Dissertations / Theses on the topic 'Sudoku'

The purpose of this bachelor thesis is to create and implement a Sudoku solver based on human strategies. We want to see how our solver compares to a brute-force solver and in which aspects it is the most efficient. We tested the two solvers in terms of solving speed, number of misses or wrong moves required to find a solution, and ability to solve harder Sudokus. Our conclusions are that the human solver is comparable to well known computer based Sudoku solvers and it is generally more efficient in terms of solving speed and number of misses. The human solver, however, does not guarantee solutions to advanced Sudokus, even though it solved all puzzles that matched the complexity of Sudokus found in newspapers.
Syftet med den här kandidatuppsatsen är att skapa och implementera en sudokulösare baserat på mänskliga strategier. Vi vill se hur vår lösare står sig mot en brute-force lösare och i vilka avseenden den kan anses vara mest effektiv. Vi har jämfört de två lösarnas lösningshastighet, antal missar eller felaktiga beräkningssteg och förmågan att lösa svårare sudokus. Våra slutsatser är att den mänskliga lösaren är jämförbar med välkända datorbaserade lösare och den är generellt sett effektivare när det gäller lösningshastighet och antal missar. Den mänskliga lösaren kan dock inte garantera en lösning till mer avancerade sudokus, även fast den löste alla de pussel som hade en motsvarande svårighetsgrad som de man kan hitta i tidningen.

The purpose of this report is to evaluate squares in any Sudoku puzzle. The evaluation is based on how difficult the square’s number is to solve by using manual methods i.e. methods possible to use with pen and paper.To achieve this, manual methods have been implemented as algorithms into an application. A GUI presents the results in the form of a Sudoku solution and a matrix window to present which methods were needed for each single square.A number of Sudoku solving techniques were implemented and applied on both specific and randomly generated Sudokus. With this an evaluation of the squares could be demonstrated.Even if the program could not show the difficulty for all squares in some Sudokus, the conditions for further development of new techniques can be made with ease which can solve these more difficult Sudokus at a later stage.
Denna rapport har som mål att värdera rutor i ett Sudoku. Värderingen baseras på hur lätt eller svårt det är att få fram rutans nummer med mänskliga metoder.För att nå detta mål har mänskliga metoder för att lösa Sudokus implementerats som algoritmer i en application. Ett GUI presenterar resultat i form av sudoku lösning samt vilka metoder som krävdes för att lösa varje enskild ruta.Ett antal tekniker för att lösa sudokus implementerades och med både specifika och slumpmässigt genererade sudokus kunde det påvisas att en värdering kunde göras.Även om programmet inte lyckats få fram svårighetsgraden för alla sorters rutor i vissa sudokus så har förutsättningar skapats för att vidar utveckla tills alla rutor kan graderas.

Mestrado em Engenharia Electrónica e Telecomunicações
Este trabalho, desenvolvido no âmbito dos sistemas reconfiguráveis, tem como objetivo a implementação de um solucionador de puzzles Sudoku, quer em software quer em hardware, tentando minimizar o seu tempo de solução. Deste modo, foram desenvolvidos três solucionadores: Simples, apenas capaz de resolver puzzles simples, Tentativa e Erro, que implementa um algoritmo de Breadth-First Search para solucionar puzzles mais complexos, e, por fim, o solucionador Tentativa e Erro com capacidade para processamento paralelo, também este capaz de solucionar puzzles mais complexos. Todos estes solucionadores foram implementados e testados numa FPGA da família Spartan-3E da Xilinx, usando, para isso, uma placa de prototipagem da Digilent. Os resultados obtidos foram comparados entre as várias implementações abordadas, assim como com outros solucionadores existentes.
This work, developed in the context of reconfigurable systems, has as an objective the implementation of a Sudoku solver, both in software and hardware, and attempting to minimize its solution time. Thus, three solvers were developed: Simple, only able to solve simple puzzles, Trial and Error, which implements a Breadth-First Search algorithm, being able to solve more complex puzzles, and, finally, the Trial and Error solver with the possibility of parallel processing, being also able to solve complex puzzles. All these solvers were implemented and tested on an FPGA of Xilinx Spartan- -3E family, using for this purpose a prototyping board from Digilent. The results were compared between the various implementations, as well as with other state-of-the-art solvers.

Sudoku and Jigsaw sudoku are two similar logic puzzles. The goal of the puzzles is to place numbers in a 9*9 grid until certain rules are met. In both Jigsaw sudoku and normal sudoku the numbers 1 to 9 needs to be placed in every row, column and box. The difference between the two puzzles is that in a normal sudoku every box is a symmetric 3*3 square, while in the jigsawv ariant the boxes have irregular, altough still nine cells big, boxes.When implementing algorithms for solving the normal sudoku, it normal touse the fact that all the boxes are symmetric. This will not work for the jigsaw sudoku though.In this report we will investigate the effectiveness of the three most common sudoku solving algorithms Rule Based backtracking, Human-Like solving and Dancing Links and how we arrived at the result that Human-Like solving was,in almost every case, the most effective algorithm for solving both sudoku and jigsaw sudoku.
Sudoku och Jigsaw sudoku är två likartade logik spel som går ut på att placera ut tal enligt vissa regler på en spelplan som har 9*9 rutor. I Både jigsaw sudoku och vanligt sudoku ska talen ett till nio finnas med i varje kolumn, rad och box exakt en gång. Det som skiljer dem åt är att i sudoku är boxarna symmetriska och 3*3 rutor stora medan i jigsaw sudoku har de varierande form av 9 rutor.Vid implementation av algoritmer för lösning av sudoku är det enkelt att använda symmetrin av hur de ser ut, medan det för jigsaw sudoku inte fungerar då boxarna ej är symmetriska.I denna rapport undersöker vi effektiviteterna hos de tre algoritmerna Rule Based backtracking, Human-Like solving och Dancing Link för att visa hur vi kom fram till resultatet att Human-Like solving i nästan alla fall var den effektivare algoritmen både för vanliga sudoku och jigsaw sudoku.

The goal of this essay is to determine whether or not there exists a correlation between the by a human perceived difficulty of a Sudoku puzzle and the difficulty of solving said puzzle with the help of computer programming built to imitate human solving. Initially we discuss the foundation and history of the Sudoku puzzle after which a few solving algorithms are explored in depth. In the methods chapter the methods used for solving and scoring the Sudokus are discussed, as well as how the study on which the results are based was conducted. We found a certain correlation between the two in spite of the obstacles encountered as a result of the human factor. Our study is based upon a specific group of people all with an academic background to minimize the differences in the skill of logical thinking. We believe that an expansion of the test group would yield better results, given that the expansion would target the same type of individuals.
Syftet med denna uppsats är att undersöka huruvida det finns någon korrelation mellan mänskligt upplevd svårighetsgrad av ett Sudokupussel och dess svårighet att lösas med en datorbaserad algoritm byggd för att imitera mänsklig lösning. Vi börjar med att diskutera grunderna kring Sudoku för att sedan gå in mer djupgående på några vanliga strategier. Därefter behandlas metoderna som användes vid genomförandet av såväl undersökning som programskrivning samt betygsindelning. Det visade sig finnas vissa likhetsdrag mellan de båda parterna trots de svårigheter som uppkom i och med den mänskliga faktorn. Vår undersökning riktar sig till människor av akademisk bakgrund för att minimera skiftningarna i nivå av logiskt tänkande. Vi tror att en utvidgning av testgruppen skulle ge bättre resultat, givet att utvidgningen sker riktat till samma målgrupp.

Mestrado em Matemática e Aplicações
Neste trabalho o objectivo principal é fazer um estudo de alguma da Matemática presente no conhecido puzzle Sudoku. Dado que o tema da presente dissertação foi proposto a duas alunas, e como se tratava de um assunto novo para ambas, os dois primeiros capítulos resultam de um trabalho conjunto com a minha colega Andreia Cristina Dias Morgado. Os conceitos introdutórios serão apresentados no primeiro capítulo, onde se abordarão os Quadrados Latinos e as suas principais características. No segundo capítulo exibimos as aplicações dos Quadrados Latinos à Teoria de Grupos. No terceiro capítulo abordamos alguns resultados importantes no estudo das Geometrias finitas, nomeadamente no que diz respeito aos planos afins e projectivos, mostrando-se como se pode obter um deles à custa do outro. Serão abordadas também as principais relações destes planos com os Quadrados Latinos. Por fim, no quarto capítulo faz-se uma análise da relação entre as propriedades dos Quadrados Latinos e do Sudoku, desenvolvendo-se um pouco da história do aparecimento deste puzzle, o modo como se joga e os níveis de dificuldade. Além disso, serão apresentadas algumas variantes do puzzle, finalizando-se com o problema das possíveis colorações parciais de um Sudoku.
In this work, the main aim is to make a study of some Mathematics presents in the Sudoku puzzle we know so well. Since the theme of this dissertation was purposed to two students, and since this was a new subject for both, the first two chapters resulted from a work, made by me and my colleague Andreia Cristina Dias Morgado. The introductory concepts will be presented in the first chapter, where we will make reference to the Latin Square and its main features. In the second chapter we show the applications of Latin Squares to the Theory of Groups. In the third chapter we will present some important results of the study of finite Geometries, particularly with what is concerned to affine plans and projective plans. We show how to get one from another. It also studies the main relations of these ones with the Latin Squares. Finally, the fourth chapter is an analysis of the relation between the properties of Latin Squares and Sudoku, developing a bit of history from the beginning of this puzzle and how to play it and its difficulty levels. In addition, we will present some variants of the puzzle, ending with the problem of possible partial colorations of a Sudoku.

This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.

With this thesis, we hope to motivate software developers to seek out already existing solving algorithms instead of attempting to use a bruteforce algorithm or specialized solving algorithms.The reason for choosing the Sudoku puzzle as a platform to demonstrate this is because it is well known around the world and easy to understand, while the reduction to an exact cover problem provides a challenge. Because of the challenge in the reduction and because we did not find any earlier research which explained in detail how the reduction from a Sudoku puzzle to an exact cover problem is done, we decided to focus on that subject in this thesis. Using our previous knowledge in reduction and the information found during our research, the reduction was eventually solved.Our conclusion is that Dancing Links is an effective solver for the exact cover problem and that a good reduction algorithm can greatly lower the solving time. The benchmarks also indicate that the number of clues in a Sudoku puzzle may not be the deciding factor of its difficulty rating. Since the reduction to an exact cover problem was arguably the hardest part in this thesis, future research can hopefully make use of our detailed explanation of the reduction and use the time saved to explore other topics in more depth, such as the difficulty rating of Sudoku puzzle.
Med denna rapport så hoppas vi motivera mjukvaruutvecklare att sökaefter redan existerande lösningsalgoritmer istället för att försöka använda en brute force-algoritm eller en lösningsalgoritm som är specialiserad på ett specifikt område. Anledningen till att vi valde att använda Sudoku som ett verktyg för att demonstrera detta är för att det är känt runt om i världen och lätt att förstå, men också för att det är svårt att utföra en reducering till ett exakt mängdtäckningsproblem. På grund av utmaningen i reduktionen och eftersom vi inte hittade någon tidigare forskning som detaljerat förklarade hur reduktionen från ett Sudokupussel till ett exakt mängdtäckningsproblem går till, bestämde vi oss för att fokusera kring det i denna rapport. Genom att använda vår tidigare kunskap inom reduktion och med den information vi hittade under informationssökningen kunde vi slutligen lösa reduktionen.Vår slutsats är att Dancing Links är en effektiv lösare till det exakta mängdtäckningsproblemet och att en bra implementerad reduktion kraftigt kan sänka lösningstiden. Mätningarna visar också att antalet ledtrådar i ett Sudokupussel inte behöver vara den avgörande faktorn för sin svårighet.Eftersom reduceringen till ett exakt mängdtäckningsproblem var den svåraste delen i vår rapport så hoppas vi att framtida forskninghar användning av vår genomgång av reduceringen och istället kan använda den tiden till att utforska andra ämnen mer djupgående, som exempelvis svårighetsgraden för Sudokupussel.

In this bachelor thesis we study 6 popular Sudoku solving algorithms, found through Google, to find the algorithm that has the slowest growth. The algorithms we tested are: brute-force, a pen-and-paper method, two exact cover reductions in Python and Haskell, a SAT reduction, and a constraint satisfaction algorithm. The algorithms were tried by solving Sudoku puzzles of sizes n = {2, 3, 4, 5} where we measured the solution time. We conclude that the slowest growing algorithm, by far, is the SAT reduction, followed by the exact cover reductions. Brute-force grows, unsurprisingly, the fastest.

Sudoku is a puzzle that has become popular during the last decade. A great number of algorithms have been implemented to solve the problem but many use approaches that do not correspond to how a human solves a sudoku puzzle. The purpose of this project was to evaluate how a strategy based algorithm which utilizes a more human approach compares to a so called Dancing Links-algorithm and an exhaustive search algorithm with respect to solving time and correctness. A qualitative study was conducted, with four respondents, which together with a literature study lay the foundation for the strategies in the implemented algorithm. Furthermore, a comparison was performed with 725 sudoku puzzles of which the strategy-based algorithm only managed to solve sudoku puzzles of a limited difficulty where the others solved all. The result showed though, that the strategy based algorithm was the fastest for the difficulties that it solved, but at the same time it showed a trend hinting at increased solving time with increasing difficulty. Finally, it could be determined that Dancing Links is a generally faster algorithm than the others. A strategy based algorithm could however be a fast alternative when solving sudoku puzzles of the difficulties that often appear in daily papers.
Sudoku är ett pussel som har blivit populärt det senaste decenniet. Ett stort antal algoritmer har implementerats för att lösa problemet men många använder angreppssätt som inte motsvarar hur en människa går tillväga för att lösa sudokupussel. Syftet med projektet var utvärdera hur en strategibaserad algoritm som använder ett mer mänskligt angreppsätt står sig mot en sk. Dancing Links-algoritm och en totalsökningsalgoritm med avseende på tid och korrekthet. I projektet genomfördes en kvalitativ undersökning, med fyra respondenter, som tillsammans med en litteraturstudie lade grunden för strategierna i den implementerade algoritmen. Vidare gjordes en jämförelse med 725 sudokupussel av vilka den strategibaserade algoritmen endast löste sudokupussel av en begränsad svårighetsgrad medan de övriga löste samtliga. Resultat visade däremot att den strategibaserade algoritmen var snabbast för de svårighetgrader den löste men samtidigt också en trend om förlängd lösningstid vid ökande svårighetgrad. Slutligen kunde det konstateras att Dancing Links är en generellt snabbare algoritm än de övriga. En strategibaserad algoritm kan dock vara ett snabbt alternativ vid lösning av sudokupussel av de svårighetsgrader som ofta förekommer i dagstidningar

In the last decade, solving the Sudoku puzzle has become every one’s passion. The simplicity of puzzle’s structure and the low requirement of mathematical skills caused people to have enormous interest in accepting challenges to solve the puzzle. Therefore, developers have tried to find algorithms in order to generate the variety of puzzles for human players so that they could be even solved by computer programming. In this essay, we have presented an algorithm called pencil-and-paper using human strategies. The purpose is to implement a more efficient algorithm and then compare it with another Sudoku solver named as brute force algorithm. This algorithm is a general algorithm that can be employed in to any problems. The results have proved that the pencil-and-paper algorithm solves the puzzle faster and more effective than the brute force algorithm.
Under senaste decenniet har Sudoku pusslet blivit väldigt populär runt om i världen. Sudoku-bräde har en enkel struktur med lättlärda regler som lockar fler mänskliga spelare att acceptera utmaningar för att lösa pusslet. Således har utvecklarna försökt att hitta algoritmer för att generera olika pussel för mänskliga spelare. Dessa algoritmer kan också lösa de generade pusslen med hjälp av dator programmering. I denna uppsats har vi presenterat en algoritm så kallat "pencil-and-paper" som utnyttjar mänskliga strategier. Syftet är att implementera en mer effektiv algoritm vilket sedan jämförs det med en annan känd algoritm nämligen Brute Force. Denna algoritm är en generell algoritm som kan appliceras för att lösa vilket problem som helst. Resultaten har visat att pencil-and-paper algoritm löser pusslen snabbare och effektivare än Brute Force algoritm.

This paper aims to clarify the differences in algorithm design with a goal of solving sudoku. A few algorithms were chosen suitable to the problem, yet different from one another. To take an everyday puzzle and utilize common computer science algorithms and learn more about them. Get relevant data to see how they perform in situations, how easily they can be modified and used in larger sudokus. Also how their performance scales when the puzzle grows larger. From the results Dancing links was the fastest and scaled best of the algorithms tested, while Brute-force and Simulated annealing struggled keeping consistent results.
Detta dokument syftar till att klargöra skillnaderna i algoritmer med målet att lösa sudoku. Välja ett par olika algorithmer lämpliga för problemet, men som samtidigt skiljer sig från varandra. Att ta ett dagligt pussel och utnyttja vanligt förekommande algoritmer inom datavetenskap och lära sig mer om dem. Få relevant data och se hur de presterar i olika situationer, hur lätt de kan modifieras och användas i större Sudokus. Även hur deras prestanda skalar när pusslet blir större. Dancing links var den snabbaste algoritmen och skalade bäst av de som testades. Brute-force och Simulated annealing inte var lika konsekventa genom alla tester och betydligt långsammare i överlag.

Sudoku is a discrete constraints satisfaction problem which is modeled as an underdetermined linear system. This report focuses on applying some new signal processing approaches to solve sudoku and comparisons to some of the existing approaches are implemented. As our goal is not meant for sudoku only in the long term, we applied approximate solvers using optimization theory methods. A Semi Definite Relaxation (SDR) convex optimization approach was developed for solving sudoku. The idea of Iterative Adaptive Algorithm for Amplitude and Phase Estimation (IAA-APES) from array processing is also being used for sudoku to utilize the sparsity of the sudoku solution as is the case in sensing applications. LIKES and SPICE were also tested on sudoku and their results are compared with l1-norm minimization, weighted l1-norm, and sinkhorn balancing. SPICE and l1-norm are equivalent in terms of accuracy, while SPICE is slower than l1-norm. LIKES and weighted l1-norm are equivalent and better than SPICE and l1-norm in accuracy. SDR proved to be best when the sudoku solutions are unique; however the computational complexity is worst for SDR. The accuracy for IAA-APES is somewhere between SPICE and LIKES and its computation speed is faster than both.
Sudoku är ett diskret bivillkorsproblem som kan modelleras som ett underbestämt ekvationssystem. Denna rapport fokuserar på att tillämpa ett antal nya signalbehandlingsmetoder för att lösa sudoku och att jämföra resultaten med några existerande metoder. Eftersom målet inte enbart är att lösa sudoku, implementerades approximativa lösare baserade på optimeringsteori. En positiv-definit konvex relaxeringsmetod (SDR) för att lösa sudoku utvecklades. Iterativ-adaptiv-metoden för amplitud- och fasskattning (IAA-APES) från gruppantennsignalbehandling användes också för sudoku för att utnyttja glesheten i sudokulösningen på liknande sätt som i mättillämpningen. LIKES och SPICE testades också för sudokuproblemet och resultaten jämfördes med l1-norm-minimiering, viktad l1- norm, och sinkhorn-balancering. SPICE och l1-norm är ekvivalenta i termer av prestanda men SPICE är långsammare. LIKES och viktad l1-norm är ekvivalenta och har bättre noggrannhet än SPICE och l1- norm. SDR visade sig ha bäst prestanda för sudoku med unika lösningar, men SDR är också den metod med beräkningsmässigt högst komplexitet. Prestandan för IAA-APES ligger någonstans mellan SPICE och LIKES men är snabbare än bägge dessa.

In Knuth’s example of Dancing Links and Algorithm X (DLX), pointers were used to connect the neighbors with each other. This has caused problems when DLX is used for parallelisation and to solve this some workaround is needed. One solution is to store the pointers as indicesin an array instead. The purpose of this thesis is therefore answer how a solution based on indices compares time wise to a solution with pointers. A comparison was made by implementing two versions of DLX, one with pointers and one with indices. Each version was then used to solve sudoku puzzles and the time taken was measured. The result of this was that the representations had similar complexity but the representation with indices fell behind since each recursion took longer time compared to the representation with pointers. Therefore parallelisation is needed to put the representation with indices up to par with the represnetation with pointers.
I Knuths exempel av Dancing Links och Algorithm X (DLX) användes pekare för att koppla ihop grannar med varandra. Problemet med denna lösning är att när DLX ska parallelliseras är det inte möjligt att använda sig av samma pekare. Istället måste en alternativ lösning hittas för detta problem och en lösning är att använda index i en array. Denna rapport kommer därmed ge ett svar på hur snabb en lösning med index är jämförtmed en representation med pekare genom att implementera två versioner av DLX, en med pekare och den andra med index. Resultatet av detta var att representationerna hade liknande komplexitet men array representationen tog längre tid än representationen med pekare eftersom att varje rekursion tog längre tid. Parallellisering behövs därav för att göra array representationen lika snabb som representationen med pekare.

The Cougaar distributed agent architecture, originally a DARPA-funded research project, provides a platform for developing distributed agent systems. Testing its ability to solve complex problems using a large number of agents in an interesting topic of research. In this thesis, the Cougaar distributed agent architecture is studied from the standpoint of Sudoku. Through analysis and experimentation, insight is gained into both the properties and weaknesses of Cougaar. Cougaar\'s performance when solving Sudoku puzzles is then compared with other Sudoku solving techniques. The Cougaar agent approach solves Sudoku puzzles in a human-like fashion, reaching solutions using both analysis and guessing. Cougaar is shown to be capable of solving Sudoku puzzles in a distributed agent architecture. Although not as fast as traditional techniques, the Cougaar distributed agent approach is able to provide solutions to Sudoku puzzles using fewer guesses. Additionally, solving Sudoku puzzles with Cougaar exposed some reliability issues and demonstrated the overhead required for communication. These results open the way for additional study of Cougaar.

Sudoku är ett mycket populärt pusselspel som härstammar från Japan. Sudokuproblemet har visats vara NP-fullständigt och det finns därför troligen inget effektivt sätt att lösa stora pussel. På senare år har det skett mycket forskning kring SAT-lösare. I denna rapport prövades olika SAT-lösare från ”International SAT-Competition” för att undersöka om det existerar en korrelation mellan exekveringstid och svårighetsgradering samt för att avgöra vilken av dessa som är effektivast för att lösa pussel av olika svårighetsgrad och storlek. För att undersöka detta genereradesett stort antal pussel och två tester utfördes. Ett test mätteexekveringstiden för olika SAT-lösare på pussel av olika svårighetsgrad.Det andra testet mätte tiden för SAT-lösarna på pussel av olika storlek.De prövade SAT-lösarna är Glucose, Lingeling, Minisat, Plingeling,Treengeling och Zenn.Resultaten visar på en korrelation mellan exekveringstid och svårighetsgradför de prövade SAT-lösarna när ett genomsnitt för lösarnabehandlades. Vid ett linjärt regressionstest erhölls en bestämningskoefficentpå ca 0.8. Vissa lösare hade en stor korrelation och andra lösarevisade inte någon korrelation alls. Korrelationen skulle också kunna beropå skillnaden i antalet ledtrådar mellan de olika pusslena. Det förklarardock inte den skillnad som finns mellan pussel av olika svårighetsgradmed samma antal ledtrådar.Genomsnittstiden för samtliga lösare var ca 20 ms för pussel avordning tre och ca 50 s för pussel av ordning nio. Av de prövade SATlösarnavar Minisat snabbast, både för pusslena av ordning tre och avhögre ordningar.
Sudoku is a popular puzzle game that originates from Japan. The Sudokuproblem has been shown to be NP-complete and therefore thereprobably does not exist an effecient way of solving large puzzles. In recentyears there has been a lot of research into solving the SAT problem.This report examined various SAT solvers from “The International SATCompetition” to investigate whether there exists a correlation betweenthe execution time and the difficulty level of puzzles and to determinewhich of these are most effective for solving puzzles of varying difficultyand size. To examine the above a large number of puzzles were generatedand two tests were performed. One test measured the executiontime of various SAT solvers when solving puzzles of varying difficulty.The second test measured the time that the SAT solvers took to solvepuzzles of different sizes. The tested SAT solvers are Glucose, Lingling,Minisat, Plingeling, Treengeling and Zenn.The results show a correlation between the execution time of theSAT solvers and the difficulty of the puzzles when looking at the averagetime of the solvers. A linear regression test gave a coefficent ofdetermination of approximately 0.8. Some solvers had a significant correlationand other solvers showed almost no correlation at all. Thecorrelation could also be attributed to the difference in the number ofclues between the puzzles. This however does not explain the disparitybetween puzzles of varying difficulty with the same number of clues.The average time for all solvers were approximately 20 ms for puzzlesof order three and about 50 s for puzzles of order nine. Of the testedSAT solvers, Minisat was the fastest at solving both the puzzles of orderthree and puzzles of higher order.

Two implementations of the backtracking algorithm for solving Sudoku puzzles as well as their dependence on the representations of the problem have been studied in order to ascertain pros and cons of different approaches. For each backtracking step, empty cells could be assigned numbers sequentially or, by using a greedy heuristic, by the probability that guessed numbers were more likely to be correct. Representations of the Sudoku puzzles varied from a n2 matrix to a n3 matrix, as well as a combination of both. This study shows that (1) a sequential approach has better best case times but poor worst case behaviour, and a n3 representation does not benefit over a n2 representation; (2) a greedy heuristic approach has superior worst case times but worse best case, and n3 representations sees great benefits over n2 representations. A combination of n2 and n3 representations grants the best overall performance with both approaches.

This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures. The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in a grid with more than one potential solution - a detrimental property for erasure correction purposes. Extensive investigation into the properties of these sub-structures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of sub-structures results in practically infeasible schemes. The thesis presents detailed classifications for the different cases of sub-structures observed in each of the outline erasure correction schemes. The anticipated similarities in the sub-structures of Sudoku and sub-structures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small sub-structures is calculated and a simulation comparing the recovery rates of small sub-structure free Sudoku and standard Sudoku is carried out. The analysis of sub-structures for the second erasure correction scheme involves detailed classification of a variety of small sub-structures; the thesis also derives probabilistic lower bounds for the expected numbers of case-specific sub-structures within the puzzle structure, indicating that specific types of sub-structure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction. The consequences of complex cell inter-relationships and wider issues with puzzle-based erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzle-based combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case.

Den här rapporten undersöker egenskaper hos en algoritm som är baserad på Learning Backtracking Search Optimization Algorithm (LBSA) som introducerades av Chen et. al. (2017). Undersökningen genomfördes genom att tillämpa algoritmen på Sudokuproblemet och jämföra lösningsgraden och diversiteten i den sista populationen med en algoritm som är baserad på Hybrid Genetic Algorithm (HGA) som introducerades av Deng och Li (2011). Resultaten visar att implementationen av den LBSA-baserade algoritmen har en lägre lösningsgrad än den HGA-baserade algoritmen för alla genomförda experiment, men att algoritmen håller en högre diversitet i den sista populationen för tre av de fem gjorda experimenten. Slutsatsen är att den LBSA-baserade algoritmen inte är lämplig för att lösa Sudokuproblemet på grund av en låg lösningsgrad och att implementationen har en hög komplexitet.
This report examines the properties of an algorithm based on the Learning Backtracking Optimization Algorithm (LBSA) introduced by Chen et. al. (2017). The examination was performed by applying the algorithm on the Sudoku problem and then comparing the solution rate and the diversity in the final population with an algorithm based on the Hybrid Genetic Algorithm introduced by Deng and Li (2011). The results show the implementation of the LBSA based algorithm have a lower solution rate than the HGA based algorithm for all executed experiments. But the LBSA based algorithm manage to keep a higher diversity in the final population in three of the five performed experiments. The conclusion is that the LBSA based algorithm is not suitable for solving the Sudoku problem since the algorithm has a lower solution rate and the implementation have a high complexity.

The number puzzle sudoku has been steadily increasing in popularity. As the puzzle becomes more popular, so does the demand to solve it with algorithms. To meet this demand a number of different sudoku algorithms have been developed. This report will examine the most popular algorithms and compare them in terms of efficiency when dealing with a large number of test cases.

There are many different algorithms for solving Sudoku puzzles, with one of the newer algorithms being the hybrid AC3-tabu search algorithm. Since the algorithm has not been subject of much research, the aim of this thesis is to increase the knowledge of it. This thesis evaluates the efficiency of the hybrid AC3-tabu search algorithm by analyzing how quickly it solves puzzles compared to two other solving algorithms: one using brute-force search, and one combining human solving techniques with brute-force search. This thesis also investigates if there is a correlation between the number of puzzle clues and the solving time for the hybrid AC3-tabu search algorithm. The results show that the hybrid AC3-tabu search algorithm is less efficient than the two other algorithms, and that there seems to be a correlation between the number of clues and the solving time for the algorithm. The conclusion is that due to the algorithm’s low efficiency and some of its characteristics, it is not suitable for solving Sudoku puzzles.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Iremos apresentar a um grupo de alunos do Ensino Médio da rede pública de Ensino do Estado de São Paulo, o mundialmente conhecido quebra cabeças Sudoku, e realizar com eles várias atividades buscando apresentá-lo como subsídio didático na aprendizagem de conceitos matemáticos importantes, além de proporcionar oportunidades de aprimorar a concentração e o raciocínio lógico. Iremos explorar conceitos matemáticos ocultos por trás de suas linhas, colunas e blocos, partindo de uma das primeiras perguntas que podem ser feitas: Qual é a quantidade total de jogos válidos existentes? Para responde-la, será proposto a realização de diversas atividades, primeiramente com um Shidoku (matriz 4 × 4), em seguida iremos calcular o total desses jogos. O tamanho reduzido dessa grade, facilita os cálculos manuais, permitindo visualizar e compreender o processo utilizado, aproveitando para introduzir o princípio fundamental da contagem. A discussão principal desse trabalho, concentra-se na exploração de um método para se determinar a quantidade de jogos válidos existentes para um Sudoku, e para isso, utilizaremos as demonstrações de Bertrand Felgenhauer e Frazer Jarvis. Também apresentaremos um método capaz de gerar uma grade completa de Sudoku, partindo de uma matriz quadrada de ordem 3, que em seguida, será utilizada para gerar uma solução de Sudoku ortogonal. Finalizando, iremos apresentar e explorar algumas formas diferenciadas para os quebra cabeças Sudoku, mostrando variações no formato dos blocos, no tamanho das grades e uma variação que utiliza formas geométricas em suas pistas (Shapedoku). Como desafio de leitura, pesquisa e aprofundamento, será proposto o problema ainda em aberto do número mínimo de dados iniciais para se ter um jogo válido. Podemos afirmar que um dos objetivos esperados, é que tal atividade venha interferir na concentração e raciocínio, auxiliando nas atividades propostas nesse trabalho e que possam ser utilizadas em outros problemas do cotidiano.
We will present to a group of high school students of the public Education of Sao Paulo state, the world-known puzzle Sudoku, and perform with them several activities seeking to present it as a didactic subsidy in the learning important mathematical concepts, besides opportunities to enhance concentration and logical reasoning. We will explore hidden mathematical concepts behind their lines, columns and blocks, starting from one of the rst questions that can be asked: What is the total number of valid games in existence? To answer this question, it will be proposed to perform several activities, rst with a Shidoku (4 × 4 matrix), then we will calculate the total of these games. The reduced size of this grid facilitates manual calculations, allowing to visualize and understand the process used, taking advantage to introduce the fundamental principle of counting. The main discussion of this paper focuses on the exploration of a method to determine the amount of valid games existing for a Sudoku, and for that, we will use the demonstrations of Bertrand Felgenhauer and Frazer Jarvis. We will also present a method capable of generating a complete Sudoku grid, starting from a square matrix of order 3, which will then be used to generate an orthogonal Sudoku solution. Finally, we will introduce and explore some di erent shapes for the Sudoku puzzle, showing variations in the shape of the blocks, the size of the grids and a variation that uses geometric forms in their tracks (Shapedoku). As a challenge for reading, searching and deepening, the open problem of the minimum number of initial data to have a valid game will be proposed. We can say that one of the expected objectives is that such activity will interfere in concentration and reasoning, helping in the activities proposed in this paper and that can be used in other daily problems.
3107510001F5

In this paper we compare various Sudoku solving algorithms in order to determine what kind of run-time improvements different optimizations can give. We will also examine what kind of effect the existence of multiple solutions in the puzzles has on our result.

This thesis explores the framing of coordinative experience in collocated computer-mediated communication. It highlights the importance of low- level coordinative properties through multifaceted examination of the transcript of the first minute of a constructed coordinative situation. In efforts to truly understand the culture we are creating and invoking by adding computers to peopleâ s activities in groups, and life in general.

A lab study was conducted using a computer program that allows one or more users to solve a Sudoku puzzle together, each on their own separate computer. This allowed for an investigation of what happens when people and technology are located in the same place. How do people construct their situation, in terms of who goes next, what do they do and what constitutes the behavior framing.
Master of Science

. A Escola Fundamental I tem como objetivo promover em seus alunos o desenvolvimento da capacidade de aprender e de se relacionar através da representação, da comunicação e da resolução de problemas em favor da aprendizagem da língua, da matemática, da representação espacial, temporal e gráfica. No campo da Psicologia e da Educação pesquisas demonstram que o jogo pode ser usado para criar situações-problema e assim contribuir para processos de desenvolvimento e aprendizagem em crianças e adolescentes. Esta pesquisa trata, então, de propor uma forma de intervenção que auxilie a aprendizagem da resolução de problemas, através de um jogo que implica o uso de operações lógicas. O Sudoku foi o jogo escolhido porque os problemas que ele apresenta são da natureza e uso da lógica, no sentido de que para descobrir o número de cada casa vazia o jogador deve coordenar vários aspectos ao mesmo tempo e considerar que há apenas uma resposta para cada caso. O recorte de idade feito para a presente pesquisa, crianças com 6-7 anos, se apoia na teoria piagetiana que afirma que as construções operatórias dão início, em média, aos sete anos e seguem até a vida adulta. Assim, criou-se, através de oficinas com o jogo Sudoku, situações-problema que exercitaram o uso do pensamento lógico favorecendo os processos de desenvolvimento e de aprendizagem requeridos para o alcance das expectativas previstas para sujeitos que cursam o segundo ano da Escola Fundamental I. Foram feitas 17 oficinas, sendo duas por semana e com duração de uma hora cada, em três turmas de segundo ano de uma escola particular do município de Ribeirão Preto, alcançando um total 60 participantes. A fundamentação metodológica utilizada nas oficinas se baseia nos modelos Taos, Paris, Atenas e Eldorado desenvolvidos por Gruber e Vonèche (1995) que têm como objetivo aplicar à Educação as contribuições de Piaget ao explorar o pensamento e a compreensão da criança em relação à natureza dos objetos, ao tempo, espaço, juízo moral e etc. Os dados foram analisados a partir dos seguintes eixos: 1) como os participantes resolveram e compreenderam o jogo Sudoku; 2) qual o valor das situações-problema para o primeiro eixo; 3) como e por que aplicar os Modelos Taos, Paris, Atenas e Eldorado em oficinas sobre o jogo Sudoku; e 4) como praticar uma visão construtivista, apoiada na perspectiva de Piaget, em uma situação de jogo com sujeitos de 6-7 anos. Os resultados apontam que no início do processo de intervenção poucos sujeitos conseguiam resolver o Sudoku da forma correta. No entanto, no desenrolar das oficinas foi possível identificar uma considerável aprendizagem deste jogo por parte dos participantes e, mais do que isto, observou-se um apreciável desenvolvimento dos sujeitos quanto à compreensão do jogo. Atribui-se tal desenvolvimento e aprendizagem às atividades das oficinas em resolver os jogos e às situações-problema. Conclui-se, ainda, que os modelos de Gruber e Vonèche formaram uma excelente base de intervenção para o aprendizado do jogo e de suas implicações lógicas. Assim, confiamos que tal estudo aqui apresentado possa colaborar de alguma maneira com educadores e psicólogos interessados no uso do jogo para o desenvolvimento e a aprendizagem de seus alunos e pacientes a respeito do pensamento lógico
Primary school has as a target the promotion of the development of its students capacity to learn and relate through representation, communication and problem solving in favor of language learning, mathematics and spatial, temporal and graphical representation. In the fields of Psychology and Education researches show that gaming can be used to create a problem situation contributing to the process of development and learning in children and teenagers. This research proposes a form of intervention that helps the learning of problem solving, through a game that implies the use of logical operations. Sudoku was the game/puzzle chosen because the problems that it presents are of logical nature and use, in a sense that for discovering the empty squares right number the player must coordinate several aspects at the same time while taking into consideration that there is only one right answer for each case. Children from 6 to 7 years old were chosen because of the Piagetian theory that states that operatory constructions begin at that age. Therefore, through Sudokus workshops problem situations were created to exercise the use of logical thought favoring the process of development and learning that is required for the achievement of expectations regarding the individuals going through the second year of primary school. Seventeen workshops of one hour each, were made twice a week, with three groups attending the second year of a private primary school in Ribeirão Preto, totaling in 60 participants. The methodological grounding was based on the models Taos, Paris, Athens and Eldorado developed by Gruber and Vonèche (1995) these models had an which was objective to apply Piagets contribution to Education as he explored a childs thought and comprehension of the nature of objects, time, moral judgement, etc. The data was analyzed through the following axes: 1) How participants solved and comprehended the Sudoku puzzle; 2) What is the value of the problem situations for the first axis; 3) How and why to apply the models Taos, Paris, Athens and Eldorado in the Sudoku workshops; and 4) How to practice a constructivist viewpoint, based on Piagets perspective, in game situations with children from 6 to 7 years old. The results demonstrate that at the beginning of the intervention few children were able to correctly solve the Sudoku puzzle. However, through the workshops a considerable amount of learning was identified, and more than that, a development of the game comprehension. The learning and development achieved is attributed to the workshops activities of puzzle solving and problem situation. We conclude that Gruber and Vonèches models formed an excellent intervention base for the learning of the puzzle and its logical implications. Therefore, we trust that the present study may collaborate in some ways with educators and psychologists interested in the use of games for their students and patients development and learning of logical thought

Sudoku is a popular puzzle game where the aim is to fill a board with numbers from one to nine with some mathematical rules to obey. The difficulty level of a Sudoku is affected by the amount of digits in the beginning, called clues. Mathematically there exists different algorithms and methods to solve a Sudoku. In this project some of the methods are investigated and compered to each other in time to find the fastest and most suitable for this project. A construction was built to be able to print out a non solved puzzle. Due to the current situation in society with Covid-19, the project has been affected negatively. The construction became very time consuming due to lack of tools and material. That affected the finished construction and the implementation of the code written in Python. After all the robot was able to print a Sudoku puzzle that can be solved. The printing time was decreased to 3 minutes after some tests with different delays. All the research questions were answered and the goal of the project which was to be able to print a Sudoku was reached.
Sudoku är ett populärt pussel där målet är att fylla i ett rutnät med siffror från ett till nio med vissa matematiska regler att följa. Svårighetsgraden av ett sudoku påverkas av antalet siffror från början, ledtrådar. Matematiskt finns det olika algoritmer och metoder för att lösa ett sudoku. I det här projektet undersöktes några metoder och jämfördes tidsmässigt med varandra för att hitta den snabbaste och mest passande för det här projektet. En konstruktion byggdes för att kunna skriva ut ett icke löst pussel. På grund av den rådande situationen i samhället med Covid19 så har projektet påverkats negativt. Konstruktionen blev väldigt tidskrävande på grund av brist på verktyg och material. Detta påverkade den slutgiltiga konstruktionen och implementeringen av koden skriven i Python. Trots allt så kunde roboten skriva ut ett Sudoku som kan lösas. Tiden att skriva ut ett Sudoku minskades till 3 minuter efter ett antal tester med olika fördröjningar. Alla forskningsfrågor kunde besvaras och målet med projektet som var att kunna skriva ut ett Sudoku nåddes.

We begin with some basic definitions and concepts from convex analysis and projection onto convex sets (POCS). We next introduce various algorithms for converging to the intersection of convex sets and review various results (Elser’s Difference Map is equivalent to the Douglas-Rachford and Fienup’s Hybrid Input-Output algorithms which are both equivalent to the Hybrid Projection-Reflection algorithm). Our main contribution is two-fold. First, we show how to model the 8-queens problem and following Elser, we model Sudoku as well. In both cases we use several very nonconvex sets and while the theory for convex sets does not apply, so far the algorithm finds a solution. Second, we show that the operator governing the Douglas-Rachford iteration need not be a proximal map even when the two involved resolvents are; this refines an observation of Eckstein.

Metaheuristics are used to find feasible solutions to hard Combinatorial Optimization Problems (COPs). Constraint Satisfaction Problems (CSPs) may be formulated as COPs, where the objective is to reduce the number of violated constraints to zero. The popular puzzle Sudoku is an NP-complete problem that has been used to study the effectiveness of metaheuristics in solving CSPs. Applying the Simulated Annealing (SA) metaheuristic to Sudoku has been shown to be a successful method to solve CSPs. However, the ‘easy-hard-easy’ phase-transition behavior frequently attributed to a certain class of CSPs makes finding a solution extremely difficult in the hard phase because of the vast search space, the small number of solutions and a fitness landscape marked by many plateaus and local minima. Two key mechanisms that metaheuristics employ for searching are diversification and intensification. Diversification is the method of identifying diverse promising regions of the search space and is achieved through the process of heating/reheating. Intensification is the method of finding a solution in one of these promising regions and is achieved through the process of cooling. The hard phase area of the search terrain makes traversal without becoming trapped very challenging. Running the best available method - a Constraint Propagation/Depth-First Search algorithm - against 30,000 benchmark problem-instances, 20,240 remain unsolved after ten runs at one minute per run which we classify as very hard. This dissertation studies the delicate balance between diversification and intensification in the search process and offers a hybrid SA algorithm to solve very hard instances. The algorithm presents (a) a heating/reheating strategy that incorporates the lowest solution cost for diversification; (b) a more complex two-stage cooling schedule for faster intensification; (c) Constraint Programming (CP) hybridization to reduce the search space and to escape a local minimum; (d) a three-way swap, secondary neighborhood operator for a low expense method of diversification. These techniques are tested individually and in hybrid combinations for a total of 11 strategies, and the effectiveness of each is evaluated by percentage solved and average best run-time to solution. In the final analysis, all strategies are an improvement on current methods, but the most remarkable results come from the application of the “Quick Reset” technique between cooling stages.

Les méthodes de Monte Carlo sont des méthodes probabilistes qui utilisent des ordinateurs pour résoudre de nombreux problèmes de la science à l’aide de nombres aléatoires. Leur principal inconvénient est leur convergence lente. La mise au point de techniques permettant d’accélérer la convergence est un domaine de recherche très actif. C’est l’objectif principal des méthodes déterministes quasi-Monte Carlo qui remplacent les points pseudo-aléatoires de simulation par des points quasi-aléatoires ayant une excellente répartition uniforme. Ces méthodes ne fournissent pas d’intervalles de confiance permettant d’estimer l’erreur. Nous étudions dans ce travail des méthodes stochastiques qui permettent de réduire la variance des estimateurs Monte Carlo : ces techniques de stratification le font en divisant le domaine d’échantillonnageen sous-domaines. Nous examinons l’intérêt de ces méthodes pour l’approximation des chaînes de Markov, la simulation de la diffusion physique et la résolution numérique de la fragmentation.Dans un premier chapitre, nous présentons les méthodes de Monte Carlo pour l’intégration numérique. Nous donnons le cadre général des méthodes de stratification. Nous insistons sur deux techniques : la stratification simple (MCS) et la stratification Sudoku (SS), qui place les points sur des grilles analogues à celle du jeu. Nous pressentons également les méthodesquasi-Monte Carlo qui partagent avec les méthodes de stratification certaines propriétés d'équipartition des points d’échantillonnage.Le second chapitre décrit l’utilisation des méthodes de Monte Carlo stratifiées pour la simulation des chaînes de Markov. Nous considérons des chaînes homogènes uni-dimensionnelles à espace d’états discret ou continu. Dans le premier cas, nous démontrons une réduction de variance par rapport `a la méthode de Monte Carlo classique ; la variance des schémas MCSou SS est d’ordre 3/2, alors que celle du schéma MC est de 1. Les résultats d’expériences numériques, pour des espaces d’états discrets ou continus, uni- ou multi-dimensionnels montrent une réduction de variance liée à la stratification, dont nous estimons l’ordre.Dans le troisième chapitre, nous examinons l’intérêt de la méthode de stratification Sudoku pour la simulation de la diffusion physique. Nous employons une technique de marche aléatoire et nous examinons successivement la résolution d’une équation de la chaleur, d’une équation de convection-diffusion, de problèmes de réaction-diffusion (équations de Kolmogorov et équation de Nagumo) ; enfin nous résolvons numériquement l’équation de Burgers. Dans chacun de ces cas, des tests numériques mettent en évidence une réduction de la variance due à l’emploi de la méthode de stratification Sudoku.Le quatrième chapitre décrit un schéma de Monte Carlo stratifie permettant de simuler un phénomène de fragmentation. La comparaison des performances dans plusieurs cas permet de constater que la technique de stratification Sudoku réduit la variance d’une estimation Monte Carlo. Nous testons enfin un algorithme de résolution d’un problème inverse, permettant d’approcher le noyau de fragmentation, à partir de résultats de l’évolution d’une distribution ;nous utilisons dans ce cas des points quasi-Monte Carlo pour résoudre le problème direct
Monte Carlo methods are probabilistic schemes that use computers for solving various scientific problems with random numbers. The main disadvantage to this approach is the slow convergence. Many scientists are working hard to find techniques that may accelerate Monte Carlo simulations. This is the aim of some deterministic methods called quasi-Monte Carlo, where random points are replaced with special sets of points with enhanced uniform distribution. These methods do not provide confidence intervals that permit to estimate the errordone. In the present work, we are interested with random methods that reduce the variance of a Monte Carlo estimator : the stratification techniques consist of splitting the sampling area into strata where random samples are chosen. We focus here on applications of stratified methods for approximating Markov chains, simulating diffusion in materials, or solving fragmentationequations.In the first chapter, we present Monte Carlo methods in the framework of numerical quadrature, and we introduce the stratification strategies. We focus on two techniques : the simple stratification (MCS) and the Sudoku stratification (SS), where the points repartitions are similar to Sudoku grids. We also present quasi-Monte Carlo methods, where quasi-random pointsshare common features with stratified points.The second chapter describes the use of stratified algorithms for the simulation of Markov chains. We consider time-homogeneous Markov chains with one-dimensional discrete or continuous state space. We establish theoretical bounds for the variance of some estimator, in the case of a discrete state space, that indicate a variance reduction with respect to usual MonteCarlo. The variance of MCS and SS methods is of order 3/2, instead of 1 for usual MC. The results of numerical experiments, for one-dimensional or multi-dimensional, discrete or continuous state spaces show improved variances ; the order is estimated using linear regression.In the third chapter, we investigate the interest of stratified Monte Carlo methods for simulating diffusion in various non-stationary physical processes. This is done by discretizing time and performing a random walk at every time-step. We propose algorithms for pure diffusion, for convection-diffusion, and reaction-diffusion (Kolmogorov equation or Nagumo equation) ; we finally solve Burgers equation. In each case, the results of numerical tests show an improvement of the variance due to the use of stratified Sudoku sampling.The fourth chapter describes a stratified Monte Carlo scheme for simulating fragmentation phenomena. Through several numerical comparisons, we can see that the stratified Sudoku sampling reduces the variance of Monte Carlo estimates. We finally test a method for solving an inverse problem : knowing the evolution of the mass distribution, it aims to find a fragmentation kernel. In this case quasi-random points are used for solving the direct problem

O presente trabalho consiste em uma pesquisa sobre como adolescentes jogam e resolvem situações-problemas relativas ao Sudoku. O objetivo foi analisar o raciocínio de escolares por meio de seu desempenho nesse jogo. Poucas são as pesquisas com jogos de regras para o desenvolvimento e aprendizagem de alunos de 9º ano do Ensino Fundamental II e, por isso, o desejo em pesquisar sobre o desenvolvimento do raciocínio por meio do jogo Sudoku com essa parcela da população escolar. O ponto diferenciador de nosso trabalho é a questão da dificuldade dos alunos em justificar suas respostas às situações- problema propostas. Para tanto, a professora-pesquisadora elaborou partidas de jogo Sudoku e situações-problema relativas ao mesmo jogo e as desenvolveu com 21 alunos de 9º ano do Ensino Fundamental II de uma escola pública do município de São Paulo. A coleta de dados foi realizada durante 15 aulas por meio de protocolos elaborados pela professora-pesquisadora. Na análise desses dados coletados, investigamos o desenvolvimento do raciocínio dos alunos ao longo dos encontros por meio de suas resoluções e da linguagem que utilizaram para justificar suas respostas aos jogos e aos Enigmas Sudoku propostos. A discussão dos resultados foi orientada principalmente pelos estudos de Jean Piaget quanto ao desenvolvimento e à aprendizagem e pelo estudo de Philippe Meirieu sobre como aprender por meio de situações-problema. Os alunos avançaram consideravelmente do primeiro encontro para o último em relação aos conceitos e procedimentos relativos aos jogos e às situações-problema e, além disso, desenvolveram sua justificação lógica, permitindo concluir que as experiências por que passaram ofereceram a oportunidade de tomarem consciência dos motivos que os orientaram em suas escolhas. Consideramos essa pesquisa relevante para o campo da Psicologia do Desenvolvimento e da Aprendizagem, pois, por meio de um jogo, aprendemos a trabalhar o raciocínio e uma forma de pensar, útil para a escola e para a vida
This work is a research about how teenagers play and solve problem situations related to Sudoku. The aim was to analyze the logic of students through their performance in that game. There are not so many researches on rule games for development and learning of students in 9th grade from Elementary School and, because of this, there was the desire to research the development of logic through Sudoku game with this part of the school population. The differentiator point of this work is the question of the students difficulty to justify their answers to the proposed problem situations. For that, the teacher-researcher elaborated Sudoku matches and problem situations related to the same game and developed them with 21 students in the 9th grade of the Elementary School in a public school in São Paulo city. The data collection was done during 15 classes by protocols elaborated by the teacher-researcher. In the analysis of the collected data, we investigated the development of the students´ logic during the encounters with the solutions and the language used to justify their answers in the proposed games and puzzles. The discussion of the results was oriented by the studies of Jean Piaget on development and learning and by the studies of Philippe Meirieu on how to learn with problem situations. The students had a considerable progress from the first encounter to the last one in relation to concepts and procedures related to the game and to the problem situations and, beyond that, they developed their logical justification, allowing us to conclude that the experiences that they had endured offered them an opportunity to be conscious of the reasons that oriented them on their choices. We consider this research relevant to the Developmental and Educational Psychology field because through a game we learned to work with logic and a way of thinking, useful for school and life

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work brings an approach to the basic notions of Graph Theory, presenting historical context, concepts, de nitions and examples in order to provide the reader with previous knowledge of the theory. The main objective is to perform a study of the graphs applied to the staining using the dual graph and the method of the greedy algorithm. To do so, we will present the demonstration attempt of the 4-Color Theorem that had been developed by Kempe and the proof of the 5-Color Theorem, made 11 years later by Heawood. Finally, we will seek the resolution of some situations problems that will be modeled through the coloring of vertices.
Este trabalho traz uma abordagem às noções da Teoria dos Grafos, apresentando contexto histórico, conceitos, definições e exemplos com o intuito de proporcionar ao leitor conhecimentos prévios da teoria. O principal objetivo é efetuar um estudo dos grafos aplicados à coloração mediante o uso do grafo dual e o métdo do algoritmo guloso. Para tanto, executaremos um esboço acerca da tentativa de demonstração do Teorema das 4 Cores que fora desenvolvida por Kempe e da prova do Teorema das 5 Cores, feita 11 anos mais tarde por Heawood. Por fim, buscaremos a resolução de algumas situações problemas que serão modeladas através da coloração de vértices.
São Cristóvão, SE

The main objective of this dissertation is to present an algebraic method capable of determining a solution, if any, of a non linear polynomial equation systems using Gröbner basis. In order to accomplish that, we first present some concepts and theorems linked to polynomial rings with several undetermined and monomial ideals where we highlight the division extended algorithm, the Hilbert Basis and the Buchberger´s algorithm. Beyond that, using basics of Elimination and Extension Theorems, we present an algebraic solution to the map coloring that use 3 colors as well as a general solution to the Sudoku puzzle.
O objetivo principal desse trabalho é, usando bases de Gröbner, apresentar um método algébrico capaz de determinar a solução, quando existir, de sistemas de equações polinomiais não necessariamente lineares. Para tanto, necessitamos inicialmente apresentar alguns conceitos e teoremas ligados a anéis de polinômios com várias indeterminadas e de ideais monomiais, dentre os quais destacamos o algoritmo extendido da divisão, o teorema da Base de Hilbert e o algoritmo de Buchberger. Além disso, usando noções básicas da Teoria de eliminação e extensão, apresentamos uma solução algébrica para o problema da coloração de mapas usando três cores, bem como um solução geral para o puzzle Sudoku.

Signal acquisition, signal reconstruction and analysis of spectrum of the signal are the three most important steps in signal processing and they are found in almost all of the modern day hardware. In most of the signal processing hardware, the signal of interest is sampled at uniform intervals satisfying some conditions like Nyquist rate. However, in some cases the privilege of having uniformly sampled data is lost due to some constraints on the hardware resources. In this thesis an important problem of signal reconstruction and spectral analysis from nonuniformly sampled data is addressed and a variety of methods are presented. The proposed methods are tested via numerical experiments on both artificial and real-life data sets. The thesis starts with a brief review of methods available in the literature for signal reconstruction and spectral analysis from non uniformly sampled data. The methods discussed in the thesis are classified into two broad categories - dense and sparse methods, the classification is based on the kind of spectra for which they are applicable. Under dense spectral methods the main contribution of the thesis is a non-parametric approach named LIMES, which recovers the smooth spectrum from non uniformly sampled data. Apart from recovering the spectrum, LIMES also gives an estimate of the covariance matrix. Under sparse methods the two main contributions are methods named SPICE and LIKES - both of them are user parameter free sparse estimation methods applicable for line spectral estimation. The other important contributions are extensions of SPICE and LIKES to multivariate time series and array processing models, and a solution to the grid selection problem in sparse estimation of spectral-line parameters. The third and final part of the thesis contains applications of the methods discussed in the thesis to the problem of radial velocity data analysis for exoplanet detection. Apart from the exoplanet application, an application based on Sudoku, which is related to sparse parameter estimation, is also discussed.

In this report, we review various methods for generating valid sudoku with few hints. The report begins with a bit of terminology and anoverview of various methods that can be used to generate sudoku. Subsequently we go through the results of these generating methods, where wecan see that in order to generate sudoku with few clues, one must takespecial care how to place the clues of the sudoku. Finally we come to theconclusion that one of the neighbour-generating-method wasthe fastest algorithm for generating sudoku.

Des biais méthodologiques et idéologiques ont entaché dès l’origine la conception du test de QI (quotient intellectuel) sans jamais entraver sa diffusion massive. A présent les spécialistes de la précocité s’efforcent de faire du surdouement une nouvelle catégorie psychopathologique. Etre intelligent serait-il devenu une maladie? Tel est l’enjeu actuel pour la psychologie et la psychiatrie d’« avant-garde » : constituer une clinique de l’enfant surdoué qui en retour fournirait une légitimité à l’arbitraire taxonomique de départ. Après avoir démantelé la logique à l’œuvre dans l’histoire du test, sa construction et sa diffusion, ce travail se propose d’expliquer pourquoi le public demande toujours plus de mesure et de chiffre, toujours plus de cette « évaluation généralisée » dont le test de QI est le paradigme. Une transformation du Discours du Maître explique le pouvoir de fascination du test. A l’époque de l’inconsistance de l’Autre, alors que les semblants vacillent, que devient l’identification du sujet ? Dans la logique qualifiée par Lacan du nommer-à, les signifiants-maîtres, désormais produits en série, sont installés en place de vérité. Promus ainsi à une puissance quasi divine, ils se présentent comme les « masques de fer » de l’objet plus-de-jouir. Il arrive que le sujet inventif s’en empare pour son compte propre. Souvent il en subit le poids. Donner la parole aux sujets testés surdoués et à leurs familles permet de dégager comment s’organise à grande échelle la ségrégation de ceux que ces signifiants-maîtres épinglent comme différents, mettant au jour certains aspects de la souffrance contemporaine conceptualisée par Freud sous le nom de Malaise dans la culture
As soon as it was designed, the IQ test was marred by a methodological and ideological bias. However this did not prevent it being widely spread. Today the tendency is to consider “the exceptionally gifted” as founding a new psychopathological category. Is cleverness a new illness? Such is the question at stake. The new era of psychology and psychiatry has designed a clinical approach of the exceptionally gifted child which comes down to legitimating the arbitrariness of the original taxonomy. After shedding light on the historical and logical foundations of the test, the present study means to explain why the general public crave for more and more measurements and numbers, always more of this “generalized evaluation” of which IQ test is the paradigm. A radical transformation of the Master’s Discourse (Lacan) explains the fascinating power of the test. In the era of the inconsistency of the Other, characterized by the faltering of the semblants, what becomes of the subject’s identification? Following Lacan’s logic of the nominating process, master signifiers - such as “exceptionally gifted” - nowadays mass-produced, are positioned as the truth. Granted some form of divine power they are as the “iron mask” of the plus-de-jouir (Lacan). Sometimes, the inventive subject adopts these signifiers for his own. More often they weigh heavy. Listening to the tested exceptionally gifted allows us to understand how on a large scale their segregation is organized, on the basis of their falling under master signifiers which identify them as different, throwing a new light on some aspects of the contemporary suffering which Freud considered as relevant to the discontents of Civilization

Una buona idratazione è fondamentale per l’espletamento delle funzioni fisiologiche più elementari, come ad esempio la regolazione della pressione sanguigna, della temperatura corporea e della digestione. Quando il corpo perde più acqua di quanto ne assume si può verificare il fenomeno della disidratazione. La perdita eccessiva di fluidi può causare diversi squilibri nello stato fisico di un individuo fino a portare, in casi estremi, a condizioni fatali e i soggetti maggiormente a rischio sono: bambini, anziani e atleti. I metodi di indagine attualmente esistenti finalizzati a tale scopo sono sostanzialmente test di laboratorio (sangue, urine) che forniscono dati molto precisi, ma sono invasivi, costosi e non permettono di ottenere un’informazione real-time. Un fenomeno che sta prendendo piede in questi ultimi anni è lo sviluppo di sensori indossabili coi quali è possibile tenere sotto osservazione parametri quali la frequenza cardiaca e il consumo di calorie, ma ancora sono pochi o quasi del tutto assenti i dispositivi che possono fornire attendibili informazioni circa lo stato di idratazione di un soggetto. Obiettivo di questa tesi è quello di illustrare il prototipo di un sensore indossabile, realizzato in laboratorio, in grado di produrre proprio questo tipo di informazione, ossia capace di monitorare lo stato di idratazione di un soggetto in maniera real-time sulla base della misura dell’ impedenza offerta dal suo sudore cutaneo. L’impedenza misurata viene poi trasdotta in una misura di conducibilità tramite un sensore in grado di valutare la variazione della composizione del sudore durante l’esecuzione di un esercizio fisico. Il dispositivo realizzato è stato calibrato e testato in vitro utilizzando soluzioni che riproducono il sudore artificiale. Successivamente, è stato usato per effettuare misure in vivo su un soggetto durante l’esecuzione di un esercizio fisico al fine di valutarne il funzionamento come prototipo indossabile.

Предмет докторске дисертације је рад два ванредна суда – Чрезвичајног суда над бунтовницима (1839) и Преког суда формираног поводом Катанске буне (1844). Први је формиран пошто је пропала Јованова буна, коју је подстакао кнез Милош Обреновић (1815–1839, 1858–1860) с циљем да ослаби утицај својих противника у Државном савету и васпостави своју апсолутну власт. Формирању Чрезвичајног суда претходила је истрага против осумњичених за учешће у буни, коју су водиле чак четири истражне комисије. Оне су током свог рада користила следећа доказна средства: признања окривљених, суочења окривљених, сведоке, суочења окривљених и сведока и писане исправе. Чрезвичајни суд почео је са радом 25. јула 1839. И он је спровео доказни поступак, у којем су коришћена мање-више иста доказна средства. Пошто су изведени докази, Чрезвичајни суд је приступио доношењу пресуда. Мање важни окривљени су или ослобођени кривице или осуђени на благе казне, док су они за које је Чрезвичајни суд устанио да су били покретачи и организатори буне осуђени на вишегодишње казне лишења слободе. Мање важни осуђени помиловани су још за време рада Чрезвичајног суда, да би недуго након тога уследило и помиловање важнијих осуђеника.Катанска буна, догађај који је представљао повод за формирање другог ванредног суда, представља неуспели покушај присталица династије Обреновић да оборе устваобранитељски режим, одиграо се између 22. и 25. септембра 1844. Против неких од заробљених бунтовника истрагу су водили Тома Вучић Перишић, командант војске упућене да угуши побуну, и Стеван Новаковић, судија шабачког окружног суда. Истражни поступак, и то против свих окривљених водио је и сам Преки суд. Сем доказних средстава наведених у излагању о Чрезвичајном суду, у истрази коју је водио Преки суд употребљавано је и јемство представника власти за окривљене. Организатори и предводници буне осуђени су на смрт, они који су знали за буну пре њеног избијања, а то нису пријавили властима, на доживотну робију, лица која су се придружила бунтовницима на казне лишења слободе у различитом трајању, а они који су искористили метеж настао побуном за крађе на телесне казне или затвор од две године. У току 1845. и 1846. један број осуђених ослобођен је даљег издржавања казне, а неким осуђеницима казне су ублажене. Међутим, већина осуђених наставила је да издржава казне по слову пресуда Преког суда.Разлог због којег је Преки суд био строжи него Чрезвичајни суд лежи у политичким околностима у којима су они деловали. Противници кнеза Милоша 1839. нису имали подршку у народу и због тога нису смели строгим кажњавањем да одвраћају потенцијалне присталице од себе. С друге стране, 1844. није постојала реална опасност од повратка Обреновића на српски престо. То је омогућило уставобранитељској власти да много строже казни покушај обреновићевске реакције.
Predmet doktorske disertacije je rad dva vanredna suda – Črezvičajnog suda nad buntovnicima (1839) i Prekog suda formiranog povodom Katanske bune (1844). Prvi je formiran pošto je propala Jovanova buna, koju je podstakao knez Miloš Obrenović (1815–1839, 1858–1860) s ciljem da oslabi uticaj svojih protivnika u Državnom savetu i vaspostavi svoju apsolutnu vlast. Formiranju Črezvičajnog suda prethodila je istraga protiv osumnjičenih za učešće u buni, koju su vodile čak četiri istražne komisije. One su tokom svog rada koristila sledeća dokazna sredstva: priznanja okrivljenih, suočenja okrivljenih, svedoke, suočenja okrivljenih i svedoka i pisane isprave. Črezvičajni sud počeo je sa radom 25. jula 1839. I on je sproveo dokazni postupak, u kojem su korišćena manje-više ista dokazna sredstva. Pošto su izvedeni dokazi, Črezvičajni sud je pristupio donošenju presuda. Manje važni okrivljeni su ili oslobođeni krivice ili osuđeni na blage kazne, dok su oni za koje je Črezvičajni sud ustanio da su bili pokretači i organizatori bune osuđeni na višegodišnje kazne lišenja slobode. Manje važni osuđeni pomilovani su još za vreme rada Črezvičajnog suda, da bi nedugo nakon toga usledilo i pomilovanje važnijih osuđenika.Katanska buna, događaj koji je predstavljao povod za formiranje drugog vanrednog suda, predstavlja neuspeli pokušaj pristalica dinastije Obrenović da obore ustvaobraniteljski režim, odigrao se između 22. i 25. septembra 1844. Protiv nekih od zarobljenih buntovnika istragu su vodili Toma Vučić Perišić, komandant vojske upućene da uguši pobunu, i Stevan Novaković, sudija šabačkog okružnog suda. Istražni postupak, i to protiv svih okrivljenih vodio je i sam Preki sud. Sem dokaznih sredstava navedenih u izlaganju o Črezvičajnom sudu, u istrazi koju je vodio Preki sud upotrebljavano je i jemstvo predstavnika vlasti za okrivljene. Organizatori i predvodnici bune osuđeni su na smrt, oni koji su znali za bunu pre njenog izbijanja, a to nisu prijavili vlastima, na doživotnu robiju, lica koja su se pridružila buntovnicima na kazne lišenja slobode u različitom trajanju, a oni koji su iskoristili metež nastao pobunom za krađe na telesne kazne ili zatvor od dve godine. U toku 1845. i 1846. jedan broj osuđenih oslobođen je daljeg izdržavanja kazne, a nekim osuđenicima kazne su ublažene. Međutim, većina osuđenih nastavila je da izdržava kazne po slovu presuda Prekog suda.Razlog zbog kojeg je Preki sud bio stroži nego Črezvičajni sud leži u političkim okolnostima u kojima su oni delovali. Protivnici kneza Miloša 1839. nisu imali podršku u narodu i zbog toga nisu smeli strogim kažnjavanjem da odvraćaju potencijalne pristalice od sebe. S druge strane, 1844. nije postojala realna opasnost od povratka Obrenovića na srpski presto. To je omogućilo ustavobraniteljskoj vlasti da mnogo strože kazni pokušaj obrenovićevske reakcije.
The subject of this doctoral dissertation are two irregular courts – Irregular Court for Rebels (1839) and Martial Court formed on the occasion of Katanska Rebellion (1844). The first of these two courts was formed after Jovan’s rebellion, incited by Prince Miloš Obrenović (1815–1839, 1858–1860) with the goal of weakening the authority of his opponents in State Council and renewal of the ruler’s absolute power, had been quenched. Antecedent of the Irregular Court’s establishment, four investigation boards had undertaken the investigation against the persons suspected of participation in Jovan’s Rebellion. In the course of the inquiry the boards produced following evidence: suspects’ confessions, confrontations of suspects, witnesses, confrontations of suspects with witnesses and documentary evidence. Irregular Court commenced its work on July 25th 1839. This institution also performed production of evidence, during which more or less above-cited sorts of evidence were produced. After the evidence had been shown, Irregular Court turned to deliberation. Less important suspects were either acquitted or sentenced to mild punishments, as those who Irregular Court found organizers and instigators of Jovan’s Rebellion are condemned to multiyear prison sentences. The convicts of less significance were pardoned while Irregular Court’s activity was still in progress. Not long after, more important convicts were granted pardon as well. Katane (Hussars)’s Rebellion, the event that occasioned the formation of the second irregular court, represents an unsuccessful attempt of Obrenović dynasty's followers to overthrow Constitution-Defenders' regime. The inquiry against some of the suspects was conducted by Toma Vučić Perišić, the commander of the troops sent to put down Katane's Rebellion, and Stevan Novaković, a judge of Šabac District Court. Martial Court also carried out investigations, of which all suspects were subjects. Besides evidence mentioned in previous paragraph, vouchments for a suspects' moral integrity and rightful political attitude, given by the representatives of local authorities, were also used in the proceedings led by Martial Court. The organizers and instigators of Katane's Rebellion were sentenced to death, the persons who knew that the rebellion would break out and did not report it to the authorities were condemned to perpetual forced labor, the individuals who joined the rebells were sentenced to prison whose duration varied. The people who used Rebellion-provoked tumultation to commit thefts and burgalries were, according to verdicts of Court Martial, to undertake corporal punishments or two-year prison. In 1845 and 1846 a certain number of convicts was pardonned, as some sentences were mitigated. Nevertheless, most of them were not granted pardon.The reason of Martial Court's greater harshness in comparison with Irregular Court lies in political circumstances in which the two institutions worked. Prince Miloš’opponents were not favorite among the people. Therefore they did not want to even more deteriorate their low popularity by admitting Irregular Court to pronounce severe punishments. On the other hand, in 1844 Obrenovićs’ partisans were not serious threat to Constitution-Defenders regime. It enabled power-holders to punish an attempt of Obrenović’s reaction more severely.

L’obiettivo di tale tesi è la caratterizzazione impedenziometrica di elettrodi flessibili, partendo dagli studi che trattano la possibilità di individuare un tumore della pelle tramite una misura di impedenza non invasiva, piuttosto che tramite biopsia. Si sottoporranno quindi 8 elettrodi, presi come campioni, a vari test, per verificare l’andamento del loro modulo e della loro fase in un determinato range di frequenze. Si testeranno le loro misure prima in una soluzione salina al 0.9% di NaCl e poi in 5 soluzioni di sudore artificiale con diversa molarità. Si andrà a valutare anche quale elettrodo mantiene le sue caratteristiche anche in una prova a lungo termine. Infine, si osserverà quale elettrodo risponde in maniera migliore a una prova su pelle, variando anche la quantità di gel elettrolita applicato.

Background Heat acclimation and precooling are strategies commonly used to mitigate heat stress during exercise in the heat. Physiological adaptations during heat acclimation include lower core temperature (Tcore), lower heart rate (HR), and increased sweat output during exercise at a given workload. Adjusting the training intensity to meet specific energetic demands during heat acclimation may be as important for performance improvements. However, the challenge of maintaining the quality of training during heat exposure without concomitant accumulative fatigue remains. Precooling presents a potential strategy to maintain the quality of training during heat exposure but may have some inhibitory effects on thermoregulatory adaptations. Of the various precooling techniques, cold water immersion (CWI) and ingestion of ice slushy (ICE) are different in terms of application (external versus internal) and their ensued effects on the sweat response, skin temperature (Tsk) and Tcore. Therefore, the primary purpose of this thesis was to examine the effects of CWI and ICE on sudo- and vasomotor responses and adaptations to heat acclimation. Aims Study 1 aimed to determine the effects of ICE and CWI on the psychophysiological responses and endurance exercise performance through meta-analysis. Subsequently, two studies were conducted to: 1) examine the effects of CWI and ICE on the changes in rectal temperature (Tre) and Tsk, perceived thermal sensation and sweat responses during constant-paced exercise in the heat; and 2) determine the effects of altered physical thermal state (Tre and Tsk) and perceived thermal sensation following ICE and CWI on thermoregulatory behaviour (i.e., total work output and mean power output [MPO]) during cycling in the heat. Finally, the purpose of study 4 was to investigate the influence of regular precooling by CWI as part of a heat acclimation regimen on thermoregulatory adaptations and changes in exercise performance. Methods For study 1, 22 studies were included in the meta-analysis based on the following criteria: 1) cooling was performed with ICE or CWI before the exercise; 2) exercise longer than 6 min was performed in ambient temperature ≥ 26°C; and 3) crossover study design with a noncooling passive control condition. Weighted average effect sizes in Hedges’ g and 95% confidence intervals (CIs) were calculated from the mean difference and pooled SD. Studies 2 and 3 were randomised crossover studies with three conditions (ICE, CWI and no cooling control [CON]). The participants in studies 2 and 3 were recreationally active males aged between 19-40 y. Each trial was preceded by 30 min of CWI (22.0 ± 0.2°C), ICE (- 0.3 ± 0.4°C) or CON. In study 2, 11 men cycled at 40 or 50% of peak aerobic power for 60 min (33.2 ± 0.3°C, 45.9 ± 0.5% relative humidity [RH]). In study 3, 11 men cycled for 60 min at perceived exertion (RPE) equivalent to 15 (i.e., “hard”) (33.9 ± 0.2°C and 42.5 ± 3.9% RH). Local sweat rate was measured by capacitance hygrometry. Using near-infrared spectroscopy and laser Doppler flowmetry, changes in muscle blood volume and oxygenation and skin perfusion were examined. In study 4, 20 male recreational triathletes and cyclists (27-50 y) completed 10 sessions of 60-min cycling at RPE 15 within 14 days in the heat (35.3 ± 0.3°C, 53.4 ± 1.9 % RH), preceded by no cooling (CON, n = 10) or 30 min of CWI at 21.9 ± 0.5°C (PRECOOL, n = 10). Only 19 participants (n = 9 and 10 for CON and PRECOOL, respectively) completed heat stress tests before and after heat acclimation, which involved 25 min of cycling at 60% V̇O2peak and a 20- km time trial in the heat (35.3 ± 0.2°C, 53.8 ± 0.7% RH). Results The meta-analysis (study 1) revealed that CWI improved exercise performance (Hedges’ g [95CI] +0.53 [0.28; 0.77]) and resulted in greater increase (ΔEX) in Tsk (+4.15 [3.1; 5.21]) during the exercise. Additionally, lower peak Tcore (-0.93 [-1.18; -0.67]), whole body sweat loss (-0.74 [-1.18; -0.3]), and thermal sensation (-0.5 [-0.8; -0.19]) were observed without concomitant changes in ΔEX-Tcore (+0.19 [-0.22; 0.6]), peak Tsk (-0.67 [-1.52; 0.18]), peak HR (-0.14 [-0.38; 0.11]), and RPE (-0.14 [-0.39; 0.12]). ICE had no clear effect on exercise performance (+0.2 [-0.07; 0.46]) but resulted in greater ΔEX-Tcore (+1.02 [0.59; 1.45]) and ΔEX-Tsk (+0.34 [0.02; 0.67]) without concomitant changes in peak Tcore (-0.1 [-0.48; 0.28]), peak Tsk (+0.1 [-0.22; 0.41]), peak HR (+0.08 [-0.19; 0.35]), whole body sweat loss (-0.12 [- 0.42; 0.18]), thermal sensation (-0.2 [-0.49; 0.1]) and RPE (-0.01 [-0.33; 0.31]). In studies 2 and 3, ICE decreased Tre by ~0.3°C during precooling, compared with CON and CWI (p < 0.05). CWI decreased Tsk by ~4°C (p < 0.05) during precooling, compared with CON but did not have any significant cooling effect on Tre. In both studies, ICE decreased Tre- Tsk gradient during the first 5 min of exercise when compared with CON (p < 0.05), and CWI increased Tre-Tsk gradient during the initial 15-20 min of exercise when compared with CON and ICE (p < 0.05). In both studies, CWI (p < 0.001) and ICE (p = 0.019) delayed sweat recruitment by 1-5 min, compared with CON but did not significantly affect the body temperature threshold for sweating. In studies 2 and 3, muscle blood volume was decreased during CWI and during the initial 10-20 min of exercise when compared with CON and ICE (p < 0.05); however, there was no significant condition effect on muscle oxygenation. In study 2, mean HR during the exercise was decreased by ~5 bpm in CWI when compared with CON only (p = 0.025). In study 3, thermal sensation was lower in CWI for up to 35-40 min during the exercise, compared with CON and ICE (p < 0.05). Additionally, thermal sensation was lower in ICE than in CON during the first 20 min of exercise (p < 0.05). Thigh skin perfusion was decreased during CWI (p = 0.012) and ICE (p = 0.044), compared with CON but was not different between conditions during the exercise (p > 0.05, study 3). MPO was greater in CWI when compared with CON only (p = 0.024, CON: 130 ± 20 W, ICE: 128 ± 25 W, CWI: 138 ± 18 W, study 3). In study 4, changes in MPO (p = 0.024) and HR (p = 0.028) during heat acclimation were lower in CON (MPO: 97.4 ± 8.1%, ΔHR: -7 ± 4 bpm) than in PRECOOL (MPO: 102.9 ± 6.6%, ΔHR: -1 ± 7 bpm). HR during cycling at 60% V̇O2peak was decreased from the first heat stress test in both groups (p < 0.001). Tre, Tsk, sweat responses, Tre threshold and sensitivity for sweating, thigh skin perfusion, thermal sensation and RPE during the heat stress tests were not affected by heat acclimation in both groups (all p > 0.05). MPO (p = 0.016, Cohen’s effect size [d] = 0.93) and finish time (p = 0.013, d = 0.97) for the 20-km time trials were improved from the first heat stress test in PRECOOL but were not significantly changed in CON (MPO: p = 0.052 and d = 0.76, finish time: p = 0.140 and d = 0.54).

La hiperhidrosis primaria esencial es una entidad clínica caracterizada, principalmente, por una sudoración excesiva a nivel palmar, plantar y axilar, asociándose una sintomatología general sugestiva de hiperactividad simpática, como es el enrojecimiento facial, palpitaciones, temblor, cefalea y un elevado nivel de ansiedad, síntomas difíciles de considerar como causa o consecuencia. No se conoce la etiología de este trastorno; sin embargo, existen diferentes explicaciones acerca del mecanismo de producción del mismo, y tampoco se conoce con exactitud la anatomía del sistema nervioso simpático de la vía ocular. Los tratamientos médicos son ineficaces y/o temporales, lo cual ha motivado la búsqueda de una solución quirúrgica. Por el momento, la denervación simpática torácica es un procedimiento eficaz para el control de la sudoración palmar, axilar y plantar. La simpaticolisis torácica superior puede presentar el inconveniente de presentar efectos colaterales secundarios a la propia denervación simpática, tanto a nivel sistémico, como sobre la región craneofacial, siendo la función oculomotora una de ellas. La simpaticolisis lumbar puede presentar complicaciones graves como eyaculación precoz en el caso de los hombres, o problemas en el control de esfínteres en el caso de las mujeres. Al estar implicados en el tratamiento quirúrgico de este trastorno, una vez confirmado y ratificado el tratamiento quirúrgico como tratamiento estándar nos vemos obligados a enfocar nuestra investigación sobre los efectos secundarios de la técnica quirúrgica y sus repercusiones. Por todo ello hemos dirigido la atención al estudio de la denervación simpática T2-T3 y su efecto sobre la vía óculo-simpática y la redistribución del sudor en pacientes con hiperhidrosis primaria.

Дискурс анализа је интердисциплинарно подручје истраживања којепосматра језик као делатност. Она се бави питањима разговора и текста и то такошто је фокус пажње подједнако и на саговорницима, и на контексту, и навербалној поруци.Њу у домаћу академску заједницу уводи Свенка Савић, најпре у оквирунаставе на основним студијама Одсека за српски језик и лингвистикуФилозофског факултета у Новом Саду. За овај предмет на Универзитету у НовомСаду објављује уџбеник под називом Дискурс анализа (1993) и формира, заједноса бројним сарадницама, пројекат „Новосадски корпус разговорног српскогјезика”. Осим на Одсеку за српски језик и лингвистику, данас се анализадискурса као наставни предмет изучава и на Одсеку за журналистику иделимично на Одсеку за англистику.Крајем 20. и почетком 21. века у анализи говорних и писаних обликадискурса јавља се нов приступ проучавања под називом критичка анализадискурса (КАД). У оквиру критичке анализе дискурса, истраживачи се највишебаве приказом демонстрације моћи, контроле и друштвених неједнакости уразличитим институцијама, а једну такву институцију представља и суд.Примену у истраживању дискурсних особина разговора у суду значајнијевидимо у радовима са енглеског говорног подручја, док су друга језичкаподручја мање истражена. Предмет проучавања ових радова су различитеграматичке и дискурсне какрактеристике разговора у суду, као што су: употребаноминализација, пасива и техничких термина током размена у судском поступку(Gibbons, 1999), доминантан положај судије/пороте у простору суднице као идемонстрацију моћи првенством права говорења током судског поступка(Přidalová, 1999), анализа типова питања током судског поступка и њихова улогау усмеравању исказа учесника (Cotterill, 2003).У литератури на српском језику радови који се баве правном и судскомпроблематиком у фокусу пажње углавном имају текст – писани облик судскогдискурса, који се манифестује кроз законе и разне прописе у којима се закон примењује (Јанићијевић, 2010) или се баве одликама жанра текста судскихпресуда (Макевић, 2014), а мали је број радова који се баве особинама разговорау суду током судског поступка (Јанковић, 2002).Предмет овог рада јесу особине дискурса разговора у суду (ДРС). Терминдискурс разговора у суду подразумева онај тип разговора у којем се један(раз)говорни догађај остварује просторно у јавној сфери (у судници), у којојучествује више особа са одређеним социјалним и дискурсним улогама. У центрупажње су дискурсне стратегије током размена судије са другим учесницима усудском поступку током судске расправе, са посебним освртом на интеракцијуизмеђу судије и (оп)туженог.Циљ овог истраживања је да се анализира, опише и објасни дискурс судскепраксе у институцији суда у Србији и покажу односи друштвене моћисаговорника укључених у судску расправу.Хипотеза је да ће анализа разговора судије са (оп)туженим бити добарпоказатељ начина на који се у суду спроводе у праксу законодавне одредбе(о дискриминацији, равноправности и сл.) и како се интерпретира друштвенамоћ.Теоријско-методолошки оквир коришћен у овом раду је у сагласности саанализом употребе језика, са језичком делатности, пре свега са учењемхоландског лингвисте Тојнa ван Дајка (Van Dijk, 2009) о моћи, и у сагласности стеоријом учтивости Пенелопи Браун и Стивена Левинсона (Brown and Levinson,1987). Обе теорије прати дескриптивни приказ одабраних узорака емпиријскогматеријала.У раду користим метод прикупљања и анализе материјала устаљен уанализи дискурса (Савић, 1993). Емпиријски материјал представља узорак од 9судских расправа из два временска периода: 4 судске расправе снимљене 1991.године и 5 судских расправа снимљених након 24 године (2015). Укупно јеснимљено 180,13 минута разговора, односно 140 страна текста трансркибованогу писану форму припремљену за анализу. Јединице анализе су речи, размене ипараграфи (Савић, 1993: 57–61).Резултати истраживања показују да је у разговору у суду доминантна улогасуткиње, која има институционално дату моћ да води судску расправу и доносирешења и пресуде. Из доминантне позиције произлази и њена комуникативна идруштвена моћ коју остварује применом различитих разговорних стратегија каошто су: стратегија постављања питања, усмеравања разговора, одређивањапонашања других у разговору, започињања и завршавања разговора, употребапрофесионалне терминологије, стратегија ословљавања, извођења закључка,причања прича, прекидања и преклапања разговора са саговорницима.За разлику од суткиње, (оп)тужени је правни лаик са малим дискурснимучинком. Његова подређена улога огледа се у стратегијама: одговарања напитања, покушају усмеравања разговора, покушају постављања питања,принципу сарадње, ословљавању, понављању и самопонављању, прекидању ипреклапању, причању приче и оклевању.На основу резултата анализе судских расправа може се закључити да једискурс разговора у суду хибридни жанр. У њему се на граматичком, лексичком,семантичком и прагматичком нивоу сједињавају формални писани правнидискурс и неформални разговорни језик свакодневне комуникације.Предлог за непосредну праксу. Потребно је успоставити успешнији моделкомуникације у суду током интеракција између правних стручњака (судија, јавних тужилаца, адвоката) и правних лаика: избегавањем непознатетерминoлогије, употребом једноставних реченица (избегавањем пасивне ибезличне конструкције и номинализације), коришћењем учтивих фраза и родноосетљивог језика, како би се језик у службеној употреби у институцији судасаобразио говору саговорника који нису део судске хијерархије. 
Diskurs analiza je interdisciplinarno područje istraživanja kojeposmatra jezik kao delatnost. Ona se bavi pitanjima razgovora i teksta i to takošto je fokus pažnje podjednako i na sagovornicima, i na kontekstu, i naverbalnoj poruci.NJu u domaću akademsku zajednicu uvodi Svenka Savić, najpre u okvirunastave na osnovnim studijama Odseka za srpski jezik i lingvistikuFilozofskog fakulteta u Novom Sadu. Za ovaj predmet na Univerzitetu u NovomSadu objavljuje udžbenik pod nazivom Diskurs analiza (1993) i formira, zajednosa brojnim saradnicama, projekat „Novosadski korpus razgovornog srpskogjezika”. Osim na Odseku za srpski jezik i lingvistiku, danas se analizadiskursa kao nastavni predmet izučava i na Odseku za žurnalistiku idelimično na Odseku za anglistiku.Krajem 20. i početkom 21. veka u analizi govornih i pisanih oblikadiskursa javlja se nov pristup proučavanja pod nazivom kritička analizadiskursa (KAD). U okviru kritičke analize diskursa, istraživači se najvišebave prikazom demonstracije moći, kontrole i društvenih nejednakosti urazličitim institucijama, a jednu takvu instituciju predstavlja i sud.Primenu u istraživanju diskursnih osobina razgovora u sudu značajnijevidimo u radovima sa engleskog govornog područja, dok su druga jezičkapodručja manje istražena. Predmet proučavanja ovih radova su različitegramatičke i diskursne kakrakteristike razgovora u sudu, kao što su: upotrebanominalizacija, pasiva i tehničkih termina tokom razmena u sudskom postupku(Gibbons, 1999), dominantan položaj sudije/porote u prostoru sudnice kao idemonstraciju moći prvenstvom prava govorenja tokom sudskog postupka(Přidalová, 1999), analiza tipova pitanja tokom sudskog postupka i njihova ulogau usmeravanju iskaza učesnika (Cotterill, 2003).U literaturi na srpskom jeziku radovi koji se bave pravnom i sudskomproblematikom u fokusu pažnje uglavnom imaju tekst – pisani oblik sudskogdiskursa, koji se manifestuje kroz zakone i razne propise u kojima se zakon primenjuje (Janićijević, 2010) ili se bave odlikama žanra teksta sudskihpresuda (Makević, 2014), a mali je broj radova koji se bave osobinama razgovorau sudu tokom sudskog postupka (Janković, 2002).Predmet ovog rada jesu osobine diskursa razgovora u sudu (DRS). Termindiskurs razgovora u sudu podrazumeva onaj tip razgovora u kojem se jedan(raz)govorni događaj ostvaruje prostorno u javnoj sferi (u sudnici), u kojojučestvuje više osoba sa određenim socijalnim i diskursnim ulogama. U centrupažnje su diskursne strategije tokom razmena sudije sa drugim učesnicima usudskom postupku tokom sudske rasprave, sa posebnim osvrtom na interakcijuizmeđu sudije i (op)tuženog.Cilj ovog istraživanja je da se analizira, opiše i objasni diskurs sudskeprakse u instituciji suda u Srbiji i pokažu odnosi društvene moćisagovornika uključenih u sudsku raspravu.Hipoteza je da će analiza razgovora sudije sa (op)tuženim biti dobarpokazatelj načina na koji se u sudu sprovode u praksu zakonodavne odredbe(o diskriminaciji, ravnopravnosti i sl.) i kako se interpretira društvenamoć.Teorijsko-metodološki okvir korišćen u ovom radu je u saglasnosti saanalizom upotrebe jezika, sa jezičkom delatnosti, pre svega sa učenjemholandskog lingviste Tojna van Dajka (Van Dijk, 2009) o moći, i u saglasnosti steorijom učtivosti Penelopi Braun i Stivena Levinsona (Brown and Levinson,1987). Obe teorije prati deskriptivni prikaz odabranih uzoraka empirijskogmaterijala.U radu koristim metod prikupljanja i analize materijala ustaljen uanalizi diskursa (Savić, 1993). Empirijski materijal predstavlja uzorak od 9sudskih rasprava iz dva vremenska perioda: 4 sudske rasprave snimljene 1991.godine i 5 sudskih rasprava snimljenih nakon 24 godine (2015). Ukupno jesnimljeno 180,13 minuta razgovora, odnosno 140 strana teksta transrkibovanogu pisanu formu pripremljenu za analizu. Jedinice analize su reči, razmene iparagrafi (Savić, 1993: 57–61).Rezultati istraživanja pokazuju da je u razgovoru u sudu dominantna ulogasutkinje, koja ima institucionalno datu moć da vodi sudsku raspravu i donosirešenja i presude. Iz dominantne pozicije proizlazi i njena komunikativna idruštvena moć koju ostvaruje primenom različitih razgovornih strategija kaošto su: strategija postavljanja pitanja, usmeravanja razgovora, određivanjaponašanja drugih u razgovoru, započinjanja i završavanja razgovora, upotrebaprofesionalne terminologije, strategija oslovljavanja, izvođenja zaključka,pričanja priča, prekidanja i preklapanja razgovora sa sagovornicima.Za razliku od sutkinje, (op)tuženi je pravni laik sa malim diskursnimučinkom. NJegova podređena uloga ogleda se u strategijama: odgovaranja napitanja, pokušaju usmeravanja razgovora, pokušaju postavljanja pitanja,principu saradnje, oslovljavanju, ponavljanju i samoponavljanju, prekidanju ipreklapanju, pričanju priče i oklevanju.Na osnovu rezultata analize sudskih rasprava može se zaključiti da jediskurs razgovora u sudu hibridni žanr. U njemu se na gramatičkom, leksičkom,semantičkom i pragmatičkom nivou sjedinjavaju formalni pisani pravnidiskurs i neformalni razgovorni jezik svakodnevne komunikacije.Predlog za neposrednu praksu. Potrebno je uspostaviti uspešniji modelkomunikacije u sudu tokom interakcija između pravnih stručnjaka (sudija, javnih tužilaca, advokata) i pravnih laika: izbegavanjem nepoznateterminologije, upotrebom jednostavnih rečenica (izbegavanjem pasivne ibezlične konstrukcije i nominalizacije), korišćenjem učtivih fraza i rodnoosetljivog jezika, kako bi se jezik u službenoj upotrebi u instituciji sudasaobrazio govoru sagovornika koji nisu deo sudske hijerarhije. 
Discourse analysis is an interdisciplinary research area which observes language as an activity. It deals with issues of conversation and text focusing its attention evenly on interlocutors, context and verbal message.It was introduced to our academic community by Svenka Savić, firstly as teaching within undergraduate studies at Department of Serbian language and linguistics, at the Faculty of Philosophy in Novi Sad.  She published a course book Discourse Analysis (1993) for this subject at the University of Novi Sad and established, with numerous associates, a project „The Corpus of Novi Sad conversational Serbian language”. Today, apart from Department of Serbian language and linguistics, discourse analysis as a subject is taught at Department of journalism and partly at Department of English language and literature.At the end of the XX and the beginning of the XXI century, a new approach of analysing spoken and written forms of discourse appeared, under the name critical discourse analysis (CDA). Within CDA, the researchers mainly deal with the representation of demonstration of power, control and social inequalities in various institutions, one of which is the court.Its application in the study of discourse aspects in courtroom, CDA has particularly found in the works from Anglosphere, while other language spheres have not been researched enough. The subject matter of these works are different grammatical and discourse features of talk in the courtroom such as the use of nominalization, passive construction and technical terms during judical proceedings (Gibbons, 1999), dominant position of a judge/jury in the courtroom as well as  demonstration of power by priority turn-taking during judical proceedings (Přidalová, 1999), analysis of types of questions during judical proceedings and their role in guiding the participants’ statements (Cotterill, 2003).In the literature in Serbian language, the works dealing with legal and judical matters mainly focus on the text- written form of courtroom discourse, which manifests itself through laws and their various regulations (Janićijević, 2010) or deal with the aspects of the genre of the verdict text (Makević, 2014), and very few works deal with the aspects of talk in the courtroom during judical proceedings (Janković, 2002).The features of courtroom discourse (CD) are the subject of this work. The term courtroom discourse means the type of talk where one spoken event is realized in spatially public sphere (in a courtroom), where several persons with different social and discourse roles participate. Discourse strategies during interaction of a judge with other participants in judical proceeding during hearing are in the spotlight, with particular reference to the interaction between the judge and the defendant/accused.The aim of this research is to analyse, describe and explain the discourse of case-law in the institution of court in Serbia and to show relations of social power of participants involved in judical proceedings.It is supposed that tha analysis of conversation between the judge and the defendant/accused will be an excellent indicator of the manner in which the court implements legislative provisions (оn discrimination, equality and etc.) and how social power is defined.The theoretical and methodological framework in this study is in compliance with analysis of use of language, with linguistic activity, above all with the approach of Dutch linguist Teun van Dijk (2009) on power, and in accordance with the Politeness theory by Penelope Brown and Stephen Levinson (1987). Both thories are accompanied by descriptive review of selected examples of empirical material.I have used the method of collecting and analysing material rooted in analysis of discourse (Savić, 1993). The empirical material represents nine courtroom hearings from two periods of time: 4 in 1991 and 5 courtroom hearings recorded 24 years later (2015). There are 180.13 minutes of recorded conversation, that is 140 pages of text transcribed into written form prepared for analysis. The units of analysis are words, exchanges and paragraphs (Savić, 1993: 57–61).The results of the research show that in a courtroom discourse the role of the judge is undoubtedly dominant, having the institutionally given power to lead the hearing and reaches decisions and verdicts. Her communicative as well as social power arises from the domination which she realizes this applying various conversation strategies such as: strategy of posing questions, directing the talk, adjusting behaviour of other interlocutors, starting and ending the talk, use of professional terminology, addresssing strategy, drawing the conclusions, storytelling, interupting and overlapping the interlocutors.Unlike the judge, the defendant/accused is a law layman with small discoursive contribution. Their subordinated role is reflected in the following strategies: question answering, attempting to direct the talk, attempting to pose a question, principle of cooperation, addressing, repeating and self-repeating, interupting and overlapping, storytelling and hesitating.Based on the results of the analysis of the courtroom hearings, we can draw the conclusion that the courtroom discourse is rather hybrid in its genre. It represents, on grammatic, lexic, semantic and pragmatic level, merging of  formal written legal discourse and informal spoken language of everday conversation.Suggestion for direct practice. It is essential to establish more successful model of communication in a courtroom during the interaction among law experts (judges, Abstract:ABDiscourse analysis is an interdisciplinary research area which observes language as an activity. It deals with issues of conversation and text focusing its attention evenly on interlocutors, context and verbal message.It was introduced to our academic community by Svenka Savić, firstly as teaching within undergraduate studies at Department of Serbian language and linguistics, at the Faculty of Philosophy in Novi Sad.  She published a course book Discourse Analysis (1993) for this subject at the University of Novi Sad and established, with numerous associates, a project „The Corpus of Novi Sad conversational Serbian language”. Today, apart from Department of Serbian language and linguistics, discourse analysis as a subject is taught at Department of journalism and partly at Department of English language and literature.At the end of the XX and the beginning of the XXI century, a new approach of analysing spoken and written forms of discourse appeared, under the name critical discourse analysis (CDA). Within CDA, the researchers mainly deal with the representation of demonstration of power, control and social inequalities in various institutions, one of which is the court.Its application in the study of discourse aspects in courtroom, CDA has particularly found in the works from Anglosphere, while other language spheres have not been researched enough. The subject matter of these works are different grammatical and discourse features of talk in the courtroom such as the use of nominalization, passive construction and technical terms during judical proceedings (Gibbons, 1999), dominant position of a judge/jury in the courtroom as well as  demonstration of power by priority turn-taking during judical proceedings (Přidalová, 1999), analysis of types of questions during judical proceedings and their role in guiding the participants’ statements (Cotterill, 2003).In the literature in Serbian language, the works dealing with legal and judical matters mainly focus on the text- written form of courtroom discourse, which manifests itself through laws and their various regulations (Janićijević, 2010) or deal with the aspects of the genre of the verdict text (Makević, 2014), and very few works deal with the aspects of talk in the courtroom during judical proceedings (Janković, 2002).The features of courtroom discourse (CD) are the subject of this work. The term courtroom discourse means the type of talk where one spoken event is realized in spatially public sphere (in a courtroom), where several persons with different social and discourse roles participate. Discourse strategies during interaction of a judge with other participants in judical proceeding during hearing are in the spotlight, with particular reference to the interaction between the judge and the defendant/accused.The aim of this research is to analyse, describe and explain the discourse of case-law in the institution of court in Serbia and to show relations of social power of participants involved in judical proceedings.It is supposed that tha analysis of conversation between the judge and the defendant/accused will be an excellent indicator of the manner in which the court implements legislative provisions (оn discrimination, equality and etc.) and how social power is defined.The theoretical and methodological framework in this study is in compliance with analysis of use of language, with linguistic activity, above all with the approach of Dutch linguist Teun van Dijk (2009) on power, and in accordance with the Politeness theory by Penelope Brown and Stephen Levinson (1987). Both thories are accompanied by descriptive review of selected examples of empirical material.I have used the method of collecting and analysing material rooted in analysis of discourse (Savić, 1993). The empirical material represents nine courtroom hearings from two periods of time: 4 in 1991 and 5 courtroom hearings recorded 24 years later (2015). There are 180.13 minutes of recorded conversation, that is 140 pages of text transcribed into written form prepared for analysis. The units of analysis are words, exchanges and paragraphs (Savić, 1993: 57–61).The results of the research show that in a courtroom discourse the role of the judge is undoubtedly dominant, having the institutionally given power to lead the hearing and reaches decisions and verdicts. Her communicative as well as social power arises from the domination which she realizes this applying various conversation strategies such as: strategy of posing questions, directing the talk, adjusting behaviour of other interlocutors, starting and ending the talk, use of professional terminology, addresssing strategy, drawing the conclusions, storytelling, interupting and overlapping the interlocutors.Unlike the judge, the defendant/accused is a law layman with small discoursive contribution. Their subordinated role is reflected in the following strategies: question answering, attempting to direct the talk, attempting to pose a question, principle of cooperation, addressing, repeating and self-repeating, interupting and overlapping, storytelling and hesitating.Based on the results of the analysis of the courtroom hearings, we can draw the conclusion that the courtroom discourse is rather hybrid in its genre. It represents, on grammatic, lexic, semantic and pragmatic level, merging of  formal written legal discourse and informal spoken language of everday conversation.Suggestion for direct practice. It is essential to establish more successful model of communication in a courtroom during the interaction among law experts (judges, prosecutors, lawyers) and law laymen: avoiding unfamiliar terms, using simple sentences (avoiding passive and impersonal constructions and nominalizations), using polite and gender-sensitive language, so as to assimilate the use of official institutional language with the speech of interlocutors who are not part of the court hierarchy.