Journal articles on the topic 'Problème Max-SAT'

The simplicity of the maximum satisfiability problem (MAX-SAT) combined with its applicability in many areas of artificial intelligence and computing science made it one of the fundamental optimization problems. This NP-complete problem refers to the task of finding a variable assignment that satisfies the maximum number of clauses (or the sum of weights of satisfied clauses) in a Boolean formula. The Walksat algorithm is considered to be the main skeleton underlying almost all local search algorithms for MAX-SAT. Most local search algorithms including Walksat rely on the 1-flip neighborhood structure. This paper introduces a variable neighborhood walksat-based algorithm. The neighborhood structure can be combined easily using any local search algorithm. Its effectiveness is compared with existing algorithms using 1-flip neighborhood structure and solvers such as CCLS and Optimax from the eighth MAX-SAT evaluation.

In this paper, a genetic model based on the operations of recombination and mutation is studied and applied to combinatorial optimization problems. Results are: The equations of the deterministic dynamics in the thermodynamic limit (infinite populations) are derived and, for a sufficiently small mutation rate, the attractors are characterized; A general approximation algorithm for combinatorial optimization problems is designed. The algorithm is applied to the Max Ek-Sat problem, and the quality of the solution is analyzed. It is proved to be optimal for k≥3 with respect to the worst case analysis; for Max E3-Sat the average case performances are experimentally compared with other optimization techniques.

Combinatorial optimization problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with a preference function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show – in a particular context – whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism. We provide learnability results within the realizable and agnostic settings, as well as hassle, an implementation based on syntax-guided synthesis and showcase its promise on recovering synthetic and benchmark instances from examples.

We prove that the sequential approximation algorithms for the problems [Formula: see text] and [Formula: see text] proposed in [9] are [Formula: see text]-hard with respect to the logarithmic space reducibility. As a corollary, these two algorithms cannot be implemented efficiently in parallel unless [Formula: see text].

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log2⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost.

Considerable effort has been spent extending the scope of planning beyond propositional domains to include, for example, time and numbers. Each extension has been designed as a separate specific semantic enrichment of the underlying planning model, with its own syntax and customised integration into a planning algorithm. Inspired by work on SAT Modulo Theories (SMT) in the SAT community, we develop a modelling language and planner that treat arbitrary first order theories as parameters. We call the approach Planning Modulo Theories (PMT). We introduce a modular language to represent PMT problems and demonstrate its benefits over PDDL in expressivity and compactness. We present a generalisation of the $h_{max}$ heuristic that allows our planner, PMTPlan, to automatically reason about arbitrary theories added as modules. Over several new and existing benchmarks, exploiting different theories, we show that PMTPlan can significantly out-perform an existing planner using PDDL models.

We give a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT as well as problems where the objective function is a weighted sum of products of Ising variables, all terms of the same degree D; this problem is called weighted MAX-ED-LIN2. We require that the optimal solution be unique for odd D and doubly degenerate for even D; however, we expect that the algorithm still works without this condition and we show how to reduce to the case without this assumption at the cost of an additional overhead. While the time required is still exponential, the algorithm provably outperforms Grover's algorithm assuming a mild condition on the number of low energy states of the target Hamiltonian. The detailed analysis of the runtime dependence on a tradeoff between the number of such states and algorithm speed: fewer such states allows a greater speedup. This leads to a natural hybrid algorithm that finds either an exact or approximate solution.

MAX k-SAT is one of the archetypal NP-hard problems. Its variation called random MAX k-SAT problem was introduced in order to understand how hard it is to solve instances of the problem on average. The most common model to sample random instances is the uniform model, which has received a large amount of attention. However, the uniform model often fails to capture important structural properties we observe in the real-world instances. To address these limitations, a more general (in a certain sense) model has been proposed, the configuration model, which is able to produce instances with an arbitrary distribution of variables' degrees, and so can simulate biases in instances appearing in various applications. Our overall goal is to expand the theory built around the uniform model to the more general configuration model for a wide range of degree distributions. This includes locating satisfiability thresholds and analysing the performance of the standard heuristics applied to instances sampled from the configuration model. In this paper we analyse the performance of the pure literal elimination rule. We provide an equation that given an underlying degree distribution gives the number of clauses the pure literal elimination rule satisfies w.h.p. We also show how the distribution of variable degrees changes over time as the algorithm is being executed.

We show that the NP-complete problems max cut and independent set can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. The 5-local Hamiltonian problem was the first problem to be shown to be complete for the quantum complexity class QMA — the quantum analog of NP. Subsequently, it was shown that 3-locality is already sufficient for QMA-completeness. It is still not known whether the 2-local Hamiltonian problem is QMA-complete. Therefore it is interesting to determine what problems can be reduced to the 2-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulated as a 3-local Hamiltonian problem. We extend his result by showing that 2-locality is sufficient in order to encompass NP.

Goal utility dependencies arise when the utility of achieving a goal depends on the other goals that are achieved with it. This complicates the planning procedure because achieving a new goal can potentially alter the utilities of all the other goals currently achieved. In this paper, we present an encoding procedure that enables general-purpose Max-SAT solvers to be used to solve planning problems with goal utility dependencies. We compare this approach to one using integer programming via an empirical evaluation using benchmark problems from past international planning competitions. Our results indicate that this approach is competitive and sometimes more successful than an integer programming one -- solving two to three times more subproblems in some domains, while being outperformed by only a significantly smaller margin in others.

Modern metaheuristic methodologies rely on well defined neighborhood structures and efficient means for evaluating potential moves within these structures. Move mechanisms range in complexity from simple 1-flip procedures where binary variables are “flipped” one at a time, to more expensive, but more powerful, r-flip approaches where “r” variables are simultaneously flipped. These multi-exchange neighborhood search strategies have proven to be effective approaches for solving a variety of combinatorial optimization problems. In this paper, we present a series of theorems based on partial derivatives that can be readily adopted to form the essential part of r-flip heuristic search methods for Pseudo-Boolean optimization. To illustrate the use of these results, we present preliminary results obtained from four simple heuristics designed to solve a set of Max 3-SAT problems.

Magic squares, chess-like problems, cryptarithmetic puzzles, and similar classes of problems have been extensively used to challenge human reasoning capabilities. Lo Shu magic square can be traced back to 650 B.C., the eight-queens problem was proposed in 1848 by the chess player Max Bazzel TWO × TWO = THREE puzzle appeared in Strand Magazine in 1924. These puzzles are nowadays widely used in constraint programming courses. The first programming language provided with constraint modelling primitives (Sketchpad) has been proposed by the Turing award winner Ivan Sutherland in his PhD thesis (1963). Logemann and Loveland, when implementing the Davis–Putnam procedure (Davis and Putnam 1960) for testing the satisfiability of a propositional formula (SAT), devised an algorithm (Davis–Putnam–Logemann–Loveland (DPLL)) that has become the core of all SAT/and Answer Set Programming solvers (50 years later). It consists in choosing an un-assigned variable, assigning it a value 0 or 1, propagating the chosen value (unit propagation), and proceeding with the alternative value, if the original assignment leads to a contradiction (backtracking). Some years later Waltz (1975) introduced the notion of domain filtering (arc-consistency-based constraint propagation). With this idea the same DPLL scheme can be used for verifying the satisfiability of a constraint satisfaction problem, where the assignment is no longer 0/1 and the unit propagation is replaced by constraint propagation. For a detailed history of these early years achievements, we refer the reader to the works by Loveland et al. (2017), Jaffar and Maher (1994), and Freuder and Mackworth (2006).

Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the hardness of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.

Optimization problems pervade essentially every scientific discipline and industry. A common form requires identifying a solution satisfying the maximum number among a set of many conflicting constraints. Often, these problems are particularly difficult to solve, requiring resources that grow exponentially with the size of the problem. Over the past decades, research has focused on developing heuristic approaches that attempt to find an approximation to the solution. However, despite numerous research efforts, in many cases even approximations to the optimal solution are hard to find, as the computational time for further refining a candidate solution also grows exponentially with input size. In this paper, we show a noncombinatorial approach to hard optimization problems that achieves an exponential speed-up and finds better approximations than the current state of the art. First, we map the optimization problem into a Boolean circuit made of specially designed, self-organizing logic gates, which can be built with (nonquantum) electronic elements with memory. The equilibrium points of the circuit represent the approximation to the problem at hand. Then, we solve its associated nonlinear ordinary differential equations numerically, towards the equilibrium points. We demonstrate this exponential gain by comparing a sequential MATLAB implementation of our solver with the winners of the 2016 Max-SAT competition on a variety of hard optimization instances. We show empirical evidence that our solver scales linearly with the size of the problem, both in time and memory, and argue that this property derives from the collective behavior of the simulated physical circuit. Our approach can be applied to other types of optimization problems, and the results presented here have far-reaching consequences in many fields.

Generalized planning is concerned with the computation of general policies that solve multiple instances of a planning domain all at once. It has been recently shown that these policies can be computed in two steps: first, a suitable abstraction in the form of a qualitative numerical planning problem (QNP) is learned from sample plans, then the general policies are obtained from the learned QNP using a planner. In this work, we introduce an alternative approach for computing more expressive general policies which does not require sample plans or a QNP planner. The new formulation is very simple and can be cast in terms that are more standard in machine learning: a large but finite pool of features is defined from the predicates in the planning examples using a general grammar, and a small subset of features is sought for separating “good” from “bad” state transitions, and goals from non-goals. The problems of finding such a “separating surface” while labeling the transitions as “good” or “bad” are jointly addressed as a single combinatorial optimization problem expressed as a Weighted Max-SAT problem. The advantage of looking for the simplest policy in the given feature space that solves the given examples, possibly non-optimally, is that many domains have no general, compact policies that are optimal. The approach yields general policies for a number of benchmark domains.

We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability (MAX-SAT) problem and weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate (MAX-)2-SAT. Our work shows the potential of SDP also for other satisfiability problems by being competitive with some of the best solvers in the yearly MAX-SAT competition. Our solver combines sum of squares (SOS)–based SDP bounds and an efficient parser within a branch-and-bound scheme. On the theoretical side, we propose a family of semidefinite feasibility problems and show that a member of this family provides the rank-two guarantee. We also provide a parametric family of semidefinite relaxations for MAX-SAT and derive several properties of monomial bases used in the SOS approach. We connect two well-known SDP approaches for (MAX)-SAT in an elegant way. Moreover, we relate our SOS-SDP relaxations for partial MAX-SAT to the known SAT relaxations. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.0036 .

We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random k-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown, while for formulae with ratios greater than some constant, algorithms under the random walk framework require substantially different heuristics. In light of these results, we propose a novel probabilistic approach for random Max-SAT called ProMS. Experimental results illustrate that ProMS outperforms many state-of-the-art local search solvers on random Max-SAT benchmarks.

We introduce the problem Max#SAT, an extension of model counting (#SAT). Given a formula over sets of variables X, Y, and Z, the Max#SAT problem is to maximize over the variables X the number of assignments to Y that can be extended to a solution with some assignment to Z. We demonstrate that Max#SAT has applications in many areas, showing how it can be used to solve problems in probabilistic inference (marginal MAP), planning, program synthesis, and quantitative information flow analysis. We also give an algorithm which by making only polynomially many calls to an NP oracle can approximate the maximum count to within any desired multiplicative error. The NP queries needed are relatively simple, arising from recent practical approximate model counting and sampling algorithms, which allows our technique to be effectively implemented with a SAT solver. Through several experiments we show that our approach can be successfully applied to interesting problems.

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of has been extensively studied for more than two decades, resulting in various extensions to the original technique and beautiful algorithms for a wide range of applications. Despite the fact that this approach yields tight approximation guarantees for some problems, e.g. , Max-Cut , for many others, e.g. , Max-SAT and Max-DiCut , the tight approximation ratio is still unknown. One of the main reasons for this is the fact that very few techniques for rounding semi-definite relaxations are known. In this work, we present a new general and simple method for rounding semi-definite programs, based on Brownian motion. Our approach is inspired by recent results in algorithmic discrepancy theory. We develop and present tools for analyzing our new rounding algorithms, utilizing mathematical machinery from the theory of Brownian motion, complex analysis, and partial differential equations. Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut , Max-2SAT , and Max-DiCut , and derive new algorithms that are competitive with the best known results. To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration results for the Sticky Brownian Motion, a feature missing from hyperplane rounding and its generalizations.

AbstractNeuromorphic hardware implementation of Boltzmann Machine using a network of stochastic neurons can allow non-deterministic polynomial-time (NP) hard combinatorial optimization problems to be efficiently solved. Efficient implementation of such Boltzmann Machine with simulated annealing desires the statistical parameters of the stochastic neurons to be dynamically tunable, however, there has been limited research on stochastic semiconductor devices with controllable statistical distributions. Here, we demonstrate a reconfigurable tin oxide (SnOx)/molybdenum disulfide (MoS2) heterogeneous memristive device that can realize tunable stochastic dynamics in its output sampling characteristics. The device can sample exponential-class sigmoidal distributions analogous to the Fermi-Dirac distribution of physical systems with quantitatively defined tunable “temperature” effect. A BM composed of these tunable stochastic neuron devices, which can enable simulated annealing with designed “cooling” strategies, is conducted to solve the MAX-SAT, a representative in NP-hard combinatorial optimization problems. Quantitative insights into the effect of different “cooling” strategies on improving the BM optimization process efficiency are also provided.

AbstractThe Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, prior work on designing dynamical systems as Ising machines has primarily considered quadratic interactions among the nodes. Dynamical systems and models considering higher order interactions among the Ising spins remain largely unexplored, particularly for applications in computing. Therefore, in this work, we propose Ising spin-based dynamical systems that consider higher order (> 2) interactions among the Ising spins, which subsequently, enables us to develop computational models to directly solve many COPs that entail such higher order interactions (i.e., COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K ≥ 4) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired ‘toolbox’ for solving COPs.

Abstract An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

Abstract The introduction of Informatics and Computing as a compulsory subject for students from the fifth to the eighth grade of elementary school, and programming as a basic content of the curriculum represents a major advance in elementary education in the Republic of Serbia. In this study we conduct research on N = 58 primary school students of the sixth grade. In the 2016/17 school year students studied the programming language Scratch, and in the school year 2017/18, they learned Python programming language. The programming courses were realized once a week (45 minutes) during 17 weeks. This study aims to monitor the flow of learning visual and textual programming language following the new elementary school curriculum in Republic of Serbia, that is, the achievement and motivation of students to continue learning programming. The research instrument used was a questionnaire. The results of this study showed that it was easier for students to master the visual programming language Scratch than the textual programming language Python. However, the research results show that algorithmic way of thinking and motivation to learn by programming a text language are satisfactory given that students have not had previous experience with it. Key words: computational thinking; elementary education; textual programming; visual programming.Istraživanje postignuća i motivacije učenja jezika programskog teksta kod učenika osnovne škole SažetakUvođenje informatike i računarstva kao obaveznog predmeta za učenike od petog do osmog razreda osnovne škole, a programiranje kao osnovni sadržaj nastavnog programa predstavlja veliki napredak u osnovnom obrazovanju Republike Srbije. U ovoj studiji provodimo istraživanje sa N = 58 učenika osnovne škole šestog razreda. U školskoj 2016/17 godini učenici su proučavali programski jezik Scratch, a u školskoj 2017/18 godini su učili programski jezik Python. Tečaj programiranja odvijao se jednom tjedno (45 minuta) tijekom 17 tjedana. Ova studija želi pratiti tok učenja vizualnog i tekstualnog programskog jezika prateći novi nastavni plan i program osnovne škole u Republici Srbiji, odnosno postignuća i motivacija učenika za nastavak učenja programa. Korišteni istraživački instrument bio je upitnik. Rezultati ove studije pokazali su da je studentima bilo lakše savladati vizualni programski jezik Scratch nego tekstualni programski jezik Python. Međutim, rezultati istraživanja pokazuju da je algoritamski način razmišljanja i motivacija za učenje programiranja tekstualnog jezika zadovoljavajući s obzirom da učenici s njim nisu imali prethodno iskustvo.Ključne riječi: računsko razmišljanje; osnovno obrazovanje; tekstualno programiranje; vizualno programiranje. UvodU posljednjem desetljeću došlo je do širenja informacijsko komunikacijske tehnologije što je rezultiralo pojavom novih digitalnih uređaja. Djeca televizijskih i slikovnica predškolske i osnovnoškolske dobi sve se više zamjenjuju računalima, tabletima i pametnim telefonima. Dakle, djeca provode više vremena igrajući se na računalu i gledajući video isječke (koji mogu biti obrazovni ili drugi sadržaji). Međutim, ovi digitalni uređaji i Internet postaju važno okruženje za učenje djece. Računalo, kao jedan od digitalnih uređaja, ima važnu ulogu u poboljšanju obrazovanja (Salomon, 1985; Lenhart, Simon i Graziano, 2001).Ako djeca žele razumjeti i aktivno sudjelovati u novom digitalnom svijetu, moraju naučiti "Računalno razmišljanje" (Wing, 2006). Novi nacionalni kurikulum za računarstvo omogućit će djeci u Engleskoj da razumiju i steknu računalne vještine koje će im trebati u budućnosti. Na temelju novog računalnog programa djeca će stjecati znanje o strukturi i radu računala i razvijati svoje ideje koristeći novu tehnologiju (Berry, 2013). Clements i Meredith (1993) analiziraju zaključke radova (Hillel 1984; Carmichael, 1985; Kull, 1986; Hillel i Kieran, 1988) zaključak da programiranje Logo-a ima određene matematičke sadržaje koji se mogu koristiti s Logo-om. Dakle, pored tradicionalnog pristupa razumijevanju matematike, mogućnost usvajanja pomoću Logo-a. Štoviše, prema autorima Lye i Koh (2014) autori (Pea, 1983; Kurland, Pea, Clement i Mawby, 1986) vjeruju da empirijska istraživanja na kraju nisu pokazala da Logo poboljšava način razmišljanja djece.Ako smo željeli naučiti tradicionalni način programiranja u programskom jeziku, potrebno je poznavati upute tog jezika kako bi nas računalo razumjelo. Osnovna zadaća programiranja je naučiti naredbu programskog jezika (deklarativno znanje) i omogućiti korištenje tih podataka na različite načine (proceduralno znanje) (Palumbo, 1990). Autor je, na temelju (Pea, 1984), izrazio sumnju u statističku ovisnost između nastavnog jezika i metoda rješavanja problema. Devedesetih godina počinje se pojavljivati ​​zanimanje ljudi za programe koji koriste grafičko okruženje za programiranje, uklanjanje pogrešaka itd. Nastanak grafičkog okruženja bio je očekivan, jer je dobro poznato da je tradicionalno programiranje složenije za učenje jer zahtijeva određenu sposobnost koju nemaju svi ljudi. Stoga je potrebno realizirati grafičko okruženje koje će korisnicima biti lako i jednostavno kako bi privukli više ljudi zainteresiranih za "grafičko programiranje" (Halbert, 1984; Lewis i Olson, 1987; Myers, 1990). Informatika u osnovnoj školiStrategija: računarskih znanosti i programiranjaU računalnoj znanosti 1980-ih proučavala se struktura računala i njezin princip rada (hardver, logika, binarnost itd.). Devedesete su škole primijenile princip rada kao i korištenje računala i njegovih aplikacija, dok se programiranje samo spominje. Od 2011. godine dolazi do značajnih promjena, razvijaju se e-vještine i neke su organizacije uključene u definiranje informatike u školi uz zaključak da bi one trebale biti sastavni dio školskog kurikuluma (Doyle, 1988; e-skills UK, 2012; Livingstone i Hope, 2011; Crick i Sentance, 2011).Studij računarskih znanosti i programiranja itd. i uvođenje njihovih nastavnih planova i programa u osnovne škole provodili su Velika Britanija i Australija. Jedan od osnovnih ciljeva je bolja prilagodba ovih nastavnih planova i programa djeci u osnovnim školama (Duncan i Bell, 2015; Brown, Sentance, Crick i Humphreys, 2014; Falkner, Vivian i Falkner, 2014). Model kurikuluma informatike K-12 sastoji se od tri razine studija pri čemu svaka odgovara određenoj dobi učenika (Seehorn, 2011). Prva razina, K-8, namijenjena je određenoj dobi učenika, što u sustavu Republike Srbije odgovara učenicima u osnovnoj školi (prvenstveno za više razrede). Primjetna prednost nastavnog plana i programa K-12, gledajući strukturu nivoa, je jedan obavezni tečaj (barem) na osnovnoj razini, koji je bio nedostatak obrazovnog sustava u Srbiji (iako se do određene mjere izučava kroz tečajeve Tehničke i informatičko obrazovanje) (Frost, Verno, Burkhart, Hutton, North i Houston, 2009; K12, 2011).Prvi put nakon školske 2017./18. računarske znanosti se predaju u predmetu Informatika i računarstvo kao obvezni predmet za učenike od petog do osmog razreda u Republici Srbiji. Sadržaj ovog predmeta razlikuje se od prethodnog koji je bio izborni. Informatika i računarstvo sastoje se od tri teme: tehnologija informacijske komunikacije, digitalna pismenost i računarstvo. U okviru teme računarstva najvažnija novost je učenje vizualnog programskog jezika. Cilj kolegija je razvijanje digitalne pismenosti kao jedne od najvažnijih vještina 21. stoljeća. Novi program poštuje činjenicu da generacije rođene u digitalnom dobu dolaze u obrazovni sustav koji ima bogato iskustvo u korištenju tehnologije iz svakodnevnog života. Informatika i računarstvo približit će studentima informatičku tehnologiju i naučiti ih kako ih sigurno koristiti. S druge strane, programiranje studentima omogućuje razvijanje računalnog načina razmišljanja i rješavanja problema. Računalni način razmišljanja usmjeren je na rješavanje problema i primjenjiv je na svim područjima ljudske aktivnosti. Ovaj koncept kombinira dekompoziciju problema na manje, lakše riješene dijelove, identifikaciju uzoraka i općih rješenja, algoritam generiranja generalizacije i apstrakcije, rješavanje problema (MESTD, 2018).S pojavom programskih jezika dizajniranih tako da omoguće vizualno programiranje, gdje ne treba poznavati sintaksu programa, poput tekstualnih programskih jezika, zanimanje za njih počinje se širiti. Jedan od tih jezika je i Scratch koji djeci u osnovnoj školi omogućuje da samostalno i bez straha dobiju osnove programiranja. Scratch je dizajnirao Mitchel Resnick iz Massachusetts instituta tehnologa. Vrlo je jednostavan za upotrebu jer su kontrole (blokovi) na ekranu i mogu se međusobno prilagoditi i dobiti odgovarajuće značenje. Nema sintaksnog koda i poruka o pogrešci kao u tekstualnom programiranju (Resnick, Maloney, Monroy-Hernández, Rusk, Eastmond, Brennan i Kafai, 2009; Wilson i Moffat, 2010; Moreno i Robles, 2016).Učenjem programiranja djeca stječu računalno utemeljen način razmišljanja koji će im kasnije biti od pomoći u daljnjem obrazovanju. Kad napišu kod, stalno vode bitku sa kompajlerom hoće li se njihov kod izvršiti. Na taj način stječu bolje obrazovne mogućnosti i potiču ih da savladaju dojam da je pisanje koda izvan njihovih mogućnosti (Duncan, Bell i Tanimoto, 2014; Tsukamoto, Takemura, Nagumo, Ikeda, Monden i Matsumoto, 2015). Također, Lopez, Whalley, Robbins i Lister (2008)) pokazuju da je vještina pisanja u korelaciji s vještinom čitanja koda. Jedan od jednostavnih tekstualnih jezika je Python. Python je dizajnirao Guido van Rossum početkom 1990. Nudi sve što zahtijevamo od programskog jezika i lako ga je naučiti i razumjeti. Treba samo spomenuti: „Moja 10-godišnja kćer programira domaću zadaću iz matematike na Pythonu (upravo je napisala rutinu za pretvaranje stupnjeva Celzijusa u stupnjeve Fahrenheita)“ (Lindstrom, 2005). Pregled literatureScratch je vrlo popularan programski jezik. Moreno-León, Robles i Román-González (2015) izveli su pregled objavljenih radova u polju programskih jezika u razdoblju od 2007. do 2015. Primjena integriranja kodiranja i vizualnog blok programiranja u programu Scratch za 5. i 6. razrede osnovne škole u razdoblju od dvije školske godine istraživali su Sáez-López, Román-González i Vázquez-Cano (2016).KalelioÄŸlu i Gülbahar (2014) ispitali su utjecaj programa Scratch na vještine rješavanja problema učenika u 5. razredu osnovne škole. Rezultati istraživanja pokazuju da su studenti zainteresirani za programiranje, ali nije bilo većih razlika u vještini rješavanja problema. Kaleoglu (2015) ponovno je ispitao kako web stranica code.org utjecala na vještine rješavanja problema kod učenika oba spola u osnovnoj školi. Rezultati istraživanja ponovno su pokazali interes učenika za programiranje. Web-lokacija code.org nije pokazala razlike u razmišljanju među učenicima različitog spola. No, neznatna je razlika u reflektivnom razmišljanju spolova (u korist ženskog spola).Motivacijom i angažmanom učenika osnovnih škola (u dobi između 8 i 11 godina) upotrebom programskog jezika (Scratch) u Škotskoj upravljao je nastavnim planom i programom, temeljenom na konceptu učenja temeljenom na igrama. Autori rada prezentiraju empirijske dokaze i daljnje smjernice o procjeni sposobnosti vršenja programiranja temeljenog na igrama (Wilson, Hainey i Connolly, 2012). Klub srednjoškolaca pod nazivom „Code club“ osnovan je u Velikoj Britaniji 2012. godine radi pružanja potpore osnovnoj školi u području programiranja. Studenti se obučavaju (kreiranje igara u programu Scratch) od strane volontera programera i učitelja, svaki iz svog područja stručnosti (Smith, Sutcliffe i Sandvik, 2014). Četiri preddiplomska studija magisterija informatike prolazila su programiranje igara koristeći Scratch na Sveučilištu Washington Bothel kako bi mogli prenijeti znanje studentima (od 6. do 8. razreda), jer se smatra da nema dovoljno stručnjaka za to područje (Gruenbaum, 2014. ).Složenost strukture tekstualnih programskih jezika na C-u, koja se predaje na fakultetu, može izazvati nezainteresiranost i nedostatak motivacije za studente da nastave programirati učenje. Kako bi se olakšala obuka učenika za jezik C, studentima se uvodi Scratch kao podrška u okolišu, paralelno s klasičnim predavanjima (Ozoran, Cagiltay i Topalli, 2012). Analizu prelaska s učenja vizualnog programiranja na tekstualni programski jezik (C # ili Java) za studente (od 15 do 16 godina) ispitali su Armoni, Meerbaum-Salant i Ben-Ari (2015). Autori su zaključili da znanje i iskustvo učenika u programiranju koji su podučavali Scratch uvelike olakšava učenje naprednijeg programskog jezika. Oni su također bolje razumjeli temu od učenika koji ranije nisu proučavali Scratch. Erol i Kurt (2017) analizirali su motivaciju i rezultate koje su postigli studenti Pedagoškog fakulteta u Turskoj, istovremeno učeći programske jezike Scratch i C # tijekom 7 tjedana. Pregled literature povezan s hipotezamaCilj studije predstavljene u ovom radu je ukazati na interes učenika osnovne škole za informatiku: prije svega programiranje. Budući da se programiranje može smatrati važnim dijelom nastave informatike (Schulte, 2013.), posebno je važno odabrati pravu nastavnu metodologiju za studente koji se prvi put susreću s programiranjem - programere početnike (Gilmore, 1990; Lahtinen, Ala-Mutka i Järvinen 2005; Kelleher i Pausch, 2005; Robins, 2019). Hipoteze definirane u ovoj studiji temelje se na sljedećim istraživačkim nalazima:Hipoteza 1 - U posljednjim razdobljima većina zemalja uvodi učenje programskog jezika kao sastavni dio osnovnoškolskog obrazovanja (kao što je rečeno u ranijoj literaturi). S prvim programskim koracima učenici osnovne škole uče uz pomoć jezika vizualnog programiranja - blok programiranja (Serafini, 2011; Pardamean, 2014; Taheri, Sasaki, Chu i Ngetha, 2016; Mladenović, Krpan i Mladenović, 2017; Papavlasopoulou , Giannakos i Jaccheri, 2019; Cheng, 2019). Nakon tečaja programiranja zasnovanog na blokovima, studenti počinju učiti osnove tekstualnog programiranja (Borne, 1991; Ferrari, Poggi i Tomaiuolo, 2016; García-Peñalvo, Hughes, Rees, Jormanainen, Toivonen, Reimann i Virnes, 2016 ; So i Kim, 2018). Međutim, postoje i istraživački radovi koji se bave komparativnim studijama postignuća djece, a koja su stekla učenjem vizualnog i tekstualnog programskog jezika (Hromkovič, Kohn, Komm i Serafini, 2016; Mladenović, Boljat, i Žanko 2018; Nitko i Mooney, 2018). Olakšavanje primjene Python programskog jezika na uvodnim tečajevima informatike predstavili su Ranum, Miller, Zelle i Guzdial (2010), dok su Kölling, Brown i Altadmri (2015) predstavili prijelaz s učenja vizualnog programskog jezika na tekstualni u osnovna škola.Hipoteza 2 - Osnove učenja, algoritamsko razmišljanje djeteta osnovnoškolskog uzrasta shvatili su Futschek i Moschitz (2011). Predstavili su takozvani scenarij učenja Tim the Train koji uključuje materijalne objekte na temelju kojih se zadaci podučavaju za učenje algoritamskog mišljenja. Međutim, autori su također pokazali blagi prijelaz s objekata na virtualno Scratch/BYOB okruženje zbog čega se studenti osjećaju bolje u svojim prvim koracima programiranja. Ko i Park (2011) ističu da će osnovnoškolci izvoditi različite aktivnosti u procesu programiranja, bez obzira na ishod. Tako će se tijekom ovog procesa poboljšati sposobnost rješavanja problema i logičkog razmišljanja. Na temelju Tutorial Graphic Tutorial System (TGTS), mrežnog sustava učenja temeljenog na zagonetkama, Hsu i Wang (2018) vjeruju da će potaknuti algoritamsko razmišljanje učenika. Prema Kátai (2015), pravilno postavljeni alati za e-učenje utječu na razvoj algoritmičkog razmišljanja i kod učenika usmjerenih na znanost i na ljude.Hipoteza 3 - Podučavanje početnicima programiranja korištenjem I/O instrukcija, petlji i odluka u osnovnom programskom jeziku analizirano je od 1986 (Dalbey, Tourniaire i Linn, 1986; vidi sliku 1; Perkins, Hancock, Hobbs, Martin i Simmons, 1986 ; vidi stranice 8 i 9). Pérez-Marín, Hijón-Neira i Martín-Lope (2018; vidi tablicu 2) proučavali su nastavu programiranja učenika osnovnih škola (upute za ulaz/ izlaz, uvjeti, petlje ...) na temelju metafora. Također, Sanford, Tietz, Farooq, Guyer i Shapiro (2014) istražili su koriste li nastavnici metafore na uvodnim tečajevima programiranja (Sanford et all., 2014; vidi tablicu 2). Podučavanje studenata programiranju osnova (programski jezik Paskal) čiji dio koda sadrži dvije petlje i ulazne izlazne upute predstavljeni su od Sajaniemi i Kuittinen (2005).Hipoteza 4 - Međutim, u realizaciji nastave informatike potrebno je uzeti u obzir metode, didaktiku i pedagogiku i dinamiku razmišljanja. Predmet matematičkog obrazovanja u školama treba biti usmjeren na algoritme kako bi se učenici približili i lakše podučavali informatiku (to je njihov osnovni dio programiranja učenja). Izgradnja algoritama i potprograma trebala bi biti sastavni dio učenja programiranja, a ne samo popis programskih jezika (Kerner, 1986). Du Boulay (1980) analizirao je problem gdje su učenici s nižim vještinama matematike naučili LOGO programski jezik i njegovu primjenu u matematičkim modelima. Analiza da su matematički tečajevi prikladni za računarstvo predočena je u (Churchhouse, 1993). Calao, Moreno-León, Correa i Robles (2015) istraživali su da li kodiranje poboljšava matematičke vještine učenika u nastavi matematike. Klymchuk (2017) u svojoj studiji ispituje učenje inženjerske matematike pomoću zagonetki kao jednu od pedagoških strategija za poboljšanje sposobnosti razmišljanja. Također, polaznici koji su razumjeli logiku programiranja mogli su prenijeti stečeno znanje učenju drugih programskih jezika (Wolz, Leitner, Malan, & Maloney, 2009). Dok pregledna studija Popat i Starkey (2019), navodi da programiranje učenja uključuje rješavanje problema iz matematike, kritičko razmišljanje, akademske vještine.Hipoteza 5 - Robins, Rountree i Rountree (2003) postavljaju pitanje: "Je li moguće prepoznati specifične nedostatke neučinkovitih novaka i pomoći im da postanu učinkoviti učenici programiranja?" Postoji nekoliko čimbenika (motivacija, emocionalni odgovori, općenita ili specifična znanja) koji utječu na učenje programiranja. Na temelju točno definiranih vještina koje bi trebalo razviti za učenike koji uče programiranje, potrebno je pravilno osmisliti igru učenja (Lin i Chen, 2016). Fincher (1999) kaže da stilovi učenja, sposobnosti i vještine mogu biti prediktivni faktori uspjeha u programiranju učenja. Perković, Settle, Hwang, i Jones (2010) ističu potrebu za intelektualnim vještinama potrebnim za računalnim tehnikama i aplikacijama. Prema Bruceu, Buckinghamu, Hyndu, McMahonu, Roggenkampu i Stoodleyu (2004), studenti rado pišu programe ako znaju da će dobiti ocjenu. Metod Cilj i problem istraživanjaUvođenje informatike i računarstva kao obveznog predmeta za učenike od petog do osmog razreda osnovne škole, a programiranje kao osnovni sadržaj nastavnog programa predstavlja veliki napredak u osnovnom obrazovanju u Republici Srbiji. Cilj studije je procijeniti motivaciju za učenje i postignuća učenika stečena učenjem programskih jezika. Ova studija usporedila je analizu učenja prvog tekstualnog jezika (Python) u odnosu na jezik vizualnog programiranja (Scratch) od strane učenika osnovne škole. HipotezeU ovoj su studiji testirane sljedeće hipoteze:H1: Učenici imaju pozitivan stav prema učenju vizualnog i svom prvom tekstualnom programskom jeziku.H2: Učenici imaju pozitivan stav prema svladavanju jednostavnih algoritamskih zadataka tijekom učenja programskog jezika.H3: Studenti imaju pozitivan stav prema savladavanju osnovnih elemenata (naredbe ulaz/izlaza, relacijski operatori, kontrola toka) tijekom učenja programskog jezika.H4: Studenti imaju pozitivan stav da znanje iz matematike utječe na bolje savladavanje njihovog prvog tekstualnog programskog jezika.H5: Razlike u postignućima učenika i njihovo zanimanje za predmet utječu na učenje programskog jezika. UzorakPedeset osam učenika bilo je uključeno u ovu studiju. Učenici su šestih razreda osnovne škole „Dositej Obradović“ iz Sombora, Republika Srbija. Starost sudionika kretala se u rasponu od 12 do 13 godina (53,3% dječaka i 46,7% devojčica). Od sedamdeset i sedam učenika petih razreda u 2016/17 školskoj godini, njih 58 odabralo je izborni predmet Informatika i računarstvo. Kako bi se zadovoljila potreba za istraživačkom etikom, svako sudjelovanje u istraživanju bilo je dobrovoljno, a ocjene učenika nisu ovisile o rezultatima ispitivanja. InstrumentNaša studija koristila je eksperimentalni dizajn: pred test, post-test i završni test. Korišteni istraživački instrument bio je upitnik. Pitanja koja su sadržana u pred-testiranju i nakon ispitivanja uključuju nastavne materijale koje su studenti naučili na tečajevima Scratch i Python. No, pitanja i njihov broj definiraju se u dogovoru s nastavnikom u vezi s odgovarajućim nastavnim planom i programom, a u nekim elementima su ograničeni i dobi učenika. Završni test sadrži izjave o učenju o motivaciji i vještinama koje su studenti stekli učenjem programskih jezika. U tijeku pred-testa i nakon testa, znanje sudionika koji su se testirali u: deklariranju varijabli, funkcija ulaza i izlaza, algoritmi, logički operatori, uvjeti i petlje. Studenti od kojih se traži da prepoznaju: vrstu deklaracije ako je data vrsta broja, te metode i vrste algoritama (opisanih pseudo jezikom i blok dijagramom). Svako je pitanje sadržavalo tekstualni opis (ponekad i grafičku sliku) i tri ponuđena odgovora (od kojih je samo jedan točan). Konačni test sadržavao je komparativne izjave o Scratch i Python-u (Dodatak 1) i pet ponuđenih odgovora (Likertova skala).Za obradu prikupljenih podataka korištene su sljedeće statističke metode: opisne statističke mjere (mjere središnje tendencije, mjere varijabilnosti, parametri raspodjele) i mjere statističkog zaključivanja (Pearsonov Chi-Square test i Spearmanova relacijska analiza). ProceduraUčenje programskih jezika provedeno je prema (KalelioÄŸlu, 2015) i (Erol i Kurt, 2017), dok se analiza rezultata temelji na (KalelioÄŸlu, 2015). Svi učenici koji su sudjelovali u ovom istraživanju tijekom školske 2016./17. naučili su programski jezik Scratch. Tečaj se realizirao jednom tjedno (45 minuta) tijekom 17 tjedana u razdoblju od siječnja do svibnja. Učenici su imali jedan školski sat tjedno (45 minuta) u skladu s nastavnim planom i programom za osnovnoškolce (u sklopu izbornog predmeta Informatika i računarstvo). Također, na istom principu, u školskoj 2017./18. godini od siječnja do svibnja organiziran je tečaj programskog jezika Python. Međutim, ovaj se programski jezik proučava kao dio obveznog predmeta Informatika i računarstvo. Nije bilo neočekivanih događaja ili poteškoća s postupkom. Slika 1 prikazuje model ove studije. Sadržaj tečaja i aktivnosti vezane uz tečaj predstavljeni su u tablici 1 (Erol i Kurt, 2017). Slika 1Model studije Tablica 1Sadržaj i aktivnosti predmetaRadne nedjelje Teme nedjelja 1 Uvod u Python nedjelja 2 Variable nedjelja 3 i 4 Aritmetičke operacije nedjelja 5 - 7 Ugrađene funkcije (min, max, aps) nedjelja 8 & 9 Nizovi nedjelja 10 – 12 Petlje nedjelja 13 – 15 Dijagrami toka nedjelja 16 i 17 Osnovni algoritmi ResultatiRezultati su dati u Tablici 2, Tablici 3 and Tablici 4.Tablica 2Statistika tvrdnji završnog testa S1 i S4 Scratch Python Mean SD Mean SD Pearson Corr. Spearman's rho p N (važeći) S1 3.31 1.19 3.43 1.30 0.61 0.572 <0.001 51 S4 3.10 1.48 3.10 1.54 0.51 0.5 <0.001 51 Tablica 3Statistika pre- i post-testa χ2 p

Drawing upon popular magazines, newspapers, blogs, Web sites, and videos, this essay compares the media framing of six, “fat” political figures from around the world. Framing refers to the suggested interpretations that are imbedded in media reports (Entman; McCombs and Ghanem; Seo, Dillard and Shen). As Robert Entman explains, framing is the process of culling a few elements of perceived reality and assembling a narrative that highlights connections among them to promote a particular interpretation. Frames introduce or raise the salience of certain ideas. Fully developed frames typically perform several functions, such as problem definition and moral judgment. Framing is connected to the [covert] wielding of power as, for example, when a particular frame is intentionally applied to obscure other frames. This comparative international study is an inquiry into “what people and societies make of the reality of [human weight]” (Marilyn Wann as quoted in Rothblum 3), especially in the political arena. The cultural and historical dimensions of human weight are illustrated by the practice of force-feeding girls and young women in Mauritania, because “fat” women have higher status and are more sought after as brides (Frenkiel). The current study, however, focuses on “fat” politics. The research questions that guide the study are: [RQ1] which terms do commentators utilize to describe political figures as “fat”? [RQ2] Why is the term “fat” utilized in the political arena? [RQ3] To what extent can one detect gender, national, or other differences in the manner in which the term “fat” is used in the political arena? After a brief introduction to the current media obsession with fat, the analysis begins in 1908 with William Howard Taft, the 330 pound, twenty-seventh President of the United States. The other political figures are: Chris Christie (Governor of New Jersey), Bill Clinton (forty-second President of the United States), Michelle Obama (current First Lady of the United States), Carla Bruni (former First Lady of France), and Julia Gillard (former Prime Minister of Australia). The final section presents some conclusions that may help readers and viewers to take a more critical perspective on “fat politics.” All of the individuals selected for this study are powerful, rich, and privileged. What may be notable is that their experiences of fat shaming by the media are different. This study explores those differences, while suggesting that, in some cases, their weight and appearance are being attacked to undercut their legitimate and referent power (Gaski). Media Obsession with Fat “Fat,” or “obesity,” the more scientific term that reflects the medicalisation of “fat” (Sobal) and which seems to hold sway today, is a topic with which the media currently is obsessed, both in Asia and in the United States. A quick Google search using the word “obesity” reports over 73 million hits. Ambady Ramachandran and Chamukuttan Snehalatha report on “The Rising Burden of Obesity in Asia” in a journal article that emphasizes the term “burden.” The word “epidemic” is featured prominently in a 2013 medical news report. According to the latter, obesity among men was at 13.8 per cent in Mongolia and 19.3 per cent in Australia, while the overall obesity rate has increased 46 per cent in Japan and has quadrupled in China (“Rising Epidemic”). Both articles use the word “rising” in their titles, a fear-laden term that suggests a worsening condition. In the United States, obesity also is portrayed as an “epidemic.” While some progress is being made, the obesity rate nonetheless increased in sixteen states in 2013, with Louisiana at 34.7 per cent as the highest. “Extreme obesity” in the United States has grown dramatically over thirty years to 6.3 per cent. The framing of obesity as a health/medical issue has made obesity more likely to reinforce social stereotypes (Saguy and Riley). In addition, the “thematic framing” (Shugart) of obesity as a moral failure means that “obesity” is a useful tool for undermining political figures who are fat. While the media pay considerable attention to the psychological impact of obesity, such as in “fat shaming,” the media, ironically, participate in fat shaming. Shame is defined as an emotional “consequence of the evaluation of failure” and often is induced by critics who attack the person and not the behavior (Boudewyns, Turner and Paquin). However, in a backlash against fat shaming, “Who you callin' fat?” is now a popular byline in articles and in YouTube videos (Reagan). Nevertheless, the dynamics of fat are even more complicated than an attack-and-response model can capture. For example, in an odd instance of how women cannot win, Rachel Frederickson, the recent winner of the TV competition The Biggest Loser, was attacked for being “too thin” (Ceja and Valine). Framing fat, therefore, is a complex process. Fat shaming is only one way that the media frame fat. However, fat shaming does not appear to be a major factor in media coverage of William Howard Taft, the first person in this study. William Howard Taft William Howard Taft was elected the 27th President of the United States in 1908 and served 1909-1913. Whitehouse.com describes Taft as “Large, jovial, conscientious…” Indeed, comments on the happy way that he carried his “large” size (330 pounds) are the main focus here. This ‹happy fat› framing is much different than the media framing associated with ‹fat shaming›. His happy personality was often mentioned, as can be seen in his 1930 obituary in The New York Times: “Mr. Taft was often called the most human President who ever sat in the White House. The mantle of office did not hide his winning personality in any way” (“Taft Gained Peaks”). Notice how “large” and “jovial” are combined in the framing of Taft. Despite his size, Taft was known to be a good dancer (Bromley 129). Two other words associated with Taft are “rotund” (round, plump, chubby) and “pudgy.” These terms seem a bit old-fashioned in 2015. “Rotund” comes from the Latin for “round,” “circular,” “spherical.” “Pudgy,” a somewhat newer term, comes from the colloquial for “short and thick” (Etymology Online). Taft was comfortable with being called “pudgy.” A story about Taft’s portrait in the Smithsonian’s National Portrait Gallery in Washington, D.C. illustrates the point: Artist William Schevill was a longtime acquaintance of Taft and painted him several times between 1905 and 1910. Friendship did not keep Taft from criticizing the artist, and on one occasion he asked Schevill to rework a portrait. On one point, however, the rotund Taft never interfered. When someone said that he should not tolerate Schevill's making him look so pudgy in his likenesses, he simply answered, "But I am pudgy." (Kain) Taft’s self-acceptance, as seen in the portrait by Schevill (circa 1910), stands in contrast to the discomfort caused by media framing of other fat political figures in the era of more intense media scrutiny. Chris Christie Governor Christie has tried to be comfortable with his size (300+ pounds), but may have succumbed to the medicalisation of fat and the less than positive framing of his appearance. As Christie took the national stage in the aftermath of Hurricane Sandy (2012), and subsequently explored running for President, he may have felt pressure to look more “healthy” and “attractive.” Even while scoring political points for his leadership in the aftermath of Superstorm Sandy, Christie’s large size was apparent. Filmed in his blue Governor jacket during an ABC TV News report that can be accessed as a YouTube video, Christie obviously was much larger than the four other persons on the speakers’ platform (“Jersey Shore Devastated”). In the current media climate, being known for your weight may be a political liability. A 2015 Rutgers’ Eagleton Poll found that 53 percent of respondents said that Governor Christie did not have “the right look” to be President (Capehart). While fat traditionally has been associated with laziness, it now is associated with health issues, too. The media framing of fat as ‹morbidly obese› may have been one factor that led Christie to undergo weight loss surgery in 2013. After the surgery, he reportedly lost a significant amount of weight. Yet his new look was partially tarnished by media reports on the specifics of lap-band-surgery. One report in The New York Daily News stressed that the surgery is not for everyone, and that it still requires much work on the part of the patient before any long-term weight loss can be achieved (Engel). Bill Clinton Never as heavy as Governor Christie, Bill Clinton nonetheless received considerable media fat-attention of two sorts. First, he could be portrayed as a kind of ‹happy fat “Bubba”› who enjoyed eating high cholesterol fast food. Because of his charm and rhetorical ability (linked to the political necessity of appearing to understand the “average person”), Clinton could make political headway by emphasizing his Arkansas roots and eating a hamburger. This vision of Bill Clinton as a redneck, fast-food devouring “Bubba” was spoofed in a popular 1992 Saturday Night Live skit (“President-Elect Bill Clinton Stops by a McDonald's”). In 2004, after his quadruple bypass surgery, the media adopted another way to frame Bill Clinton. Clinton became the poster-child for coronary heart disease. Soon he would be framed as the ‹transformed Bubba›, who now consumed a healthier diet. ‹Bill Clinton-as-vegan› framing fit nicely with the national emphasis on nutrition, including the widespread advocacy for a largely plant-based diet (see film Forks over Knives). Michelle Obama Another political figure in the United States, whom the media has connected both to fast food and healthy nutrition, is Michelle Obama. Now in her second term as First Lady, Michelle Obama is associated with the national campaign for healthier school lunches. At the same time, critics call her “fat” and a “hypocrite.” A harsh diatribe against Obama was revealed by Media Matters for America in the personal attacks on Michelle Obama as “too fat” to be a credible source on nutrition. Dr. Keith Ablow, a FOX News medical adviser said, Michelle Obama needs to “drop a few” [pounds]. “Who is she to be giving nutrition advice?” Another biting attack on Obama can be seen in a mocking 2011 Breitbart cartoon that portrayed Michelle Obama devouring hamburgers while saying, “Please pass the bacon” (Hahn). Even though these attacks come from conservative media utterly opposed to the presidency of Barack Obama, they nonetheless reflect a more widespread political use of media framing. In the case of Michelle Obama, the media sometimes cannot decide if she is “statuesque” or “fat.” She is reported to be 5’11 tall, but her overall appearance has been described as “toned” (in her trademark sleeveless dresses) yet never as “thin.” The media’s ambivalence toward tall/large women is evident in the recent online arguments over whether Robyn Lawley, named one of the “rookies of the year” by the Sports Illustrated Swimsuit issue, has a “normal” body or a “plus-size” body (Blair). Therefore, we have two forms of media framing in the case of Michelle Obama. First, there is the ‹fat hypocrite› frame, an ad hominem framing that she should not be a spokesperson for nutrition. This first form of framing, perhaps, is linked to the traditional tendency to tear down political figures, to take them off their pedestals. The second form of media framing is a ‹large woman ambiguity› frame. If you are big and tall, are you “fat”? Carla Bruni Carla Bruni, a model and singer/songwriter, was married in 2008 to French President Nicolas Sarkozy (who served 2007 to 2012). In 2011, Bruni gave birth to a daughter, Giulia. After 2011, Bruni reports many attacks on her as being too “fat” (Kim; Strang). Her case is quite interesting, because it goes beyond ‹fat shaming› to illustrate two themes not previously discussed. First, the attacks on Bruni seem to connect age and fat. Specifically, Bruni’s narrative introduces the frame: ‹weight loss is difficult after giving birth›. Motherhood is taxing enough, but it becomes even more difficulty when the media are watching your waist line. It is implied that older mothers should receive more sympathy. The second frame represents an odd form of reverse fat shaming: ‹I am so sick and tired of skinny people saying they are fat›. As Bruni explains: “I’m kind of tall, with good-size shoulders, and when I am 40 pounds overweight, I don’t even look fat—I just look ugly” (Orth). Critics charge that celebs like Bruni not only do not look fat, they are not fat. Moreover, celebs are misguided in trying to cultivate sympathy that is needed by people who actually are fat. Several blogs echo this sentiment. The site Whisper displays a poster that states: “I am so sick and tired of skinny people saying they are fat.” According to Anarie in another blog, the comment, “I’m fat, too,” is misplaced but may be offered as a form of “sisterhood.” One of the best examples of the strong reaction to celebs’ fat claims is the case of actress Jennifer Lawrence. According The Gloss, Lawrence isn’t chubby. She isn’t ugly. She fits the very narrow parameters for what we consider beautiful, and has been rewarded significantly for it. There’s something a bit tone deaf in pretending not to have thin or attractive privilege when you’re one of the most successful actresses in Hollywood, consistently lauded for your looks. (Sonenshein) In sum, the attempt to make political gain out of “I’m fat” comments, may backfire and lead to a loss in political capital. Julia Gillard The final political figure in this study is Julia Eileen Gillard. She is described on Wikipedia as“…a former Australian politician who served as the 27th Prime Minister of Australia, and the Australian Labor Party leader from 2010 to 2013. She was the first woman to hold either position” (“Julia Gillard”). Gillard’s case provides a useful example of how the media can frame feminism and fat in almost opposite manners. The first version of framing, ‹woman inappropriately attacks fat men›, is set forth in a flashback video on YouTube. Political enemies of Gillard posted the video of Gillard attacking fat male politicians. The video clip includes the technique of having Gillard mouth and repeat over and over again the phrase, “fat men”…”fat men”…”fat men” (“Gillard Attacks”). The effect is to make Gillard look arrogant, insensitive, and shrill. The not-so-subtle message is that a woman should not call men fat, because a woman would not want men to call her fat. The second version of framing in the Gillard case, ironically, has a feminist leader calling Gillard “fat” on a popular Australian TV show. Australian-born Germaine Greer, iconic feminist activist and author of The Female Eunuch (1970 international best seller), commented that Gillard wore ill-fitting jackets and that “You’ve got a big arse, Julia” (“You’ve Got”). Greer’s remarks surprised and disappointed many commentators. The Melbourne Herald Sun offered the opinion that Greer has “big mouth” (“Germaine Greer’s”). The Gillard case seems to support the theory that female politicians may have a more difficult time navigating weight and appearance than male politicians. An experimental study by Beth Miller and Jennifer Lundgren suggests “weight bias exists for obese female political candidates, but that large body size may be an asset for male candidates” (p. 712). Conclusion This study has at least partially answered the original research questions. [RQ1] Which terms do commentators utilize to describe political figures as “fat”? The terms include: fat, fat arse, fat f***, large, heavy, obese, plus size, pudgy, and rotund. The media frames include: ‹happy fat›, ‹fat shaming›, ‹morbidly obese›, ‹happy fat “Bubba›, ‹transformed “Bubba›, ‹fat hypocrite›, ‹large woman ambiguity›, ‹weight gain women may experience after giving birth›, ‹I am so sick and tired of skinny people saying they are fat›, ‹woman inappropriately attacks fat men›, and ‹feminist inappropriately attacks fat woman›. [RQ2] Why is the term “fat” utilized in the political arena? Opponents in attack mode, to discredit a political figure, often use the term “fat”. It can imply that the person is “unhealthy” or has a character flaw. In the attack mode, critics can use “fat” as a tool to minimize a political figure’s legitimate and referent power. [RQ3] To what extent can one detect gender, national, or other differences in the manner in which the term “fat” is used in the political arena? In the United States, “obesity” is the dominant term, and is associated with the medicalisation of fat. Obesity is linked to health concerns, such as coronary heart disease. Weight bias and fat shaming seem to have a disproportionate impact on women. This study also has left many unanswered questions. 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