Dissertations / Theses on the topic 'Lattice code'

This thesis is part of a larger qualification effortperformed at Westinghouse Electric Sweden AB of the PHOENIX5 latticephysics code. The aim of the thesis is to validate PHOENIX5 withregards to cold criticality tests performed at the Toshiba NCAfacility in 2010-2011. For this, 26 different models were built torepresent the experiments performed by Toshiba in PHOENIX5. As anindependent reference, models were also built for the probabilisticMonte Carlo code SERPENT. The parameters examined in this thesis arethe criticality of the system, as well as the pin fission rates forselected experiments. Two different PHOENIX5 libraries were utilized,along with a HELIOS library. The results show that there is a Kinf trend between the differentlibraries. Furthermore, a void trend was found. This void trend waspresent for all models, including the SERPENT models. Pin fissionrate predictions give results close to those of the experiments forboth PHOENIX5 libraries. The system also proved sensitive to meshingchanges, as well as for the chosen water reflector width.

Topological order is a new field of research involving exotic physics. Among other things it has been suggested as a means for realising fault-tolerant quantum computation. Topological degeneracy, i.e. the ground state degeneracy of a topologically ordered state, is one of the quantities that have been used to characterize such states. Topological order has also been suggested as a possible quantum information storage. We study two-dimensional lattice models defined on a closed manifold, specifically on a torus, and find that these systems exhibit topological degeneracy proportional to the genus of the manifold on which they are defined. We also find that the addition of lattice dislocations increases the ground state degeneracy, a behaviour that can be interpreted as artificially increasing the genus of the manifold. We derive the fusion and braiding rules of the model, which are then used to calculate the braiding properties of the dislocations themselves. These turn out to resemble non-abelian anyons, a property that is important for the possibility to achieve universal quantum computation. One can also emulate lattice dislocations synthetically, by adding an external field. This makes them more realistic for potential experimental realisations.
Topologisk ordning är ett nytt område inom fysik som bland annat verkar lovande som verktyg för förverkligandet av kvantdatorer. En av storheterna som karakteriserar topologiska tillstånd är det totala antalet degenererade grundtillstånd, den topologiska degenerationen. Topologisk ordning har också föreslagits som ett möjligt sätt att lagra kvantdata. Vi undersöker tvådimensionella gittermodeller definierade på en sluten mångfald, specifikt en torus, och finner att dessa system påvisar topologisk degeneration som är proportionerlig mot mångfaldens topologiska genus. När dislokationer introduceras i gittret finner vi att grundtillståndets degeneration ökar, något som kan ses som en artificiell ökning av mångfaldens genus. Vi härleder sammanslagningsregler och flätningsregler för modellen och använder sedan dessa för att räkna ut flätegenskaperna hos själva dislokationerna. Dessa visar sig likna icke-abelska anyoner, en egenskap som är viktiga för möjligheten att kunna utföra universella kvantberäkningar. Det går också att emulera dislokationer i gittret genom att lägga på ett yttre fält. Detta gör dem mer realistiska för eventuella experimentella realisationer.

A framework for constructing kinetic monte carlo (KMC) simulations of diffusive events on a lattice was developed. This code was then tested by running simulations of Fe adatom diffusion on graphene and graphene-boron nitride surfaces. The results from these simulations was then used to show that the modeled diffusion adheres to the laws of brownian motion and generates results similar to recent research findings.

Abstract Lattice codes achieve AWGN capacity and naturally fit in many multi-terminal networks because of their inherited structure. Although extensive information theoretic research has been done to prove the importance of lattice codes for these networks, the progress in finding practical low-complexity lattice schemes is limited. Hence, the motivation of this thesis is to develop several methods to make lattice codes practical for communication networks. First, we propose an efficient lattice coding scheme for real-valued, full-duplex one- and two-way relay channels. Lattice decomposition, superposition, and block Markov encoding are used to propose a simple, yet near capacity achieving encoding/decoding schemes for these relay channels. By using information theoretic tools, we prove the achievable rates of these schemes, which are equal to the best known rates. Then, we construct practical, low-complexity implementations of the proposed relay schemes using low-density lattice codes. Numerical evaluation is presented and they show that our schemes achieve performance as close as 2.5dB away from theoretical limits. The effect of shaping/coding loss on the performance of relay channels is studied. Then, we propose a low complexity lattice code construction that provides high shaping and coding gains. First, integer information is encoded to shaped integers. Two methods are proposed for this task: ''Voronoi integers'' and ''non uniform integers''. These shaped integers have shaping gains over the integer lattice. Then for the second step, we present a general framework to systematically encode these integers, using any high dimensional lattice with lower-triangular generator or parity check matrices, retaining the same shaping gain. The proposed scheme can be used to shape high dimensional lattices such as low density lattice codes, LDA-lattice, etc. Comprehensive analysis is presented using low density lattice codes. By using E8 and BW16 as shaping lattices, we numerically show the Voronoi integers result in the shaping gain of these lattices, that is, as much as 0.65dB and 0.86dB. It is numerically observed that non-uniform integers have shaping gains of up to 1.25dB. These shaping operations can be implemented with less complexity than previous low density lattice codes shaping approaches and shaping gains are higher than in previously reported cases, which are in the order of 0.4dB. Lastly, we propose a low complexity practical code construction for compute-and-forward. A novel code construction called ''mixed nested lattice code construction'' is developed. This code construction uses a pair of distinct nested lattices to encode the integers where shaping is provided by a small dimensional lattice with high shaping gain and coding is performed using a high coding gain and a high dimensional lattice. This construction keeps the shaping and the coding gains of respective shaping and coding lattices. Further, we prove an existence of an isomorphism in this construction such that linear combination of lattice codes can be mapped to a linear combination of integers over a finite field. Hence, this construction can be readily used for any compute-and-forward applications. A modified LDLC decoder is proposed to estimate a linear combination of messages. Performance is numerically evaluated
Tiivistelmä Hilakoodit saavuttavat AWGN kapasiteetin ja sopivat luonnollisesti moniin monen päätelaitteen verkkoihin niihin sisältyvän rakenteen vuoksi. Vaikka lukuisat informaatioteoreettiset tutkimustyöt todistavat hilakoodien tärkeyden näille verkoille, käytännössä alhaisen kompleksisuuden hilajärjestelmiä on vielä vähän. Näin ollen tämän tutkielman tarkoitus on kehittää useita metodeja, jotta hilakoodeista saadaan käytännöllisiä viestintäverkkoihin. Aluksi, ehdotamme tehokkaan hilakoodausjärjestelmän reaaliarvoisille, full duplexisille yksi- ja kaksisuuntaisille välittäjäkanaville. Käytämme hilan hajottamista, superpositiota ja lohko-Markov -koodausta ehdottaessamme yksinkertaiset ja siltikin kapasiteetin saavuttavat koodaus- ja dekoodausjärjestelmät näihin välityskanaviin. Käyttämällä informaatioteoreettisia työkaluja, osoitamme näiden järjestelmien saavutettavat nopeudet, jotka ovat yhtä suuret kuin parhaimmat tunnetut nopeudet. Sitten rakennamme käytännölliset ja alhaisen monimutkaisuuden toteutukset ehdotetuille välitysjärjestelmille käyttäen alhaisen tiheyden hilakoodeja. Esitämme näille järjestelmille numeeriset arvioinnit, jotka näyttävät että nämä toteutukset saavuttavat tehokkuuden, joka on 2.5dB:n päässä teoreettisista rajoista. Tutkimme muotoilu- ja koodaushäviön vaikutusta välityskanavien tehokkuuteen. Sitten, ehdotamme alhaisen monimutkaisuuden hilakoodirakenteen, joka tarjoaa korkean muotoilu- ja koodausvahvistuksen. Ensin, kokonaislukuinformaatio on koodattu muotoiltuihin kokonaislukuihin. Esitämme kaksi metodia tähän tehtävään; 'Voronoi kokonaisluvut' ja 'ei yhtenäiset kokonaisluvut'. Näillä muotoilluilla kokonaisluvuilla on muotoiluvahvistusta kokonaislukuhilalle. Toisena askeleena, esitämme yleiset puitteet systemaattiseen kokonaislukujen koodaukseen käyttäen korkeaulotteisia hiloja alhaisen kolmiogeneraattori- tai pariteettivarmistusmatriiseja, jotka säilyttävät samalla muotoiluvahvistuksen. Ehdotettua järjestelmää voidaan käyttää muotoilemaan korkeaulotteisia hiloja kuten alhaisen tiheyden hilakoodeja, LDA-hiloja, jne. Esitämme kattavan analyysin käyttäen alhaisen tiheyden hilakoodeja. Käyttämällä muotoiluhiloina E8aa ja BW16a, näytämme numeerisesti 'Voronoi kokonaislukujen' käyttämisen seurauksena saavutettavat hilojen muotoiluvahvistukset, jotka ovat jopa 0.65dB ja 0.86dB. Näytämme myös numeerisesti että 'ei yhtenäisillä kokonaisluvuilla' on muotoiluvahvistusta jopa 1.25dB. Nämä muotoiluoperaatiot voidaan toteuttaa alhaisemmalla monimutkaisuudella kuin aikaisemmat 'alhaisen tiheyden hilakoodien muotoilumenetelmät' ja muotoiluvahvistukset ovat suuremmat kuin aikaisemmin raportoidut tapaukset, jotka ovat suuruusluokaltaan 0.4dB. Viimeiseksi, ehdotamme käytännöllisen koodikonstruktion alhaisella monimutkaisuudella 'laske ja lähetä' -menetelmään. Kehitämme uuden koodikonstruktion, jota kutsumme 'sekoitetuksi sisäkkäiseksi hilakoodikonstruktioksi'. Tämä koodikonstruktio käyttää kahta eroteltavissa olevaa sisäkkäistä hilaa koodaamaan kokonaisluvut siellä, missä muotoilu tehdään pienen ulottuvuuden hiloilla korkean muotoiluvahvistuksella ja koodaus toteutetaan käyttäen korkean koodausvahvistuksen omaavaa korkeaulottuvuuksista hilaa. Tämä konstruktio säilyttää muotoilu- ja koodausvahvistukset kullekin muotoilu- ja koodaushilalle. Lisäksi, todistamme isomorfismin olemassaolon tässä konstruktiossa siten, että lineaarisen hilakoodien kombinaatio voidaan kuvata lineaarisena kokonaislukujen kombinaationa äärellisessä kunnassa. Näin ollen tätä konstruktiota voidaan helposti käyttää missä tahansa 'laske ja lähetä' -sovelluksessa. Esitämme muokatun LDLC dekooderin lineaarisen viestikombinaation estimointiin. Arvioimme tehon numeerisesti

Doctor of Philosophy
Department of Mathematics
Gerald H. Höhn
We classify the genera of doubly even binary codes, the genera of even lattices, and the genera of rational vertex operator algebras (VOAs) arising from the modular tensor categories (MTCs) of rank up to 4 and central charges up to 16. For the genera of even lattices, there are two types of the genera: code type genera and non code type genera. The number of the code type genera is finite. The genera of the lattices of rank larger than or equal to 17 are non code type. We apply the idea of a vector valued modular form and the representation of the modular group SL[subscript]2(Z) in [Bantay2007] to classify the genera of the VOAs arising from the MTCs of ranks up to 4 and central charges up to 16.

Organic molecular crystals form a condensed solid phase offering a rich vein of physical phenomena which are open to investigation. The desire to harness these properties for technological and biological purposes has led to extensive experimental and theoretical investigations. The naturally occurring ɑ-amino acids form molecular crystals in the solid state; to date there have been very few studies of these systems. The work in this thesis is concerned with attempting to understand the relationship between the properties of the molecular crystal, and how these relate to the properties of the constituent molecules in isolation. To this end, density functional calculations of the structural and electronic properties of amino acids in both the crystalline and gaseous states are performed, and the results reported. The bonding mechanisms responsible for the crystal being stable are elucidated, and used to explain the zwitterionisation of the molecules upon formation of the solid state. In order to investigate the lattice dynamical and dielectric properties, the implementation of a variational density functional perturbation theory (DFPT) scheme within the plane wave pseudopotential formalism is described in detail. This scheme is fully self-consistent, and its computational cost is comparable to that of a single-point self-consistent total energy calculation. The long wave method is used to alleviate well-known problems associated with the application of homogeneous fields to crystal systems, viz. that such fields break the crystal symmetry, and the adequate treatment of electronic screening. Calculation of the first order perturbed wavefunctions and the second order change in the Kohn-Sham functional allows properties such as the polarisability, dielectric matrix, dynamical matrix and Born effective charge tensors to be determined. The treatment of crystalline symmetries is described in detail. The DFPT formalism is extended to allow IR absorption spectra to be obtained. The lattice dynamical and dielectric behaviour of the isolated molecules and the molecular crystals are obtained; calculation of the IR spectra facilitates an insight into the effects of the crystalline environment and zwitterionisation upon the lattice dynamics. Results indicate the importance of the molecular shape and structure upon the intermolecular interactions, and hence the crystal structure formed. It is these intermolecular interactions that are found to play the major part in modification of the lattice dynamical and dielectric behaviour.

Cette thèse aborde deux problèmes liés aux réseaux de points, un vieux problème et un nouveau.Tous deux sont des problèmes de décodage de réseaux de points : À savoir, étant donné un point dans l'espace, trouver le point du réseau le plus proche.Le premier problème est lié au codage de canal en dimensions intermédiaires. Alors que des systèmes efficaces basés sur les réseaux de points existent dans les petites dimensions n < 30 et les grandes dimensions n > 1000, ce n'est pas le cas des dimensions intermédiaires. Nous étudions le décodage de réseaux de points intéressants dans ces dimensions intermédiaires. Nous introduisons de nouvelles familles de réseaux de points obtenues en appliquant le contrôle de parité de manière récursive. Ces familles comprennent des réseaux de points célèbres, tels que les réseaux Barnes-Wall, les réseaux Leech et Nebe, ainsi que de nouveaux réseaux de parité.Nous montrons que tous ces réseaux de points peuvent être décodés efficacement avec un nouveau décodeur récursif par liste.Le deuxième problème concerne les réseaux de neurones. Depuis 2016, d'innombrables articles ont tenté d'utiliser l'apprentissage profond pour résoudre le problème de décodage/détection rencontré dans les communications numériques. Nous proposons d'étudier la complexité du problème que les réseaux de neurones doivent résoudre. Nous introduisons une nouvelle approche du problème de décodage afin de l'adapter aux opérations effectuées par un réseau de neurones. Cela permet de mieux comprendre ce qu'un réseau de neurones peut et ne peut pas faire dans le cadre de ce problème, et d'obtenir des indications concernant la meilleure architecture du réseau de neurones. Des simulations informatiques validant notre analyse sont fournies
This thesis discusses two problems related to lattices, an old problem and a new one.Both of them are lattice decoding problems: Namely, given a point in the space, find the closest lattice point.The first problem is related to channel coding in moderate dimensions. While efficient lattice schemes exist in low dimensions n < 30 and high dimensions n > 1000, this is not the case of intermediate dimensions. We investigate the decoding of interesting lattices in these intermediate dimensions. We introduce new families of lattices obtained by recursively applying parity checks. These families include famous lattices, such as Barnes-Wall lattices, the Leech and Nebe lattices, as well as new parity lattices.We show that all these lattices can be efficiently decoded with an original recursive list decoder.The second problem involves neural networks. Since 2016 countless papers tried to use deep learning to solve the decoding/detection problem encountered in digital communications. We propose to investigate the complexity of the problem that neural networks should solve. We introduce a new approach to the lattice decoding problem to fit the operations performed by a neural network. This enables to better understand what a neural network can and cannot do in the scope of this problem, and get hints regarding the best architecture of the neural network. Some computer simulations validating our analysis are provided

Fases topológicas da matéria são caracterizadas por terem uma degenerescên- cia do estado fundamental que depende da topologia da variedade em que o sistema físico é definido, além disso apresentam estados excitados no interior do sistema que são interpretados como sendo quase-partículas com estatística de tipo anyonica. Estes sistemas apresentam também excitações sem gap de energia em sua borda. Fases topologicamente ordenadas distintas não podem ser distinguidas pelo esquema usual de quebra de simetria de Ginzburg-Landau. Nesta dissertação apresentamos como exemplo o modelo mais simples de um sistema com Ordem Topológica, a saber, o Toric Code (TC), introduzido originalmente por A. Kitaev em [1]. O estado fundamental deste modelo ap- resenta degenerescência igual a 4 quando incorporado à superfície de um toro. As excitações elementares são interpretadas como sendo quase-partículas com estatística do tipo anyonica. O TC é um caso especial de uma classe mais geral de models chamados de Quantum Double Models (QDMs), estes modelos podem ser entendidos como sendo uma implementação de Teorias de gauge na rede em (2 + 1) dimensões na formulação Hamiltoniana, em que os graus de liberdade vivem nas arestas da rede e são elementos do grupo de gauge G. Nós generalizamos estes modelos com a inclusão de campos de matéria nos vértices da rede. Também apresentamos uma construção detalhada de tais modelos e mostramos que eles são exatamente solúveis. Em particular, exploramos o modelo que corresponde à escolher o grupo de gauge como sendo o grupo cíclico Z2 e os graus de liberdade de matéria como sendo elementos de um espaço vetorial bidimensional V2. Além disso, mostramos que a degenerescência do estado fundamental não depende da topologia da variedade e obtemos os estados excitados mais elementares deste modelo.
Topological phases of matter are characterized for having a topologically dependent ground state degeneracy, anyonic quasi-particle bulk excitations and gapless edge excitations. Different topologically ordered phases of matter can not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the \\Toric Code (TC) introduced by A. Kitaev in [1]. Its ground state is 4-fold degenerate when embedded on the surface of a torus and its elementary excited states are interpreted as quasi-particle anyons. The TC is a particular case of a more general class of lattice models known as Quantum Double Models (QDMs) which can be interpreted as an implementation of (2+1) Lattice Gauge Theories in the Hamiltonian formulation with discrete gauge group G. We generalize these models by the inclusion of matter fields at the vertices of the lattice. We give a detailed construction of such models, we show they are exactly solvable and explore the case when the gauge group is set to be the abelian Z_2 cyclic group and the matter degrees of freedom to be elements of a 2-dimensional vector space V_2. Furthermore, we show that the ground state degeneracy is not topologically dependent and obtain the most elementary excited states.

Lattice codes find good use as higher dimensional signal constellations. When used with QAM, the constituent 2-D constellations of a lattice code determine important properties of the transmitted signal. Using multidimensional Fourier techniques, this work presents a robust method to efficiently generate the point distribution of all the constituent 2-D constellations of a lattice code. The multidimensional discrete Fourier transform (MDFT) is computed for a periodic extension of the lattice code. The MDFT is used in conjunction with a version of the Projection-Slice theorem, derived for the discrete case, to obtain the point distribution of all the constituent 2-D constellations. The implementation of the MDFT is via a multidimensional generalization of the FFT using the Cooley-Tukey decomposition, well matched to lattice properties. Numerical results show that for signal constellations which are not large, the continuous approximation technique is not accurate, and therefore the exact calculations should be used.

In this thesis, using lattice codes and channel codes, we propose several solutions to improve the performance of physical-layer network coding (PNC) schemes over the two-way relay network as well as the multi-way relay network. In the first part of our work, we propose an efficient equation-coefficient search algorithm for compute-and-forward over complex-valued channels, which guarantees to find the optimal coefficients over the ring of Gaussian integers as well as the ring of Eisenstein integers. We also propose an optimal coefficient search algorithm for the Integer-Forcing compute-and-forward receiver, when multiple receive antennas are available at the relay. The proposed algorithms are shown to have low polynomial complexity in transmitting user number and we use numerical results to verify the performance of our algorithms against other competitive search algorithms in literature. In the second part of our work we investigate the performance of popular PNC schemes for the two-way relay network and derive their end-to-end achievable rates with channel inversion precoding over the Rayleigh fading channel. We also propose a power efficient precoding scheme based on compute-and forward-to improve the network throughput. In the third part of our work, after introducing the novel concept of compatibility between channel code and lattice code, we propose several low complexity joint channel coded network coding (JCCNC) schemes for PAM and QAM two-way relay networks. Firstly, using LDPC codes, we propose the lattice-decoded JCCNC (LD-JCCNC) scheme. Secondly, we propose two JCCNC schemes using low density construction A (LDA) lattices and polar lattices, which we call LDA-JCCNC and PLA-JCCNC respectively. In both JCCNC schemes, channel coding and network coding operations are integrated through the use of lattice decoding at the relay, where the arithmetic addition of lattice codewords is directly decoded using their corresponding lattice decoding algorithm. In contrast with most existing JCCNC schemes which are restricted to set types of modulation schemes, we also give clear methodology on how our JCCNC schemes can be applied to general types of higher order PAM and QAM modulation schemes. In the final part of our work, we extend our novel JCCNC schemes to the general multi-way relay network for the compute-and-forward scheme, and show how they can be used with general types of PAM and QAM modulation systems. Detailed simulation analysis are carried out to evaluate and compare the performance of all proposed JCCNC schemes in relation to existing schemes in literature.

Multi-Terminal Source Coding (MTSC) addresses the problem of compressing correlated sources without communication links among them. In this thesis, the constructive approach of this problem is considered in an algebraic framework and a system design is provided that can be applicable in a variety of settings. Wyner-Ziv problem is first investigated: coding of an independent and identically distributed (i.i.d.) Gaussian source with side information available only at the decoder in the form of a noisy version of the source to be encoded. Theoretical models are first established and derived for calculating distortion-rate functions. Then a few novel practical code implementations are proposed by using the strategy of multi-dimensional nested lattice/trellis coding. By investigating various lattices in the dimensions considered, analysis is given on how lattice properties affect performance. Also proposed are methods on choosing good sublattices in multiple dimensions. By introducing scaling factors, the relationship between distortion and scaling factor is examined for various rates. The best high-dimensional lattice using our scale-rotate method can achieve a performance less than 1 dB at low rates from the Wyner-Ziv limit; and random nested ensembles can achieve a 1.87 dB gap with the limit. Moreover, the code design is extended to incorporate with distributed compressive sensing (DCS). Theoretical framework is proposed and practical design using nested lattice/trellis is presented for various scenarios. By using nested trellis, the simulation shows a 3.42 dB gap from our derived bound for the DCS plus Wyner-Ziv framework.

In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two cyclic constructions.

In this paper, we introduce and characterize the class of lattices that arise as the family of lowersets of the incidence poset for a hypergraph. In particular, we show that the following statements are logically equivalent: 1. A lattice L is order isomorphic to the frame of opens for a hypergraph endowed with the Classical topology. 2. A lattice L is bialgebraic, distributive, and its subposet of completely joinprime elements forms the incidence poset for a hypergraph. 3. A lattice L is a cone lattice.

We conclude the paper by extending a well-known Stone-type duality to the categories of hypergraphs coupled with finite-based HP-morphisms and cone lattices coupled with frame homomorphisms that preserve compact elements.

Westinghouse Electric Sweden AB’s three-dimensional reactor core simulation program POLCA uses a large number of tables containing various fuel dependent data, such as cross sections, pin power maps with power distribution etc. POLCA uses quadratic and linear interpolation to extract the values needed for the simulation. However, finding the correct values to interpolate between takes time. This master thesis describes a method of compacting the tables by removing values, in order to shorten the needed simulation time. This is done so that no significant accuracy is lost in the interpolations. The method also finds deviant values and replaces these with new, interpolated values. The thesis shows that approximately 90 % of all values can be removed without losing significant accuracy. These results are however heavily dependent on the choice of accuracy loss criterion; a lower allowance for accuracy loss lowers the amount of values which can be removed sharply.

The use of accelerator technology, particularly Graphics Processing Units (GPUs), for scientific computing has increased greatly over the last decade. While this technology allows larger and more complicated problems to be solved faster than before it also presents another opportunity: the real-time and interactive solution of problems. This work aims to investigate the progress that GPU technology has made towards allowing fluid-structure interaction (FSI) problems to be solved in real-time, and to facilitate user interaction with such a solver. A mesoscopic scale fluid flow solver is implemented on third generation nVidia ‘Kepler’ GPUs in two and three dimensions, and its performance studied and compared with existing literature. Following careful optimisation the solvers are found to be at least as efficient as existing work, reaching peak efficiencies of 93% compared with theoretical values. These solvers are then coupled with a novel immersed boundary method, allowing boundaries defined at arbitrary coordinates to interact with the structured fluid domain through a set of singular forces. The limiting factor of the performance of this method is found to be the integration of forces and velocities over the fluid and boundaries; the arbitrary location of boundary markers makes the memory accesses during these integrations largely random, leading to poor utilisation of the available memory bandwidth. In sample cases, the efficiency of the method is found to be as low as 2.7%, although in most scenarios this inefficiency is masked by the fact that the time taken to evolve the fluid flow dominates the overall execution time of the solver. Finally, techniques to visualise the fluid flow in-situ are implemented, and used to allow user interaction with the solvers. Initially this is achieved via keyboard and mouse to control the fluid properties and create boundaries within the fluid, and later by using an image based depth sensor to import real world geometry into the fluid. The work concludes that, for 2D problems, real-time interactive FSI solvers can be implemented on a single laptop-based GPU. In 3D the memory (both size and bandwidth) of the GPU limits the solver to relatively simple cases. Recommendations for future work to allow larger and more complicated test cases to be solved in real-time are then made to complete the work.

Sandwich panels are extensively used in constructional, naval and aerospace structures due to their high stiffness and strength-to-weight ratios. In contrast, sound transmission properties of sandwich panels are adversely influenced by their low effective mass. Phase velocity matching of structural waves propagating within the panel and the incident pressure waves from the surrounding fluid medium lead to coincidence effects (often within the audible range) resulting in reduced impedance and high sound transmission. Truss-like lattice cores with porous microarchitecture and \emph{reduced} inter panel connectivity relative to honeycomb cores promise the potential to satisfy the conflicting structural and vibroacoustic response requirements. This study combines Bloch-wave analysis and the Finite Element Method (FEM) to understand wave propagation and hence sound transmission in sandwich panels with a truss lattice core. Three dimensional coupled fluid-structure finite element simulations are conducted to compare the performance of a representative set of lattice core topologies. Potential advantages of sandwich structures with a lattice core over the traditional shear wall panel designs are identified. The significance of partial band gaps is evident in the sound transmission loss characteristics of the panels studied. This work demonstrates that, even without optimization, significant enhancements in STL performance can be achieved in truss lattice core sandwich panels compared to a traditional sandwich panel employing a honeycomb core under constant mass constraint.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

Предмет  истраживања  тезе  је  из области  паралелног  програмирања,имплементација  CFD  (Computational Fluid  Dynamics)  методе  на  вишехетерогених  вишејезгарних  уређаја истовремено.  У  раду  је  приказанонеколико  алгоритама  чији  је  циљ убрзање  CFD  симулације  на персоналним  рачунарима.  Показано је  да  описано  решење  постиже задовољавајуће  перформансе  и  на HPC  уређајима  (Тесла  графичким картицама).  Направљена  је симулација  у  микросервис архитектури  која  је  портабилна  и флексибилна и додатно олакшава рад на персоналним рачунарима.
Predmet  istraživanja  teze  je  iz oblasti  paralelnog  programiranja,implementacija  CFD  (Computational Fluid  Dynamics)  metode  na  višeheterogenih  višejezgarnih  uređaja istovremeno.  U  radu  je  prikazanonekoliko  algoritama  čiji  je  cilj ubrzanje  CFD  simulacije  na personalnim  računarima.  Pokazano je  da  opisano  rešenje  postiže zadovoljavajuće  performanse  i  na HPC  uređajima  (Tesla  grafičkim karticama).  Napravljena  je simulacija  u  mikroservis arhitekturi  koja  je  portabilna  i fleksibilna i dodatno olakšava rad na personalnim računarima.
The  case  study  of  this  dissertation belongs  to  the  field  of  parallel programming,  the  implementation  of CFD  (Computational  Fluid  Dynamics) method  on  several  heterogeneous multiple  core  devices  simultaneously. The  paper  presents  several  algorithms aimed  at  accelerating  CFD  simulation on common computers. Also it has been shown  that  the  described  solution achieves  satisfactory  performance  onHPC  devices  (Tesla  graphic  cards). Simulation is  created    in  micro-service architecture that is portable and flexible and  makes  it  easy  to  test  CFDsimulations on common computers.

Thesis advisor: Udayan Mohanty
The high surface area and atomic-level tunability offered by nanoparticles has defined their promise as heterogeneous catalysts. While initial studies began with nanoparticles of a single metal assuming thermodynamic shapes, modern work has focused on using nanoparticle composition and geometry to optimize nanocatalysts for a wide variety of reactions. Further optimization of these refined nanocatalysts remains difficult, however, as the factors that determine catalytic activity are intertwined and a fundamental understanding of each remains elusive. In this work, precise synthetic methods are used to tune a number of factors, including composition, strain, metal-to-metal charge transfer, atomic order, and surface faceting, and understand their impact on catalysis. The first chapter focuses on current achievements and challenges in the synthesis of intermetallic nanocatalysts, which offer long-range order that allows for total control of surface structure. A particular focus is given to the impact of the synthetic approach on the activity of the resulting nanoparticles. In the second chapter, multilayered Pd-(Ni-Pt)x nanoparticles serve as a controlled arena for the study of metallic mixing and order formation on the nanoscale. The third chapter controls the shell thickness of Au@PdPt core-alloyed shell nanoparticles on a nanometer scale to isolate strain at the nanoparticle surface. In the fourth chapter, the synthetic approaches of chapters two and three are applied to catalysis. In totality, the work presented here represents a brick in the foundation of understanding and exploiting structure-function relationships on the nanoscale, with an eye toward the rational design of tailored nanocatalysts
Thesis (PhD) — Boston College, 2020
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Chemistry

In the past several decays, lattice codes played an important role in coding theory and information theory. Lattice codes with good performance in communication and source compression have attracted considerable interest. A typical method of constructing good lattice codes is to use existing linear codes. For instance, the famous Barnes-Wall lattices are generated by Reed-Muller (RM) codes, and more recently, the emerging low density Construction-A (LDA) lattices are resulted from low density parity check (LDPC) codes. In this thesis, we develop a new class of lattices, called polar lattices, based on polar codes. The invention of polar codes is considered to be one of the major breakthroughs in coding theory for the past ten years. We show that polar lattices provide explicit solutions for many interesting problems in information theory. For channel coding, we prove that polar lattices are capable of achieving the capacity of the additive white Gaussian noise (AWGN) channel. For the dual side, i.e., source compression, polar lattices can also achieve the rate-distortion bound for the independent and identically distributed (i.i.d.) Gaussian source. Moreover, a combining design of polar lattices for both channel coding and source coding gives us explicit solutions to the Gaussian version of the Wyner-Ziv and Gelfand-Pinsker problems. For physical layer security, we prove that polar lattices are able to approach the secrecy capacity of the Gaussian wiretap channel under the strong secrecy criterion. Two more applications of polar lattices are achieving the capacity of the i.i.d. fading channel and extracting the common information of two joint Gaussian sources. The explicit construction of polar lattices provides us better insights on the study of lattice coding. Many interesting problems of lattice coding, such as AWGN goodness, secrecy-goodness, lattice shaping, and lattice Gaussian distribution will be addressed from the perspective of polar lattices.

Value-range analysis is a static analysis technique based on arguing about the values that a variable may take on a given program point. It can be used to prove absence of run-time errors such as out-of-bound array accesses. Since value-range analysis collects information on each program point, data-flow analysis can be used in association with it. The main goal of this work is designing and implementing such a value-range analysis tool. The work begins with an introduction into the topic, an explanation of data-flow and value-range analyses and a description of abstract interpretation, which provides the formal basis of the analyser. The core of this work is the design, implementation, testing and evaluation of the analyser. In the conclusion, our personal experience obtained in the area of the thesis is mentioned, along with a discussion of a possible future development of the designed tool.

This thesis focuses on detection algorithms of radar targets, namely on group of techniques for removing of disturbing reflections from static objects - clutter and for suppression of distortion products caused by the phase noise of the transmitter and receiver. Methods for distortion suppression in received signal are designed for implementation in the developed active multistatic radar, which operates in the code division multiplex of several transmitters on single frequency. The aim of the doctoral thesis is to design, implement in tool for technical computing MATLAB and analyze the effectiveness and computational complexity of these techniques on simulated and real data.

Un graphe métrique G(X;D) est un graphe dont l’ensemble des sommets est l’ensemble X des points d’un espace métrique (X; d), et dont les arêtes relient les paires fx; yg de sommets telles que d(x; y) 2 D. Dans cette thèse, nous considérons deux problèmes qui peuvent être interprétés comme des problèmes de graphes métriques dans Rn. Premièrement, nous nous intéressons au célèbre problème d’empilements de sphères, relié au graphe métrique G(Rn; ]0; 2r[) pour un rayon de sphère r donné. Récemment, Venkatesh a amélioré d’un facteur log log n la meilleure borne inférieure connue pour un empilement de sphères donné par un réseau, pour une suite infinie de dimensions n. Ici nous prouvons une version effective de ce résultat, dans le sens où l’on exhibe, pour la même suite de dimensions, des familles finies de réseaux qui contiennent un réseaux dont la densité atteint la borne de Venkatesh. Notre construction met en jeu des codes construits sur des corps cyclotomiques, relevés en réseaux grâce à un analogue de la Construction A. Nous prouvons aussi un résultat similaire pour des familles de réseaux symplectiques. Deuxièmement, nous considérons le graphe distance-unité G associé à une norme k_k. Le nombre m1 (Rn; k _ k) est défini comme le supremum des densités réalisées par les stables de G. Si la boule unité associée à k _ k pave Rn par translation, alors il est aisé de voir que m1 (Rn; k _ k) > 1 2n . C. Bachoc et S. Robins ont conjecturé qu’il y a égalité. On montre que cette conjecture est vraie pour n = 2 ainsi que pour des régions de Voronoï de plusieurs types de réseaux en dimension supérieure, ceci en se ramenant à la résolution de problèmes d’empilement dans des graphes discrets
A distance graph G(X;D) is a graph whose set of vertices is the set of points X of a metric space (X; d), and whose edges connect the pairs fx; yg such that d(x; y) 2 D. In this thesis, we consider two problems that may be interpreted in terms of distance graphs in Rn. First, we study the famous sphere packing problem, in relation with thedistance graph G(Rn; (0; 2r)) for a given sphere radius r. Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor log log n for infinitely many dimensions n. We prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A. We also prove a similar result for families of symplectic lattices. Second, we consider the unit distance graph G associated with a norm k _ k. The number m1 (Rn; k _ k) is defined as the supremum of the densities achieved by independent sets in G. If the unit ball corresponding with k _ k tiles Rn by translation, then it is easy to see that m1 (Rn; k _ k) > 1 2n . C. Bachoc and S. Robins conjectured that the equality always holds. We show that this conjecture is true for n = 2 and for several Voronoï cells of lattices in higher dimensions, by solving packing problems in discrete graphs

This PhD study, developed at Universitat Politècnica de València (UPV), aims to cover the first phase of the benchmark released by the expert group on Uncertainty Analysis in Modeling (UAM-LWR). The main contribution to the benchmark, made by the thesis' author, is the development of a MATLAB program requested by the benchmark organizers. This is used to generate neutronic libraries to distribute among the benchmark participants. The UAM benchmark pretends to determine the uncertainty introduced by coupled multi-physics and multi-scale LWR analysis codes. The benchmark is subdivided into three phases: 1. Neutronic phase: obtain collapsed and homogenized problem-dependent cross sections and criticality analyses. 2. Core phase: standalone thermohydraulic and neutronic codes. 3. System phase: coupled thermohydraulic and neutronic code. In this thesis the objectives of the first phase are covered. Specifically, a methodology is developed to propagate the uncertainty of cross sections and other neutronic parameters through a lattice physics code and core simulator. An Uncertainty and Sensitivity (U&S) analysis is performed over the cross sections contained in the ENDF/B-VII nuclear library. Their uncertainty is propagated through the lattice physics code SCALE6.2.1, including the collapse and homogenization phase, up to the generation of problem-dependent neutronic libraries. Afterward, the uncertainty contained in these libraries can be further propagated through a core simulator, in this study PARCSv3.2. The module SAMPLER -available in the latest release of SCALE- and DAKOTA 6.3 statistical tool are used for the U&S analysis. As a part of this process, a methodology to obtain neutronic libraries in NEMTAB format -to be used in a core simulator- is also developed. A code-to-code comparison with CASMO-4 is used as a verification. The whole methodology is tested using a Boiling Water Reactor (BWR) reactor type. Nevertheless, there is not any concern or limitation regarding its use in any other type of nuclear reactor. The Gesellschaft für Anlagen und Reaktorsicherheit (GRS) stochastic methodology for uncertainty quantification is used. This methodology makes use of the high-fidelity model and nonparametric sampling to propagate the uncertainty. As a result, the number of samples (determined using the revised Wilks' formula) does not depend on the number of input parameters but only on the desired confidence and uncertainty of output parameters. Moreover, the output Probability Distribution Functions (PDFs) are not subject to normality. The main disadvantage is that each input parameter must have a pre-defined PDF. If possible, input PDFs are defined using information found in the related literature. Otherwise, the uncertainty definition is based on expert judgment. A second scenario is used to propagate the uncertainty of different thermohydraulic parameters through the coupled code TRACE5.0p3/PARCSv3.0. In this case, a PWR reactor type is used and a transient control rod drop occurrence is simulated. As a new feature, the core is modeled chan-by-chan following a fully 3D discretization. No other study is found using a detailed 3D core. This U&S analysis also makes use of the GRS methodology and DAKOTA 6.3.
Este trabajo de doctorado, desarrollado en la Universitat Politècnica de València (UPV), tiene como objetivo cubrir la primera fase del benchmark presentado por el grupo de expertos Uncertainty Analysis in Modeling (UAM-LWR). La principal contribución al benchmark, por parte del autor de esta tesis, es el desarrollo de un programa de MATLAB solicitado por los organizadores del benchmark, el cual se usa para generar librerías neutrónicas a distribuir entre los participantes del benchmark. El benchmark del UAM pretende determinar la incertidumbre introducida por los códigos multifísicos y multiescala acoplados de análisis de reactores de agua ligera. El citado benchmark se divide en tres fases: 1. Fase neutrónica: obtener los parámetros neutrónicos y secciones eficaces del problema específico colapsados y homogenizados, además del análisis de criticidad. 2. Fase de núcleo: análisis termo-hidráulico y neutrónico por separado. 3. Fase de sistema: análisis termo-hidráulico y neutrónico acoplados. En esta tesis se completan los principales objetivos de la primera fase. Concretamente, se desarrolla una metodología para propagar la incertidumbre de secciones eficaces y otros parámetros neutrónicos a través de un código lattice y un simulador de núcleo. Se lleva a cabo un análisis de incertidumbre y sensibilidad para las secciones eficaces contenidas en la librería neutrónica ENDF/B-VII. Su incertidumbre se propaga a través del código lattice SCALE6.2.1, incluyendo las fases de colapsación y homogenización, hasta llegar a la generación de una librería neutrónica específica del problema. Luego, la incertidumbre contenida en dicha librería puede continuar propagándose a través de un simulador de núcleo, para este estudio PARCSv3.2. Para el análisis de incertidumbre y sensibilidad se ha usado el módulo SAMPLER -disponible en la última versión de SCALE- y la herramienta estadística DAKOTA 6.3. Como parte de este proceso, también se ha desarrollado una metodología para obtener librerías neutrónicas en formato NEMTAB para ser usadas en simuladores de núcleo. Se ha realizado una comparación con el código CASMO-4 para obtener una verificación de la metodología completa. Esta se ha probado usando un reactor de agua en ebullición del tipo BWR. Sin embargo, no hay ninguna preocupación o limitación respecto a su uso con otro tipo de reactor nuclear. Para la cuantificación de la incertidumbre se usa la metodología estocástica Gesellschaft für Anlagen und Reaktorsicherheit (GRS). Esta metodología hace uso del modelo de alta fidelidad y un muestreo no paramétrico para propagar la incertidumbre. Como resultado, el número de muestras (determinado con la fórmula revisada de Wilks) no depende del número de parámetros de entrada, sólo depende del nivel de confianza e incertidumbre deseados de los parámetros de salida. Además, las funciones de distribución de probabilidad no están limitadas a normalidad. El principal inconveniente es que se ha de disponer de las distribuciones de probabilidad de cada parámetro de entrada. Si es posible, las distribuciones de probabilidad de entrada se definen usando información encontrada en la literatura relacionada. En caso contrario, la incertidumbre se define en base a la opinión de un experto. Se usa un segundo escenario para propagar la incertidumbre de diferentes parámetros termo-hidráulicos a través del código acoplado TRACE5.0p3/PARCSv3.0. En este caso, se utiliza un reactor tipo PWR para simular un transitorio de una caída de barra. Como nueva característica, el núcleo se modela elemento a elemento siguiendo una discretización totalmente en 3D. No se ha encontrado ningún otro estudio que use un núcleo tan detallado en 3D. También se usa la metodología GRS y el DAKOTA 6.3 para este análisis de incertidumbre y sensibilidad.
Aquest treball de doctorat, desenvolupat a la Universitat Politècnica de València (UPV), té com a objectiu cobrir la primera fase del benchmark presentat pel grup d'experts Uncertainty Analysis in Modeling (UAM-LWR). La principal contribució al benchmark, per part de l'autor d'aquesta tesi, es el desenvolupament d'un programa de MATLAB sol¿licitat pels organitzadors del benchmark, el qual s'utilitza per a generar llibreries neutròniques a distribuir entre els participants del benchmark. El benchmark del UAM pretén determinar la incertesa introduïda pels codis multifísics i multiescala acoblats d'anàlisi de reactors d'aigua lleugera. El citat benchmark es divideix en tres fases: 1. Fase neutrònica: obtenir els paràmetres neutrònics i seccions eficaces del problema específic, col¿lapsats i homogeneïtzats, a més de la anàlisi de criticitat. 2. Fase de nucli: anàlisi termo-hidràulica i neutrònica per separat. 3. Fase de sistema: anàlisi termo-hidràulica i neutrònica acoblats. En aquesta tesi es completen els principals objectius de la primera fase. Concretament, es desenvolupa una metodologia per propagar la incertesa de les seccions eficaces i altres paràmetres neutrònics a través d'un codi lattice i un simulador de nucli. Es porta a terme una anàlisi d'incertesa i sensibilitat per a les seccions eficaces contingudes en la llibreria neutrònica ENDF/B-VII. La seua incertesa es propaga a través del codi lattice SCALE6.2.1, incloent les fases per col¿lapsar i homogeneïtzar, fins aplegar a la generació d'una llibreria neutrònica específica del problema. Després, la incertesa continguda en la esmentada llibreria pot continuar propagant-se a través d'un simulador de nucli, per a aquest estudi PARCSv3.2. Per a l'anàlisi d'incertesa i sensibilitat s'ha utilitzat el mòdul SAMPLER -disponible a l'última versió de SCALE- i la ferramenta estadística DAKOTA 6.3. Com a part d'aquest procés, també es desenvolupa una metodologia per a obtenir llibreries neutròniques en format NEMTAB per ser utilitzades en simuladors de nucli. S'ha realitzat una comparació amb el codi CASMO-4 per obtenir una verificació de la metodologia completa. Aquesta s'ha provat utilitzant un reactor d'aigua en ebullició del tipus BWR. Tanmateix, no hi ha cap preocupació o limitació respecte del seu ús amb un altre tipus de reactor nuclear. Per a la quantificació de la incertesa s'utilitza la metodologia estocàstica Gesellschaft für Anlagen und Reaktorsicherheit (GRS). Aquesta metodologia fa ús del model d'alta fidelitat i un mostreig no paramètric per propagar la incertesa. Com a resultat, el nombre de mostres (determinat amb la fórmula revisada de Wilks) no depèn del nombre de paràmetres d'entrada, sols depèn del nivell de confiança i incertesa desitjats dels paràmetres d'eixida. A més, las funcions de distribució de probabilitat no estan limitades a la normalitat. El principal inconvenient és que s'ha de disposar de les distribucions de probabilitat de cada paràmetre d'entrada. Si és possible, les distribucions de probabilitat d'entrada es defineixen utilitzant informació trobada a la literatura relacionada. En cas contrari, la incertesa es defineix en base a l'opinió d'un expert. S'utilitza un segon escenari per propagar la incertesa de diferents paràmetres termo-hidràulics a través del codi acoblat TRACE5.0p3/PARCSv3.0. En aquest cas, s'utilitza un reactor tipus PWR per simular un transitori d'una caiguda de barra. Com a nova característica, cal assenyalar que el nucli es modela element a element seguint una discretizació totalment 3D. No s'ha trobat cap altre estudi que utilitze un nucli tan detallat en 3D. També s'utilitza la metodologia GRS i el DAKOTA 6.3 per a aquesta anàlisi d'incertesa i sensibilitat.¿
Mesado Melia, C. (2017). Uncertainty Quantification and Sensitivity Analysis for Cross Sections and Thermohydraulic Parameters in Lattice and Core Physics Codes. Methodology for Cross Section Library Generation and Application to PWR and BWR [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86167
TESIS

Thesis advisor: Chia-kuang Frank Tsung
Pt-based alloy and core-shell nanoparticles have been intensively studied to regulate its size and shape. It has known that these nanoparticles show enhanced catalytic activity in various important fields such as heterogeneous catalysis, and electrochemical energy storage including fuel cells and metal-air batteries. Here, we report a facile hydrothermal synthesis of sub-10 nm PdPt alloy and sub-20 nm Au@PdPt core-shell structures. By using a mild reducing agent in aqueous solution, metal precursors are co-reduced. Specific gases are introduced during the synthesis to optimize the reaction conditions. The PdPt alloy and Au@PdPt core-shell nanostructures were characterized and confirmed by TEM, HRTEM, EDS, ICP-OES and XRD. The resulting PdPt and Au@PdPt particles are monodispersed single crystalline and octahedral shape enclosed by (111) facets. The electrocatalytic activity for the oxidation of formic acid was tested. It was found that the catalytic activity toward the formic acid oxidation of Au@PdPt core-shell particles were much higher than those of PdPt alloy particles. In addition, Pt-rich compositions were the most active in both PdPt alloy and Au@PdPt core-shell nanoparticles. Further studies on thinner alloy-shell core-shell nanoparticles reveal that there is a volcano-curve relationship between the lattice strain strength related to alloy-shell thickness and the catalytic performance. It is proposed that there are three key parameters that can determine the catalytic activity: the alloy composition, the presence of the gold core, and the thickness of alloy-shell
Thesis (MS) — Boston College, 2012
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Chemistry

With the usage of biometrics becoming commonly used in a variety of applications, keeping those biometrics private and secure is an important issue. Indeed, the convenience of using biometrics for authentication is counteracted by the fact that they cannot easily be modified or changed. This can have dire consequences to a person if their biometrics are leaked. In the past decades, various techniques have been proposed to solve this problem. Such techniques range from using and storing randomized templates, using homomorphic encryption, or using biometric encryption techniques such as fuzzy extractors. Fuzzy extractors are a construction that allows the extraction of cryptographic keys from noisy data like biometrics. The key can then be rebuilt from some helper data and another biometric, provided that it is similar enough to the biometrics used to generate the key. This can be achieved through various approaches like the use of a quantizer or an error correcting code. In this thesis, we consider specifically fuzzy extractors for facial images. The first part of this thesis focuses on improving the security, privacy and performance of the extractor for faces first proposed by Sutcu et al. Our improvements make their construction more resistant to partial and total leaks of secure information, as well as improve the performance in a biometric authentication setting. The second part looks at using low density lattice codes (LDLC) as a quantizer in the fuzzy extractor, instead of using component based quantization. Although LDLC have been proposed as a quantizer for a general fuzzy extractor, they have yet to be used or tested for continuous biometrics like face images. We present a construction for a fuzzy extractor scheme using LDLC and we analyze its performance on a publicly available data set of images. Using an LDLC quantizer on this data set has lower accuracy than the improved scheme from the first part of this thesis. On the other hand, the LDLC scheme performs better when the inputs have additive white Gaussian noise (AWGN), as we show through simulated data. As such, we expect it to perform well in general on data and biometrics with variance akin to a AWGN channel.

Orientadores: Walter da Cunha Borelli, Emilia de Mendonça Rosa Marques
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Esta tese apresenta contribuições aos esquemas de modulação codificada para os códigos de treliça sobre partições de reticulados. Uma das principais contribuições é a construção dos códigos de treliça sobre novas partições de reticulados e também em cadeias de partições. Para otimizar a procura dos códigos de treliça ótimos, é construído um algoritmo de procura. É proposta uma classe de equivalência utilizada para excluir as matrizes geradoras de códigos equivalentes, sendo que esta classe de equivalência quando aplicada ao algoritmo de procura dos códigos de treliça ótimos diminui a quantidade de matrizes geradoras a ser investigada. Apresentam-se, vários exemplos de códigos de treliça sobre reticulados quociente nos espaços bi-dimensional, tridimensional e tetra-dimensional com satisfatórios ganhos de codificação e menor energia média das constelações de sinais.
Abstract: This thesis presents some contributions to the coded modulation schemes for the trellis codes based on lattices partitioning. One of the main contributions is the construction of the trellis codes based on novel lattices partitioning and also on chains partitioning. In order to optimize the search for the optimum trellis codes, a search algorithm was proposed. An equivalence class is proposed to exclude the generator matrix of equivalent codes. This equivalence class, when applied to the search algorithm for optimum trellis codes, reduces quite strongly the number of generator matrices to be investigated. Several examples of trellis codes on lattices quotient are shown in bi-dimensional, three-dimensional and tetra-dimensional spaces with satisfactory coding gain and lower average energy of the signal constellations.
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica

Channel coding has been largely used for the purpose of improving error performance on a communications system. Typical methods based on added redundancy allow for error detection and correction, this improvement however comes at a cost of bandwidth. This thesis focuses on channel coding for the bandwidth-limited channel where no bandwidth expansion is allowed. We first discuss the idea of coding for the bandwidth-limited channel as seen from the signal space point of view where the purpose of coding is to maximize the Euclidian distance between constellation points without increasing the total signal power and under the condition that no extra bits can be added. We then see the problem from another angle and identify the tradeoffs related to bandwidth and error performance. This thesis intends to find a simple way of achieving an improvement in error performance for the bandwidth-limited channel without the use of lattice codes or trellis-coded modulation. The proposed system is based on convolutional coding followed by multilevel transmission. It achieved a coding gain of 2 dB on Eb/No or equivalently, a coding gain of approximately 2.7 dB on SNRnorm without increase in bandwidth. This coding gain is better than that obtained by a more sophisticated lattice code Gosset E8 at the same error rate.

In this thesis, we investigate physical-layer network coding in an L × M × K relay network, where L source nodes want to transmit messages to K sink nodes via M relay nodes. We focus on the information processing at the relay nodes and the compute-and-forward framework. Nested lattice codes are used, which have the property that every linear combination of codewords is a valid codeword. This property is essential for physical-layer network coding. Because the actual network coding occurs on the physical layer, the network coding coefficients are determined by the channel realizations. Finding the optimal network coding coefficients for given channel realizations is a non-trivial optimization problem. In this thesis, we provide an algorithm to find network coding coefficients that result in the highest data rate at a chosen relay. The solution of this optimization problem is only locally optimal, i.e., it is optimal for a particular relay. If we consider a multi-hop network, each potential receiver must get enough linear independent combinations to be able to decode the individual messages. If this is not the case, outage occurs, which results in data loss. In this thesis, we propose a new strategy for choosing the network coding coefficients locally at the relays without solving the optimization problem globally. We thereby reduce the solution space for the relays such that linear independence between their decoded linear combinations is guaranteed. Further, we discuss the influence of spatial correlation on the optimization problem. Having solved the optimization problem, we combine physical-layer network coding with physical-layer secrecy. This allows us to propose a coding scheme to exploit untrusted relays in multi-user relay networks. We show that physical-layer network coding, especially compute-and-forward, is a key technology for simultaneous and secure communication of several users over an untrusted relay. First, we derive the achievable secrecy rate for the two-way relay channel. Then, we enhance this scenario to a multi-way relay channel with multiple antennas. We describe our implementation of the compute-and-forward framework with software-defined radio and demonstrate the practical feasibility. We show that it is possible to use the framework in real-life scenarios and demonstrate a transmission from two users to a relay. We gain valuable insights into a real transmission using the compute-and-forward framework. We discuss possible improvements of the current implementation and point out further work
In dieser Arbeit untersuchen wir Netzwerkcodierung auf der Übertragungsschicht in einem Relay-Netzwerk, in dem L Quellen-Knoten Nachrichten zu K Senken-Knoten über M Relay-Knoten senden wollen. Der Fokus dieser Arbeit liegt auf der Informationsverarbeitung an den Relay-Knoten und dem Compute-and-Forward Framework. Es werden Nested Lattice Codes eingesetzt, welche die Eigenschaft besitzen, dass jede Linearkombination zweier Codewörter wieder ein gültiges Codewort ergibt. Dies ist eine Eigenschaft, die für die Netzwerkcodierung von entscheidender Bedeutung ist. Da die eigentliche Netzwerkcodierung auf der Übertragungsschicht stattfindet, werden die Netzwerkcodierungskoeffizienten von den Kanalrealisierungen bestimmt. Das Finden der optimalen Koeffizienten für gegebene Kanalrealisierungen ist ein nicht-triviales Optimierungsproblem. Wir schlagen in dieser Arbeit einen Algorithmus vor, welcher Netzwerkcodierungskoeffizienten findet, die in der höchsten Übertragungsrate an einem gewählten Relay resultieren. Die Lösung dieses Optimierungsproblems ist zunächst nur lokal, d. h. für dieses Relay, optimal. An jedem potentiellen Empfänger müssen ausreichend unabhängige Linearkombinationen vorhanden sein, um die einzelnen Nachrichten decodieren zu können. Ist dies nicht der Fall, kommt es zu Datenverlusten. Um dieses Problem zu umgehen, ohne dabei das Optimierungsproblem global lösen zu müssen, schlagen wir eine neue Strategie vor, welche den Lösungsraum an einem Relay soweit einschränkt, dass lineare Unabhängigkeit zwischen den decodierten Linearkombinationen an den Relays garantiert ist. Außerdem diskutieren wir den Einfluss von räumlicher Korrelation auf das Optimierungsproblem. Wir kombinieren die Netzwerkcodierung mit dem Konzept von Sicherheit auf der Übertragungsschicht, um ein Übertragungsschema zu entwickeln, welches es ermöglicht, mit Hilfe nicht-vertrauenswürdiger Relays zu kommunizieren. Wir zeigen, dass Compute-and-Forward ein wesentlicher Baustein ist, um solch eine sichere und simultane Übertragung mehrerer Nutzer zu gewährleisten. Wir starten mit dem einfachen Fall eines Relay-Kanals mit zwei Nutzern und erweitern dieses Szenario auf einen Relay-Kanal mit mehreren Nutzern und mehreren Antennen. Die Arbeit wird abgerundet, indem wir eine Implementierung des Compute-and-Forward Frameworks mit Software-Defined Radio demonstrieren. Wir zeigen am Beispiel von zwei Nutzern und einem Relay, dass sich das Framework eignet, um in realen Szenarien eingesetzt zu werden. Wir diskutieren mögliche Verbesserungen und zeigen Richtungen für weitere Forschungsarbeit auf

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Dissertacao (Mestrado)
IPEN/D
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Il periodo di transizione (TP) delle vacche da latte è caratterizzata da disfunzione del sistema immunitario e dalla comparsa di fenomeni infiammatori. La tesi ha presentato una vasta revisione della letteratura seguita da 3 articoli sperimentali. Nel capitolo II sono stati investigati i cambiamenti delle citochine pro-infiammatorie (PIC) nel TP. I livelli di PIC hanno mostrato una elevata variabilità in tarda gravidanza, ma i livelli più alti hanno mostrato un’associazione con i problemi di salute e le prestazioni dopo il parto. Nel capitolo III, l'attività immunitaria di vacche in transizione è stata valutata utilizzando un test ex vivo di stimolazione del sangue con lipopolisaccaridi (WBA) e un test cutaneo alla carragenina. I risultati hanno rivelato che il sistema immunitario è molto sensibile in prossimità del parto. Entrambi i test descrivono i cambiamenti del sistema immunitario durante il TP. Nel capitolo IV, è stata valutata l’espressione genica dei leucociti durante il TP con la tecnica dell’ RNA-Seq. Confrontando i geni differenzialmente espressi con i risultati del capitolo II e III sono stati resi noti i cambiamenti funzionali dei leucociti. Complessivamente, queste ricerche contribuiscono a definire meglio la fisiologia della fase di transizione della vacche da latte.
The transition period of dairy cows is characterized by immune dysfunction and inflammatory like conditions. The thesis presented a wide review literature followed by 3 research papers. Chapter II investigated the pattern of changes of pro-inflammatory cytokines (PIC) around parturition and discovered an association with periparturient health status. PIC levels showed a high variability in late pregnancy but the highest levels demonstrated a good relationship with health troubles and performance after calving. In Chapter III, immune activity of transition cows were evaluated using: an ex vivo whole blood stimulation assay (WBA) with lipopolysaccharides and a carrageenan skin test. Results revealed that immune system is very sensitive around calving in respect to both tests, with a significant increase of pro-inflammatory cytokines and a reduction of the skin thickness after carrageenan challenge. Thus, both tests are able to describe the complex changes of the immune system combined to conventional metabolic and immune parameters. In Chapter IV, changes of leukocyte gene expression were evaluated from 20 days before to 7 days after calving using RNA-seq technique. Comparing the differentially expressed genes with the results of Chapter II and III were disclosed fundamental functional changes in leukocytes. Overall, these researches contribute to define better the physiology of the most vulnerable phase of dairy cows.

Utvecklingen av framtidens flerbostadshus ställer höga krav på en bjälklagslösnings tekniska egenskaper. Plattbärlagsbjälklaget som idag utgör det vanligaste förekommande bjälklagsvalet vid uppförandet av flerbostadshus kan ses som en lösning som kombinerar en god bärförmåga med stora möjligheter ur teknisk synpunkt. Målet med denna undersökning har varit att jämföra det traditionella plattbärlaget med en nyutvecklad bjälklagslösning baserad på produkten förspänt håldäcksbjälklag (HD/F). Jämförelsen har utgått från de aktuella kraven som enligt Boverkets byggregler (BBR) idag ställs på bjälklag och fokuserat på aspekter ur ljud, brand och fuktsynpunkt. Dessutom har jämförelsen beaktat de maximala spännvidder som respektive lösning kan dimensioneras för. Resultatet av de genomförda undersökningarna visade på att den nyutvecklade bjälklagslösningen är tillräckligt konkurrenskraftig för att i framtiden få ett större användande inom flerbostadshus. Medan plattbärlagets fördelar utmärker sig ur ljudsynpunkt möjliggör dock användandet av den nyutvecklade lösningen längre spännvidder och kortare torktider.
The development of apartment buildings puts high demands on the technical characteristics of floor systems. The lattice girder system which today represents the most commonly utilized floor system when building apartment buildings, is characterized by a good load-bearing ability along with great opportunities from a technical point of view. The aim of this analysis was to compare the traditional lattice girder system with a newly developed floor system based on hollow core slabs. The comparison is based on the current technical requirements set by Boverkets byggregler (BBR) and has its main focus on subjects related to sound, fire and moisture matters. The comparison has also accounted for the maximum spans which can be used for each solution respectively. The results of the investigation show that the newly developed floor system is competitive enough to be used in future apartment buildings. While the advantages of the lattice girder system are distinctive from a sound point of view, the utilization of the newly developed floor solution enables longer spans and shorter curing time.

Orientador: Sueli Irene Rodrigues Costa
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Essa dissertação possui como objetivo abordar as teorias de códigos e de reticulados e o uso recente destas na proposição de sistemas criptográficos que fazem o uso de chaves públicas dentro da chamada criptografia pós-quântica. No primeiro capítulo introduzimos a teoria dos códigos corretores de erros, incluindo definições e particularmente propriedades de códigos bastante utilizados como os de Hamming, códigos cíclicos, códigos BCH e códigos de Goppa. No segundo capítulo apresentamos a caracterização de dois problemas difíceis (NP-completos) baseados na estrutura de códigos que são o problema de decodificação geral (GDP) e o problema de decodificação por síndromes (SDP), os quais fundamentam algoritmos baseados na dificuldade de resolvê-los, como os criptossistemas de McEliece e Niederreiter. O Capítulo 3 é dedicado à teoria de reticulados, seus conceitos básicos e à caracterização dos problemas difíceis de se determinar nesta estrutura - o problema do vetor mais curto (SVP) e o problema do vetor mais próximo (CVP). Apresentamos também um modo de se obter reticulados a partir de códigos lineares, utilizando a chamada Construção A e ferramentas de geometria dos números para explicar métodos que avaliam a implementação da criptografia baseada em reticulados. No último capítulo descrevemos algoritmos desta subárea da criptografia , como os criptossistemas GGH e NTRU. Todos esses fundamentos embasam temas muito recentes de pesquisa em criptografia, que visam não somente a busca de sistemas que possivelmente resistirão à implementação de computadores quânticos mas que sejam mais eficientes na evolução prevista para computadores clássicos atuais
Abstract: This dissertation has the aim of approaching the theory of codes and lattices and their recent use to propose public key cryptosystems in the so called post-quantum cryptography. In the first chapter we introduce the theory of error correcting codes, including definitons and particularly properties of larged used codes such as Hamming codes, cyclic codes, BCH codes and Goppa codes. In the second chapter we present a characterization of two hard problems (NP-complete) based on the code structure which are the general decoding problem (GDP) and the syndrome decoding problem (SDP), which underlie algorithms based on the difficulty of solving them, as the McEliece and the Niederreiter cryptosystems. Chapter 3 is devoted to lattice theory, its basic concepts and the characterization of hard problems in this structure ¿ the shortest vector problem (SVP) and the closest vector problem (CVP). We also present a way to obtain lattices from linear codes using the so called Construction A and some tools of geometry of numbers to explain methods to evaluate the implementation of encryption schemes based on lattices. In the last chapter, we describe algorithms of this subarea of cryptography, such as GGH and NTRU. All these fundaments give support to recent research topics in cryptography, intended not only to search for secure systems that will probably resist to the introduction of quantum computers but also to be more efficient considering the the evolution of the classical computers
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada

This thesis presents the project for the optimization of the APOLLO3® neutronic calculation scheme applied to the 4th generation fast neutron reactor ASTRID. APOLLO3® is the new multipurpose neutronic platform developed by the CEA. It incorporates many of the previous generation codes used in the French reactor core design supply chain. Like all deterministic codes, APOLLO3® solves the neutron transport equation with a discretization of the variables of interest: multi-group method for the energy, discrete ordinates and spherical harmonics for the angular variable, collision probabilities and characteristics methods for the spatial variable. The resolution of the transport equation handles useful quantities such as the neutron flux and multiplication factor, fission rates and cross sections to understand the physical behaviour of the reactor core. Currently it is not possible to use deterministic codes to simulate an entire reactor with a heterogeneous 3D geometry and a fine energy description, so to simplify the study of complete neutron field at core level, the calculation scheme is divided into two phases: lattice and core calculation. The main purpose of this work is to find an optimal degree of approximations of the calculation scheme for the evaluation of a desired physical effect and of the user constraints. In order to reach this optimum, several studies have been carried out with different levels of approximations. The results have been benchmarked with the ones obtained using the stochastic code TRIPOLI4®, used as a reference and to ensure a good accuracy. Furthermore, several sensitivity studies have been carried out to understand how the different approximations affect the macroscopic cross sections evaluation, because these dependences are not yet fully understood.

Estruturas treliçadas de linhas de transmissão submetidas à ação do vento têm sido utilizadas de forma rotineira em aplicações da engenharia estrutural há mais de um século. Entretanto, o conhecimento dos efeitos do vento sobre este tipo de estrutura é, ainda hoje, imperfeito e as prescrições das normas a respeito destes efeitos são, em muitos casos, mutuamente inconsistentes e em desacordo com os dados experimentais. Partindo deste contexto, no caso particular de estruturas para linhas de transmissão, podemos acrescentar que as normas existentes não são, em princípio, aplicáveis à maior parte das geometrias utilizadas nos projetos das torres. Além disso, maiores níveis de segurança e confiabilidade são atingidos quando a consideração criteriosa dos efeitos do vento é feita a partir da etapa de concepção sendo, geralmente, este o processo de menor custo e de maior eficiência. Sabe-se também que o modelo físico adotado para consideração dos carregamentos difere do real, seja pela forma de atuação ou pela complexidade para estimativa da interação entre fluido-estrutura. Nesse sentido, através do presente trabalho procurou-se: desenvolver e aperfeiçoar instrumentos e técnicas de medição de coeficientes de arrasto; verificar a aplicabilidade dos critérios de estimativa do carregamento devido ao vento sobre trechos de estruturas treliçadas; propor coeficientes de arrasto compatíveis com geometrias tradicionalmente utilizadas em torres de linhas de transmissão determinados a partir da aplicação de dois critérios de área de referência, a saber, área calculada e área projetada; além de comparar os resultados experimentais com outras referências como normas técnicas de projeto. Este trabalho de pesquisa contempla o estudo de duas torres de suspensão autoportantes em túnel de vento. Para a realização dos ensaios, através de modelos reduzidos, cada torre foi dividida em módulos. Os módulos foram ensaiados para diferentes ângulos de incidência do vento e também para diferentes níveis de velocidade do vento. As forças de arrasto sobre os modelos foram determinadas através de uma balança de forças unidirecional instalada na base da câmara de ensaios.
Transmission lines lattice structures submitted to wind action have been widely used in structural engineering applications for more than a century. However, the knowledge of the wind effect on this type of structure is yet imperfect, being the codes recommendations, in several cases, inconsistent and in disagreement with the experimental data. From this point of view, in the particular case of transmission lines structures, we can add that the existing codes are not, in principle, applicable to a large amount of geometries used in the towers design. Furthermore, largest safety and reliability levels are reached when careful consideration of the wind effects is made from the conception stage, being this process, in general, the less costly and the most efficient. It is also known that the physical model adopted for the consideration of the loads differs from the real, either for the way in which the load is really applied or the complexity for an accurate estimate of the fluid-structure interaction. In this sense, the present work had the aim of: developing and improving instrumentation and measurement techniques for drag coefficients; verifying the applicability of the criteria for estimating wind loads on modules of lattice structures; proposing drag coefficients applicable to geometries traditionally adopted in transmission lines towers, obtained from the application of the two reference areas criteria, calculated area and projected area; as well as comparing experimental results with other references such as design codes. The research contemplates wind tunnel studies of two self-supported suspension towers. For the accomplishment of the tests, through scaled models, each tower was divided in modules. The modules had been tested for different angles of incidence of the wind and also for different wind speeds. The drag forces on the models were measured through a unidirectional force balance installed in the base of the models.

Orientador: Sueli Irene Rodrigues Costa
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Este trabalho está dividido em duas partes. A primeira e dedicada ao problema de encontrar o menor vetor não nulo de um reticulado. Este é um problema de alta complexidade computacional e que tem grande interesse tanto para a Teoria dos Códigos, como para diversas outras áreas. Esse mínimo está associado a performance do reticulado em termos da codificação: quanto maior for a razão entre este mínimo e o determinante do reticulado, melhor e a distribuição dos pontos no espaço (alta densidade de empacotamento). Nesta tese demos ênfase ao caso especial dos reticulados obtidos por uma projeção ortogonal do reticulado n-dimensional dos inteiros na direção de seus elementos. Tais reticulados estão associados ao problema de codificação contínua fonte/canal. Mostramos nos casos tri e quadridimensionais em que condições podemos garantir reticulados bons, ou seja, com alta densidade de empacotamento. Neste processo foram também construídos dois novos algoritmos, um para cálculo da base de Minkowski de um reticulado e outro específico para a busca da norma mínima do reticulado-projeção. Na segunda parte trabalhamos com grafos em toros planares que são quocientes de reticulados, os quais são isomorfos a grafos circulantes. Estabelecemos a conexão entre estes códigos esféricos rotulados por grupos cíclicos e códigos perfeitos na métrica de Lee. A partir de tal associação foram também obtidos resultados sobre o gênero 1 e a determinação do dos gênero de uma classe especial de grafos circulantes que tem número arbitrariamente grande de conexões (grau)
Abstract: The research developed here is related and inspired by problems in coding theory. It is presented in two parts. In the first we focus on the search for the minimum nonvanishing vector of a lattice, specially in the case of a projection of the ndimensional integer lattice in the direction of one of its vectors. This is a problem of high computational complexity which is related to the search for efficient joint sourcechannel continuous coding. In the second part we deal with flat torus graphs generated by a quotient of lattices and which are labeled by a a cyclic group of isometries. We show that any circulant graph is isomorphic to one of these graphs and hence associated to a spherical code. Through these isomorphism a complete classification of circulant graphs of genus one and the genus of an arbitrarily high order class of circulant graphs is obtained.
Doutorado
Geometria Topologia
Doutor em Matemática

Orientadores: Sueli Irene Rodrigues Costa, Simone Maria de Moraes
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho está dividido essencialmente em quatro tópicos. O primeiro capítulo é dedicado a uma introdução à teoria dos códigos corretores de erros com algumas propriedades e exemplos. No segundo capítulo abordamos reticulados e suas propriedades com foco na análise do quociente de reticulados gerando grafos em toros planares, grafos circulantes obtidos através de quociente de reticulados e ladrilhamentos associados. O terceiro capítulo é dedicado a códigos esféricos, com ênfase na obtenção de códigos ótimos. Foram introduzidos alguns limitantes importantes como o de Rankim, e a demonstração de que alguns códigos esféricos como o simplex e biortogonal são ótimos. No capítulo quatro apresentamos uma construção de reticulados através de códigos binários e também a construção de códigos esféricos a partir de reticulados que possuem sub-reticulados com base ortogonal. Analisamos o caso especial do reticulado BCC que é o de melhor densidade no espaço e pode ser gerado por código binário. Mostramos que o quociente deste por um sub reticulado especial produz o melhor código esférico associado ao grupo comutativo Z2 2 ×Z4 . Também identificamos o reticulado que é associado ao melhor código de grupo comutativo de 16 elementos em R6
Abstract: In this work it is presented through examples a connection between inary codes, lattices and spherical codes. A brief introduction to coding theory, properties and examples is included in the first chapter. In Chapter 2 lattices are approached with focus on the quotient of lattices, graphs on flat tori and connections with circulant graphs. An introduction to spherical codes and some of their bounds, as the Ranking bound, are described in Chapter 3. Finally in Chapter 4 the three topics above are connected. The construction of lattices from linear binary codes and the construction of spherical codes from the lattices which have orthogonal sub-lattices are presented. We analyze specifically the case of the three dimensional BCC lattice, which has the best packing density for this dimension, and show that a quotient of this lattice give rise to the best spherical code associate to the commutative group Z2 2 ×Z4. We also identify the lattice which is associate to the best commutative group code with 16 elements in em R6
Mestrado
Mestre em Matemática

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this dissertation, a way to build dense STBCs with full diversity of maximal order in central simple algebra will be presented. We constructed a retriculated ST code with a nonzero determinant for a quad antenna MISO transmission. Also, we will present a general algorithm to test the limit of a given order, since by the use of a maximum order instead of just the algebraic integer ring, we can increase the capacity of the code without a loss in the minimum determinant. Furthermore, by using the ideal of a maximum order we can further improve the code, as we increase the minimum determinant.
Nesta dissertação, será apresentada uma maneira para construir STBCs denso com diversidade completa, de ordem maximal em álgebras centrais simples. Construiremos um código reticulado ST com determinante não nulo para uma aplicação de quatro an- tenas de transmissão MISO. Apresentaremos também, um algoritmo geral para testar a maximalidade de uma ordem dada, uma vez que com o uso de uma ordem maximal em vez de apenas o anel dos inteiros algébricos, conseguimos um aumento na capacidade do código sem perda no determinante mínimo. Além disso, utilizando o ideal de uma ordem maximal melhoramos ainda mais o código, à medida que aumentamos o determinante mínimo.

Nelle applicazioni Lattice QCD l'operatore di Dirac rappresenta una delle principali operazioni, ottimizzarne l'efficienza si riflette in un incremento delle prestazioni globali dell'algoritmo. In tal senso i Tensor Core rappresentano una soluzione che incrementa le prestazioni del calcolo dell'operatore di Dirac ottimizzando in particolare la moltiplicazione tra matrici e vettori. Si è analizzata nel dettaglio l'architettura dei Tensor Core studiando il modello di esecuzione e il layout della memoria. Sono quindi state formulate e analizzate in dettaglio alcune soluzioni che sfruttano i Tensor Core per accelerare l'operatore di Dirac.

Les cœurs de réacteur à neutrons rapides refroidi au sodium (RNR-Na ) sont constitués d’assemblages combustibles disposés selon un réseau hexagonal régulier, compact en régime de fonctionnement nominal.Sous l’effet de l’irradiation et de la température, les assemblages sont amenés à se déformer axialement et radialement.Les objectifs de cette thèse sont la compréhension des phénomènes neutroniques intervenant lors d’une telle déformation du cœur, l’impact sur la conception ainsi que la mise au point de schémas de calcul neutroniques déterministes innovants aptes à en évaluer l’amplitude.La première partie de ces travaux est dédiée au développement d’une modélisation analytique des causes de variations de réactivité lors de la déformation du cœur. Cette analyse a permis d’identifier à la fois les causes de ces variations de réactivité et l’impact du déplacement des assemblages en fonction de leurs directions et de leurs positions dans le cœur.Un premier schéma neutronique basé sur la méthode de projection de maillage a été conçu et développé à l’aide des codes ERANOS (BISTRO, H3D et VARIANT) et du solveur SNATCH Le deuxième schéma conçu se base sur la transformation géométrique du maillage de calcul : le maillage est modifié en fonction du champ des déformations des assemblages. Cette fonctionnalité a été implémentée pour le solveur SNATCH, initialement prévu pour la résolution de l’équation de Boltzmann pour de mailles régulières.Enfin un modèle itératif basé sur la méthode de projection de maillage a été mis en place afin de déterminer les champs de déformations les plus réactifs en fonction de l’énergie mécanique fournie au cœur dans sa configuration nominale
The fuel assemblies of SFR cores (sodium fast reactors) are normally arranged in hexagonal regular lattices, whose compactness is ensured in nominal operating conditions by thermal expansion of assemblies pads disposed on the six assembly wrapper faces.During the reactor operations, thermal expansion phenomena and irradiation creep phenomena occur and they cause the fuel assemblies to bow and to deform both radially and axially.The main goal of this PhD is the understanding of the neutronic aspects and phenomena occurring in case of core and lattice deformations, as much as the design and implementation of deterministic neutronic calculation schemes and methods in order to evaluate the consequences for the core design activities and the safety analysis.The first part of this work is focused on the development of an analytical model with the purpose to identify the neutronic phenomena that are the main contributors to the reactivity changes induced by lattice and core deformations.A first scheme based on the spatial mesh projection method has been conceived and implemented for the ERANOS codes (BISTRO, H3D and VARIANT) and to the SNATCH solver.The second calculation scheme propose is based on mesh deformation: the computing mesh is deformed as a function of the assembly displacement field. This methodology has been implemented for the solver SNATCH, which normally allows the Boltzmann equation to be solved for a regular mesh. Finally, an iterative method has been developed in order to fulfill an a-priori estimation of the maximal reactivity insertion as a function of the postulated mechanical energy provided to the core, as much as the deformation causing it