Queue buildup is a problem that every fast food restaurant would like to reduce, as its effect on customer satisfaction and restaurant revenue is obviously negative. This thesis looks at how a dynamic menu management system would affect fast food restaurants, specifically how the promotion of fast products, in certain situations, would affect total revenue and queue lengths. A neural network was used to categorize products depending on their preparation time and to predict queue waiting times. A simulation approach was used to find out how the menu management system would affect the restaurant. The results are that in situations where long queues are formed, the promotion of fast products increases revenue by 7.8% and decreases queue lengths by 13.3%. In situations where little to no queues are formed, the same system still decreases queue lengths by 4.7%, but also decreases revenue by 0.2%

Les oxydes de métaux de transition sont largement utilisés en raison de leurs propriétés fondamentales intéressantes et de leurs applications importantes. En particulier, CuCrO2 est d’un intérêt particulier parce qu’il possède un état multiferroïque en absence de champ magnétique. Dans cette thèse, nous modélisons les propriétés magnéto-électriques de CuCrO2 par simulations Monte Carlo basées sur des paramètres magnétiques déterminés par calculs ab initio. Nous étudions également l’effet du dopage du Ga sur les propriétés magnéto-électriques du composé CuCr1-xGaxO2 (0 ≤ x ≤ 0:3). Nos résultats sontqualitativement en accord avec les observations expérimentales. / Transition metal oxides are widely used due to their interesting fundamental properties and important applications. In particular, CuCrO2 is of special interest because it enters the multiferroic state in zero magnetic fields. In this thesis we model the magnetoelectric properties of CuCrO2 using Monte Carlo simulations with the help of ab initio calculations.We also investigate the effect of Ga doping on the magnetoelectric properties of CuCr1-xGaxO2 (0 ≤ x ≤ 0:3). Our results are well comparable to the experimental observations.

The optimum ordering strategies for the coded V-BLAST system with capacity achieving temporal codes on each stream are studied in this thesis. Mathematical representations of the optimum detection ordering strategies for the coded V-BLAST under instantaneous rate allocation (IRA), uniform power/rate allocation (URA), instantaneous power allocation(IPA) and instantaneous power/rate allocation (IPRA) are derived. For two transmit antennas, it is shown that the optimum detection strategies are based on the per-stream before-processing channel gains. Based on approximations of the per-stream capacity equation, closed-form expressions of the optimal ordering strategy under the IRA at low and high signal to noise ratio (SNR) are derived. Necessary optimality conditions under the IRA are given. Thresholds for the low, intermediate and high SNR regimes in the 2-Tx-antenna system under the IPRA are determined, and the SNR gain of the ordering is studied for each regime. Performances of simple suboptimal ordering strategies are analysed, some of which perform very close to the optimum one.

Avec des motivations venant du domaine de la Vérification, nous définissons une notion de WQO effectifs pour lesquels il est possible de représenter les ensembles clos et de calculer les principales opérations ensemblistes sur ces représentations. Dans une première partie, nous montrons que de nombreuses constructions naturelles sur les WQO préservent notre notion d'effectivité, prouvant ainsi que la plupart des WQOs utilisés en pratique sont effectifs. Cette partie est basée sur un article non publié dont Jean Goubault-Larrecq, Narayan Kumar, Prateek Karandikar et Philippe Schnoebelen sont co-auteurs.Dans une seconde partie, nous étudions les conséquences qu'a notre notion sur la logique du première ordre interprété sur un WQO. Bien que le fragment existentiel positif soit décidable pour tous les WQOs effectif, les perspectives de généralisation sont limitées par le résultat suivant: le fragment existentiel de la logique du première ordre sur les mots finis, ordonnés par plongement, est déjà indécidable. Ce résultat a été publié à LICS 2017 avec Philippe Schnoebelen et Georg Zetzsche. / With motivations coming from Verification, we define a notionof effective WQO for which it is possible to represent closed subsetsand to compute basic set-operations on these representations. In a firstpart, we show that many of the natural constructions that preserve WQOsalso preserve our notion of effectiveness, proving that a large class ofcommonly used WQOs are effective. This part is based on an unpublishedarticle with Jean Goubault-Larrecq, Narayan Kumar, Prateek Karandikarand Philippe Schnoebelen.In a second part, we investigate the consequences of our notion onfirst-order logics over WQOs. Although the positive existential fragmentis decidable for any effective WQO, the perspective of extension tolarger fragments is hopeless since the existential fragment is alreadyundecidable for the first-order logic over words with the subwordordering. This last result has been published in LICS 2017 with PhilippeSchnoebelen and Georg Zetzsche.

This thesis presents a novel approach to reconstructing ancestral genomes of a number of descendant species related by a phylogeny. Traditional methods face challenges due to cycles of whole genome doubling followed by fractionation in plant lineages. In response, the thesis proposes a new approach that first accumulates a large number of candidate gene adjacencies specific to each ancestor in a phylogeny. A subset of these which to produces long ancestral contigs are chosen through maximum weight matching. The strategy results in more complete reconstructions than existing methods, and a number of quality measures are deployed to assess the results. The thesis also presents a new computational technique for estimating the ancestral monoploid number of chromosomes, involving a "g-mer" analysis to resolve a bias due to long contigs and gap statistics to estimate the number. The method is applied to a set of phylogenetically related descendant species, and the monoploid number is found to be 9 for all rosid and asterid orders. Additionally, the thesis demonstrates that this result is not an artifact of the method, by deriving a monoploid number of approximately 20 for the metazoan ancestor. The reconstructed ancestral genomes are functionally annotated and visualized through painting ancestral projections on descendant genomes and highlighting syntenic ancestor-descendant relationships. The proposed method is applied to genomes drawn from a broad range of plant orders. The Raccroche pipeline reconstructs ancestral gene orders and chromosomal contents of the ancestral genomes at all internal vertices of a phylogenetic tree, and constructs chromosomes by counting the frequencies of ancestral contig co-occurrence on the extant genomes, clustering these for each ancestor, and ordering them. Overall, this thesis presents a significant contribution to the field of ancestral genome reconstruction, offering a new approach that produces more complete reconstructions and provides valuable insights into the evolutionary process giving rise to the gene content and order of extant genomes.

The rise of cryptocurrencies has brought with it new math problems with new sets of constraints. The MEV problem entails solving for the ordering of pending trades that maximizes a block creator's profit. In decentralized finance, time is a big constraint, so an exhaustive search of all possible orderings is impossible. I propose a solution to the MEV problem that gives a near optimal result that can be solved in a reasonable amount of time. I layout the method and the formulas required for my solution. Additionally, I test my solution on synthesized data to show that it works as desired.

We study the unusual phases seen in charge transfer salts (CTS) at 1/2 and 1/4 filling. We use the Holstein-Hubbard model (HHM) and the Peierls extended Hubbard model (PEH) to study competing phases in CTS. In the 1/2illed HHM the Holstein coupling promotes a Peierls charge-density wave phase while the on-site Coulomb repulsion U gives rise to antiferromagnetic correlations and a Mott insulating state. Takada et al. have shown possibility of a third metallic phase between the Mott and the Peierls phase. We investigate the presence of an intermediate phase between the Mott and Peierls phase using Stochastic Series Expansion (SSE) method. We used charge and spin susceptibilities to determine the phase boundaries. As the coupling is increased a spin gap opens followed by the Peierls transition. The intermediate phase is metallic and has a spin gap but no charge gap. Transitions from the Mott to intermediate and intermediate to Peierls state are Kosterlitz-Thouless type (KT). As the coulomb repulsion is increaed beyond certain value the two KT transitions fuse to give a single first order transition. Similar behavior is seen at 1/4illed HHM. We also studied the temperature dependence of charge ordering (CO) in 1/4illed CTS. Most previous theoretical studies of the on CTS have concentrated on ground state or T=0 properties. Here we show the evolution of charge ordered (CO) state with temperature and directly related the experimental phase diagram with our theoretical results. Our calculations show that as temperature is lowered the Wigner crystal state gives way to spin-Peierls state with a different pattern of CO. Also we show that the critical value of nearest neighbor Coulomb repulsion is depends on the total spin and is different for different spin subspace.

No description available.

<p dir="ltr">A novel computational electromagnetic (CEM) solver using potential-based formulations and discrete exterior calculus (DEC) is proposed. The proposed solver consists of two parts: the DEC A-Phi solver and the DEC F-Psi solver. A and Phi are the magnetic vector potential and electric scalar potential of the electromagnetic (EM) field, respectively; F and Psi are the electric vector potential and magnetic scalar potential, respectively. The two solvers are dual to each other, and most research is carried out with respect to the DEC A-Phi solver.</p><p dir="ltr">Systematical approach for constructing the DEC A-Phi matrix equations is provided in this thesis, including the construction of incidence matrices, Hodge star operators and different boundary conditions. The DEC A-Phi solver is proved to be broadband stable from DC to optics, while classical CEM solvers suffer from stability issues at low frequencies (also known as the low-frequency breakdown). The proposed solver is ideal for broadband and multi-scale analysis, which is of great importance in modern industry.</p><p dir="ltr">To empower the proposed solver with the ability to solve industry problems with large number of unknowns, iterative solvers are preferred. The error-minimization mechanism buried in iterative solvers allows user to control the effect of numerical error accumulation to the solution vector. Proper preconditioners are almost always needed to accelerate the convergence of iterative solvers in large scale problems. In this thesis, preconditioning schemes for the proposed solver are studied.</p><p dir="ltr">In the DEC A-Phi solver, current sources can be applied easily, but it is difficult to implement voltage sources. To incorporate voltage sources in the potential-based solver, the DEC F-Psi solver is proposed. The DEC A-Phi and F-Psi solvers are dual formulations to each other, and the construction of the F-Psi solver can be generalized from the A-Phi solver straightforward.</p>

We present a methodology of an agile formal method named eXtreme Formal Modeling (XFM) recently developed by us, based on Extreme Programming concepts to construct abstract models from a natural language specification of a complex system. In particular, we focus on Prescriptive Formal Models (PFMs) that capture the specification of the system under design in a mathematically precise manner. Such models can be used as golden reference models for formal verification, test generation, etc. This methodology for incrementally building PFMs work by adding user stories (expressed as LTL formulae) gleaned from the natural language specifications, one by one, into the model. XFM builds the models, retaining correctness with respect to incrementally added properties by regressively model checking all the LTL properties captured theretofore in the model. We illustrate XFM with a graded set of examples including a traffic light controller, a DLX pipeline and a Smart Building control system. To make the regressive model checking steps feasible with current model checking tools, we need to keep the model size increments under control. We therefore analyze the effects of ordering LTL properties in XFM. We compare three different property-ordering methodologies: 'arbitrary ordering', 'property based ordering' and 'predicate based ordering'. We experiment on the models of the ISA bus monitor and the arbitration phase of the Pentium Pro bus. We experimentally show and mathematically reason that predicate based ordering is the best among these orderings. Finally, we present a GUI based toolbox for users to build PFMs using XFM. / Master of Science