Cette thèse s’inscrit dans le cadre de la conception, l’analyse et la mise en œuvre d’algorithmes efficaces et fiables pour la résolution de problèmes d’optimisation non linéaire avec contraintes. Nous présentons trois nouveaux algorithmes fortement primaux-duaux pour résoudre ces problèmes. La première caractéristique de ces algorithmes est que le contrôle des itérés s’effectue dans l’espace primal-dual tout au long du processus de la minimisation, d’où l’appellation “fortement primaux-duaux”. En particulier, la globalisation est effectuée par une méthode de recherche linéaire qui utilise une fonction de mérite primale-duale. La deuxième caractéristique est l’introduction d’une régularisation naturelle du système linéaire qui est résolu à chaque itération pour calculer une direction de descente. Ceci permet à nos algorithmes de bien se comporter pour résoudre les problèmes dégénérés pour lesquels la jacobienne des contraintes n’est pas de plein rang. La troisième caractéristique est que le paramètre de pénalisation est autorisé à augmenter au cours des itérations internes, alors qu’il est généralement maintenu constant. Cela permet de réduire le nombre d’itérations internes. Une étude théorique détaillée incluant l’analyse de convergence globale des itérations internes et externes, ainsi qu’une analyse asymptotique a été présentée pour chaque algorithme. En particulier, nous montrons qu’ils jouissent d’un taux de convergence rapide, superlinéaire ou quadratique. Ces algorithmes sont implémentés dans un nouveau solveur d’optimisation non linéaire qui est appelé SPDOPT. Les bonnes performances de ce solveur ont été montrées en effectuant des comparaisons avec les codes de références IPOPT, ALGENCAN et LANCELOT sur une large collection de problèmes. / This thesis focuses on the design, analysis, and implementation of efficient and reliable algorithms for solving nonlinearly constrained optimization problems. We present three new strongly primal-dual algorithms to solve such problems. The first feature of these algorithms is that the control of the iterates is done in both primal and dual spaces during the whole minimization process, hence the name “strongly primal-dual”. In particular, the globalization is performed by applying a backtracking line search algorithm based on a primal-dual merit function. The second feature is the introduction of a natural regularization of the linear system solved at each iteration to compute a descent direction. This allows our algorithms to perform well when solving degenerate problems for which the Jacobian of constraints is rank deficient. The third feature is that the penalty parameter is allowed to increase along the inner iterations, while it is usually kept constant. This allows to reduce the number of inner iterations. A detailed theoretical study including the global convergence analysis of both inner and outer iterations, as well as an asymptotic convergence analysis is presented for each algorithm. In particular, we prove that these methods have a high rate of convergence : superlinear or quadratic. These algorithms have been implemented in a new solver for nonlinear optimization which is called SPDOPT. The good practical performances of this solver have been demonstrated by comparing it to the reference codes IPOPT, ALGENCAN and LANCELOT on a large collection of test problems.

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There is an ever-increasing usage of mobile data with global traffic having reached 115 exabytes per month at the end of 2022 for mobile data traffic including fixed wireless access. This is projected to grow up to 453 exabytes at the end of 2028, according to Ericssons 2022 mobile data traffic outlook report. To meet the increasing demand radio access networks (RAN) used for mobile communication are continuously being improved with the current generation enabling larger virtualization of the network through the Cloud RAN (C-RAN) architecture. This facilitates the usage of commercial off-the-shelf servers (COTS) in the network replacing specialized hardware servers and making it easier to scale up or down the network capacity after traffic demand. This thesis looks at how we can efficiently identify servers needed to meet traffic demand in a network consisting of both COTS servers and specialized hardware servers while trying to reduce the energy consumption of the network. We model the problem as a network where the antennas and radio heads are connectedto the core network through a C-RAN and a specialized hardware layer. The network is then represented using a graph where the nodes represent servers in the network. Using this problem model as a base we then generate problem instances with varying topologies, server profiles, and traffic demands. To find out how the traffic should be passed through the network we test two different methods: A mixed integer linear programming (MILP) method focused on energy minimization and a graph attention network (GAT) predictor combined with the energy minimization MILP. To help evaluate the results we also create three other methods: a MILP model that tries to spread the traffic as evenly as possible, a random predictor combined with the energy minimization MILP and a greedy method. Our results show that the energy optimization MILP method can be used to create optimal solutions, but it suffer from a slow computation time compared to the other methods. The GAT model shows promising results in making predictions regarding what servers should be included in a network making it possible to reduce the problem size and solve it faster with MILP. The mean energy cost of the solutions created using the combined GAT/MILP method was 4% more than just using MILP but the time gain was substantial for problems of similar size as the GAT was trained on. With regards to computation time the combined GAT/MILP method used was 85% faster than using only MILP. For networks of almost double the size than the ones that the GAT model was trained on the solutions of the combined GAT and MILP methods had a mean energy cost increase of 7% while still showing a strong speedup, being 93% faster than when only using MILP.

Due to the high cost of manual content creation within the game development industry, methods for procedural generation of content such as game maps and levels have emerged. However, methods for generating game maps have remained relatively unexplored in competitive multiplayer contexts. Presumably, this is due to the opposing goals of generating game maps that are both interesting and fair. This study aims to explore the possibility of satisfying both these goals simultaneously by separating the generative phase from the phase that enforces fairness. In this endeavor, simple game maps for a generic multiplayer grand strategy game are generated using noise-based methods. The task of partitioning the game map fairly between the players is then modeled as a constrained categorical multiobjective minimization problem that is subsequently solved by two genetic algorithms, the reference-point-based algorithm NSGA-III and the decomposition-based algorithm MOEA/D-IEpsilon. In a primary study, the proposed partitioning method is evaluated based on the quality of the solutions produced, its scalability, and its ability to find symmetrical partitions of symmetrical game maps. The results show that the proposed method makes significant improvement from the initial guess but fails to produce completely fair partitions in general. Explanations and possible solutions to this are presented. The timing results indicate that the proposed method is not applicable in real-time contexts. However, the proposed method might still be applicable in online contexts if smaller game maps are considered and in offline contexts if larger game maps are considered. Finally, the partitioning results show that the proposed method successfully finds fair partitions of symmetrical game maps but fails to find the obvious symmetrical partitions. In a secondary study, the two genetic algorithms are compared to determine which algorithm produces dominating solutions and which algorithm produces most diverse solution. The results indicate that, for the partitioning problems considered in this study, the reference-point-based algorithm is both dominant and produces the most diverse solutions.

We discuss a full-waveform based material profile reconstruction in two-dimensional heterogeneous semi-infinite domains. In particular, we try to image the spatial variation of shear moduli/wave velocities, directly in the time-domain, from scant surficial measurements of the domain's response to prescribed dynamic excitation. In addition, in one-dimensional media, we try to image the spatial variability of elastic and attenuation properties simultaneously. To deal with the semi-infinite extent of the physical domains, we introduce truncation boundaries, and adopt perfectly-matched-layers (PMLs) as the boundary wave absorbers. Within this framework we develop a new mixed displacement-stress (or stress memory) finite element formulation based on unsplit-field PMLs for transient scalar wave simulations in heterogeneous semi-infinite domains. We use, as is typically done, complex-coordinate stretching transformations in the frequency-domain, and recover the governing PDEs in the time-domain through the inverse Fourier transform. Upon spatial discretization, the resulting equations lead to a mixed semi-discrete form, where both displacements and stresses (or stress histories/memories) are treated as independent unknowns. We propose approximant pairs, which numerically, are shown to be stable. The resulting mixed finite element scheme is relatively simple and straightforward to implement, when compared against split-field PML techniques. It also bypasses the need for complicated time integration schemes that arise when recent displacement-based formulations are used. We report numerical results for 1D and 2D scalar wave propagation in semi-infinite domains truncated by PMLs. We also conduct parametric studies and report on the effect the various PML parameter choices have on the simulation error. To tackle the inversion, we adopt a PDE-constrained optimization approach, that formally leads to a classic KKT (Karush-Kuhn-Tucker) system comprising an initial-value state, a final-value adjoint, and a time-invariant control problem. We iteratively update the velocity profile by solving the KKT system via a reduced space approach. To narrow the feasibility space and alleviate the inherent solution multiplicity of the inverse problem, Tikhonov and Total Variation (TV) regularization schemes are used, endowed with a regularization factor continuation algorithm. We use a source frequency continuation scheme to make successive iterates remain within the basin of attraction of the global minimum. We also limit the total observation time to optimally account for the domain's heterogeneity during inversion iterations. We report on both one- and two-dimensional examples, including the Marmousi benchmark problem, that lead efficiently to the reconstruction of heterogeneous profiles involving both horizontal and inclined layers, as well as of inclusions within layered systems. / text

Le développement simultané de terminaux mobiles multimédia (smartphones, tablettes) et de réseaux d’accès offrant des débits élevés conduit à une explosion du trafic liés aux contenus multimédia. Cette croissance nécessite un partage efficace des ressources radio entre fournisseurs de contenus (dans le cas de la diffusion) ou entre récepteurs (dans le cas de services de vidéo à la demande). Cette thèse propose des outils de partage équitable des ressources en termes de qualité des contenus multimédia reçu et de délai de transmission dans les deux contextes précédents. La variété des compromis débit-distorsion des contenus multimédia est exploitée à cet effet. Dans un premier temps, une solution centralisée de contrôle conjoint du débit de codage et de transmission de plusieurs programmes transmis sur un même canal est considérée. L’objectif est de fournir des flux de qualités similaires avec des variations limitées, tout en assurant des délais de transmission comparables. Ce problème est résolu en synthétisant une commande prédictive à l’aide d’outils d’optimisation sous contrainte. Dans un second temps, seule l’allocation de bande est centralisée, le contrôle des caractéristiques de compression de chaque flux est réalisé de manière distribuée. Le contrôleur centralisé ne renvoie que le niveau de remplissage des tampons associés à chaque flux aux fournisseurs de contenus distants. Une stratégie de régulation des débits de codage est alors mise en place par ces fournisseurs, de manière à réguler le niveau en bits ou en image des tampons. La stabilité de ce système de régulation couplé est étudiée en détails. Enfin, l’optimisation inter-couches d’une chaine de transmission de contenus multimédia scalable est considérée. Ce problème est formulé dans le contexte de la programmation dynamique. Lorsque des modèles de complexité raisonnable sont considérés et avec des caractéristiques du système bien connues, des solutions optimales peuvent être obtenues. Des techniques d’apprentissage sont mises en œuvre, lorsque le système n’est que partiellement connu, par exemple, lorsque l’état du canal de transmission parvient avec du retard à l’organe de commande. / Due to the emergence of new generation mobiles and media streaming services, data traffic on mobile networks is continuously exploding. Despite the emergence of standards such as LTE, resources still remain scarce and limited. Thus, efficiently sharing resources among broadcasters or between unicast receivers connected to the same base station is necessary. An efficient resources allocation, where a fair received video quality between users and an equal transmission delay are achieved, is targeted. To that end, the variety of the rate-distortion trade-off of multimedia content is exploited. First, a centralized joint encoding and transmission rate control of multiple programs sharing the same channel is considered. A satisfactory and a comparable video quality among the transmitted programs, with limited variations, as well as a comparable transmission delay are targeted. The problem is solved using constrained optimization tools. Second, only the bandwidth allocation control is centralized, the control of the encoding rate characteristics of each stream is carried in a distributed manner. By modeling the problem as a feedback control system, the centralized bandwidth allocation is required to feed back only the buffer level to its associated remote content provider. The equilibrium and stability issues are addressed for both bit and second buffer control. In the case of simple unicast connection, a cross-layer optimization of scalable video delivery over wireless channel is performed. The optimization problem is cast in the context of dynamic programming. When low complex model are considered and when the system characteristics are known, optimal solutions can be obtained. When the system is partially known, for example, when the state of the channel reaches the control process with delay, learning techniques are implemented.

La finesse de la résolution spectrale et spatiale des images hyperspectrales en font des données de très grande dimension. C'est également le cas d'autres types de données, où leur taille tend à augmenter pour de plus en plus d'applications. La complexité des données provenant de l'hétérogénéité spectrale et spatiale, de la non gaussianité du bruit et des processus physiques sous-jacents, renforcent la richesse des informations présentes sur une image hyperspectrale. Exploiter ces informations demande alors des outils statistiques adaptés aux grandes données mais aussi à leur nature non gaussienne. Des méthodes reposant sur la théorie des matrices aléatoires, théorie adaptée aux données de grande dimension, et reposant sur la robustesse, adaptée aux données non gaussiennes, sont ainsi proposées dans cette thèse, pour des applications à l'imagerie hyperspectrale. Cette thèse propose d'améliorer deux aspects du traitement des images hyperspectrales : l'estimation du nombre d'endmembers ou de l'ordre du modèle et le problème du démélange spectral. En ce qui concerne l'estimation du nombre d'endmembers, trois nouveaux algorithmes adaptés au modèle choisi sont proposés, le dernier présentant de meilleures performances que les deux autres, en raison de sa plus grande robustesse.Une application au domaine de la finance est également proposée. Pour le démélange spectral, trois méthodes sont proposées, qui tiennent comptent des diff érentes particularités possibles des images hyperspectrales. Cette thèse a permis de montrer que la théorie des matrices aléatoires présente un grand intérêt pour le traitement des images hyperspectrales. Les méthodes développées peuvent également s'appliquer à d'autres domaines nécessitant le traitement de données de grandes dimensions. / Hyperspectral imaging generates large data due to the spectral and spatial high resolution, as it is the case for more and more other kinds of applications. For hyperspectral imaging, the data complexity comes from the spectral and spatial heterogeneity, the non-gaussianity of the noise and other physical processes. Nevertheless, this complexity enhances the wealth of collected informations, that need to be processed with adapted methods. Random matrix theory and robust processes are here suggested for hyperspectral imaging application: the random matrix theory is adapted to large data and the robustness enables to better take into account the non-gaussianity of the data. This thesis aims to enhance the model order selection on a hyperspectral image and the unmixing problem. As the model order selection is concerned, three new algorithms are developped, and the last one, more robust, gives better performances. One financial application is also presented. As for the unmixing problem, three methods that take into account the peculierities of hyperspectral imaging are suggested. The random matrix theory is of great interest for hyperspectral image processing, as demonstrated in this thesis. Differents methods developped here can be applied to other field of signal processing requiring the processing of large data.

Cette thèse est consacrée à étudier les applications potentielles de véhicules autonomes et communications V2X pour construire les systèmes de transport intelligents. Premièrement, le comportement de caravane dans un environnement de véhicule connecté est étudié. Un algorithme de commande de caravane est conçu pour obtenir l'espacement sécuritaire ainsi que la conformité de la vitesse et de l'accélération. Deuxièmement, à plus grande échelle, les caravanes autour d'une intersection sont considérées. Le débit pendant une période de signal de trafic peut être amélioré en tirant profit de la capacité redondante de la route. Dans diverses contraintes, les véhicules peuvent choisir d'accélérer et rejoindre la caravane précédente ou à décélérer de déroger à l'actuel. Troisièmement, une intersection sans signalisation en VANET est considérée. Dans des conditions de faible trafic, les véhicules peuvent réguler leur vitesse avant d'arriver à l'intersection en fonction du temps d'occupation de la zone de conflit (TOZC) stocké au niveau du gestionnaire, afin qu'ils puissent traverser l'intersection sans collision ni arrêt. Le délai peut être réduit en conséquence. Enfin, un algorithme de gestion d'intersection autonome universelle, qui peut fonctionner même avec le trafic lourd, est développé. Le véhicule cherche à sécuriser les fenêtres entrant dans le TOZC. Ensuite, sur la base des fenêtres trouvées et le mouvement du véhicule qui précède, les trajectoires des véhicules peuvent être planifiées en utilisant une méthode de programmation dynamique segmentée. Tous les algorithmes conçus sont testés et vérifiés avec succès par des simulations dans scénarios différents / This thesis is devoted to study the potential applications of autonomous vehicles and V2X communications to construct the intelligent transportation systems. Firstly, the behavior of platoon in connected vehicle environment is studied. A platoon control algorithm is designed to obtain safe spacing as well as accordance of velocity and acceleration for vehicles in the same lane. Secondly, in larger scale, the platoons around an intersection are considered. The throughput in a traffic signal period can be improved by taking advantage of the redundant road capacity. Within diverse constraints, vehicles can choose to accelerate to join in the preceding platoon or to decelerate to depart from the current one. Thirdly, an unsignalized intersection in VANET is considered. In light traffic conditions, vehicles can regulate their velocities before arriving at the intersection according to the conflict zone occupancy time (CZOT) stored at the manager, so that they could get through the intersection without collision or stop. The delay can be reduced accordingly. Finally, an universal autonomous intersection management algorithm, which can work even with heavy traffic, is developed. The vehicle searches for safe entering windows in the CZOT. Then based on the found windows and the motion of preceding vehicle, the trajectories of vehicles can be planned using a segmented dynamic programming method. All the designed algorithms are successfully tested and verified by simulations in various scenarios

Environ trois quarts des ressources globales sont aujourd'hui consommés dans les aires urbaines. Le processus d'urbanisation induit des changements sévères du climat local, de la qualité environnementale des espaces, ainsi qu'une augmentation significative de la demande énergétique des bâtiments. Les projections statistiques sur la croissance de la population urbaine indiquent que cette situation tendra à s'aggraver dans les années à venir. Il devient donc impératif de chercher d'autres stratégies pour mieux adapter les environnements urbains aux nouvelles demandes énergétiques, afin de réduire l'empreinte environnementale des villes. Dans ce contexte, ce travail est une contribution à la recherche énergétique urbaine, plus particulièrement en ce qui concerne l'énergie consommée et potentiellement produite parles bâtiments à l'échelle urbaine locale. La morphologie urbaine est ici considérée comme un paramètre crucial dans le processus d'amélioration de l'efficacité énergétique du cadre bâti. Dans les zones de basses latitudes, sous climat tropical, l'énergie solaire incidente est extrêmement abondante. Toutefois, la bonne utilisation de cette ressource dans les bâtiments peut suggérer l'adoption de formes urbaines très peu denses et étales, en vue de réduire les obstructions produites par l'environnement proche. A rebours, ces formes urbaines très peu denses peuvent entrainer une augmentation des apports solaires sur les façades,élevant la demande énergétique. Le contrôle des gains solaires sur les façades pour la réduction de la demande énergétique peut ainsi représenter une perte potentielle en terme d'éclairement naturel des espaces, et une réduction du potentiel de production d'énergie solaire. Afin de quantifier le potentiel de ces stratégies conflictuelles, il devient indispensable de convoquer des modèles d'analyse pluridisciplinaires, permettant de mettre en oeuvre des approches multicritères dans le processus de conception de la forme urbaine. Cette thèse s'appuie sur une réflexion prospective sur les quartiers de la ville de Maceió, Alagoas, au Brésil. Dans un premier temps, un ensemble de paramètres morphologiques caractéristiques sont employés pour identifier et caractériser le potentiel solaire de typologies de référence de la ville. Ensuite, ces paramètres sont soumis à une analyse de sensibilité via un plan d'expérience. Les paramètres statistiquement significatifs sont alors intégrés à une méthode paramétrique d'optimisation dans laquelle l'algorithme génétique NSGA-II est couplé à un algorithme simplifiée de radiosité, visant à maximiser le potentiel de production d'énergie sur les toitures des bâtiments, tout en minimisant les apports solaires sur ses façades. Nous considérons des seuils d'éclairement naturel et intégrons des règles locales d'urbanisme comme contraintes aux projets. Cinq typologies représentatives du tissu urbain de Maceió ont ainsi été identifiées. L'ensemble des indicateurs les plus influents sur le potentiel solaire des formes urbaines a été hiérarchisé, en mettant l'accent notamment sur le rôle du prospect moyen ou de l'albédo des surfaces. La méthode d'optimisation a permis de tester plus de 80 000configurations d'ilots urbains et les résultats obtenus font apparaître une grande diversité de morphologies «optimum». Ces projets ont des performances solaires supérieures à celles des typologies existantes dans la ville. Cette intégration de stratégies énergétiques contradictoires montre qu'au-delà de l'intégration de contraintes variées et d'une meilleure adaptation à la complexité du processus de design urbain, l'approche utilisée ici apparaît très utile pour la recherche de solutions urbaines performantes à l'échelle des quartiers. Cette approche peut ainsi participer au renouvellement de l'Architecture de la Ville / At the beginning of 21th century, the world was faced with unprecedented environmental transformations. The urbanization process reached record levels and it keeps increasing, especiallyin developing countries. Around 3/4 of global resources are currently consumed in urban settlements, with corresponding adverse environmental consequences which leads to severe local climate changes, affecting environmental quality of spaces and leading to a significant increase of energy demand in buildings. A projection of the world urban population indicates that this situation will worsen in the coming years. It is therefore imperative that we understand how to design less resource intensive urban settlements. This research consists of a contribution to the energy debate in cities, focusing on the energy potentially consumed and produced by the built environment in the neighborhood scale. Urban morphology has been pointed out as a pivotal issue on shifting to climate adapted urban environments towards energy efficiency of buildings. In tropical climate regions, solar energy represents a high potential for renewable electric production in buildings, recording high levels of irradiation throughout the year. Though, engaging such a strategy may suggest applying sparsely low-density urban forms, aiming at reducing obstructions caused by the urban built surroundings. On one hand, scattered and less dense urban forms may result in significant increase of solar thermal load in buildings vertical facades, but on the other hand, the control of the solar heat gains in urban facades may represent significant losses on indoors daylight levels andalso reducing solar energy harness. Estimating the relative potential of these conflicting design strategies, taking into account the constrained parameters related to local building regulation, requires coupling multidisciplinary and multiobjective models of analysis in order to integrate multi-criteria approach in the urban design process. This thesis aims to contribute to a prospective energy debate toward sustainable urban districts for the city of Maceió in Brazil. Firstly, a set of energy-related morphological parameters are applied to identify, classify and characterize the solarpotential of local urban typologies. Then, these parameters are analyzed by means of a sensitivity analysis using a design of experiments reduced factorial method. The statistically most significant parameters are then submitted to a parametric design methodology via optimization, in which thenon-dominated sorting genetic algorithm (NSGA-II) is coupled with a simplified radiosity algorithm.The solar constraints are integrated as design criteria aiming at maximizing the solar energy potential on building roofs and minimizing solar gains on the their vertical facades. Daylight threshold levels as well as local building regulation parameters are taken into account as design constraints. Five representative types of urban fabric of Maceió were identified which allowed examining and adapting them from the use of energy-related indicators of the urban form. A set of most influential indicators of solar potential of urban forms was hierarchized, highlighting the role of the aspect ratio and albedo of urban surfaces. The application of optimization algorithm allowed testing more than 80,000 urban settings, pointing out a great diversity of "optimum" morphologies of urban blocks. The urban block designs obtained behaved better compared to the existing local typologies. Dealing with conflicting energy strategies by means of a constrained evolutionary optimization design process offered a great opportunity in searching for new solutions to the urban design in the neighborhood scale, helping to guide urban designers' decisions and allowing arenewal of the Architecture of the city

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work some classical methods for constrained nonlinear optimization are studied. The mathematical formulations for the optimization problem with equality and inequality constrained, convergence properties and algorithms are presented. Furthermore, optimality conditions of rst order (Karush-Kuhn-Tucker conditions) and of second order. These conditions are essential for the demonstration of many results. Among the methods studied, some techniques transform the original problem into an unconstrained problem (Penalty Methods, Augmented Lagrange Multipliers Method). In others methods, the original problem is modeled as one or as a sequence of quadratic subproblems subject to linear constraints (Quadratic Programming Method, Sequential Quadratic Programming Method). In order to illustrate and compare the performance of the methods studied, two nonlinear optimization problems are considered: a bi-dimensional problem and a problem of mass minimization of a coil spring. The obtained results are analyzed and confronted with each other. / Neste trabalho são estudados alguns métodos clássicos de otimização restrita não linear. São abordadas a formulação matemática para o problema de otimização com restrições de igualdade e desigualdade, propriedades de convergência e algoritmos. Além disso, são relatadas as condições de otimalidade de primeira ordem (condições de Karush-Kuhn-Tucker) e de segunda ordem. Estas condições são essenciais para a demonstração de muitos resultados. Dentre os métodos estudados, algumas técnicas transformam o problema original em um problema irrestrito (Métodos de Penalidade, Método dos Multiplicadores de Lagrange Aumentado). Em outros métodos, o problema original é modelado como um ou uma seqüência de subproblemas quadráticos sujeito _a restrições lineares (Método de Programação Quadrática, Método de Programação Quadrática Seqüencial). A fim de ilustrar e comparar o desempenho dos métodos estudados são considerados dois problemas de otimização não linear: um problema bidimensional e o problema de minimização da massa de uma mola helicoidal. Os resultados obtidos são examinados e confrontados entre si. / Mestre em Matemática