Dissertations / Theses: 'Embedding space'

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Zhang, Xinhua, and xinhua zhang cs@gmail com. "Graphical Models: Modeling, Optimization, and Hilbert Space Embedding." The Australian National University. ANU College of Engineering and Computer Sciences, 2010. http://thesis.anu.edu.au./public/adt-ANU20100729.072500.

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Over the past two decades graphical models have been widely used as powerful tools for compactly representing distributions. On the other hand, kernel methods have been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. Graphical models are a powerful underlying formalism in machine learning. Their graph theoretic properties provide both an intuitive modular interface to model the interacting factors, and a data structure facilitating efficient learning and inference. The probabilistic nature ensures the global consistency of the whole framework, and allows convenient interface of models to data. Kernel methods, on the other hand, provide an effective means of representing rich classes of features for general objects, and at the same time allow efficient search for the optimal model. Recently, kernels have been used to characterize distributions by embedding them into high dimensional feature space. Interestingly, graphical models again decompose this characterization and lead to novel and direct ways of comparing distributions based on samples. Among the many uses of graphical models and kernels, this thesis is devoted to the following four areas: Conditional random fields for multi-agent reinforcement learning Conditional random fields (CRFs) are graphical models for modelling the probability of labels given the observations. They have traditionally been trained with using a set of observation and label pairs. Underlying all CRFs is the assumption that, conditioned on the training data, the label sequences of different training examples are independent and identically distributed (iid ). We extended the use of CRFs to a class of temporal learning algorithms, namely policy gradient reinforcement learning (RL). Now the labels are no longer iid. They are actions that update the environment and affect the next observation. From an RL point of view, CRFs provide a natural way to model joint actions in a decentralized Markov decision process. They define how agents can communicate with each other to choose the optimal joint action. We tested our framework on a synthetic network alignment problem, a distributed sensor network, and a road traffic control system. Using tree sampling by Hamze & de Freitas (2004) for inference, the RL methods employing CRFs clearly outperform those which do not model the proper joint policy. Bayesian online multi-label classification Gaussian density filtering (GDF) provides fast and effective inference for graphical models (Maybeck, 1982). Based on this natural online learner, we propose a Bayesian online multi-label classification (BOMC) framework which learns a probabilistic model of the linear classifier. The training labels are incorporated to update the posterior of the classifiers via a graphical model similar to TrueSkill (Herbrich et al., 2007), and inference is based on GDF with expectation propagation. Using samples from the posterior, we label the test data by maximizing the expected F-score. Our experiments on Reuters1-v2 dataset show that BOMC delivers significantly higher macro-averaged F-score than the state-of-the-art online maximum margin learners such as LaSVM (Bordes et al., 2005) and passive aggressive online learning (Crammer et al., 2006). The online nature of BOMC also allows us to effciently use a large amount of training data. Hilbert space embedment of distributions Graphical models are also an essential tool in kernel measures of independence for non-iid data. Traditional information theory often requires density estimation, which makes it unideal for statistical estimation. Motivated by the fact that distributions often appear in machine learning via expectations, we can characterize the distance between distributions in terms of distances between means, especially means in reproducing kernel Hilbert spaces which are called kernel embedment. Under this framework, the undirected graphical models further allow us to factorize the kernel embedment onto cliques, which yields efficient measures of independence for non-iid data (Zhang et al., 2009). We show the effectiveness of this framework for ICA and sequence segmentation, and a number of further applications and research questions are identified. Optimization in maximum margin models for structured data Maximum margin estimation for structured data, e.g. (Taskar et al., 2004), is an important task in machine learning where graphical models also play a key role. They are special cases of regularized risk minimization, for which bundle methods (BMRM, Teo et al., 2007) and the closely related SVMStruct (Tsochantaridis et al., 2005) are state-of-the-art general purpose solvers. Smola et al. (2007b) proved that BMRM requires O(1/έ) iterations to converge to an έ accurate solution, and we further show that this rate hits the lower bound. By utilizing the structure of the objective function, we devised an algorithm for the structured loss which converges to an έ accurate solution in O(1/√έ) iterations. This algorithm originates from Nesterov's optimal first order methods (Nesterov, 2003, 2005b).

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Gibert, Domingo Jaume. "Vector Space Embedding of Graphs via Statistics of Labelling Information." Doctoral thesis, Universitat Autònoma de Barcelona, 2012. http://hdl.handle.net/10803/96240.

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El reconeixement de patrons és la tasca que pretén distingir objectes entre diferents classes. Quan aquesta tasca es vol solucionar de forma automàtica un pas crucial és el com representar formalment els patrons a l'ordinador. En funció d'aquests formalismes, podem distingir entre el reconeixement estadístic i l'estructural. El primer descriu objectes com un conjunt de mesures col·locats en forma del que s'anomena un vector de característiques. El segon assumeix que hi ha relacions entre parts dels objectes que han de quedar explícitament representades i per tant fa servir estructures relacionals com els grafs per codificar la seva informació inherent. Els espais vectorials són una estructura matemàtica molt flexible que ha permès definir diverses maneres eficients d'analitzar patrons sota la forma de vectors de característiques. De totes maneres, la representació vectorial no és capaç d'expressar explícitament relacions binàries entre parts dels objectes i està restrigida a mesurar sempre, independentment de la complexitat dels patrons, el mateix nombre de característiques per cadascun d'ells. Les representacions en forma de graf presenten la situació contrària. Poden adaptar-se fàcilment a la complexitat inherent dels patrons però introdueixen un problema d'alta complexitat computational, dificultant el disseny d'eines eficients per al procés i l'anàlisis de patrons. Resoldre aquesta paradoxa és el principal objectiu d'aquesta tesi. La situació ideal per resoldre problemes de reconeixement de patrons seria el representar-los fent servir estructures relacionals com els grafs, i a l'hora, poder fer ús del ric repositori d'eines pel processament de dades del reconeixement estadístic. Una solució elegant a aquest problema és la de transformar el domini dels grafs en el domini dels vectors, on podem aplicar qualsevol algorisme de processament de dades. En altres paraules, assignant a cada graf un punt en un espai vectorial, automàticament tenim accés al conjunt d'algorismes del món estadístic per aplicar-los al domini dels grafs. Aquesta metodologia s'anomena graph embedding. En aquesta tesi proposem de fer una associació de grafs a vectors de característiques de forma simple i eficient fixant l'atenció en la informació d'etiquetatge dels grafs. En particular, comptem les freqüències de les etiquetes dels nodes així com de les aretes entre etiquetes determinades. Tot i la seva localitat, aquestes característiques donen una representació prou robusta de les propietats globals dels grafs. Primer tractem el cas de grafs amb etiquetes discretes, on les característiques són sencilles de calcular. El cas continu és abordat com una generalització del cas discret, on enlloc de comptar freqüències d'etiquetes, ho fem de representants d'aquestes. Ens trobem que les representacions vectorials que proposem pateixen d'alta dimensionalitat i correlació entre components, i tractem aquests problems mitjançant algorismes de selecció de característiques. També estudiem com la diversitat de diferents representacions pot ser explotada per tal de millorar el rendiment de classificadors base en el marc d'un sistema de múltiples classificadors. Finalment, amb una extensa evaluació experimental mostrem com la metodologia proposada pot ser calculada de forma eficient i com aquesta pot competir amb altres metodologies per a la comparació de grafs.
Pattern recognition is the task that aims at distinguishing objects among different classes. When such a task wants to be solved in an automatic way a crucial step is how to formally represent such patterns to the computer. Based on the different representational formalisms, we may distinguish between statistical and structural pattern recognition. The former describes objects as a set of measurements arranged in the form of what is called a feature vector. The latter assumes that relations between parts of the underlying objects need to be explicitly represented and thus it uses relational structures such as graphs for encoding their inherent information. Vector spaces are a very flexible mathematical structure that has allowed to come up with several efficient ways for the analysis of patterns under the form of feature vectors. Nevertheless, such a representation cannot explicitly cope with binary relations between parts of the objects and it is restricted to measure the exact same number of features for each pattern under study regardless of their complexity. Graph-based representations present the contrary situation. They can easily adapt to the inherent complexity of the patterns but introduce a problem of high computational complexity, hindering the design of efficient tools to process and analyze patterns. Solving this paradox is the main goal of this thesis. The ideal situation for solving pattern recognition problems would be to represent the patterns using relational structures such as graphs, and to be able to use the wealthy repository of data processing tools from the statistical pattern recognition domain. An elegant solution to this problem is to transform the graph domain into a vector domain where any processing algorithm can be applied. In other words, by mapping each graph to a point in a vector space we automatically get access to the rich set of algorithms from the statistical domain to be applied in the graph domain. Such methodology is called graph embedding. In this thesis we propose to associate feature vectors to graphs in a simple and very efficient way by just putting attention on the labelling information that graphs store. In particular, we count frequencies of node labels and of edges between labels. Although their locality, these features are able to robustly represent structurally global properties of graphs, when considered together in the form of a vector. We initially deal with the case of discrete attributed graphs, where features are easy to compute. The continuous case is tackled as a natural generalization of the discrete one, where rather than counting node and edge labelling instances, we count statistics of some representatives of them. We encounter how the proposed vectorial representations of graphs suffer from high dimensionality and correlation among components and we face these problems by feature selection algorithms. We also explore how the diversity of different embedding representations can be exploited in order to boost the performance of base classifiers in a multiple classifier systems framework. An extensive experimental evaluation finally shows how the methodology we propose can be efficiently computed and compete with other graph matching and embedding methodologies.

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Sandvick, Joshua Sandvick. "Machine Translation Through the Creation of a Common Embedding Space." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531420294211248.

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Bishop, Jonathan R. B. "Embedding population dynamics in mark-recapture models." Thesis, St Andrews, 2009. http://hdl.handle.net/10023/718.

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Dube, Matthew P. "An Embedding Graph for 9-Intersection Topological Spatial Relations." Fogler Library, University of Maine, 2009. http://www.library.umaine.edu/theses/pdf/DubeMP2009.pdf.

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Donald, Andrew. "Embedding 3-manifolds in 4-space and link concordance via double branched covers." Thesis, University of Glasgow, 2013. http://theses.gla.ac.uk/4425/.

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The double branched cover is a construction which provides a link between problems in knot theory and other questions in low-dimensional topology. Given a knot in a 3-manifold, the double branched cover gives a natural way of associating a 3-manifold to the knot. Similarly, the double branched cover of a properly embedded surface in a 4-manifold is a 4-manifold whose boundary is the double branched cover of the boundary link of the surface. Consequently, whenever a link in S^3 bounds certain types of surfaces, its double branched cover will bound a 4-manifold of an appropriate type. The most familiar situation in which this connection is used is the application to slice knots as the double branched cover of a smoothly slice knot is the boundary of a smooth rational ball. Examples of 3-manifolds which bound rational balls can therefore easily be constructed by taking the double branched covers of slice knots while obstructions to a 3-manifold bounding a rational ball can be interpreted as slicing obstructions. This thesis is primarily concerned with two different extensions of this idea. Given a closed, orientable 3-manifold, it is natural to ask whether it admits a smooth embedding in the four-sphere $S^4$. Examples can be obtained by taking the double branched covers of doubly slice links. These are links which are cross-sections of an unknotted embedding of a two-sphere in S^4. Certain links can be shown to be doubly slice via ribbon diagrams with appropriate properties. Other embeddings can be obtained via Kirby calculus. On the other hand, many obstructions to a 3-manifold bounding a rational ball can be adapted to give stronger obstructions to embedding smoothly in S^4. Using an obstruction based on Donaldson's theorem on the intersection forms of definite 4-manifolds, we determine precisely which connected sums of lens spaces smoothly embed. This method also gives strong constraints on the Seifert invariants of Seifert manifolds which embed when either the base orbifold is non-orientable or the first Betti number is odd. Other applicable methods, also based on obstructions to bounding a rational ball, include the d invariant from Ozsvath and Szabo's Heegaard-Floer homology and the Neumann-Siebenmann mu-bar invariant. These are used, in conjunction with some embedding results derived from doubly slice links, to examine the question of when the double branched cover of a 3 or 4 strand pretzel link embeds. The fact that the double branched cover of a slice knot bounds a rational ball has a second interpretation in terms of knot concordance. In this viewpoint, the double branched cover gives a homomorphism from the concordance group of knots to the rational cobordism group of rational homology 3-spheres. This can be extended to a concordance group of links using a notion of concordance based on Euler characteristic. This yields link concordance groups which contain the knot concordance group as a direct summand with an infinitely generated complement. The double branched cover homomorphism extends to large subgroups containing the knot concordance group.

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Strickrodt, Marianne [Verfasser], and Tobias [Akademischer Betreuer] Meilinger. "The impossible puzzle : No global embedding in environmental space memory / Marianne Strickrodt ; Betreuer: Tobias Meilinger." Tübingen : Universitätsbibliothek Tübingen, 2019. http://d-nb.info/1190639653/34.

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Stewart, Nigel Timothy, and nigels@nigels com. "An Image-Space Algorithm for Hardware-Based Rendering of Constructive Solid Geometry." RMIT University. Aerospace, Mechanical and Manufacturing Engineering, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080721.144757.

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A new approach to image-space hardware-based rendering of Constructive Solid Geometry (CSG) models is presented. The work is motivated by the evolving functionality and performance of computer graphics hardware. This work is also motivated by a specific industrial application --- interactive verification of five axis grinding machine tool programs. The goal is to minimise the amount of time required to render each frame in an animation or interactive application involving boolean combinations of three dimensional shapes. The Sequenced Convex Subtraction (SCS) algorithm utilises sequenced subtraction of convex objects for the purpose of interactive CSG rendering. Concave shapes must be decomposed into convex shapes for the purpose of rendering. The length of Permutation Embedding Sequences (PESs) used as subtraction sequences are shown to have a quadratic lower bound. In many situations shorter sequences can be used, in the best case linear. Approaches to s ubtraction sequence encoding are presented including the use of object-space overlap information. The implementation of the algorithm is experimentally shown to perform better on modern commodity graphics hardware than previously reported methods. This work also examines performance aspects of the SCS algorithm itself. Overall performance depends on hardware characteristics, the number and spatial arrangement of primitives, and the structure and boolean operators of the CSG tree.

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BELLAVITA, CARLO. "FUNCTIONAL PROPERTIES OF P-DE BRANGES SPACES." Doctoral thesis, Università degli Studi di Milano, 2022. http://hdl.handle.net/2434/924712.

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This Ph.D. final dissertation studies some analytical properties of the p-de Branges spaces, Hp(E), made up of entire functions and extensively studied in the last thirty years. Besides the first two chapters, where I recall the main properties of the p-de Branges spaces, the rest of the thesis gathers my research work: in the second part, Boundedness of operators, I look for some necessary and sufficient conditions for the boundedness of the translation operators in H2(E) and subsequently for the continuity of the embedding operator ιp,q from Hp(E) into Hq(E). In the third part, Duality results, I characterize the dual of some 1-de Branges spaces. Firstly, I describe the dual of the 1-Bernstein spaces and then I extend the reasonings to some others 1-de Branges spaces.

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Sinnokrot, Mohanned Omar. "Space-time block codes with low maximum-likelihood decoding complexity." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31752.

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Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Barry, John; Committee Co-Chair: Madisetti, Vijay; Committee Member: Andrew, Alfred; Committee Member: Li, Ye; Committee Member: Ma, Xiaoli; Committee Member: Stuber, Gordon. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Quintanar, Cortes Patricia Tanessi. "Plongements polyédriques du tore carré plat." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1354.

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En 1996, Burago et Zalgaller ont montré le théorème suivant : Théorème (Burago et Zalgaller) : Soit S une surface polyédrique, alors S admet un plongement isométrique PL dans E3 . Ce théorème nous montre en particulier que le tore plat carré admet un plongement isométrique PL dans E3. En 1997, Zalgaller construit un tel plongement de tore rectangulaires plats longs. Dans la première partie de cette thèse, on fait un plongement isométrique du tore carré plat T2 dans E3. Ce premier résultat est énoncé dans le théorème suivant : Théorème : Il y a un plongement isométrique PL du tore carré plat T2 avec au plus 48 points. On sait que la triangulation minimale du tore plat est le tore de Moebius M. Le 1-squelette du tore de Moebius est le graphe K7. On considère l’ensemble GE(M, T2) de toutes les triangulations géodésiques de T2 isomorphes à M, modulo translations. Dans la deuxième partie de la thèse, on donne une description complète de cet ensemble : - L’espace de configurations GE(M, T2) est l’union disjointe de 12 produits de 6-simplexes. On dénote par LT(E3) l’ensemble de plongements linéaires isométriques d’une triangulation T de T2 dans E3, on a dans la troisième partie de la thèse le résultat suivant : -Il existe un voisinage N(S) de dimension 12 d’un certain ensemble S tel que pour chaque T in N(S), on a LT(E3)=Ø
In 1996 Burago and Zalgaller showed the following theorem: Theorem (Burago and Zalgaller): Let S be a polyhedral surface, then S admits an isometric PL embedding in E3. This theorem shows in particular that the Flat Square Torus admits an isometric PL embedding in E3. In 1997 Zalgaller constructs such an embedding of Flat Rectangular Torii into E3. In the first part of this work, we do show an isometric embedding du Flat Square Torus in E3. This first result is stated as follows: Theorem: There is an isometric PL embedding of the flat Square Torus with at most 48 points. We know that the minimal triangulation of the flat torus is the Moebius Torus M. The 1-skeleton of the Moebius Torus is the graph K7. We consider GE(M, T2) the set of all geodesic triangulations of T2 isomorphic to M modulo translations. In the second part of this work, we give a complete description of this set : - The configuration space GE(M, T2) is the disjoint union of 12 products of 6-simplex. We writte LT(E3) the set of lineal isometric embeddings of a triangulation T of T2 in E3, in the third part of this worg, we have the following result : - There is a 12-dimensional neighborhood N(S) of a 6-diensional set S such that for every T in E3, we have LT(E3)= Ø

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Muller, Carole. "Minor-closed classes of graphs: Isometric embeddings, cut dominants and ball packings." Doctoral thesis, Universite Libre de Bruxelles, 2021. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/331629.

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Une classe de graphes est close par mineurs si, pour tout graphe dans la classe et tout mineur de ce graphe, le mineur est ́egalement dans la classe. Par un fameux th ́eor`eme de Robertson et Seymour, nous savons que car- act ́eriser une telle classe peut ˆetre fait `a l’aide d’un nombre fini de mineurs exclus minimaux. Ceux-ci sont des graphes qui n’appartiennent pas `a la classe et qui sont minimaux dans le sens des mineurs pour cette propri ́et ́e.Dans cette thèse, nous étudions trois problèmes à propos de classes de graphes closes par mineurs. Les deux premiers sont reliés à la caractérisation de certaines classes de graphes, alors que le troisième étudie une relation de “packing-covering” dans des graphes excluant un mineur.Pour le premier problème, nous étudions des plongements isométriques de graphes dont les arêtes sont pondérées dans des espaces métriques. Principalement, nous nous intêressons aux espaces ell_2 et ell_∞. E ́tant donné un graphe pondéré, un plongement isométrique associe à chaque sommet du graphe un vecteur dans l’autre espace de sorte que pour chaque arête du graphe le poids de celle-ci est égal à la distance entre les vecteurs correspondant à ses sommets. Nous disons qu’une fonction de poids sur les arêtes est une fonction de distances réalisable s’il existe un tel plongement. Le paramètre f_p(G) détermine la dimension k minimale d’un espace ell_p telle que toute fonction de distances réalisable de G peut être plongée dans ell_p^k. Ce paramètre est monotone dans le sens des mineurs. Nous caractérisons les graphes tels que f_p(G) a une grande valeur en termes de mineurs inévitables pour p = 2 et p = ∞. Une famille de graphes donne des mineurs inévitables pour un invariant monotone pour les mineurs, si ces graphes “expliquent” pourquoi l’invariant est grand.Le deuxième problème étudie les mineurs exclus minimaux pour la classe de graphes avec φ(G) borné par une constante k, où φ(G) est un paramètre lié au dominant des coupes d’un graphe G. Ce polyèdre contient tous les points qui, composante par composante, sont plus grands ou égaux à une combination convexe des vecteurs d’incidence de coupes dans G. Le paramètre φ(G) est égal au membre de droite maximum d’une description linéaire du dominant des coupes de G en forme entière minimale. Nous étudions les mineurs exclus minimaux pour la propriété φ(G) <= 4 et montrons une nouvelle borne sur φ(G) en termes du “vertex cover number”.Le dernier problème est d’un autre type. Nous étudions une relation de “packing-covering” dans les classes de graphes excluant un mineur. Étant donné un graphe G, une boule de centre v et de rayon r est l’ensemble de tous les sommets de G qui sont à distance au plus r de v. Pour un graphe G et une collection de boules donnés nous pouvons définir un hypergraphe H dont les sommets sont ceux de G et les arêtes correspondent aux boules de la collection. Il est bien connu que dans l’hypergraphe H, le “transversal number” τ(H) vaut au moins le “packing number” ν(H). Nous montrons une borne supérieure sur ν(H) qui est linéaire en τ(H), résolvant ainsi un problème ouvert de Chepoi, Estellon et Vaxès.
A class of graphs is closed under taking minors if for each graph in the class and each minor of this graph, the minor is also in the class. By a famous result of Robertson and Seymour, we know that characterizing such a class can be done by identifying a finite set of minimal excluded minors, that is, graphs which do not belong to the class and are minor-minimal for this property.In this thesis, we study three problems in minor-closed classes of graphs. The first two are related to the characterization of some graph classes, while the third one studies a packing-covering relation for graphs excluding a minor.In the first problem, we study isometric embeddings of edge-weighted graphs into metric spaces. In particular, we consider ell_2- and ell_∞-spaces. Given a weighted graph, an isometric embedding maps the vertices of this graph to vectors such that for each edge of the graph the weight of the edge equals the distance between the vectors representing its ends. We say that a weight function on the edges of the graph is a realizable distance function if such an embedding exists. The minor-monotone parameter f_p(G) determines the minimum dimension k of an ell_p-space such that any realizable distance function of G is realizable in ell_p^k. We characterize graphs with large f_p(G) value in terms of unavoidable minors for p = 2 and p = ∞. Roughly speaking, a family of graphs gives unavoidable minors for a minor-monotone parameter if these graphs “explain” why the parameter is high.The second problem studies the minimal excluded minors of the class of graphs such that φ(G) is bounded by some constant k, where φ(G) is a parameter related to the cut dominant of a graph G. This unbounded polyhedron contains all points that are componentwise larger than or equal to a convex combination of incidence vectors of cuts in G. The parameter φ(G) is equal to the maximum right-hand side of a facet-defining inequality of the cut dominant of G in minimum integer form. We study minimal excluded graphs for the property φ(G) <= 4 and provide also a new bound of φ(G) in terms of the vertex cover number.The last problem has a different flavor as it studies a packing-covering relation in classes of graphs excluding a minor. Given a graph G, a ball of center v and radius r is the set of all vertices in G that are at distance at most r from v. Given a graph and a collection of balls, we can define a hypergraph H such that its vertices are the vertices of G and its edges correspond to the balls in the collection. It is well-known that, in the hypergraph H, the transversal number τ(H) is at least the packing number ν(H). We show that we can bound τ(H) from above by a linear function of ν(H) for every graphs G and ball collections H if the graph G excludes a minor, solving an open problem by Chepoi, Estellon et Vaxès.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Larsson, Leo. "Carlson type inequalities and their applications." Doctoral thesis, Uppsala : Univ. : Matematiska institutionen, Univ. [distributör], 2003. http://publications.uu.se/theses/91-506-1654-4/.

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Drezga, Irislav. "A generalized ANN-based model for short-term load forecasting." Diss., This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-06062008-151653/.

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Bird, Gregory David. "Linear and Nonlinear Dimensionality-Reduction-Based Surrogate Models for Real-Time Design Space Exploration of Structural Responses." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8653.

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Design space exploration (DSE) is a tool used to evaluate and compare designs as part of the design selection process. While evaluating every possible design in a design space is infeasible, understanding design behavior and response throughout the design space may be accomplished by evaluating a subset of designs and interpolating between them using surrogate models. Surrogate modeling is a technique that uses low-cost calculations to approximate the outcome of more computationally expensive calculations or analyses, such as finite element analysis (FEA). While surrogates make quick predictions, accuracy is not guaranteed and must be considered. This research addressed the need to improve the accuracy of surrogate predictions in order to improve DSE of structural responses. This was accomplished by performing comparative analyses of linear and nonlinear dimensionality-reduction-based radial basis function (RBF) surrogate models for emulating various FEA nodal results. A total of four dimensionality reduction methods were investigated, namely principal component analysis (PCA), kernel principal component analysis (KPCA), isometric feature mapping (ISOMAP), and locally linear embedding (LLE). These methods were used in conjunction with surrogate modeling to predict nodal stresses and coordinates of a compressor blade. The research showed that using an ISOMAP-based dual-RBF surrogate model for predicting nodal stresses decreased the estimated mean error of the surrogate by 35.7% compared to PCA. Using nonlinear dimensionality-reduction-based surrogates did not reduce surrogate error for predicting nodal coordinates. A new metric, the manifold distance ratio (MDR), was introduced to measure the nonlinearity of the data manifolds. When applied to the stress and coordinate data, the stress space was found to be more nonlinear than the coordinate space for this application. The upfront training cost of the nonlinear dimensionality-reduction-based surrogates was larger than that of their linear counterparts but small enough to remain feasible. After training, all the dual-RBF surrogates were capable of making real-time predictions. This same process was repeated for a separate application involving the nodal displacements of mode shapes obtained from a FEA modal analysis. The modal assurance criterion (MAC) calculation was used to compare the predicted mode shapes, as well as their corresponding true mode shapes obtained from FEA, to a set of reference modes. The research showed that two nonlinear techniques, namely LLE and KPCA, resulted in lower surrogate error in the more complex design spaces. Using a RBF kernel, KPCA achieved the largest average reduction in error of 13.57%. The results also showed that surrogate error was greatly affected by mode shape reversal. Four different approaches of identifying reversed mode shapes were explored, all of which resulted in varying amounts of surrogate error. Together, the methods explored in this research were shown to decrease surrogate error when performing DSE of a turbomachine compressor blade. As surrogate accuracy increases, so does the ability to correctly make engineering decisions and judgements throughout the design process. Ultimately, this will help engineers design better turbomachines.

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Liste, Erika. "Orders of Geo-Kinetic Manifestation in Ivan Doig´s The Sea Runners." Thesis, Stockholms universitet, Engelska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-86913.

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This phenomenological study presents a map of spatial forces in Ivan Doig’s The Sea Runners. The investigation calls attention to forms of space-experience that come across as a sense of embeddedness in environment. Events, places, feelings, and moods materialize as being nested within greater events and places that are likewise nested in even larger ones. The study shows that experience, place, memory, hope, and narrative have nested structures. The embedding of narrated realities within larger realities is identified as a mode of organization central to the text’s complexity. Even the smallest acts, events, moods, and feelings are set within larger ones with greater scope, reach, or extension. The literary force of The Sea Runners is made possible by a sustained presentation of complexly interlocking orders of embedding. These orders are co-ordinated and synchronized in terms of movement. The study shows how kinetic systems of circulation, vanishing, encircling, and transformation overlap and reinforce each other so as to create a comprehensive co-ordination effect that colours the presentation of landscape and travel. Movement is highlighted in the essay as a factor that makes it possible for these kinetic structures to be fused in various patterns of co-ordination. In The Sea Runners, place and motion complexly combine to shape the narrated flow of lived experience. In its various orders of fluctuation, space-experience flows in intimate association with life-feeling and movement-sensation. Certain basic kinetic categories are delineated as being at the heart of the text’s overall structure. The study brings its findings to a conclusion by discussing these kinetic categories of lived space as running parallel to categories of lived temporality.

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Fogaça, Isis Caroline Oliveira de Sousa. "Análise da evolução temporal de dados métricos." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/8661.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
The expansion of different areas of knowledge through many types of information brought the necessity to support complex data (images, sounds, videos, strings, DNA chains, etc.), that do not have a Total Order Relationship and need other management mechanisms, like the contentbased retrieval. In general, they are represented in metric space domains, where we have only the elements and the distances between them. Through the characteristics extracted from them, we perform the similarity search. Considering the necessity to associate temporal information on these data in many applications, this work aims to analyze the temporal evolve of metric data. One alternative for this is embedding them into a multidimensional space to allow trajectories estimates. We studied different methods of embedding and analyzed how this affected the data’s distribution and, consequently, the estimates. Two new methods were purposed to estimate an element’s status on a different time from that available in database, in order to reduce the number of non-relevant elements on search results. These methods are based on radius search reduction (range) and evaluation of retrieved element’s proximity by using an approximation of reverse k- NN. We performed experiments which showed that purposed methods could improve the estimate’s result, that used to be performed only using k-NN searches.
A expansão de diferentes áreas do conhecimento com os diversos tipos de informação tornou necessário o suporte a dados complexos (imagens, sons, vídeos, cadeias de DNA, entre outros), que por não possuírem uma Relação de Ordem Total (ROT), necessitam de outros mecanismos de gerenciamento, como a recuperação por conteúdo. Em geral, esses dados são representados em domínios de espaços métricos, onde apenas se tem os elementos e as distâncias entre eles. Através das características extraídas dos mesmos, realiza-se consultas por similaridade. Considerando a necessidade de associar a informação temporal a esses dados em muitas aplicações, este trabalho visa analisar a evolução temporal dos dados métricos. Para isso, uma alternativa é mapeá-los para um espaço multidimensional, a fim possibilitar a estimativa de trajetórias. Neste trabalho, foram estudados diferentes métodos de mapeamento, sendo também analisado como o mapeamento afetou a distribuição dos mesmos e, por conseguinte, a realização das estimativas. Foram propostos dois novos métodos para estimar o estado de um elemento em um tempo diferente daqueles disponíveis na base de dados, com o objetivo de reduzir no conjunto resposta a quantidade de elementos não relevantes. Os métodos propostos são baseados na redução do raio de consulta na região estimada pela delimitação do raio de consulta (range) e a avaliação da proximidade dos elementos retornados utilizando verificação (aproximação) do k-NN reverso. Foram realizados experimentos que mostraram que os métodos propostos melhoraram o resultado final das estimativas, que anteriormente eram realizadas apenas com consultas aos vizinhos mais próximos.

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Arzhantsev, I. V., D. A. Timashev, and Andreas Cap@esi ac at. "Affine Embeddings of Homogeneous Spaces." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi929.ps.

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19

Abdikalikova, Zamira. "Embedding theorems for spaces with multiweighted derivatives." Licentiate thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-26092.

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This Licentiate Thesis consists of four chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we consider and analyze some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we present and prove analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are crucially for the proofs of the main results of this Licentiate Thesis. In Chapter 3 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of spaces. However, with the help of our new embedding theorems we can extend these results to the case of strong degeneration. In Chapter 4 we prove some new estimates for each function in a Tchebychev system. In order to be able to study also compactness of the embeddings from Chapter 3 such estimates are crucial. I plan to study this question in detail in my further PhD studies.

Godkänd; 2007; 20071107 (ysko)

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Abdikalikova, Zamira T. "Embedding theorems for spaces with multiweighted derivatives /." Luleå : Luleå University of Technology, 2007. http://epubl.ltu.se/1402-1757/2007/53/.

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Carroll, Douglas Edmonds. "Embedding parameterized graph classes into normed spaces." Diss., Restricted to subscribing institutions, 2007. http://proquest.umi.com/pqdweb?did=1324389171&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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22

Zheng, Bentuo. "Embeddings and factorizations of Banach spaces." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1551.

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Neves, Julio Severino. "Fractional Sobolev-type spaces and embeddings." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341514.

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Algervik, Robert. "Embedding Theorems for Mixed Norm Spaces and Applications." Doctoral thesis, Karlstads universitet, Avdelningen för matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-5646.

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This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. We study different structural, integrability, and smoothness properties of functions satisfying certain mixed norm conditions. Conditions of this type are determined by the behaviour of linear sections of functions. The work in this direction originates in a paper due to Gagliardo (1958), and was further developed by Fournier (1988), by Blei and Fournier (1989), and by Kolyada (2005). Here we continue these studies. We obtain some refinements of known embeddings for certain mixed norm spaces introduced by Gagliardo, and we study general properties of these spaces. In connection with these results, we consider a scale of intermediate mixed norm spaces, and prove intrinsic embeddings in this scale. We also consider more general, fully anisotropic, mixed norm spaces. Our main theorem states an embedding of these spaces to Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic Sobolev-Besov spaces, and anisotropic fractional Sobolev spaces. The methods used are based on non-increasing rearrangements, and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces by Bourgain, Brezis, and Mironescu, and for anisotropic Besov spaces by Kolyada. We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces, and in the description of Sobolev type embeddings. In the last chapter, we study mixed norm spaces consisting of functions that have smooth sections. We prove embeddings of these spaces to Lorentz spaces. From this result, known properties of Sobolev-Liouville spaces follow.

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Algervik, Robert. "Embedding Theorems for Mixed Norm Spaces and Applications." Licentiate thesis, Karlstad : Faculty of Technology and Science, Mathematics, Karlstads universitet, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-2874.

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Rilk, Albrecht Johannes. "The flicker electroretinogram in phase space embeddings and techniques /." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969749384.

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Pelatt, Kristine, and Kristine Pelatt. "Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots." Thesis, University of Oregon, 2012. http://hdl.handle.net/1794/12423.

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We produce explicit geometric representatives of non-trivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live off of the vanishing line of a homology spectral sequence due to Sinha. We use con figuration space integrals to show our classes pair non-trivially with cohomology classes due to Longoni. We then give an alternate formula for the first differential in the homology spectral sequence due to Sinha. This differential connects the geometry of the cycles we define to the combinatorics of the spectral sequence. The new formula for the differential also simplifies calculations in the spectral sequence.

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Hume, David S. "Embeddings of infinite groups into Banach spaces." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde.

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In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifolds and to higher dimensional analogues of graph manifolds. In Chapter 4 we give an explicit method of embedding relatively hyperbolic groups into certain Banach spaces, which yields optimal bounds on the compression exponent of such groups relative to their peripheral subgroups. From this we deduce that the fundamental group of every closed three-manifold has Hilbert compression exponent one. In Chapter 5 we prove that relatively hyperbolic spaces with a tree-graded quasi-isometry representative can be characterised by a relative version of Manning's bottleneck property. This applies to the Bestvina-Bromberg-Fujiwara quasi-trees of spaces, yielding an embedding of each mapping class group of a closed surface into a finite product of simplicial trees. From this we obtain explicit embeddings of mapping class groups into certain Banach spaces and deduce that these groups have finite Assouad-Nagata dimension. It also applies to relatively hyperbolic groups, proving that such groups have finite Assouad-Nagata dimension if and only if each peripheral subgroup does.

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Buckingham, Lawrence. "K-mer based algorithms for biological sequence comparison and search." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/236377/1/Buckingham%2BThesis%281%29.pdf.

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The present thesis develops novel algorithms for biological sequence comparison and accelerated sequence database search, motivated by the need to work effectively with the rapidly expanding volume of sequence data which is available as the result of continuing advances in sequencing technology. Empirical tests using datasets of realistic size and content demonstrate that these algorithms are approximately an order of magnitude faster than standard sequence database search tools, while attaining higher precision. While the algorithms have been developed and tested in a biological context, they are applicable to any problem involving comparison of sequential data series.

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Fearnley, David L. "Dense embeddings of #sigma#-discrete #pi#-based spaces." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244550.

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Clavero, Nadia F. "Optimal Sobolev Embeddings in Spaces with Mixed Norm." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/292613.

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Este proyecto hace referencia a estimaciones, en espacios funcionales, que relacionan la norma de una función y la de sus derivadas. Concretamente, nuestro principal objetivo es estudiar las estimaciones clásicas de las inclusiones de Sobolev, probadas por Gagliardo y Nirenberg, para derivadas de orden superior y espacios más generales. En particular, estamos interesados en describir el dominio y el rango óptimos para estas inclusiones entre los espacios invariantes por reordenamiento (r.i.) y espacios de normas mixtas.
This thesis project concerns estimates, in function spaces, that relate the norm of a function and that of its derivatives. Speci.cally, our main purpose is to study the classical Sobolev-type inequalities due to Gagliardo and Nirenberg for higher order derivatives and more general spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between rearrangement-invariant spaces (r.i.) and mixed norm spaces.

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Carpenter, Timothy E. "Algorithms For Low-Distortion Embeddings Into Geometrically Restricted Spaces." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555337435997622.

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Kilbane, James. "Finite metric subsets of Banach spaces." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/288272.

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The central idea in this thesis is the introduction of a new isometric invariant of a Banach space. This is Property AI-I. A Banach space has Property AI-I if whenever a finite metric space almost-isometrically embeds into the space, it isometrically embeds. To study this property we introduce two further properties that can be thought of as finite metric variants of Dvoretzky's Theorem and Krivine's Theorem. We say that a Banach space satisfies the Finite Isometric Dvoretzky Property (FIDP) if it contains every finite subset of $\ell_2$ isometrically. We say that a Banach space has the Finite Isometric Krivine Property (FIKP) if whenever $\ell_p$ is finitely representable in the space then it contains every subset of $\ell_p$ isometrically. We show that every infinite-dimensional Banach space \emph{nearly} has FIDP and every Banach space nearly has FIKP. We then use convexity arguments to demonstrate that not every Banach space has FIKP, and thus we can exhibit classes of Banach spaces that fail to have Property AI-I. The methods used break down when one attempts to prove that there is a Banach space without FIDP and we conjecture that every infinite-dimensional Banach space has Property FIDP.

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Desai, Palash. "Embeddings of a cray T3D supercomputer onto a free-space optical backplane." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23743.

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The rapid increase in the demands for high bandwidth systems has motivated research in optoelectronic technologies and architectures. At McGill University, a five year five Major Project in Photonic Devices and Systems has been undertaken, with funding from the Canadian Institute for Telecommunications Research. One of the main goals of the project is to develop an optical backplane architecture capable of interconnecting several electronic printed circuit boards with an aggregate bandwidth on the order of 1 Terabit per second. Currently, the project is in its third year in which a representative subset of a Terabit Photonic Backplane is under development.
The objectives of this thesis are three fold. First, we motivate the study of optical backplanes by demonstrating that the interconnection network of a Cray T3D Supercomputer can be embedded onto the optical backplane. In particular, we demonstrate that the 3D mesh interconnect of the Cray T3D can be embedded into the "Dual Stream Linear HyperPlane" (9). Secondly, having established a motivation we then provide a detailed review of the functional specifications of an optical backplane. In particular, we provide a detailed review of the June 1995 backplane design (31). Thirdly, having established a motivation and a detailed design we then develop a executable software model of the June 1995 backplane using the VHDL hardware description language. The VHDL model is used to establish the functional correctness of the design. In addition, the VHDL model is used to develop a real-time simulator for the photonic backplane using 4013 Field Programmable Gate Arrays (FPGAs). The real time simulator can operate at a 4 MHz clock rate and can be used to test other electronic components such as the Message-Processors at realistic clock rates. (Abstract shortened by UMI.)

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Samuel, Javed K. K. "Lower bounds for embedding the Earth Mover Distance metric into normed spaces." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33346.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.
Includes bibliographical references (p. 71-73).
This thesis presents a lower bounds for embedding the Earth Mover Distance (EMID) metric into normed spaces. The EMID is a metric over two distributions where one is a mass of earth spread out in space and the other is a collection of holes in that same space. The EMD between these two distributions is defined as the least amount of work needed to fill the holes with earth. The EMD metric is used in a number of applications, for example in similarity searching and for image retrieval. We present a simple construction of point sets in the ENID metric space over two dimensions that cannot be embedded from the ED metric exactly into normed spaces, namely l1 and the square of l2. An embedding is a mapping f : X --> V with X a set of points in a metric space and ' Va set of points in some normed vector space. When the Manhattan distance is used as the underlying metric for the EMD, it can be shown that this example is isometric to K2,4 which has distortion equal to 1.25 when it is embedded into I and( 1.1180 when embedded into the square of 12. Other constructions of points sets in the EMID metric space over three and higher dimensisions are also discussed..
by Javed K.K. Samuel.
M.Eng.

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Sidiropoulos, Anastasios. "Approximation algorithms for low-distortion embeddings into low-dimensional spaces." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/34126.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.
Includes bibliographical references (p. 33-35).
We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. We give an O([square root] n)-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. For the same problem, we give an exact algorithm, with running-time exponential in the distortion. We complement these results by showing that the problem is NP-hard to [alpha]-approximate, for some constant [alpha] > 1. For the two-dimensional case, we show a O([square root] n) upper bound for the distortion required to embed an n-point subset of the two-dimensional sphere, into the plane. We prove that this bound is asymptotically tight, by exhibiting n-point subsets such that any embedding into the plane has distortion [omega]([square root] n). These techniques yield a O(1)-approximation algorithm for the problem of embedding an n-point subset of the sphere into the plane.
by Anastasios Sidiropoulos.
S.M.

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Prang, Mathieu. "Representation learning for symbolic music." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS489.

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Un élément clé du récent succès des modèles d'apprentissage profond de traitement du langage réside dans la capacité à apprendre des "embeddings" de mots efficaces. Ces méthodes fournissent des espaces vectoriels structurés de dimension réduite ayant des relations métriques intéressantes. Ceux-ci, à leur tour, peuvent être utilisés comme des représentations d'entrées efficaces pour traiter des tâches plus complexes. Dans cette thèse, nous nous concentrons sur la tâche d'apprentissage d'espaces "d'embedding" pour la musique polyphonique dans le domaine symbolique. Pour ce faire, nous explorons deux approches différentes.Tout d'abord, nous introduisons un modèle d'embedding basé sur un réseau convolutif avec un nouveau type de mécanisme d'attention hiérarchique auto-modulée, qui est calculé à chaque couche afin d'obtenir une vision hiérarchique de l'information musicale.Puis, nous proposons un autre système basé sur les VAE, un type d'auto-encodeur qui contraint la distribution des données de l'espace latent à être proche d'une distribution préalablement choisie. La musique polyphonique étant un type d'information complexe, le choix de la représentation d'entrée est un processus crucial. Nous introduisons donc une nouvelle représentation de données musicales symboliques, qui transforme une partition polyphonique en un signal continu.Enfin, nous montrons le potentiel de nos espaces d'embedding à travers le développement de plusieurs applications créatives utilisées pour améliorer la connaissance et l'expression musicales, à travers des tâches telles que la modification de mélodies ou l'identification de compositeurs
A key part in the recent success of deep language processing models lies in the ability to learn efficient word embeddings. These methods provide structured spaces of reduced dimensionality with interesting metric relationship properties. These, in turn, can be used as efficient input representations for handling more complex tasks. In this thesis, we focus on the task of learning embedding spaces for polyphonic music in the symbolic domain. To do so, we explore two different approaches.We introduce an embedding model based on a convolutional network with a novel type of self-modulated hierarchical attention, which is computed at each layer to obtain a hierarchical vision of musical information.Then, we propose another system based on VAEs, a type of auto-encoder that constrains the data distribution of the latent space to be close to a prior distribution. As polyphonic music information is very complex, the design of input representation is a crucial process. Hence, we introduce a novel representation of symbolic music data, which transforms a polyphonic score into a continuous signal.Finally, we show the potential of the resulting embedding spaces through the development of several creative applications used to enhance musical knowledge and expression, through tasks such as melodies modification or composer identification

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Boavida, de Brito Pedro. "Homotopy sheaves on manifolds and applications to spaces of smooth embeddings." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=215123.

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This thesis explores connections between homotopy sheaves, manifold calculus of functors and operad theory. We argue that there is a deep overlap between these, and as evidence we give a new operadic description of the homotopy theoretical obstructions to deforming a smooth immersion into a smooth embedding. We then discuss an application which improves on some aspects of recent results of Arone-Turchin and Dwyer-Hess concerning spaces of long knots and high-dimensional variants. Along the way, we define fibrewise complete Segal spaces, a mild generalisation of Rezk's notion of complete Segal spaces. Also in the context of Segal spaces, we define right fibrations and prove a Grothendieck construction theorem for presheaves with values in spaces. Finally, we prove a result of independent interest which states that weakly k-reduced operads (those with contractible space of operations in arity j ? k) can be strictified when k = 0, 1.

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Shaker, Jomaa K. M. A. "Algebraic computing in general relativity and supergravity : space-time embeddings and higher dimensional theories." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37849.

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Sanomiya, Thais Akemi Tokubo. "Sobre o teorema de Campbell-Magaard e o problema de Cauchy na relatividade." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9542.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
After the formulation of general relativity differential geometry has become an increasing important tool in theoretical physics. This is even more clear in the investigation of the so-called embedding space-time theories. In this work we focus our attention in the Cauchy problem. These have played a crucial role in our understanding of the mathematical structure of general relativity and embedding theories. We investigate the similarities and differences between the two approaches. We also study an extension of the Campbell-Magaard theorem and give two examples of both formalisms.
A geometria diferencial passou a ser uma ferramenta fundamental na fisica com o surgimento da relatividade geral. Em particular, destacamos sua importância na investigado das chamadas teorias de imersdo do espaco-tempo. Neste trabalho analisamos dois grandes formalismos fundamentados de forma direta ou indireta na teoria de imersões: o teorema de Campbell-Magaard e o problema de Cauchy para a relatividade geral. Tendo como principal objetivo tracar um paralelo entre esses dois formalismos, estudamos, nesta dissertacdo, o problema de valor inicial (pvi) para a relatividade geral mostrando que alem de admitir a formulae-do de pvi, a mesma é bem posta. Ademais, aplicamos este formalismo para o caso de uma metrica do tipo Friedmann-Robertson-Walker em (3+1). Estudamos tambem o teorema de Campbell-Magaard e sua extensdo para o espaco-tempo de Einstein e aplicamos este teorema para uma metrica do tipo de Sitter em (2+1).

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Voigtlaender, Felix Verfasser], Hartmut [Akademischer Betreuer] Führ, Hans G. [Akademischer Betreuer] [Feichtinger, and Holger [Akademischer Betreuer] Rauhut. "Embedding theorems for decomposition spaces with applications to wavelet coorbit spaces / Felix Voigtlaender ; Hartmut Führ, Hans G. Feichtinger, Holger Rauhut." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/112733719X/34.

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Voigtlaender, Felix [Verfasser], Hartmut Akademischer Betreuer] Führ, Hans G. [Akademischer Betreuer] [Feichtinger, and Holger [Akademischer Betreuer] Rauhut. "Embedding theorems for decomposition spaces with applications to wavelet coorbit spaces / Felix Voigtlaender ; Hartmut Führ, Hans G. Feichtinger, Holger Rauhut." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/112733719X/34.

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Choudhary, Rishabh R. "Construction and Visualization of Semantic Spaces for Domain-Specific Text Corpora." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1627666092811419.

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44

Abdikalikova, Zamira. "Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives." Doctoral thesis, Luleå, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25800.

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This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions.Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we prove some new estimates for each function in a Tchebychev system. In order to be able to study compactness of the embeddings from Chapter 3 such estimates are crucial.In Chapter 3 we rewrite and present some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we rewrite and discuss some analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are not available in the Western literatures in this way and they are crucial for the proofs of the main results in Chapter 4. In Chapter 4 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of the spaces. However, with the help of our new embedding theorems we can extend theseresults to the case of strong degeneration.The main aim of Chapter 5 is to establish boundedness and compactness of the embedding considered in Chapter 4.In Chapter 4 basically only sufficient conditions for boundedness of this embedding were obtained. In Chapter 5 we obtain necessary and sufficient conditions for boundedness and compactness of this embedding and the main results are proved in a different way.
Godkänd; 2009; 20090429 (zamira); DISPUTATION Ämnesområde: Matematik/Mathematics Opponent: Professor Victor Burenkov, Cardiff University, United Kingdom Ordförande: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Fredag den 12 juni 2009, kl 10.00 Plats: D 2214, Luleå tekniska universitet

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Abdikalikova, Zamira T. "Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivates /." Luleå : Department of Mathematics, Luleå University of Technology, 2009. http://pure.ltu.se/ws/fbspretrieve/2745822.

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Melo, Givanildo Donizeti de [UNESP]. "Sobre a dimensão do quadrado de um espaço métrico compacto X de dimensão n e o conjunto dos mergulhos de X em R2n." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/138318.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Neste trabalho nós estudamos o seguinte resultado: para um espaço métrico compacto X, de dimensão n, o subespaço dos mergulhos de X em R2n é denso no espaço das funções contínuas de X em R2n se, e somente se, dim(X x X)<2n. A demonstração apresentada é aquela dada por J. Krasinkiewicz e por S. Spiez.
In this work we study the following result: given a compact metric space X of dimension n, the subspace consisting of all embeddings of X into R2n is dense in the space of all continuous maps of X into R2n if and only if dim(X x X)<2n. The presented proof is the one given by J. Krasinkiewicz e por S. Spiez.

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James, Morrison-Knight. "Experiences of Immigrant Entrepreneurs in the Falafel Trade in Malmö." Thesis, Malmö universitet, Fakulteten för kultur och samhälle (KS), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-23641.

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This research investigates how immigrant entrepreneurs in the falafel business in Malmö position themselves in relation to the host society. Interviews with five immigrant entrepreneurs in the falafel trade were conducted to explore their life stories, business endeavours and their relations with the host society. The data was then analysed to establish the degree to which they feel embedded in different arenas of the host society and their society of origin. This study confirms the disadvantageous position of immigrants in Swedish society, though demonstrates the various strategies they utilise to improve their situation through entrepreneurship. The study, the first of its kind in Malmö, is important in the context of rising xenophobia in Sweden and segregation in the city.

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Couairon, Guillaume. "Text-Based Semantic Image Editing." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS248.

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L’objectif de cette thèse est de proposer des algorithmes pour la tâche d’édition d’images basée sur le texte (TIE), qui consiste à éditer des images numériques selon une instruction formulée en langage naturel. Par exemple, étant donné une image d’un chien et la requête "Changez le chien en un chat", nous voulons produire une nouvelle image où le chien a été remplacé par un chat, en gardant tous les autres aspects de l’image inchangés (couleur et pose de l’animal, arrière- plan). L’objectif de l’étoile du nord est de permettre à tout un chacun de modifier ses images en utilisant uniquement des requêtes en langage naturel. Une des spécificités de l’édition d’images basée sur du texte est qu’il n’y a pratiquement pas de données d’entraînement pour former un algorithme supervisé. Dans cette thèse, nous proposons différentes solutions pour l’édition d’images, basées sur l’adaptation de grands modèles multimodaux entraînés sur d’énormes ensembles de données. Nous étudions tout d’abord une configuration d’édition simplifiée, appelée édition d’image basée sur la recherche, qui ne nécessite pas de modifier directement l’image d’entrée. Au lieu de cela, étant donné l’image et la requête de modification, nous recherchons dans une grande base de données une image qui correspond à la modification demandée. Nous nous appuyons sur des modèles multimodaux d’alignement image/texte entraînés sur des ensembles de données à l’échelle du web (comme CLIP) pour effectuer de telles transformations sans aucun exemple. Nous proposons également le cadre SIMAT pour évaluer l’édition d’images basée sur la recherche. Nous étudions ensuite comment modifier directement l’image d’entrée. Nous proposons FlexIT, une méthode qui modifie itérativement l’image d’entrée jus- qu’à ce qu’elle satisfasse un "objectif d’édition" abstrait défini dans un espace d’intégration multimodal. Nous introduisons des termes de régularisation pour imposer des transformations réalistes. Ensuite, nous nous concentrons sur les modèles de diffusion, qui sont des modèles génératifs puissants capables de synthétiser de nouvelles images conditionnées par une grande variété d’invites textuelles. Nous démontrons leur polyvalence en proposant DiffEdit, un algorithme qui adapte les modèles de diffusion pour l’édition d’images sans réglage fin. Nous proposons une stratégie "zero-shot" pour trouver automatiquement où l’image initiale doit être modifiée pour satisfaire la requête de transformation de texte
The aim of this thesis is to propose algorithms for the task of Text-based Image Editing (TIE), which consists in editing digital images according to an instruction formulated in natural language. For instance, given an image of a dog, and the query "Change the dog into a cat", we want to produce a novel image where the dog has been replaced by a cat, keeping all other image aspects unchanged (animal color and pose, background). The north-star goal is to enable anyone to edit their images using only queries in natural language. One specificity of text-based image editing is that there is practically no training data to train a supervised algorithm. In this thesis, we propose different solutions for editing images, based on the adaptation of large multimodal models trained on huge datasets. We first study a simplified editing setup, named Retrieval-based image edit- ing, which does not require to directly modify the input image. Instead, given the image and modification query, we search in a large database an image that corresponds to the requested edit. We leverage multimodal image/text alignment models trained on web-scale datasets (like CLIP) to perform such transformations without any examples. We also propose the SIMAT framework for evaluating retrieval-based image editing. We then study how to directly modify the input image. We propose FlexIT, a method which iteratively changes the input image until it satisfies an abstract "editing objective" defined in a multimodal embedding space. We introduce a variety of regularization terms to enforce realistic transformations. Next, we focus on diffusion models, which are powerful generative models able to synthetize novel images conditioned on a wide variety of textual prompts. We demonstrate their versatility by proposing DiffEdit, an algorithm which adapts diffusion models for image editing without finetuning. We propose a zero-shot strategy for finding automatically where the initial image should be changed to satisfy the text transformation query. Finally, we study a specific challenge useful in the context of image editing: how to synthetize a novel image by giving as constraint a spatial layout of objects with textual descriptions, a task which is known as Semantic Image Synthesis. We adopt the same strategy, consisting in adapting diffusion models to solve the task without any example. We propose the ZestGuide algorithm, which leverages the spatio-semantic information encoded in the attention layers of diffusion models

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Batson, Scott Christopher. "On the Relationship Between Two Embeddings of Ideals into Geometric Space and the Shortest Vector Problem in Principal Ideal Lattices." Thesis, North Carolina State University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3710729.

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An ideal lattice is the geometric embedding of an ideal in the algebraic integer ring of some number field. Many recent developments in lattice-based cryptography are centered around the use of ideal lattices. The shortest vector problem (SVP) is the most important hard lattice problem. Few algorithms that find a short vector in ideal lattices exploit their additional algebraic structure, and whether or not the SVP can be solved algebraically in ideal lattices remains unknown. We study the relationship between the canonical and coefficient embeddings of ideals in algebraic integer rings of cyclotomic number fields. We examine the algebraic structure of principal ideal lattices under the coefficient embedding by considering them as principal ideals of a cyclotomic quotient ring. Finally, empirical evidence is provided to exhibit a relationship between the algebraic structure of a principal ideal in this quotient ring and the geometric structure of its corresponding ideal lattice. These results demonstrate progress towards solving the SVP in ideal lattices algebraically.

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Duquenne, Paul-Ambroise. "Sentence Embeddings for Massively Multilingual Speech and Text Processing." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS039.

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L'apprentissage de représentations mathématiques des phrases, sous forme textuelle, a été largement étudié en traitement automatique des langues (TAL). Alors que de nombreuses recherches ont exploré différentes fonctions d'objectif de pré-entraînement pour créer des représentations contextuelles des mots à partir des phrases, d'autres se sont concentrées sur l'apprentissage de représentations des phrases par des vecteurs uniques, ou représentations de taille fixe (par opposition à une séquence de vecteurs dont la longueur dépend de la longueur de la phrase), pour plusieurs langues. Le but étant d'encoder par des vecteurs proches entre eux les paraphrases et les traductions d'une même phrase. Dans cette thèse, nous étudions d'abord comment étendre ces espaces de représentations de phrases à la modalité de la parole afin de construire un espace de représentation de phrases multilingue pour la parole et le texte. Ensuite, nous explorons comment utiliser cet espace de représentation de phrase multilingue et multimodal pour de la recherche de similarité sémantique entre des phrases parlées et écrites à grande échelle. Ceci nous permet de créer automatiquement des alignements entre des phrases écrites et parlées dans différentes langues. Pour des seuils de similarité élevés dans l'espace de représentation, les phrases alignées peuvent être considérées comme des traductions. Si les alignements impliquent d'un côté des phrases écrites et de l'autre des phrases parlées, il s'agit alors de potentielles traductions parole-texte. Si les alignements impliquent des deux côtés des phrases parlées, il s'agit alors de potentielles traductions parole-parole. Pour valider la qualité des données collectées automatiquement, nous entraînons des modèles de traduction de la parole vers le texte et des modèles de traduction parole vers parole. Nous montrons qu'ajouter les données alignées automatiquement améliore significativement la qualité du modèle de traduction appris, démontrant la qualité des alignements et l'utilité des données automatiquement alignées. Ensuite, nous étudions comment décoder ces représentations vectorielles de phrases en texte ou parole dans différentes langues. Nous explorons plusieurs méthodes d'apprentissage de modèles décodeurs et analysons leur robustesse pour décoder des représentations de phrases de langues/modalités non observées pendant leur apprentissage, afin de quantifier leur capacité de généralisation et le transfert entre langues et entre modalités des capacités de décodage. Nous mettons en évidence que l'on peut atteindre des résultats de traduction d'une modalité à l'autre proches de systèmes appris de manière supervisée avec un mécanisme d'attention. La compatibilité des représentations parole/texte dans différentes langues permet ces très bonnes performances, malgré une représentation intermédiaire composée d'un seul vecteur. Enfin, nous montrons comment nous avons développé un nouvel espace de représentation de phrases pour la parole et le texte qui améliore l'état de l'art nommé SONAR, grâce aux enseignements tirés de nos travaux précédents. Nous étudions différentes fonctions d'objectif pour l'apprentissage de cet espace et nous analysons leur impact sur l'organisation de l'espace ainsi que sur les capacités de décodage des représentations. Nous montrons que ce nouvel espace de représentation de phrases améliore significativement l'état de l'art pour la recherche de similarité entre langues et entre modalités ainsi que les capacités de décodage de ces représentations. Ce nouvel espace couvre 200 langues écrites et 37 langues parlées. Il offre également des résultats en traduction du texte proche du système de traduction NLLB sur lequel il se base, et en traduction de la parole compétitifs avec le système supervisé Whisper. Nous présentons également SONAR EXPRESSIVE, qui introduit une représentation supplémentaire encodant des propriétés de la parole non sémantiques telles que la voix ou l'expressivité
Representation learning of sentences has been widely studied in NLP. While many works have explored different pre-training objectives to create contextual representations from sentences, several others have focused on learning sentence embeddings for multiple languages with the aim of closely encoding paraphrases and translations in the sentence embedding space.In this thesis, we first study how to extend text sentence embedding spaces to the speech modality in order to build a multilingual speech/text sentence embedding space. Next, we explore how to use this multilingual and multimodal sentence embedding space for large-scale speech mining. This allows us to automatically create alignments between written and spoken sentences in different languages. For high similarity thresholds in the latent space, aligned sentences can be considered as translations. If the alignments involve written sentences on one side and spoken sentences on the other, then these are potential speech-to-text translations. If the alignments involve on both sides spoken sentences, then these are potential speech-to-speech translations. To validate the quality of the mined data, we train speech-to-text translation models and speech-to-speech translation models. We show that adding the automatically mined data significantly improves the quality of the learned translation models, demonstrating the quality of the alignments and the usefulness of the mined data.Then, we study how to decode these sentence embeddings into text or speech in different languages. We explore several methods for training decoders and analyze their robustness to modalities/languages not seen during training, to evaluate cross-lingual and cross-modal transfers. We demonstrate that we could perform zero-shot cross-modal translation in this framework, achieving translation results close to systems learned in a supervised manner with a cross-attention mechanism. The compatibility between speech/text representations from different languages enables these very good performances, despite an intermediate fixed-size representation.Finally, we develop a new state-of-the-art massively multilingual speech/text sentence embedding space, named SONAR, based on conclusions drawn from the first two projects. We study different objective functions to learn such a space and we analyze their impact on the organization of the space as well as on the capabilities to decode these representations. We show that such sentence embedding space outperform previous state-of-the-art methods for both cross-lingual and cross-modal similarity search as well as decoding capabilities. This new space covers 200 written languages and 37 spoken languages. It also offers text translation results close to the NLLB system on which it is based, and speech translation results competitive with the Whisper supervised system. We also present SONAR EXPRESSIVE, which introduces an additional representation encoding non-semantic speech properties, such as vocal style or expressivity of speech

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Dissertations / Theses on the topic 'Embedding space'

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