Relevant bibliographies by topics / Embedding space

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Embedding space'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Embedding space"

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Takehara, Daisuke, and Kei Kobayashi. "Representing Hierarchical Structured Data Using Cone Embedding." Mathematics 11, no. 10 (May 15, 2023): 2294. http://dx.doi.org/10.3390/math11102294.

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Extracting hierarchical structure in graph data is becoming an important problem in fields such as natural language processing and developmental biology. Hierarchical structures can be extracted by embedding methods in non-Euclidean spaces, such as Poincaré embedding and Lorentz embedding, and it is now possible to learn efficient embedding by taking advantage of the structure of these spaces. In this study, we propose embedding into another type of metric space called a metric cone by learning an only one-dimensional coordinate variable added to the original vector space or a pre-trained embedding space. This allows for the extraction of hierarchical information while maintaining the properties of the pre-trained embedding. The metric cone is a one-dimensional extension of the original metric space and has the advantage that the curvature of the space can be easily adjusted by a parameter even when the coordinates of the original space are fixed. Through an extensive empirical evaluation we have corroborated the effectiveness of the proposed cone embedding model. In the case of randomly generated trees, cone embedding demonstrated superior performance in extracting hierarchical structures compared to existing techniques, particularly in high-dimensional settings. For WordNet embeddings, cone embedding exhibited a noteworthy correlation between the extracted hierarchical structures and human evaluation outcomes.
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Samko, Natasha. "Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets." Fractional Calculus and Applied Analysis 22, no. 5 (October 25, 2019): 1203–24. http://dx.doi.org/10.1515/fca-2019-0064.

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Abstract We study embeddings of weighted local and consequently global generalized Morrey spaces defined on a quasi-metric measure set (X, d, μ) of general nature which may be unbounded, into Lebesgue spaces Ls(X), 1 ≤ s ≤ p < ∞. The main motivation for obtaining such an embedding is to have an embedding of non-separable Morrey space into a separable space. In the general setting of quasi-metric measure spaces and arbitrary weights we give a sufficient condition for such an embedding. In the case of radial weights related to the center of local Morrey space, we obtain an effective sufficient condition in terms of (fractional in general) upper Ahlfors dimensions of the set X. In the case of radial weights we also obtain necessary conditions for such embeddings of local and global Morrey spaces, with the use of (fractional in general) lower and upper Ahlfors dimensions. In the case of power-logarithmic-type weights we obtain a criterion for such embeddings when these dimensions coincide.
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Paston, Sergey, and Taisiia Zaitseva. "Nontrivial Isometric Embeddings for Flat Spaces." Universe 7, no. 12 (December 4, 2021): 477. http://dx.doi.org/10.3390/universe7120477.

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Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.
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Ravindran, Renjith P., and Kavi Narayana Murthy. "Syntactic Coherence in Word Embedding Spaces." International Journal of Semantic Computing 15, no. 02 (June 2021): 263–90. http://dx.doi.org/10.1142/s1793351x21500057.

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Word embeddings have recently become a vital part of many Natural Language Processing (NLP) systems. Word embeddings are a suite of techniques that represent words in a language as vectors in an n-dimensional real space that has been shown to encode a significant amount of syntactic and semantic information. When used in NLP systems, these representations have resulted in improved performance across a wide range of NLP tasks. However, it is not clear how syntactic properties interact with the more widely studied semantic properties of words. Or what the main factors in the modeling formulation are that encourages embedding spaces to pick up more of syntactic behavior as opposed to semantic behavior of words. We investigate several aspects of word embedding spaces and modeling assumptions that maximize syntactic coherence — the degree to which words with similar syntactic properties form distinct neighborhoods in the embedding space. We do so in order to understand which of the existing models maximize syntactic coherence making it a more reliable source for extracting syntactic category (POS) information. Our analysis shows that syntactic coherence of S-CODE is superior to the other more popular and more recent embedding techniques such as Word2vec, fastText, GloVe and LexVec, when measured under compatible parameter settings. Our investigation also gives deeper insights into the geometry of the embedding space with respect to syntactic coherence, and how this is influenced by context size, frequency of words, and dimensionality of the embedding space.
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Li, Pandeng, Yan Li, Hongtao Xie, and Lei Zhang. "Neighborhood-Adaptive Structure Augmented Metric Learning." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 2 (June 28, 2022): 1367–75. http://dx.doi.org/10.1609/aaai.v36i2.20025.

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Most metric learning techniques typically focus on sample embedding learning, while implicitly assume a homogeneous local neighborhood around each sample, based on the metrics used in training ( e.g., hypersphere for Euclidean distance or unit hyperspherical crown for cosine distance). As real-world data often lies on a low-dimensional manifold curved in a high-dimensional space, it is unlikely that everywhere of the manifold shares the same local structures in the input space. Besides, considering the non-linearity of neural networks, the local structure in the output embedding space may not be homogeneous as assumed. Therefore, representing each sample simply with its embedding while ignoring its individual neighborhood structure would have limitations in Embedding-Based Retrieval (EBR). By exploiting the heterogeneity of local structures in the embedding space, we propose a Neighborhood-Adaptive Structure Augmented metric learning framework (NASA), where the neighborhood structure is realized as a structure embedding, and learned along with the sample embedding in a self-supervised manner. In this way, without any modifications, most indexing techniques can be used to support large-scale EBR with NASA embeddings. Experiments on six standard benchmarks with two kinds of embeddings, i.e., binary embeddings and real-valued embeddings, show that our method significantly improves and outperforms the state-of-the-art methods.
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Bhowmik, Kowshik, and Anca Ralescu. "Clustering of Monolingual Embedding Spaces." Digital 3, no. 1 (February 23, 2023): 48–66. http://dx.doi.org/10.3390/digital3010004.

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Suboptimal performance of cross-lingual word embeddings for distant and low-resource languages calls into question the isomorphic assumption integral to the mapping-based methods of obtaining such embeddings. This paper investigates the comparative impact of typological relationship and corpus size on the isomorphism between monolingual embedding spaces. To that end, two clustering algorithms were applied to three sets of pairwise degrees of isomorphisms. It is also the goal of the paper to determine the combination of the isomorphism measure and clustering algorithm that best captures the typological relationship among the chosen set of languages. Of the three measures investigated, Relational Similarity seemed to capture best the typological information of the languages encoded in their respective embedding spaces. These language clusters can help us identify, without any pre-existing knowledge about the real-world linguistic relationships shared among a group of languages, the related higher-resource languages of low-resource languages. The presence of such languages in the cross-lingual embedding space can help improve the performance of low-resource languages in a cross-lingual embedding space.
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Hawley, Scott H., Zach Evans, and Joe Baldridge. "Audio (vector) algebra: Vector space operations on neural audio embeddings." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A178. http://dx.doi.org/10.1121/10.0015957.

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Ever since the work of Castellon, Donahue, and Liang (ISMIR 2021) showed that latent space “embedding” representations encoded by OpenAI's Jukebox model contain semantically meaningful information about the music, many have wondered whether such embeddings support vector relations akin to the famous “king—man + woman = queen” result seen in word vector embeddings. Such an “audio (vector) algebra” would provide a way to perform operations on the audio by displacing the embeddings in certain directions, and then decoding them to new sounds. The nonlinear aspects of the encoding process suggest that this may not be possible in general, however, for certain kinds of operations in finite regions of embedding spaces, such embedding vector transformations may indeed have musically relevant counterparts. In this talk we investigate the feasibility of such schemes for the cases of mixing and audio effects.
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Hashimoto, Tatsunori B., David Alvarez-Melis, and Tommi S. Jaakkola. "Word Embeddings as Metric Recovery in Semantic Spaces." Transactions of the Association for Computational Linguistics 4 (December 2016): 273–86. http://dx.doi.org/10.1162/tacl_a_00098.

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Continuous word representations have been remarkably useful across NLP tasks but remain poorly understood. We ground word embeddings in semantic spaces studied in the cognitive-psychometric literature, taking these spaces as the primary objects to recover. To this end, we relate log co-occurrences of words in large corpora to semantic similarity assessments and show that co-occurrences are indeed consistent with an Euclidean semantic space hypothesis. Framing word embedding as metric recovery of a semantic space unifies existing word embedding algorithms, ties them to manifold learning, and demonstrates that existing algorithms are consistent metric recovery methods given co-occurrence counts from random walks. Furthermore, we propose a simple, principled, direct metric recovery algorithm that performs on par with the state-of-the-art word embedding and manifold learning methods. Finally, we complement recent focus on analogies by constructing two new inductive reasoning datasets—series completion and classification—and demonstrate that word embeddings can be used to solve them as well.
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Marinari, Maria Grazia, and Mario Raimondo. "On Complete Intersections Over an Algebraically Non-Closed Field." Canadian Mathematical Bulletin 29, no. 2 (June 1, 1986): 140–45. http://dx.doi.org/10.4153/cmb-1986-024-0.

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AbstractWe give a criterion in order that an affine variety defined over any field has a complete intersection (ci.) embedding into some affine space. Moreover we give an example of a smooth real curve C all of whose embeddings into affine spaces are c.i.; nevertheless it has an embedding into ℝ3 which cannot be realized as a c.i. by polynomials.
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Minemyer, Barry. "Isometric embeddings of polyhedra into Euclidean space." Journal of Topology and Analysis 07, no. 04 (September 22, 2015): 677–92. http://dx.doi.org/10.1142/s179352531550020x.

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In this paper we consider piecewise linear (pl) isometric embeddings of Euclidean polyhedra into Euclidean space. A Euclidean polyhedron is just a metric space [Formula: see text] which admits a triangulation [Formula: see text] such that each n-dimensional simplex of [Formula: see text] is affinely isometric to a simplex in 𝔼n. We prove that any 1-Lipschitz map from an n-dimensional Euclidean polyhedron [Formula: see text] into 𝔼3n is ϵ-close to a pl isometric embedding for any ϵ > 0. If we remove the condition that the map be pl, then any 1-Lipschitz map into 𝔼2n + 1 can be approximated by a (continuous) isometric embedding. These results are extended to isometric embedding theorems of spherical and hyperbolic polyhedra into Euclidean space by the use of the Nash–Kuiper C1 isometric embedding theorem ([9] and [13]).
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Dissertations / Theses on the topic "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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Books on the topic "Embedding space"

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Froehlich, Annette, ed. Embedding Space in African Society. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06040-4.

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Riesen, Kaspar. Graph classification and clustering based on vector space embedding. New Jersey: World Scientific, 2010.

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1975-, Parcet Javier, ed. Mixed-norm inequalities and operator space Lp embedding theory. Providence, R.I: American Mathematical Society, 2010.

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Timashev, D. A. Homogeneous Spaces and Equivariant Embeddings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18399-7.

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service), SpringerLink (Online, ed. Homogeneous Spaces and Equivariant Embeddings. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Edmunds, David E., and W. Desmond Evans. Hardy Operators, Function Spaces and Embeddings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-07731-3.

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Edmunds, David E. Hardy Operators, Function Spaces and Embeddings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004.

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1942-, Hong Jia-Xing, ed. Isometric embedding of Riemannian manifolds in Euclidean spaces. Providence, R.I: American Mathematical Society, 2006.

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Bernard, Maurey, ed. H [delta]-embeddings in Hilbert space and optimization on G [delta]-sets. Providence, R.I., USA: American Mathematical Society, 1986.

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Envelopes and sharp embeddings of function spaces. Boca Raton, FL: Chapman & Hall/CRC, 2007.

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Book chapters on the topic "Embedding space"

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Martens, Bas, Alexander Gairiseb, and Carl Eriksen. "Embedding Space in Society." In Southern Space Studies, 335–56. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05980-4_20.

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Vempala, Santosh. "Embedding metrics in Euclidean space." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 15–25. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/dimacs/065/03.

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Uncu, Baran Alp. "Embedding the prefigurations of the Gezi protests." In Public Space Democracy, 47–73. London: Routledge, 2022. http://dx.doi.org/10.4324/9781003193753-5.

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Gallier, Jean. "Embedding an Affine Space in a Vector Space." In Texts in Applied Mathematics, 70–86. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0137-0_4.

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Gallier, Jean. "Embedding an Affine Space in a Vector Space." In Texts in Applied Mathematics, 85–101. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9961-0_4.

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Siebrits, André, Bas Martens, and Carl Eriksen. "Initiatives for Embedding Space Applications in African Societies." In Southern Space Studies, 357–73. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05980-4_21.

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Bunke, Horst, and Kaspar Riesen. "Graph Classification on Dissimilarity Space Embedding." In Lecture Notes in Computer Science, 2. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-89689-0_2.

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Smola, Alex, Arthur Gretton, Le Song, and Bernhard Schölkopf. "A Hilbert Space Embedding for Distributions." In Lecture Notes in Computer Science, 13–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75225-7_5.

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Hou, Haiwei, Shifei Ding, Xiao Xu, and Lili Guo. "Deep Friendly Embedding Space for Clustering." In IFIP Advances in Information and Communication Technology, 92–105. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57808-3_7.

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Feintuch, Avraham. "Orthogonal Embedding of Time-Varying Systems." In Robust Control Theory in Hilbert Space, 207–16. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0591-3_11.

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Conference papers on the topic "Embedding space"

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Pereira, João, Albert K. Groen, Erik S. G. Stroes, and Evgeni Levin. "Graph Space Embedding." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/451.

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We propose the Graph Space Embedding (GSE), a technique that maps the input into a space where interactions are implicitly encoded, with little computations required. We provide theoretical results on an optimal regime for the GSE, namely a feasibility region for its parameters, and demonstrate the experimental relevance of our findings. Next, we introduce a strategy to gain insight on which interactions are responsible for the certain predictions, paving the way for a far more transparent model. In an empirical evaluation on a real-world clinical cohort containing patients with suspected coronary artery disease, the GSE achieves far better performance than traditional algorithms.
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Zhang, Yizhou, Guojie Song, Lun Du, Shuwen Yang, and Yilun Jin. "DANE: Domain Adaptive Network Embedding." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/606.

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Recent works reveal that network embedding techniques enable many machine learning models to handle diverse downstream tasks on graph structured data. However, as previous methods usually focus on learning embeddings for a single network, they can not learn representations transferable on multiple networks. Hence, it is important to design a network embedding algorithm that supports downstream model transferring on different networks, known as domain adaptation. In this paper, we propose a novel Domain Adaptive Network Embedding framework, which applies graph convolutional network to learn transferable embeddings. In DANE, nodes from multiple networks are encoded to vectors via a shared set of learnable parameters so that the vectors share an aligned embedding space. The distribution of embeddings on different networks are further aligned by adversarial learning regularization. In addition, DANE's advantage in learning transferable network embedding can be guaranteed theoretically. Extensive experiments reflect that the proposed framework outperforms other state-of-the-art network embedding baselines in cross-network domain adaptation tasks.
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Dghais, Wael, Luis Nero Alves, Joana Catarina Mendes, Jonathan Rodriguez, and Jose Carlos Pedro. "Memristor state-space embedding." In 2015 European Conference on Circuit Theory and Design (ECCTD). IEEE, 2015. http://dx.doi.org/10.1109/ecctd.2015.7300040.

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Ioannou, Yani, Limin Shang, Robin Harrap, and Michael Greenspan. "Local PotentialWell Space Embedding." In 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops. IEEE, 2009. http://dx.doi.org/10.1109/iccvw.2009.5457491.

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Ding, Chuntao, Li Zhang, and Bangjun Wang. "Hidden space discriminant neighborhood embedding." In 2014 International Joint Conference on Neural Networks (IJCNN). IEEE, 2014. http://dx.doi.org/10.1109/ijcnn.2014.6889365.

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Dar, Guy, Mor Geva, Ankit Gupta, and Jonathan Berant. "Analyzing Transformers in Embedding Space." In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). Stroudsburg, PA, USA: Association for Computational Linguistics, 2023. http://dx.doi.org/10.18653/v1/2023.acl-long.893.

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Ko, Byungsoo, and Geonmo Gu. "Embedding Expansion: Augmentation in Embedding Space for Deep Metric Learning." In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2020. http://dx.doi.org/10.1109/cvpr42600.2020.00728.

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Yang, Liang, Yuexue Wang, Junhua Gu, Chuan Wang, Xiaochun Cao, and Yuanfang Guo. "JANE: Jointly Adversarial Network Embedding." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/192.

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Motivated by the capability of Generative Adversarial Network on exploring the latent semantic space and capturing semantic variations in the data distribution, adversarial learning has been adopted in network embedding to improve the robustness. However, this important ability is lost in existing adversarially regularized network embedding methods, because their embedding results are directly compared to the samples drawn from perturbation (Gaussian) distribution without any rectification from real data. To overcome this vital issue, a novel Joint Adversarial Network Embedding (JANE) framework is proposed to jointly distinguish the real and fake combinations of the embeddings, topology information and node features. JANE contains three pluggable components, Embedding module, Generator module and Discriminator module. The overall objective function of JANE is defined in a min-max form, which can be optimized via alternating stochastic gradient. Extensive experiments demonstrate the remarkable superiority of the proposed JANE on link prediction (3% gains in both AUC and AP) and node clustering (5% gain in F1 score).
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Chen, Ying-Nong, Gang-Feng Ho, Kuo-Chin Fan, Chi-Hung Chuang, and Chih-Chang Yu. "Orthogonal Nearest Neighbor Feature Space Embedding." In 2012 Eighth International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP). IEEE, 2012. http://dx.doi.org/10.1109/iih-msp.2012.46.

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Shang, Limin, and Michael Greenspan. "Pose Determination By PotentialWell Space Embedding." In Sixth International Conference on 3-D Digital Imaging and Modeling (3DIM 2007). IEEE, 2007. http://dx.doi.org/10.1109/3dim.2007.40.

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Reports on the topic "Embedding space"

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Holzapfel, Rolf-Peter. Jacobi Theta Embedding of a Hyperbolic 4-Space with Cusps. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-11-63.

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Bano, Masooda, and Zeena Oberoi. Embedding Innovation in State Systems: Lessons from Pratham in India. Research on Improving Systems of Education (RISE), December 2020. http://dx.doi.org/10.35489/bsg-rise-wp_2020/058.

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The learning crisis in many developing countries has led to searches for innovative teaching models. Adoption of innovation, however, disrupts routine and breaks institutional inertia, requiring government employees to change their way of working. Introducing and embedding innovative methods for improving learning outcomes within state institutions is thus a major challenge. For NGO-led innovation to have largescale impact, we need to understand: (1) what factors facilitate its adoption by senior bureaucracy and political elites; and (2) how to incentivise district-level field staff and school principals and teachers, who have to change their ways of working, to implement the innovation? This paper presents an ethnographic study of Pratham, one of the most influential NGOs in the domain of education in India today, which has attracted growing attention for introducing an innovative teaching methodology— Teaching at the Right Level (TaRL) – with evidence of improved learning outcomes among primary-school students and adoption by a number of states in India. The case study suggests that while a combination of factors, including evidence of success, ease of method, the presence of a committed bureaucrat, and political opportunity are key to state adoption of an innovation, exposure to ground realities, hand holding and confidence building, informal interactions, provision of new teaching resources, and using existing lines of communication are core to ensuring the co-operation of those responsible for actual implementation. The Pratham case, however, also confirms existing concerns that even when NGO-led innovations are successfully implemented at a large scale, their replication across the state and their sustainability remain a challenge. Embedding good practice takes time; the political commitment leading to adoption of an innovation is often, however, tied to an immediate political opportunity being exploited by the political elites. Thus, when political opportunity rather than a genuine political will creates space for adoption of an innovation, state support for that innovation fades away before the new ways of working can replace the old habits. In contexts where states lack political will to improve learning outcomes, NGOs can only hope to make systematic change in state systems if, as in the case of Pratham, they operate as semi-social movements with large cadres of volunteers. The network of volunteers enables them to slow down and pick up again in response to changing political contexts, instead of quitting when state actors withdraw. Involving the community itself does not automatically lead to greater political accountability. Time-bound donor-funded NGO projects aiming to introduce innovation, however large in scale, simply cannot succeed in bringing about systematic change, because embedding change in state institutions lacking political will requires years of sustained engagement.
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McReynolds, Stephanie JH, Peter Verheyen, Terriruth Carrier, and Scott Warren. Library Impact Research Report: Distinct Academic Learning Communities at Syracuse University Libraries. Association of Research Libraries, July 2022. http://dx.doi.org/10.29242/report.syracuse2022.

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As part of ARL’s Research Library Impact Framework initiative, a team at Syracuse University Libraries conducted a study to explore the impact of embedding three “distinct academic learning communities” in Syracuse University’s Bird Library: the Blackstone LaunchPad; the Center for Learning and Student Success; and the Syracuse Office of Undergraduate Research and Creative Engagement. Three objectives guided the team: (1) explore how the libraries impact the communities; (2) determine how the communities impact the libraries; and (3) identify methods/metrics that could demonstrate reciprocal impact and be useful to the Association of Research Libraries (ARL). Impact was explored from multiple perspectives, including community directors, community participants, the libraries’ dean, and libraries’ staff. Results point to the value of the library as a central and interdisciplinary academic space for the communities, one that helps break down disciplinary borders by allowing community participants to more easily meet and collaborate with students from other schools and colleges.
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