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Journal articles on the topic 'Representations of space'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Brattka, Vasco. "Effective representations of the space of linear bounded operators." Applied General Topology 4, no. 1 (April 1, 2003): 115. http://dx.doi.org/10.4995/agt.2003.2014.

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<p>Representations of topological spaces by infinite sequences of symbols are used in computable analysis to describe computations in topological spaces with the help of Turing machines. From the computer science point of view such representations can be considered as data structures of topological spaces. Formally, a representation of a topological space is a surjective mapping from Cantor space onto the corresponding space. Typically, one is interested in admissible, i.e. topologically well-behaved representations which are continuous and characterized by a certain maximality condition. We discuss a number of representations of the space of linear bounded operators on a Banach space. Since the operator norm topology of the operator space is nonseparable in typical cases, the operator space cannot be represented admissibly with respect to this topology. However, other topologies, like the compact open topology and the Fell topology (on the operator graph) give rise to a number of promising representations of operator spaces which can partially replace the operator norm topology. These representations reflect the information which is included in certain data structures for operators, such as programs or enumerations of graphs. We investigate the sublattice of these representations with respect to continuous and computable reducibility. Certain additional conditions, such as finite dimensionality, let some classes of representations collapse, and thus, change the corresponding graph. Altogether, a precise picture of possible data structures for operator spaces and their mutual relation can be drawn.</p>

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Shapiro, Vadim. "Maintenance of Geometric Representations Through Space Decompositions." International Journal of Computational Geometry & Applications 07, no. 01n02 (February 1997): 21–56. http://dx.doi.org/10.1142/s0218195997000041.

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The ability to transform between distinct geometric representations is the key to success of multiple-representation modeling systems. But the existing theory of geometric modeling does not directly address or support construction, conversion, and comparison of geometric representations. A study of classical problems of CSG ↔ b-rep conversions, CSG optimization, and other representation conversions suggests a natural relationship between a representation scheme and an appropriate decomposition of space. We show that a hierarchy of space decompositions corresponding to different representation schemes can be used to enhance the theory and to develop a systematic approach to maintenance of geometric representations.

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3

Lee, Min Ho. "Theta functions on Hermitian symmetric domains and fock representations." Journal of the Australian Mathematical Society 74, no. 2 (April 2003): 201–34. http://dx.doi.org/10.1017/s1446788700003256.

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AbstractOne way of realizing representations of the Heisenberg group is by using Fock representations, whose representation spaces are Hilbert spaces of functions on complex vector space with inner products associated to points on a Siegel upper half space. We generalize such Fock representations using inner products associated to points on a Hermitian symmetric domain that is mapped into a Seigel upper half space by an equivariant holomorphic map. The representations of the Heisenberg group are then given by an automorphy factor associated to a Kuga fiber variety. We introduce theta functions associated to an equivariant holomorphic map and study connections between such generalized theta functions and Fock representations described above. Furthermore, we discuss Jacobi forms on Hermitian symmetric domains in connection with twisted torus bundles over symmetric spaces.

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BERGER, ULRICH, JENS BLANCK, and PETTER KRISTIAN KØBER. "Domain representations of spaces of compact subsets." Mathematical Structures in Computer Science 20, no. 2 (March 25, 2010): 107–26. http://dx.doi.org/10.1017/s096012950999034x.

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We present a method for constructing from a given domain representation of a space X with underlying domain D, a domain representation of a subspace of compact subsets of X where the underlying domain is the Plotkin powerdomain of D. We show that this operation is functorial over a category of domain representations with a natural choice of morphisms. We study the topological properties of the space of representable compact sets and isolate conditions under which all compact subsets of X are representable. Special attention is paid to admissible representations and representations of metric spaces.

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DE JEU, MARCEL, and MARTEN WORTEL. "POSITIVE REPRESENTATIONS OF FINITE GROUPS IN RIESZ SPACES." International Journal of Mathematics 23, no. 07 (June 27, 2012): 1250076. http://dx.doi.org/10.1142/s0129167x12500760.

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In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite-dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite-dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive G-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity turns out not to hold.

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Guruprasad, K., and C. S. Rajan. "space of representations." Duke Mathematical Journal 91, no. 1 (January 1998): 137–49. http://dx.doi.org/10.1215/s0012-7094-98-09107-4.

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Carlson, Thomas A., J. Brendan Ritchie, Nikolaus Kriegeskorte, Samir Durvasula, and Junsheng Ma. "Reaction Time for Object Categorization Is Predicted by Representational Distance." Journal of Cognitive Neuroscience 26, no. 1 (January 2014): 132–42. http://dx.doi.org/10.1162/jocn_a_00476.

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How does the brain translate an internal representation of an object into a decision about the object's category? Recent studies have uncovered the structure of object representations in inferior temporal cortex (IT) using multivariate pattern analysis methods. These studies have shown that representations of individual object exemplars in IT occupy distinct locations in a high-dimensional activation space, with object exemplar representations clustering into distinguishable regions based on category (e.g., animate vs. inanimate objects). In this study, we hypothesized that a representational boundary between category representations in this activation space also constitutes a decision boundary for categorization. We show that behavioral RTs for categorizing objects are well described by our activation space hypothesis. Interpreted in terms of classical and contemporary models of decision-making, our results suggest that the process of settling on an internal representation of a stimulus is itself partially constitutive of decision-making for object categorization.

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8

JORGENSEN, PALLE E. T. "REPRESENTATIONS OF LIE ALGEBRAS BUILT OVER HILBERT SPACE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, no. 03 (September 2011): 419–42. http://dx.doi.org/10.1142/s0219025711004468.

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Starting with a complex Hilbert space, using inductive limits, we build Lie algebras, and find families of representations. They include those often studied in mathematical physics in order to model quantum statistical mechanics or quantum fields. We explore natural actions on infinite tensor algebras T(H) built with a functorial construction, starting with a fixed Hilbert space H. While our construction applies also when H is infinite-dimensional, the case with N ≔ dim H finite is of special interest as the symmetry group we consider is then a copy of the non-compact Lie group U(N, 1). We give the tensor algebra T(H) the structure of a Hilbert space, i.e. the unrestricted infinite tensor product Fock space [Formula: see text]. The tensor algebra T(H) is naturally represented as acting by bounded operators on [Formula: see text], and U (N, 1) as acting as a unitary representation. From this we built a covariant system, and we explore how the fermion, the boson, and the q on Hilbert spaces are reduced by the representations. In particular we display the decomposition into irreducible representations of the naturally defined U (N, 1) representation.

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Bridgeman, Bruce. "Implicit and explicit representations of visual space." Behavioral and Brain Sciences 22, no. 5 (October 1999): 759–60. http://dx.doi.org/10.1017/s0140525x99272184.

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The visual system captures a unique contrast between implicit and explicit representation where the same event (location of a visible object) is coded in both ways in parallel. A method of differentiating the two representations is described using an illusion that affects only the explicit representation. Consistent with predictions, implicit information is available only from targets presently visible, but, surprisingly, a two-alternative decision does not disturb the implicit representation.

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van Wassenhove, Virginie. "Minding time in an amodal representational space." Philosophical Transactions of the Royal Society B: Biological Sciences 364, no. 1525 (July 12, 2009): 1815–30. http://dx.doi.org/10.1098/rstb.2009.0023.

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How long did it take you to read this sentence? Chances are your response is a ball park estimate and its value depends on how fast you have scanned the text, how prepared you have been for this question, perhaps your mood or how much attention you have paid to these words. Time perception is here addressed in three sections. The first section summarizes theoretical difficulties in time perception research, specifically those pertaining to the representation of time and temporal processing. The second section reviews non-exhaustively temporal effects in multisensory perception. Sensory modalities interact in temporal judgement tasks, suggesting that (i) at some level of sensory analysis, the temporal properties across senses can be integrated in building a time percept and (ii) the representational format across senses is compatible for establishing such a percept. In the last section, a two-step analysis of temporal properties is sketched out. In the first step, it is proposed that temporal properties are automatically encoded at early stages of sensory analysis, thus providing the raw material for the building of a time percept; in the second step, time representations become available to perception through attentional gating of the raw temporal representations and via re-encoding into abstract representations.

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Gurunath Shivakumar, Prashanth, and Panayiotis Georgiou. "Confusion2Vec: towards enriching vector space word representations with representational ambiguities." PeerJ Computer Science 5 (June 10, 2019): e195. http://dx.doi.org/10.7717/peerj-cs.195.

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Word vector representations are a crucial part of natural language processing (NLP) and human computer interaction. In this paper, we propose a novel word vector representation, Confusion2Vec, motivated from the human speech production and perception that encodes representational ambiguity. Humans employ both acoustic similarity cues and contextual cues to decode information and we focus on a model that incorporates both sources of information. The representational ambiguity of acoustics, which manifests itself in word confusions, is often resolved by both humans and machines through contextual cues. A range of representational ambiguities can emerge in various domains further to acoustic perception, such as morphological transformations, word segmentation, paraphrasing for NLP tasks like machine translation, etc. In this work, we present a case study in application to automatic speech recognition (ASR) task, where the word representational ambiguities/confusions are related to acoustic similarity. We present several techniques to train an acoustic perceptual similarity representation ambiguity. We term this Confusion2Vec and learn on unsupervised-generated data from ASR confusion networks or lattice-like structures. Appropriate evaluations for the Confusion2Vec are formulated for gauging acoustic similarity in addition to semantic–syntactic and word similarity evaluations. The Confusion2Vec is able to model word confusions efficiently, without compromising on the semantic-syntactic word relations, thus effectively enriching the word vector space with extra task relevant ambiguity information. We provide an intuitive exploration of the two-dimensional Confusion2Vec space using principal component analysis of the embedding and relate to semantic relationships, syntactic relationships, and acoustic relationships. We show through this that the new space preserves the semantic/syntactic relationships while robustly encoding acoustic similarities. The potential of the new vector representation and its ability in the utilization of uncertainty information associated with the lattice is demonstrated through small examples relating to the task of ASR error correction.

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Lourenco, Stella F., Janellen Huttenlocher, and Marina Vasilyeva. "Toddlers' Representations of Space." Psychological Science 16, no. 4 (April 2005): 255–59. http://dx.doi.org/10.1111/j.0956-7976.2005.01524.x.

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In the present study, we examined how people code object location when an object is hidden in an enclosed space. On object location tasks involving disorientation, viewers must code the location of an object in relation to the spatial environment because they cannot directly track their changing relation to the object. Recently, we showed that viewers also code their perspective relative to the entire space (inside vs. outside) in such tasks. To determine whether viewers code perspective whenever they must locate an object, we examined young children's performance on a task in which coding perspective would be difficult. Our task involved both disorientation and translation (i.e., movement from inside to outside the space or vice versa). When translation preceded disorientation, performance was comparable to performance on tasks with no translation. However, when disorientation preceded translation, performance was at chance. The implications of these findings for location coding are discussed.

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13

Shao, Zhong, and Andrew W. Appel. "Space-efficient closure representations." ACM SIGPLAN Lisp Pointers VII, no. 3 (July 1994): 150–61. http://dx.doi.org/10.1145/182590.156783.

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14

Vogt, Dietmar. "Power Series Space Representations of Nuclear Frechet Spaces." Transactions of the American Mathematical Society 319, no. 1 (May 1990): 191. http://dx.doi.org/10.2307/2001342.

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Vogt, Dietmar. "Power series space representations of nuclear Fréchet spaces." Transactions of the American Mathematical Society 319, no. 1 (January 1, 1990): 191–208. http://dx.doi.org/10.1090/s0002-9947-1990-1008704-5.

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Arslan, Bora, Alexander P. Goncharov, and Mefharet Kocatepe. "Sequence space representations of spaces of Whitney functions." Results in Mathematics 37, no. 1-2 (March 2000): 3–12. http://dx.doi.org/10.1007/bf03322508.

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Motos, Joaquín, and María Jesús Planells. "On sequence space representations of Hörmander–Beurling spaces." Journal of Mathematical Analysis and Applications 348, no. 1 (December 2008): 395–403. http://dx.doi.org/10.1016/j.jmaa.2008.07.031.

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18

Kausar, Samina, and Andre O. Falcao. "Analysis and Comparison of Vector Space and Metric Space Representations in QSAR Modeling." Molecules 24, no. 9 (April 30, 2019): 1698. http://dx.doi.org/10.3390/molecules24091698.

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The performance of quantitative structure–activity relationship (QSAR) models largely depends on the relevance of the selected molecular representation used as input data matrices. This work presents a thorough comparative analysis of two main categories of molecular representations (vector space and metric space) for fitting robust machine learning models in QSAR problems. For the assessment of these methods, seven different molecular representations that included RDKit descriptors, five different fingerprints types (MACCS, PubChem, FP2-based, Atom Pair, and ECFP4), and a graph matching approach (non-contiguous atom matching structure similarity; NAMS) in both vector space and metric space, were subjected to state-of-art machine learning methods that included different dimensionality reduction methods (feature selection and linear dimensionality reduction). Five distinct QSAR data sets were used for direct assessment and analysis. Results show that, in general, metric-space and vector-space representations are able to produce equivalent models, but there are significant differences between individual approaches. The NAMS-based similarity approach consistently outperformed most fingerprint representations in model quality, closely followed by Atom Pair fingerprints. To further verify these findings, the metric space-based models were fitted to the same data sets with the closest neighbors removed. These latter results further strengthened the above conclusions. The metric space graph-based approach appeared significantly superior to the other representations, albeit at a significant computational cost.

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Climent, Joan-Josep, Diego Napp, Raquel Pinto, and Verónica Requena. "Minimal State-Space Representation of Convolutional Product Codes." Mathematics 9, no. 12 (June 17, 2021): 1410. http://dx.doi.org/10.3390/math9121410.

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In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

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Chornozhuk, S. "The New Geometric “State-Action” Space Representation for Q-Learning Algorithm for Protein Structure Folding Problem." Cybernetics and Computer Technologies, no. 3 (October 27, 2020): 59–73. http://dx.doi.org/10.34229/2707-451x.20.3.6.

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Introduction. The spatial protein structure folding is an important and actual problem in computational biology. Considering the mathematical model of the task, it can be easily concluded that finding an optimal protein conformation in a three dimensional grid is a NP-hard problem. Therefore some reinforcement learning techniques such as Q-learning approach can be used to solve the problem. The article proposes a new geometric “state-action” space representation which significantly differs from all alternative representations used for this problem. The purpose of the article is to analyze existing approaches of different states and actions spaces representations for Q-learning algorithm for protein structure folding problem, reveal their advantages and disadvantages and propose the new geometric “state-space” representation. Afterwards the goal is to compare existing and the proposed approaches, make conclusions with also describing possible future steps of further research. Result. The work of the proposed algorithm is compared with others on the basis of 10 known chains with a length of 48 first proposed in [16]. For each of the chains the Q-learning algorithm with the proposed “state-space” representation outperformed the same Q-learning algorithm with alternative existing “state-space” representations both in terms of average and minimal energy values of resulted conformations. Moreover, a plenty of existing representations are used for a 2D protein structure predictions. However, during the experiments both existing and proposed representations were slightly changed or developed to solve the problem in 3D, which is more computationally demanding task. Conclusion. The quality of the Q-learning algorithm with the proposed geometric “state-action” space representation has been experimentally confirmed. Consequently, it’s proved that the further research is promising. Moreover, several steps of possible future research such as combining the proposed approach with deep learning techniques has been already suggested. Keywords: Spatial protein structure, combinatorial optimization, relative coding, machine learning, Q-learning, Bellman equation, state space, action space, basis in 3D space.

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Batsakis, Sotiris, Ilias Tachmazidis, and Grigoris Antoniou. "Representing Time and Space for the Semantic Web." International Journal on Artificial Intelligence Tools 26, no. 03 (June 2017): 1750015. http://dx.doi.org/10.1142/s0218213017600156.

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Representation of temporal and spatial information for the Semantic Web often involves qualitative defined information (i.e., information described using natural language terms such as “before” or “overlaps”) since precise dates or coordinates are not always available. This work proposes several temporal representations for time points and intervals and spatial topological representations in ontologies by means of OWL properties and reasoning rules in SWRL. All representations are fully compliant with existing Semantic Web standards and W3C recommendations. Although qualitative representations for temporal interval and point relations and spatial topological relations exist, this is the first work proposing representations combining qualitative and quantitative information for the Semantic Web. In addition to this, several existing and proposed approaches are compared using different reasoners and experimental results are presented in detail. The proposed approach is applied to topological relations (RCC5 and RCC8) supporting both qualitative and quantitative (i.e., using coordinates) spatial relations. Experimental results illustrate that reasoning performance differs greatly between different representations and reasoners. To the best of our knowledge, this is the first such experimental evaluation of both qualitative and quantitative Semantic Web temporal and spatial representations. In addition to the above, querying performance using SPARQL is evaluated. Evaluation results demonstrate that extracting qualitative relations from quantitative representations using reasoning rules and querying qualitative relations instead of directly querying quantitative representations increases performance at query time.

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Hõim, Terje, and D. A. Robbins. "Sectional representation of Banach modules and their multipliers." International Journal of Mathematics and Mathematical Sciences 2003, no. 13 (2003): 817–25. http://dx.doi.org/10.1155/s0161171203207109.

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LetXbe a Banach module over the commutative Banach algebraAwith maximal ideal spaceΔ. We show that there is a norm-decreasing representation ofXas a space of bounded sections in a Banach bundleπ:ℰ→Δ, whose fibers are quotient modules ofX. There is also a representation ofM(X), the space of multipliersT:A→X, as a space of sections in the same bundle, but this representation may not be continuous. These sectional representations subsume results of various authors over the past three decades.

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CATTANEO, U., and W. F. WRESZINSKI. "CONTRACTIONS OF LIE ALGEBRA REPRESENTATIONS." Reviews in Mathematical Physics 11, no. 10 (November 1999): 1179–207. http://dx.doi.org/10.1142/s0129055x99000374.

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A theory of contractions of Lie algebra representations on complex Hilbert spaces is proposed, based on Trotter's theory of approximating sequences of Banach spaces. Its main distinguishing feature is a careful definition of the carrier space of the limit Lie algebra representation. A set of quite general conditions on the contracting representations, satisfied in all known examples, is proven to be sufficient for the existence of such a representation. In order to show how natural the suggested framework is, the general theory is applied to the contraction of [Formula: see text] into the Lie algebra [Formula: see text] of the 3-dimensional Heisenberg group and to the related study of the limit N→∞ of a quantum system of N identical two-level particles.

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Turčalo, Sead, and Ado Kulović. "Contemporary Geopolitics and Digital Representations of Space." Croatian International Relations Review 24, no. 81 (May 1, 2018): 7–22. http://dx.doi.org/10.2478/cirr-2018-0001.

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Abstract This research is premised on two theoretical constructs: that maps do not objectively depict space and that traditional cartography produces a geopolitical narrative. The research aim is to investigate geopolitical influence in modern, digital representations of space, and vice versa. This paper is divided into three parts: In the first, the digital representation of space is introduced and explained, and two widely acknowledged digital cartographic services are established as the empirical foundation of the research – Google (Google Maps and Google Earth), designed by cartographic and geo-data professionals, and OpenStreetMap, built through crowdsourcing. In the second part, the geopolitical features of traditional cartography are discussed in the context of digital mapping, including ethnocentricity and hierarchical representations of space, similarities to geopolitische karte, and “minor geopolitics.” The final part asks and answers a key question about geopolitical subjectivity: “Who benefits from the geopolitical narratives in digital representations of space?”

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McGuffin, Michael J., and Jean-Marc Robert. "Quantifying the Space-Efficiency of 2D Graphical Representations of Trees." Information Visualization 9, no. 2 (May 21, 2009): 115–40. http://dx.doi.org/10.1057/ivs.2009.4.

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A mathematical evaluation and comparison of the space-efficiency of various 2D graphical representations of tree structures is presented. As part of the evaluation, a novel metric called the mean area exponent is introduced that quantifies the distribution of area across nodes in a tree representation, and that can be applied to a broad range of different representations of trees. Several representations are analyzed and compared by calculating their mean area exponent as well as the area they allocate to nodes and labels. Our analysis inspires a set of design guidelines as well as a few novel tree representations that are also presented.

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Duchoň, Miloslav, and Peter Maličký. "A Helly theorem for functions with values in metric spaces." Tatra Mountains Mathematical Publications 44, no. 1 (December 1, 2009): 159–68. http://dx.doi.org/10.2478/v10127-009-0056-z.

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Abstract We present a Helly type theorem for sequences of functions with values in metric spaces and apply it to representations of some mappings on the space of continuous functions. A generalization of the Riesz theorem is formulated and proved. More concretely, a representation of certain majored linear operators on the space of continuous functions into a complete metric space.

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Fyfe, N. R. "Contested Visions of a Modern City: Planning and Poetry in Postwar Glasgow." Environment and Planning A: Economy and Space 28, no. 3 (March 1996): 387–403. http://dx.doi.org/10.1068/a280387.

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The author draws on the distinctions between representations of space and spaces of representation contained in Lefebvre's Production of Space, and examines the postwar modernisation of Glasgow. In the first part of the paper he considers the images of the city presented in the city's two postwar master plans; one drawn up by central government, the other by local government. These two very different representations of the space of Glasgow as a modern city sparked off a political struggle over the making of the built environment which has left its imprint on the city's contemporary urban landscape. In the second part of the paper he uses the work of several Glasgow poets to illuminate the consequences of the modernisation process for the lived spaces of the city—the spaces of representation. The poets' reading of the modern city vividly illustrates the effects of the colonisation of concrete space by the abstract spaces of the master plans. Weaving together these two different, but closely related, discourses about the city—planning and poetry—he provides a specific example of the significance of Lefebvre's conceptual framework for making sense of the urban landscape of the modern city.

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Saito, Kyoji. "Algebraic representations of Teichmüller space." Kodai Mathematical Journal 17, no. 3 (1994): 609–26. http://dx.doi.org/10.2996/kmj/1138040055.

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Furl, Nicholas, Forida Begum, Justin Sulik, Francesca Pizzorni Ferrarese, Sarah Jans, and Caroline Woolley. "Face space representations of movement." NeuroImage 212 (May 2020): 116676. http://dx.doi.org/10.1016/j.neuroimage.2020.116676.

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Funk, Will, and David Lutzer. "Branch space representations of lines." Topology and its Applications 151, no. 1-3 (June 2005): 187–214. http://dx.doi.org/10.1016/j.topol.2003.12.020.

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Greatbatch, Ian. "Representations of Time and Space." Information Visualization 3, no. 1 (March 2004): 60–61. http://dx.doi.org/10.1057/palgrave.ivs.9500064.

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McGranaghan, Matt. "Representations of Space and Time." Cartographic Perspectives, no. 46 (September 1, 2003): 66–70. http://dx.doi.org/10.14714/cp46.487.

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Cotaescu, Ion I. "Canonical quantization of the covariant fields on de Sitter space–times." International Journal of Modern Physics A 33, no. 08 (March 20, 2018): 1830007. http://dx.doi.org/10.1142/s0217751x18300077.

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The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

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Poppenberg, Markus. "Tame sequence space representations of spaces of C∞—functions." Results in Mathematics 29, no. 3-4 (May 1996): 317–34. http://dx.doi.org/10.1007/bf03322228.

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KRISHNAMURTI, RAMESH. "Explicit design space?" Artificial Intelligence for Engineering Design, Analysis and Manufacturing 20, no. 2 (March 10, 2006): 95–103. http://dx.doi.org/10.1017/s0890060406060082.

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This paper examines the need for explicit representations of the design space, in response to Woodbury and Burrow. Specifically, their proposal for a particular search strategy, by means of which one can reuse past experiences explicitly represented by previously traversed paths, is examined. This is done by exploring issues with respect to design search and representation in general, while relating these to specific issues raised by Woodbury and Burrow. The paper concludes by suggesting that their arguments essentially point to devising an appropriate “programming language” for design.

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ALAGHMANDAN, MAHMOOD, and MASSOUD AMINI. "DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS." Glasgow Mathematical Journal 59, no. 2 (June 10, 2016): 421–35. http://dx.doi.org/10.1017/s0017089516000252.

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AbstractWe characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.

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Watkins, Ceri. "Representations of Space, Spatial Practices and Spaces of Representation: An Application of Lefebvre’s Spatial Triad." Culture and Organization 11, no. 3 (September 2005): 209–20. http://dx.doi.org/10.1080/14759550500203318.

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Kupsch, Joachim, and Oleg G. Smolyanov. "Functional Representations for Fock Superalgebras." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 02 (April 1998): 285–324. http://dx.doi.org/10.1142/s0219025798000168.

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The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.

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HILDEN, HUGH M., MARÍA TERESA LOZANO, and JOSÉ MARÍA MONTESINOS-AMILIBIA. "ON REPRESENTATIONS OF 2-BRIDGE KNOT GROUPS IN QUATERNION ALGEBRAS." Journal of Knot Theory and Its Ramifications 20, no. 10 (October 2011): 1419–83. http://dx.doi.org/10.1142/s0218216511009224.

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Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as E3 (Euclidean 3-space), H3 (hyperbolic 3-space) and E2, 1 (Minkowski 3-space), using quaternion algebra theory, are studied. We study the different representations of a 2-generator group in which the generators are send to conjugate elements, by analyzing the points of an algebraic variety, that we call the variety of affine c-representations ofG. Each point in this variety corresponds to a representation in the unit group of a quaternion algebra and their affine deformations.

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Gao, Fan. "Kazhdan–Lusztig representations and Whittaker space of some genuine representations." Mathematische Annalen 376, no. 1-2 (October 31, 2019): 289–358. http://dx.doi.org/10.1007/s00208-019-01925-1.

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Cieśliński, Jan L., and Artur Kobus. "Lax Triples for Integrable Surfaces in Three-Dimensional Space." Advances in Mathematical Physics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/8386420.

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We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean spaceE3. We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameterλare trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the groupSpin(6). Finally, the obtained results are interpreted in the context of the soliton surfaces approach.

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Bryant, R. M., R. Stöhr, and R. Zerck. "Metabelian Lie powers of group representations." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 2 (April 1994): 145–68. http://dx.doi.org/10.1017/s1446788700034819.

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AbstractAny representation of a group G on a vector space V extends uniquely to a representation of G on the free metabelian Lie algebra on V. In this paper we study such representations and make some group-theoretic applications.

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Moraglio, Alberto, and Dirk Sudholt. "Principled Design and Runtime Analysis of Abstract Convex Evolutionary Search." Evolutionary Computation 25, no. 2 (June 2017): 205–36. http://dx.doi.org/10.1162/evco_a_00169.

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Geometric crossover is a formal class of crossovers that includes many well-known recombination operators across representations. In previous work, it was shown that all evolutionary algorithms with geometric crossover (but no mutation) do the same form of convex search regardless of the underlying representation, the specific selection mechanism, offspring distribution, search space, and problem at hand. Furthermore, it was suggested that the generalised convex search could perform well on generalised forms of concave and approximately concave fitness landscapes regardless of the underlying space and representation. In this article, we deepen this line of enquiry and study the runtime of generalised convex search on concave fitness landscapes. This is a first step toward linking a geometric theory of representations and runtime analysis in the attempt to (1) set the basis for a more general, unified approach for the runtime analysis of evolutionary algorithms across representations, and (2) identify the essential matching features of evolutionary search behaviour and landscape topography that cause polynomial performance. We present a general runtime result that can be systematically instantiated to specific search spaces and representations and present its specifications to three search spaces. As a corollary, we obtain that the convex search algorithm optimises LeadingOnes in [Formula: see text] fitness evaluations, which is faster than all unbiased unary black box algorithms.

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Aase, Tor H. "Symbolic Space: Representations of Space in Geography and Anthropology." Geografiska Annaler. Series B, Human Geography 76, no. 1 (1994): 51. http://dx.doi.org/10.2307/490497.

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Bansal, Suguman, Yong Li, Lucas Tabajara, and Moshe Vardi. "Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 06 (April 3, 2020): 9766–74. http://dx.doi.org/10.1609/aaai.v34i06.6528.

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LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical role in synthesis as well.Therefore, effective resolution of the bottleneck for synthesis requires the conversion to be time and memory performant, and prevent state-space explosion. Current conversion approaches, however, which are based either on explicit-state representation or symbolic-state representation, fail to address these necessities adequately at scale: Explicit-state approaches generate minimal DFA but are slow due to expensive DFA minimization. Symbolic-state representations can be succinct, but due to the lack of DFA minimization they generate such large state spaces that even their symbolic representations cannot compensate for the blow-up.This work proposes a hybrid representation approach for the conversion. Our approach utilizes both explicit and symbolic representations of the state-space, and effectively leverages their complementary strengths. In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck. A comprehensive empirical evaluation on conversion and synthesis benchmarks supports the merits of our hybrid approach.

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Popal, Haroon, Yin Wang, and Ingrid R. Olson. "A Guide to Representational Similarity Analysis for Social Neuroscience." Social Cognitive and Affective Neuroscience 14, no. 11 (November 1, 2019): 1243–53. http://dx.doi.org/10.1093/scan/nsz099.

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Abstract Representational similarity analysis (RSA) is a computational technique that uses pairwise comparisons of stimuli to reveal their representation in higher-order space. In the context of neuroimaging, mass-univariate analyses and other multivariate analyses can provide information on what and where information is represented but have limitations in their ability to address how information is represented. Social neuroscience is a field that can particularly benefit from incorporating RSA techniques to explore hypotheses regarding the representation of multidimensional data, how representations can predict behavior, how representations differ between groups and how multimodal data can be compared to inform theories. The goal of this paper is to provide a practical as well as theoretical guide to implementing RSA in social neuroscience studies.

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Byrne, Patrick, and Suzanna Becker. "A Principle for Learning Egocentric-Allocentric Transformation." Neural Computation 20, no. 3 (March 2008): 709–37. http://dx.doi.org/10.1162/neco.2007.10-06-361.

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Numerous single-unit recording studies have found mammalian hippocampal neurons that fire selectively for the animal's location in space, independent of its orientation. The population of such neurons, commonly known as place cells, is thought to maintain an allocentric, or orientation-independent, internal representation of the animal's location in space, as well as mediating long-term storage of spatial memories. The fact that spatial information from the environment must reach the brain via sensory receptors in an inherently egocentric, or viewpoint-dependent, fashion leads to the question of how the brain learns to transform egocentric sensory representations into allocentric ones for long-term memory storage. Additionally, if these long-term memory representations of space are to be useful in guiding motor behavior, then the reverse transformation, from allocentric to egocentric coordinates, must also be learned. We propose that orientation-invariant representations can be learned by neural circuits that follow two learning principles: minimization of reconstruction error and maximization of representational temporal inertia. Two different neural network models are presented that adhere to these learning principles, the first by direct optimization through gradient descent and the second using a more biologically realistic circuit based on the restricted Boltzmann machine (Hinton, 2002; Smolensky, 1986). Both models lead to orientation-invariant representations, with the latter demonstrating place-cell-like responses when trained on a linear track environment.

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Ren, Yudong. "Solving Integral Representations Problems for the Stationary Schrödinger Equation." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/715252.

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When solutions of the stationary Schrödinger equation in a half-space belong to the weighted Lebesgue classes, we give integral representations of them, which imply known representation theorems of classical harmonic functions in a half-space.

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FARSI, CARLA, ELIZABETH GILLASPY, PALLE JORGENSEN, SOORAN KANG, and JUDITH PACKER. "Monic representations of finite higher-rank graphs." Ergodic Theory and Dynamical Systems 40, no. 5 (September 6, 2018): 1238–67. http://dx.doi.org/10.1017/etds.2018.79.

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In this paper, we define the notion of monic representation for the$C^{\ast }$-algebras of finite higher-rank graphs with no sources, and we undertake a comprehensive study of them. Monic representations are the representations that, when restricted to the commutative$C^{\ast }$-algebra of the continuous functions on the infinite path space, admit a cyclic vector. We link monic representations to the$\unicode[STIX]{x1D6EC}$-semibranching representations previously studied by Farsi, Gillaspy, Kang and Packer (Separable representations, KMS states, and wavelets for higher-rank graphs.J. Math. Anal. Appl. 434 (2015), 241–270) and also provide a universal representation model for non-negative monic representations.

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Moro, Valentina, Michela Corbella, Silvio Ionta, Federico Ferrari, and Michele Scandola. "Cognitive Training Improves Disconnected Limbs’ Mental Representation and Peripersonal Space after Spinal Cord Injury." International Journal of Environmental Research and Public Health 18, no. 18 (September 12, 2021): 9589. http://dx.doi.org/10.3390/ijerph18189589.

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Paraplegia following spinal cord injury (SCI) affects the mental representation and peripersonal space of the paralysed body parts (i.e., lower limbs). Physical rehabilitation programs can improve these aspects, but the benefits are mostly partial and short-lasting. These limits could be due to the absence of trainings focused on SCI-induced cognitive deficits combined with traditional physical rehabilitation. To test this hypothesis, we assessed in 15 SCI-individuals the effects of adding cognitive recovery protocols (motor imagery–MI) to standard physical rehabilitation programs (Motor + MI training) on mental body representations and space representations, with respect to physical rehabilitation alone (control training). Each training comprised at least eight sessions administered over two weeks. The status of participants’ mental body representation and peripersonal space was assessed at three time points: before the training (T0), after the training (T1), and in a follow-up assessment one month later (T2). The Motor + MI training induced short-term recovery of peripersonal space that however did not persist at T2. Body representation showed a slower neuroplastic recovery at T2, without differences between Motor and the Motor + MI. These results show that body and space representations are plastic after lesions, and open new rehabilitation perspectives.

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