Academic literature on the topic 'Multidimensional symbolic systems'
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Journal articles on the topic "Multidimensional symbolic systems"
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Quadrat, Alban, and Eva Zerz. "Special issue on symbolic methods in multidimensional systems theory." Multidimensional Systems and Signal Processing 26, no. 2 (February 17, 2015): 337–38. http://dx.doi.org/10.1007/s11045-015-0313-z.
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Hochman, Michael. "On the dynamics and recursive properties of multidimensional symbolic systems." Inventiones mathematicae 176, no. 1 (December 4, 2008): 131–67. http://dx.doi.org/10.1007/s00222-008-0161-7.
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BERTHÉ, VALÉRIE, JÉRÉMIE BOURDON, TIMO JOLIVET, and ANNE SIEGEL. "A combinatorial approach to products of Pisot substitutions." Ergodic Theory and Dynamical Systems 36, no. 6 (March 19, 2015): 1757–94. http://dx.doi.org/10.1017/etds.2014.141.
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We define a generic algorithmic framework to prove a pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of the three-letter substitutions associated with the multidimensional continued fraction algorithms of Brun and Jacobi–Perron. Our tools consist in a reformulation of some combinatorial criteria (coincidence conditions), in terms of properties of discrete plane generation using multidimensional (dual) substitutions. We also deduce some topological and dynamical properties of the Rauzy fractals, of the underlying symbolic dynamical systems, as well as some number-theoretical properties of the associated Pisot numbers.
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Huang, Bo, and Wei Niu. "Analysis of Snapback Repellers Using Methods of Symbolic Computation." International Journal of Bifurcation and Chaos 29, no. 04 (April 2019): 1950054. http://dx.doi.org/10.1142/s0218127419500548.
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This paper presents an algebraic criterion for determining whether all the zeros of a given polynomial are outside the unit circle in the complex plane. This criterion is used to deduce critical algebraic conditions for the occurrence of chaos in multidimensional discrete dynamical systems based on a modified Marotto’s theorem developed by Li and Chen (called “Marotto–Li–Chen theorem”). Using these algebraic conditions we reduce the problem of analyzing chaos induced by snapback repeller to an algebraic problem, and propose an algorithmic approach to solve this algebraic problem by means of symbolic computation. The proposed approach is effective as shown by several examples and can be used to determine the possibility that all the fixed points are snapback repellers.
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KUZNETSOV, YU A. "PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS." International Journal of Bifurcation and Chaos 15, no. 11 (November 2005): 3535–46. http://dx.doi.org/10.1142/s0218127405014209.
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Simple computational formulas are derived for the two-, three-, and four-order coefficients of the smooth normal form on the center manifold at the Bogdanov–Takens (nonsemisimple double-zero) bifurcation for n-dimensional systems with arbitrary n ≥ 2. These formulas are equally suitable for both symbolic and numerical evaluation and allow one to classify all codim 3 Bogdanov–Takens bifurcations in generic multidimensional ODEs. They are also applicable to systems with symmetries. We perform no preliminary linear transformations but use only critical (generalized) eigenvectors of the linearization matrix and its transpose. The derivation combines the approximation of the center manifold with the normalization on it. Three known models are used as test examples to demonstrate advantages of the method.
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HOCHMAN, MICHAEL. "On notions of determinism in topological dynamics." Ergodic Theory and Dynamical Systems 32, no. 1 (September 6, 2011): 119–40. http://dx.doi.org/10.1017/s0143385710000738.
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AbstractWe examine the relations between topological entropy, invertibility, and prediction in topological dynamics. We show that topological determinism in the sense of Kamińsky, Siemaszko, and Szymański imposes no restriction on invariant measures except zero entropy. Also, we develop a new method for relating topological determinism and zero entropy, and apply it to obtain a multidimensional analog of this theory. We examine prediction in symbolic dynamics and show that while the condition that each past admits a unique future only occurs in finite systems, the condition that each past has a bounded number of futures imposes no restriction on invariant measures except zero entropy. Finally, we give a negative answer to a question of Eli Glasner by constructing a zero-entropy system with a globally supported ergodic measure in which every point has multiple preimages.
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Wójcik, Piotr, Krzysztof Obłój, Aleksandra Wąsowska, and Szymon Wierciński. "Corporate acceleration process: a systems psychodynamics perspective." Journal of Organizational Change Management 33, no. 6 (September 29, 2020): 1163–80. http://dx.doi.org/10.1108/jocm-05-2019-0136.
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PurposeThe purpose of this paper is to explore the emotional dynamics of the corporate acceleration process, using the systems psychodynamics perspective.Design/methodology/approachThe study applies inductive multiple case study of embedded 10 cases of corporate acceleration, covering both incumbent and startup perspectives, occurring in the context of a corporate accelerator.FindingsWe find that (1) the process of corporate acceleration involves three phases, each of them is dominated by a different emotional state (hope, anxiety and acceptance), triggering different behavioral responses; (2) as a means to deal with negative emotions, entrepreneurs and corporate acceleration program's team members develop different mechanisms of dealing with contradictories in subsequent acceleration phases (defense and copying mechanisms), which are reflected in their behaviors. Coping mechanisms with goal reformulation (i.e. refocus from the officially declared “open innovation” goals toward mainly symbolic ones) is an effective strategy to manage negative emotions in third phase of the acceleration.Research limitations/implicationsOur sample is limited to two relatively similar accelerators established by telecom companies, and therefore, our theoretical and practical conclusions cannot be generalized.Practical implicationsWe supplement the studies of corporate accelerators that imply how to design them better and improve decision-making rules with recommendation that in order to improve their effectiveness in terms of learning and innovations, their managers need not only to learn how to manage structural and procedural differences but also how to overcome social defenses triggered by corporate–startups cooperation.Originality/valueBy documenting a multidimensional impact of acceleration process, and especially shedding light on psychodynamic aspects behind such liaisons, this paper contributes to richer understanding of corporate–startup relationships, typically examined through a rationalistic lens of strategy literature. The study contributes to interorganizational research and open innovation literature, by showing that corporate acceleration process is marked by phases based on the type of emotions intertwined with the nature and dynamism of its life cycle. It indicates how these emotions are managed depending on their type.
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Diegmiller, Rocky, Lun Zhang, Marcio Gameiro, Justinn Barr, Jasmin Imran Alsous, Paul Schedl, Stanislav Y. Shvartsman, and Konstantin Mischaikow. "Mapping parameter spaces of biological switches." PLOS Computational Biology 17, no. 2 (February 8, 2021): e1008711. http://dx.doi.org/10.1371/journal.pcbi.1008711.
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Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection inDrosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches.
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Pokrovskaia, N. N., D. V. Golohvastov, and M. Yu Ababkova. "Innovative Growth of the Virtual Economy: A Regulatory Paradigm Shift." Economics and Management 27, no. 8 (September 21, 2021): 576–92. http://dx.doi.org/10.35854/1998-1627-2021-8-576-592.
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Aim. The presented study aims to harmonize the understanding of the innovative growth of the virtual economy within the framework of a regulatory approach from the perspective of the evolution of regulatory mechanisms.Tasks. The authors identify the major conditions and elements of the virtual economy; clarify the definition of the virtual economy; determine the essential characteristics of the innovative growth of the virtual economy; develop a multidimensional matrix of tools for measuring the innovative growth of the virtual economy within the framework of a regulatory approach.Methods. This study uses the methods of scientific analysis and synthesis as well as comparative and systems approach to examine the reflection of innovative growth in the evolution of regulatory mechanisms that determine economic behavior.Results. The acceleration of economic virtualization during the 2020–2021 pandemic has exacerbated the need for a scientific analysis of the ways and directions of innovative economic growth with allowance for intangible, primarily virtual factors, which include traditional symbolic components implemented on the basis of digital tools. The conducted analysis makes it possible to identify four main dimensions that determine directions for the innovative growth of the virtual economy: adaptation to new categories of entities to the extent of personification based on big data; development of new behavioral models; development of institutions and ecosystems; prioritization of a meaningful requirement for harmony and aesthetics on the part of users.Conclusions. A study of the multidimensional model of innovative growth of the virtual economy will make it possible to improve both the decision-making of individual and group entities, and the regulatory mechanisms used by the government.
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Martin, Andrea E. "A Compositional Neural Architecture for Language." Journal of Cognitive Neuroscience 32, no. 8 (August 2020): 1407–27. http://dx.doi.org/10.1162/jocn_a_01552.
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Hierarchical structure and compositionality imbue human language with unparalleled expressive power and set it apart from other perception–action systems. However, neither formal nor neurobiological models account for how these defining computational properties might arise in a physiological system. I attempt to reconcile hierarchy and compositionality with principles from cell assembly computation in neuroscience; the result is an emerging theory of how the brain could convert distributed perceptual representations into hierarchical structures across multiple timescales while representing interpretable incremental stages of (de)compositional meaning. The model's architecture—a multidimensional coordinate system based on neurophysiological models of sensory processing—proposes that a manifold of neural trajectories encodes sensory, motor, and abstract linguistic states. Gain modulation, including inhibition, tunes the path in the manifold in accordance with behavior and is how latent structure is inferred. As a consequence, predictive information about upcoming sensory input during production and comprehension is available without a separate operation. The proposed processing mechanism is synthesized from current models of neural entrainment to speech, concepts from systems neuroscience and category theory, and a symbolic-connectionist computational model that uses time and rhythm to structure information. I build on evidence from cognitive neuroscience and computational modeling that suggests a formal and mechanistic alignment between structure building and neural oscillations, and moves toward unifying basic insights from linguistics and psycholinguistics with the currency of neural computation.
Dissertations / Theses on the topic "Multidimensional symbolic systems"
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Johnson, Dean S. "Coprimeness in multidimensional system theory and symbolic computation." Thesis, Loughborough University, 1993. https://dspace.lboro.ac.uk/2134/31933.
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During the last twenty years the theory of linear algebraic and high-order differential equation systems has been greatly researched. Two commonly used types of system description are the so-called matrix fraction description (MFD) and the Rosenbrock system matrix (RSM); these are defined by polynomial matrices in one indeterminate. Many of the system's physical properties are encoded as algebraic properties of these polynomial matrices. The theory is well developed and the structure of such systems is well understood. Analogues of these 1-D realisations can be set up for many dimensional systems resulting in polynomial matrices in many indeterminates. The scarcity of detailed algebraic results for such matrices has limited the understanding of such systems.
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Aubrun, Nathalie. "Dynamique symbolique des systèmes 2D et des arbres infinis." Phd thesis, Université Paris-Est, 2011. http://pastel.archives-ouvertes.fr/pastel-00664331.
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Cette thèse est consacrée à l'étude des décalages, ou encore systèmes dynamiques symboliques, définis sur certains monoïdes finiment présentés, $Z^d$ d'une part et les arbres d'autre part. Le principal résultat concernant les décalages multidimensionnels établit que tout décalage effectif de dimension d est obtenu par facteur et sous-action projective d'un décalage de type fini de dimension d+1. De ce résultat nous déduisons que les décalages S-adiques multidimensionnels donnés par une suite effective de substitutions sont sofiques. Sur les décalages d'arbres nous montrons un théorème de décomposition, qui permet d'écrire une conjugaison entre deux décalages d'arbres quelconques comme une suite finie d'opérations élémentaires, les fusions entrantes et les éclatements entrants. De ce théorème, associé à la commutation des fusions entrantes, nous déduisons la décidabilité du problème de conjugaison entre deux décalages d'arbres de type fini. Nous nous intéressons ensuite à la classe des décalages d'arbres sofiques, qui sont exactement ceux reconnus par des automates d'arbres montants dans lesquels tous les états sont à la fois initiaux et finaux. Nous montrons l'existence d'un unique automate d'arbres déterministe, réduit, irréductible et synchronisé qui reconnaît un décalage d'arbres sofique. Enfin nous montrons que l'appartenance à la sous-classe des décalages d'arbres AFT est décidable
Books on the topic "Multidimensional symbolic systems"
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Johnson, Dean S. Coprimeness in multidimensional system theory and symbolic computation. 1993.
Find full textBook chapters on the topic "Multidimensional symbolic systems"
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Goldsmith, Ronald E. "Online Consumer Behavior." In End-User Computing, 141–47. IGI Global, 2008. http://dx.doi.org/10.4018/978-1-59904-945-8.ch013.
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One convenient way of describing consumer behavior both off-line and online is to present the topic as a model representing the steps typical consumers go through when they acquire the goods and services they desire. These steps are Need Recognition, Information Search, Pre-purchase Alternative Evaluation, Purchase, Consumption and Post Consumption Evaluation (Blackwell, Miniard & Engel, 2001). Although not every consumer goes through every step for every purchase, this model is a useful heuristic for organizing the study of consumer behavior and serves as a way to describe online consumer behavior as well. In the Need Recognition stage consumer behavior is stimulated by needs and wants. Needs are the abstract categories that consumers require in order to survive, function and thrive. Wants are the specific objects or mechanisms that consumers learn will enable them to satisfy their needs. Consumer needs are few, universal and inborn. Wants are acquired through individual learning histories defined by the time, place and context of the consumers’ life. Consequently, wants are many, individual and varied. Each consumer is born with the same needs and learns what will satisfy those needs through the experience of being reared within a specific society, time and place. Marketers recognize that consumers have shared needs and seek to develop brands as the specific want-satisfying ways in which consumers can gratify their needs. Table 1 presents a summary of consumer needs and wants (Foxall & Goldsmith, 1997). Physiological needs derive from the fact that consumers are physiological creatures. The social needs come from the fact that consumers are social animals. Hedonic needs describe the needs consumers have for pleasurable sensations for the five senses. Experiential needs arise because consumers are saturated with feelings and emotions that they constantly seek to modify. Cognitive needs come from the curious, inquiring cerebral cortex that wants to know about its environment. Finally, consumers have egos, a sense of self-identity, they want to express, usually through symbols. Each consumer is born with these mind/body “systems” and spends much time and energy seeking to satisfy the requirements these systems impose. Products (goods, services and information) can be multidimensional (Freiden, Goldsmith, Hofacker, & Takacs, 1998). That is, consumption of a given product can simultaneously satisfy more than one need, as buying and wearing an item of clothing protects the wearer from the elements (physiological), attracts the opposite sex (social), is comfortable to the skin (hedonic), makes the wearer feel sexy (experiential) and represents the self-concept and values of the wearer (psychological). Consuming a news magazine might satisfy cognitive needs as well as psychologically symbolic ones; the reader acquires some desired information and shows that he/she is a responsible citizen. Moreover, consumers might buy many different products to satisfy the same needs, as where designer brand names are wanted for clothing, furniture, perfumes and cars to symbolize social status. This theory of motivation can be used to explain the motivations for participation in virtual communities. Belonging to a virtual community fulfills some of the social need for belonging and fellowship. Group participation can yield feelings of fun, excitement and pleasure. The community can be an important source of information that can satisfy the cognitive need to know. Membership can be used symbolically to express identity. Thus, much like the consumption of goods, services
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Schmid, Hans-Jörg. "Association and cognitive processing." In The Dynamics of the Linguistic System, 43–73. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198814771.003.0004.
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The chapter discusses the cognitive activities which are performed in usage events and entrenched, if repeated. The key cognitive activity is association in the associative network, with four types of associations (symbolic, paradigmatic, syntagmatic, paradigmatic) being activated in predictive and probabilistic lexical and syntactic processing. Processing and representation take place in the form of entrenched patterns of associations. Language processing is explained in terms of the activation of associations. This activation is probabilistic and follows the principle of predictive coding. Lexical-semantic processing is understood in terms of dynamic and transient multidimensional activation patterns in the associative network targeting attractors in the network. A highly dynamic and flexible associative model of syntactic processing is proposed. It is first developed with reference to two examples and then described in general form. The model is very important for the understanding of entrenchment to be discussed in Part III.
Conference papers on the topic "Multidimensional symbolic systems"
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Augusta, Petr, and Zdenek Hurak. "Polmat library now within Symbolic Math Toolbox for Matlab in multidimensional systems computations." In 2009 International Workshop on Multidimensional (nD) Systems (nD. IEEE, 2009. http://dx.doi.org/10.1109/nds.2009.5191494.
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Butcher, Eric A., and S. C. Sinha. "Symbolic Bifurcation Boundaries and Time-Dependent Resonance Sets of Time-Periodic Nonlinear Systems." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8315.
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Abstract A recent computational technique is utilized for symbolic computation of local stability boundaries and bifurcation surfaces for nonlinear multidimensional time-periodic dynamical systems as an explicit function of the system parameters. This is made possible by the recent development of a symbolic computational algorithm for approximating the parameter-dependent fundamental solution matrix of linear time-periodic systems. By evaluating this matrix at the end of the principal period, the parameter-dependent Floquet Transition Matrix (FTM), or the linear part of the Poincaré map, is obtained. The subsequent use of well-known criteria for the local stability and bifurcation conditions of equilibria and periodic solutions enables one to obtain the equations for the bifurcation surfaces in the parameter space as polynomials of the system parameters. Because this method is not based on expansion in terms of a small parameter, it can successfully be applied to periodic systems whose internal excitation is strong. In addition, the time-dependent normal forms and resonance sets for one and two degree-of-freedom time-periodic nonlinear systems are analyzed. For this purpose, the Liapunov-Floquet (L-F) transformation is employed which transforms the periodic variational equations into an equivalent form in which the linear system matrix is constant. Both quadratic and cubic nonlinearities are investigated, and all possible cases for the single degree-of-freedom case are studied. The above algorithm for computing stability boundaries may also be employed to compute the time-dependent resonance sets of zero measure in the parameter space. Two illustrative example problems, viz., a parametrically excited simple pendulum and a double inverted pendulum subjected to a periodic follower force, are included.
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Cotta, Renato M., Joa˜o N. N. Quaresma, Leandro A. Sphaier, and Carolina P. Naveira-Cotta. "Unified Integral Transform Approach in the Hybrid Solution of Multidimensional Nonlinear Convection-Diffusion Problems." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22396.
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The present work summarizes the theory and describes the algorithm related to the construction of an open source mixed symbolic-numerical computational code named UNIT — Unified Integral Transforms, that provides a development platform for finding solutions of linear and nonlinear partial differential equations via integral transforms. The reported research was performed by making use of the symbolic computational system Mathematica v.7.0 and the hybrid numerical-analytical methodology Generalized Integral Transform Technique — GITT. The aim here is to illustrate the robust and precision controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source code. Test cases are selected based on nonlinear multi-dimensional formulations of the Burgers equations, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects and computational behaviors of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code.
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Fukuda, Shuichi. "Pattern Driven Decision Making Approach to Engineering Systems Design: Concept." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37989.
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This paper points out that in team decision making where members come from many different fields, pattern driven decision making approach is very much effective. It not only satisfies each member, but it also leads to thought-to-be-the most reasonable decision. AI succeeded by introducing pattern based reasoning, but in traditional AI, its patterns are expressed in the form of a list, i.e., the sequence of symbols. In other words, patterns in AI are one-dimensional. But increasing complexities and complicatedness call for many different kinds of knowledge and experience so that such one dimensional pattern matching does not really provide an adequate tool for decision making for problems which involve many different disciplines. In this paper, it is pointed out that if we introduce Mahalanobis-Taguchi System, which permits multidimensional pattern matching, it facilitates team decision making for a problem which needs a wide variety of expertise to solve and to which rational approaches are difficult to apply.