Relevant bibliographies by topics / Combinatorial dynamical systems

Academic literature on the topic 'Combinatorial dynamical systems'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Combinatorial dynamical systems"

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Wisniewski, Rafael. "Combinatorial Abstractions of Dynamical Systems." Electronic Proceedings in Theoretical Computer Science 124 (August 22, 2013): 5–8. http://dx.doi.org/10.4204/eptcs.124.2.

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Díaz, Rafael, and Sergio Villamarín. "Combinatorial micro–macro dynamical systems." São Paulo Journal of Mathematical Sciences 14, no. 1 (August 29, 2018): 66–122. http://dx.doi.org/10.1007/s40863-018-0103-2.

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NEKRASHEVYCH, VOLODYMYR. "Combinatorial models of expanding dynamical systems." Ergodic Theory and Dynamical Systems 34, no. 3 (January 24, 2013): 938–85. http://dx.doi.org/10.1017/etds.2012.163.

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AbstractWe prove homotopical rigidity of expanding dynamical systems, by showing that they are determined by a group-theoretic invariant. We use this to show that the Julia set of every expanding dynamical system is an inverse limit of simplicial complexes constructed by inductive cut-and-paste rules. Moreover, the cut-and-paste rules can be found algorithmically from the algebraic invariant.
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Forman, Robin. "Combinatorial vector fields and dynamical systems." Mathematische Zeitschrift 228, no. 4 (August 1998): 629–81. http://dx.doi.org/10.1007/pl00004638.

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Harmer, Russ, Vincent Danos, Jérôme Feret, Jean Krivine, and Walter Fontana. "Intrinsic information carriers in combinatorial dynamical systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 3 (September 2010): 037108. http://dx.doi.org/10.1063/1.3491100.

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Banzhaf, Wolfgang. "Artificial Chemistries – Towards Constructive Dynamical Systems." Solid State Phenomena 97-98 (April 2004): 43–50. http://dx.doi.org/10.4028/www.scientific.net/ssp.97-98.43.

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In this contribution we consider constructive dynamical systems, taking one particular Artificial Chemistry as an example. We argue that constructive dynamical systems are in fact widespread in combinatorial spaces of Artificial Chemistries.
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Suzuki, Tomoya. "Dynamical Combinatorial Optimization for Predicting Multivariate Complex Systems." Journal of Signal Processing 16, no. 6 (2012): 537–46. http://dx.doi.org/10.2299/jsp.16.537.

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Yang, Insoon, Samuel A. Burden, Ram Rajagopal, S. Shankar Sastry, and Claire J. Tomlin. "Approximation Algorithms for Optimization of Combinatorial Dynamical Systems." IEEE Transactions on Automatic Control 61, no. 9 (September 2016): 2644–49. http://dx.doi.org/10.1109/tac.2015.2504867.

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Dey, Tamal K., Marian Mrozek, and Ryan Slechta. "Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems." SIAM Journal on Applied Dynamical Systems 21, no. 2 (April 11, 2022): 817–39. http://dx.doi.org/10.1137/21m143162x.

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Morrison, Rebecca E., Eric J. Friedman, and Adam S. Landsberg. "Combinatorial games with a pass: A dynamical systems approach." Chaos: An Interdisciplinary Journal of Nonlinear Science 21, no. 4 (December 2011): 043108. http://dx.doi.org/10.1063/1.3650234.

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Dissertations / Theses on the topic "Combinatorial dynamical systems"

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Forrest, Alan Hunter. "Recurrence in dynamical systems : a combinatorial approach /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487682558446011.

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Tiozzo, Giulio. "Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10891.

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The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued fractions. We develop a combinatorial calculus to describe the bifurcation set of both families and prove they are isomorphic. As a corollary, we establish a series of results describing the behavior of entropy as a function of the parameter. One of the most important applications is the relation between the topological entropy of quadratic polynomials and the Hausdorff dimension of sets of external rays landing on principal veins of the Mandelbrot set.
Mathematics
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Ziegler, Caleb. "On Factors of Rank One Subshifts." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1157623/.

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Rank one subshifts are dynamical systems generated by a regular combinatorial process based on sequences of positive integers called the cut and spacer parameters. Despite the simple process that generates them, rank one subshifts comprise a generic set and are the source of many counterexamples. As a result, measure theoretic rank one subshifts, called rank one transformations, have been extensively studied and investigations into rank one subshifts been the basis of much recent work. We will answer several open problems about rank one subshifts. We completely classify the maximal equicontinuous factor for rank one subshifts, so that this factor can be computed from the parameters. We use these methods to classify when large classes of rank one subshifts have mixing properties. Also, we completely classify the situation when a rank one subshift can be a factor of another rank one subshift.
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Rothlisberger, Matthew Samuel. "Ergodic and Combinatorial Proofs of van der Waerden's Theorem." Scholarship @ Claremont, 2010. http://scholarship.claremont.edu/cmc_theses/14.

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Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.
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Tastan, Mesut. "Analysis And Prediction Of Gene Expression Patterns By Dynamical Systems, And By A Combinatorial Algorithm." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606672/index.pdf.

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Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun&rsquo
s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.
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Paskauskas, Rytis. "Chaotic Scattering in Rydberg Atoms, Trapping in Molecules." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19809.

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We investigate chaotic ionization of highly excited hydrogen atom in crossed electric and magnetic fields (Rydberg atom) and intra-molecular relaxation in planar carbonyl sulfide (OCS) molecule. The underlying theoretical framework of our studies is dynamical systems theory and periodic orbit theory. These theories offer formulae to compute expectation values of observables in chaotic systems with best accuracy available in given circumstances, however they require to have a good control and reliable numerical tools to compute unstable periodic orbits. We have developed such methods of computation and partitioning of the phase space of hydrogen atom in crossed at right angles electric and magnetic fields, represented by a two degree of freedom (dof) Hamiltonian system. We discuss extensions to a 3-dof setting by developing the methodology to compute unstable invariant tori, and applying it to the planar OCS, represented by a 3-dof Hamiltonian. We find such tori important in explaining anomalous relaxation rates in chemical reactions. Their potential application in Transition State Theory is discussed.
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Lan, Yueheng. "Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view." Diss., Available online, Georgia Institute of Technology, 2004:, 2004. http://etd.gatech.edu/theses/available/etd-10282004-154606/unrestricted/lan%5Fyueheng%5F200412%5Fphd.pdf.

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Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005.
Jean Bellissard, Committee Member ; Turgay Uzer, Committee Member ; Roman Grigoriev, Committee Member ; Konstantin Mischaikow, Committee Member ; Predrag Cvitanovic, Committee Chair. Vita. Includes bibliographical references.
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Demaeyer, Jonathan. "Escape rate theory for noisy dynamical systems." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209440.

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The escape of trajectories is a ubiquitous phenomenon in open dynamical systems and stochastic processes. If escape occurs repetitively for a statistical ensemble of trajectories, the population of remaining trajectories often undergoes an exponential decay characterised by the so-called escape rate. Its inverse defines the lifetime of the decaying state, which represents an intrinsic property of the system. This paradigm is fundamental to nucleation theory and reaction-rate theory in chemistry, physics, and biology.

In many circumstances, escape is activated by the presence of noise, which may be of internal or external origin. This is the case for thermally activated escape over a potential energy barrier and, more generally, for noise-induced escape in continuous-time or discrete-time dynamics.

In the weak-noise limit, the escape rate is often observed to decrease exponentially with the inverse of the noise amplitude, a behaviour which is given by the van't Hoff-Arrhenius law of chemical kinetics. In particular, the two important quantities to determine in this case are the exponential dependence (the ``activation energy') and its prefactor.

The purpose of the present thesis is to develop an analytical method to determine these two quantities. We consider in particular one-dimensional continuous and discrete-time systems perturbed by Gaussian white noise and we focus on the escape from the basin of attraction of an attracting fixed point.

In both classes of systems, using path-integral methods, a formula is deduced for the noise-induced escape rate from the attracting fixed point across an unstable fixed point, which forms the boundary of the basin of attraction. The calculation starts from the trace formula for the eigenvalues of the operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined by the loop formed by two heteroclinic orbits connecting back and forth the two fixed points in a two-dimensional auxiliary deterministic dynamical system. The escape rate is obtained, including the expression of the prefactor to van't Hoff-Arrhenius exponential factor./L'échappement des trajectoires est un phénomène omniprésent dans les systèmes dynamiques ouverts et les processus stochastiques. Si l'échappement se produit de façon répétitive pour un ensemble statistique de trajectoires, la population des trajectoires restantes subit souvent une décroissance exponentielle caractérisée par le taux d'échappement. L'inverse du taux d'échappement définit alors la durée de vie de l'état transitoire associé, ce qui représente une propriété intrinsèque du système. Ce paradigme est fondamental pour la théorie de la nucléation et, de manière générale, pour la théorie des taux de transitions en chimie, en physique et en biologie.

Dans de nombreux cas, l'échappement est induit par la présence de bruit, qui peut être d'origine interne ou externe. Ceci concerne en particulier l'échappement activé thermiquement à travers une barrière d'énergie potentielle, et plus généralement, l'échappement dû au bruit dans les systèmes dynamiques à temps continu ou à temps discret.

Dans la limite de faible bruit, on observe souvent une décroissance exponentielle du taux d'échappement en fonction de l'inverse de l'amplitude du bruit, un comportement qui est régi par la loi de van't Hoff-Arrhenius de la cinétique chimique. En particulier, les deux quantités importantes de cette loi sont le coefficient de la dépendance exponentielle (c'est-à-dire ``l'énergie d'activation') et son préfacteur.

L'objectif de cette thèse est de développer une théorie analytique pour déterminer ces deux quantités. La théorie que nous présentons concerne les systèmes unidimensionnels à temps continu ou discret perturbés par un bruit blanc gaussien et nous considérons le problème de l'échappement du bassin d'attraction d'un point fixe attractif. Pour s'échapper, les trajectoires du système bruité initialement contenues dans ce bassin d'attraction doivent alors traverser un point fixe instable qui forme la limite du bassin.

Dans le présent travail, et pour les deux types de systèmes, une formule est dérivée pour le taux d'échappement du point fixe attractif en utilisant des méthodes d'intégrales de chemin. Le calcul utilise la formule de trace pour les valeurs propres de l'opérateur gouvernant l'évolution temporelle de la densité de probabilité dans le système bruité. Le taux d'échappement est déterminé en considérant la boucle formée par deux orbites hétéroclines liant dans les deux sens les deux points fixes dans un système dynamique auxiliaire symplectique et bidimensionnel. On obtient alors le taux d'échappement, comprenant l'expression du préfacteur de l'exponentielle de la loi de van't Hoff-Arrhenius.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Nguyen, Rémi. "Dynamic combinatorial mesophases and self-replicating systems." Strasbourg, 2010. http://www.theses.fr/2010STRA6285.

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Mon travail de thèse a consisté à développer des systèmes de blocs amphiphiles combinatoires dynamiques pour étudier de possibles phénomènes d’auto-organisation hiérarchique dans l’espace et dans le temps. Pour cela, j’ai combiné des associations réversibles de blocs hydrophiles et hydrophobes en étudiant deux types possibles de contrôle : a) un contrôle moléculaire externe sur les liaisons entre blocs de manière à forcer l’expression d’une mésophase particulière ; et b) un contrôle supramoléculaire interne dicté par la formation préférentielle d’une mésophase, avec sélection spontanée des blocs qui la composent. Lors de ce travail, j’ai pu démontrer pour la première fois la possibilité d’étendre la chimie combinatoire dynamique aux systèmes à micro-séparation de phase. Pour y parvenir, j’ai développé un nouveau type d’objets dynamiques (Dynablocks) et j’ai pu mettre en évidence des comportements très originaux de ces derniers qu’ils soient d’ordre cinétique (auto-réplication) ou thermodynamique (sélection au sein de mélange) ; j’ai également montré que ces deux aspects pouvaient être réunis au sein de processus d’auto-organisation. Pour caractériser les mélanges, de nouvelles méthodes de combinaisons linéaires pour l’analyse des diffusions du rayonnement ont été développées. Cette étude fondamentale constitue une nouvelle ouverture de la chimie combinatoire dynamique aux frontières avec deux domaines d’importance : a) la science des matériaux et b) la chimie des systèmes – en particulier des systèmes autonomes minimaux (i. E. Autopoiétiques)
My PhD work consisted in developing combinatorial dynamic systems of amphiphilic block copolymers to study their hierarchical self-organization processes in space and time. For this I combined reversible associations between hydrophobic and hydrophilic blocks, focusing on two possible kinds of control of these responsive systems: a) an external molecular control on the reversible covalent bonds between the blocks in order to favour the expression of a particular mesophase; and b) an internal supramolecular control driven by the preferential formation of a mesophase leading to spontaneous selection of its own composing blocks. During this work, I demonstrated for the first time the possibility to extend dynamic combinatorial chemistry to systems with phase micro-separation. For this, I developed a new type of dynamic molecules (Dynablocks) and I discovered some interesting behaviours from the mesophases I obtained, such as self-replication on a kinetic point of view, or selection/adaptation process within a mixture on a thermodynamic point of view. I also demonstrated that these to aspects could be coupled together in an auto-organization process. To characterize those complex mixtures, new analytical methods were developed for scattering techniques, based on linear combinations. This fundamental study opens a new field of investigation for dynamic combinatorial chemistry in relations with two important domains: a) material science and b) system chemistry – particularly minimal autonomous systems (i. E. Autopoietics systems)
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Syzmczak, Andrzej. "Index pairs : from dynamics to combinatorics and back." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/28027.

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Books on the topic "Combinatorial dynamical systems"

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1940-, Zehnder Eduard, ed. Notes on dynamical systems. Providence, RI: American Mathematical Society, 2005.

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Fauvet, Frédéric, and Claude Mitschi, eds. From Combinatorics to Dynamical Systems. Berlin, New York: Walter de Gruyter, 2003. http://dx.doi.org/10.1515/9783110200003.

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Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. Providence, Rhode Island: American Mathematical Society, 2014.

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Bhattacharya, Siddhartha, Tarun Das, Anish Ghosh, and Riddhi Shah. Recent trends in ergodic theory and dynamical systems: International conference in honor of S.G. Dani's 65th birthday, December 26--29, 2012, Vadodara, India. Providence, Rhode Island: American Mathematical Society, 2015.

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Wirsching, Günther J. The dynamical system generated by the 3n + 1 function. Berlin: Springer, 1998.

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Fogg, N. Pytheas, S. bastien Ferenczi, Christian Mauduit, and Anne Siegel. Substitutions in Dynamics, Arithmetics and Combinatorics. Berlin: Springer-Verlag Berlin Heidelberg, 2002.

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Ferenczi, Sébastien, Joanna Kułaga-Przymus, and Mariusz Lemańczyk, eds. Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74908-2.

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Murfitt, Louise. Discrete event dynamic systems in max-algebra: Realisation and related combinatorial problems. Birmingham: University of Birmingham, 2000.

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International Congress of Chinese Mathematicians (5th 2010 Beijing, China). Fifth International Congress of Chinese Mathematicians. Edited by Ji Lizhen 1964-. Providence, R.I: American Mathematical Society, 2012.

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1964-, Ji Lizhen, ed. Fifth International Congress of Chinese Mathematicians. Providence, R.I: American Mathematical Society, 2012.

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Book chapters on the topic "Combinatorial dynamical systems"

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Lamnabhi-Lagarrigue, Françoise, Pierre Leroux, and Xavier G. Viennot. "Combinatorial Approximations of Volterra Series by Bilinear Systems." In Analysis of Controlled Dynamical Systems, 304–15. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-3214-8_27.

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Tu, Guizhang. "A Combinatorial Rule to Hirota’s Bilinear Equations." In Nonlinear Evolution Equations and Dynamical Systems, 170–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84039-5_33.

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Durand, Fabien. "Combinatorial and Dynamical Study of Substitutions Around the Theorem of Cobham." In Nonlinear Phenomena and Complex Systems, 53–94. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0345-2_3.

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Mălin, Maria, Ionel Rovenţa, and Mihai Tudor. "The Convergence of a Sequence of Iterated Polygons: A Discrete Combinatorial Analysis." In Difference Equations, Discrete Dynamical Systems and Applications, 333–49. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20016-9_14.

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Aranzubía, Solange, and Rafael Labarca. "Combinatorial Dynamics and an Elementary Proof of the Continuity of the Topological Entropy at θ =101, in the Milnor Thurston World." In Progress and Challenges in Dynamical Systems, 25–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38830-9_3.

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Bemporad, Alberto, and Nicolò Giorgetti. "SAT-Based Branch & Bound and Optimal Control of Hybrid Dynamical Systems." In Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 96–111. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24664-0_7.

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Nishimoto, Ryunosuke, and Jun Tani. "Learning to Generate Combinatorial Action Sequences Utilizing the Initial Sensitivity of Deterministic Dynamical Systems." In Computational Methods in Neural Modeling, 422–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44868-3_54.

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Moulin, Emilie, and Nicolas Giuseppone. "Dynamic Combinatorial Self-Replicating Systems." In Constitutional Dynamic Chemistry, 87–105. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/128_2011_198.

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Starke, Jens, and Michael Schanz. "Dynamical System Approaches to Combinatorial Optimization." In Handbook of Combinatorial Optimization, 1217–70. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4613-0303-9_18.

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Starke, Jens. "Dynamical System Approaches to Combinatorial Optimization∗." In Handbook of Combinatorial Optimization, 1065–124. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-7997-1_43.

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Conference papers on the topic "Combinatorial dynamical systems"

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Jiang, Chunheng, Jianxi Gao, and Malik Magdon-Ismail. "Inferring Degrees from Incomplete Networks and Nonlinear Dynamics." 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.2020/457.

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Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks. Prior studies usually focus on the structure-based estimation to infer network sizes, degree distributions, average degrees, and more. Little effort attempted to estimate the specific degree of each vertex from a sampled induced graph, which prevents us from measuring the lethality of nodes in protein networks and influencers in social networks. The current approaches dramatically fail for a tiny sampled induced graph and require a specific sampling method and a large sample size. These approaches neglect information of the vertex state, representing the dynamical behavior of the networked system, such as the biomass of species or expression of a gene, which is useful for degree estimation. We fill this gap by developing a framework to infer individual vertex degrees using both information of the sampled topology and vertex state. We combine the mean-field theory with combinatorial optimization to learn vertex degrees. Experimental results on real networks with a variety of dynamics demonstrate that our framework can produce reliable degree estimates and dramatically improve existing link prediction methods by replacing the sampled degrees with our estimated degrees.
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Oberlin, Paul, Sivakumar Rathinam, and Swaroop Darbha. "Combinatorial Motion Planning for a Dubins Vehicle With Precedence Constraints." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2720.

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This paper considers a combinatorial motion planning problem of finding a shortest tour for a Dubins’ vehicle that must visit a given set of targets and return to its initial depot while satisfying the motion constraints of the vehicle and the precedence constraints. Precedence constraints restrict the sequence in which a Dubins’ vehicle visits the given set of targets by imposing a partial ordering on the sequence in which the targets must be visited. This problem arises in applications involving fixed wing, Unmanned Aerial Vehicles (UAVs) where the vehicles have fuel and motion constraints. A fixed wing UAV may be modeled as a Dubins’ vehicle that can travel at a constant speed and has an upper bound on its turning rate. This is a difficult problem because it couples the combinatorial problem of optimally visiting a set of targets with the path planning problem of finding the shortest path that satisfies the motion constraints given the sequence in which the targets must be visited. In this paper, the sequence in which the targets must be visited is obtained by solving the combinatorial problem using a split dual algorithm. Using this sequence, the path planning problem is solved using Dynamic Programming. Computational results are given to corroborate the performance of the algorithms.
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Schwind, M., O. Gujo, and T. Stockheim. "Dynamic Resource Prices in a Combinatorial Grid System." In The 8th IEEE International Conference on E-Commerce Technology and The 3rd IEEE International Conference on Enterprise Computing, E-Commerce, and E-Services (CEC/EEE'06). IEEE, 2006. http://dx.doi.org/10.1109/cec-eee.2006.37.

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Baykasoglu, Adil, and Fehmi Burcin Ozsoydan. "A constructive search algorithm for combinatorial dynamic optimization problems." In 2015 IEEE International Conference on Evolving and Adaptive Intelligent Systems (EAIS). IEEE, 2015. http://dx.doi.org/10.1109/eais.2015.7368783.

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Pfeiffer, Friedrich. "The Idea of Complementarity in Multibody Dynamics." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21328.

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Abstract Considered in a straightforward manner multibody systems with many multiple unilateral contacts involve a combinatorial problem of huge dimensions, which can only be solved reasonably by the introduction of the complementarity idea. It states that for unilateral contacts either relative kinematics is zero and the corresponding constraint forces are not zero, or vice versa. This leads to a complementarity problem which is somehow related to linear programming problems. Paper discusses the theoretical and practical background.
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Cui, Ying, Xiao Wu, Jiao Song, and Huijiao Ma. "A Dynamic Task Equilibrium Allocation Algorithm Based on Combinatorial Auctions." In 2016 8th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC). IEEE, 2016. http://dx.doi.org/10.1109/ihmsc.2016.177.

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Gunarathna, Udesh, Renata Borovica-Gajic, Shanika Karunasekera, and Egemen Tanin. "Dynamic graph combinatorial optimization with multi-attention deep reinforcement learning." In SIGSPATIAL '22: The 30th International Conference on Advances in Geographic Information Systems. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3557915.3560956.

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Wang, Bingyu, Sivakumar Rathinam, Rajnikant Sharma, and Kaarthik Sundar. "Algorithms for Localization and Routing of Unmanned Vehicles in GPS-Denied Environments." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-8949.

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A majority of the routing algorithms for unmanned aerial or ground vehicles rely on Global Positioning System (GPS) information for localization. However, disruption of GPS signals, by intention or otherwise, can render these algorithms ineffective. This article provides a way to address this issue by utilizing landmarks to aid localization in GPS-denied environments. Specifically, given a number of vehicles and a set of targets, we formulate a joint routing and landmark placement problem as a combinatorial optimization problem: to compute paths for the vehicles that traverse every target at least once, and to place landmarks to aid the vehicles in localization while each of them traverses its route, such that the sum of the traveling cost and the landmark placement cost is minimized. A mixed-integer linear program is presented, and a set of algorithms and heuristics are proposed for different approaches to address certain issues not covered by the linear program. The performance of each proposed algorithm is evaluated and compared through extensive computational and simulation results.
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Liu, Hongzhi, Zhonghai Wu, D. Frank Hsu, and Bruce S. Kristal. "Improved Combination of Multiple Retrieval Systems Using a Dynamic Combinatorial Fusion Algorithm." In 2016 IEEE/WIC/ACM International Conference on Web Intelligence (WI). IEEE, 2016. http://dx.doi.org/10.1109/wi.2016.0102.

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10

Nezamuddin, N., David Fajardo, and S. Travis Waller. "A combinatorial algorithm and warm start method for dynamic traffic assignment." In 2011 14th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2011). IEEE, 2011. http://dx.doi.org/10.1109/itsc.2011.6083130.

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