{"title":"Localization of Floer homology of engulfed topological Hamiltonian loop","authors":"Y. Oh","doi":"10.4310/CIS.2013.V13.N4.A1","DOIUrl":"https://doi.org/10.4310/CIS.2013.V13.N4.A1","url":null,"abstract":"Localization of Floer homology is first introduced by Floer cite{floer:fixed} in the context of Hamiltonian Floer homology. The author employed the notion in the Lagrangian context for the pair $(phi_H^1(L),L)$ of compact Lagrangian submanifolds in tame symplectic manifolds $(M,omega)$ in cite{oh:newton,oh:imrn} for a compact Lagrangian submanifold $L$ and $C^2$-small Hamiltonian $H$. In this article, motivated by the study of topological Hamiltonian dynamics, we extend the localization process for any engulfable Hamiltonian path $phi_H$ whose time-one map $phi_H^1$ is sufficiently $C^0$-close to the identity (and also to the case of triangle product), and prove that the value of local Lagrangian spectral invariant is the same as that of global one. Such a Hamiltonian path naturally occurs as an approximating sequence of engulfable topological Hamiltonian loop. We also apply this localization to the graphs $Graph phi_H^t$ in $(Mtimes M, omegaoplus -omega)$ and localize the Hamiltonian Floer complex of such a Hamiltonian $H$. We expect that this study will play an important role in the study of homotopy invariance of the spectral invariants of topological Hamiltonian.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114260878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum filtering for systems driven by fermion fields","authors":"J. Gough, M. Guţă, M. James, H. Nurdin","doi":"10.4310/CIS.2011.V11.N3.A3","DOIUrl":"https://doi.org/10.4310/CIS.2011.V11.N3.A3","url":null,"abstract":"Recent developments in quantum technology mean that is it now possible to manipulate systems and measure fermion fields (e.g. reservoirs of electrons) at the quantum level. This progress has motivated some recent work on filtering theory for quantum systems driven by fermion fields by Korotkov, Milburn and others. The purpose of this paper is to develop fermion filtering theory using the fermion quantum stochastic calculus. We explain that this approach has close connections to the classical filtering theory that is a fundamental part of the systems and control theory that has developed over the past 50 years.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131963070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Entropy for Pareto-types and its Order Statistics Distributions","authors":"G. M. Borzadran, G. Yari","doi":"10.4310/CIS.2010.V10.N3.A4","DOIUrl":"https://doi.org/10.4310/CIS.2010.V10.N3.A4","url":null,"abstract":"Abstract. The aim of this paper is deriving the exact analytical expressions of entropy for the Pareto-types and related distributions. Entropy for i order statistics of these distributions corresponding to the random sample size n is introduced. We have shown that all the expressions related to finding corresponding entropy for these families and their order statistics distributions are obtained through some particular techniques via integration. Indeed, these techniques for that improper integrals has its own importance also.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126126166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal natural frames","authors":"E. Justh, P. Krishnaprasad","doi":"10.4310/CIS.2011.V11.N1.A2","DOIUrl":"https://doi.org/10.4310/CIS.2011.V11.N1.A2","url":null,"abstract":"Abstract : Problems of optimal control on Lie groups are of broad interest and application dating back to the early days of geometric control theory. We study a class of such problems defined on the special Euclidean group and demonstrate by appealing to reduction methods that the extremals in these problems admit special structure associated to the nonlinear Schrodinger equation.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121971675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Convergence of Fundamental Limitations in Feedback Communication, Estimation, and Feedback Control over Gaussian Channels","authors":"Jialing Liu, N. Elia","doi":"10.4310/CIS.2014.V14.N3.A2","DOIUrl":"https://doi.org/10.4310/CIS.2014.V14.N3.A2","url":null,"abstract":"In this paper, we establish the connections of the fundamental limitations in feedback communication, estimation, and feedback control over Gaussian channels, from a unifying perspective for information, estimation, and control. The optimal feedback communication system over a Gaussian necessarily employs the Kalman filter (KF) algorithm, and hence can be transformed into an estimation system and a feedback control system over the same channel. This follows that the information rate of the communication system is alternatively given by the decay rate of the Cramer-Rao bound (CRB) of the estimation system and by the Bode integral (BI) of the control system. Furthermore, the optimal tradeoff between the channel input power and information rate in feedback communication is alternatively characterized by the optimal tradeoff between the (causal) one-step prediction mean-square error (MSE) and (anti-causal) smoothing MSE (of an appropriate form) in estimation, and by the optimal tradeoff between the regulated output variance with causal feedback and the disturbance rejection measure (BI or degree of anti-causality) in feedback control. All these optimal tradeoffs have an interpretation as the tradeoff between causality and anti-causality. Utilizing and motivated by these relations, we provide several new results regarding the feedback codes and information theoretic characterization of KF. Finally, the extension of the finite-horizon results to infinite horizon is briefly discussed under specific dimension assumptions (the asymptotic feedback capacity problem is left open in this paper).","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124170718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stabilization of Three-Dimensional Collective Motion","authors":"L. Scardovi, Naomi Ehrich Leonard, R. Sepulchre","doi":"10.4310/CIS.2008.V8.N4.A6","DOIUrl":"https://doi.org/10.4310/CIS.2008.V8.N4.A6","url":null,"abstract":"This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical formations. We first derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116665282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computational Geometric Optimal Control of Rigid Bodies","authors":"Taeyoung Lee, M. Leok, N. McClamroch","doi":"10.4310/CIS.2008.V8.N4.A5","DOIUrl":"https://doi.org/10.4310/CIS.2008.V8.N4.A5","url":null,"abstract":"This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each rigid body is viewed as evolving on a configuration manifold that is a Lie group. Discrete-time dynamics of each rigid body are developed that evolve on the configuration manifold according to a discrete version of Hamilton's principle so that the computations preserve geometric features of the dynamics and guarantee evolution on the configuration manifold; these discrete-time dynamics are referred to as Lie group variational integrators. Rigid body optimal control problems are formulated as discrete-time optimization problems for discrete Lagrangian/Hamiltonian dynamics, to which standard numerical optimization algorithms can be applied. This general approach is illustrated by presenting results for several different optimal control problems for a single rigid body and for multiple interacting rigid bodies. The computational advantages of the approach, that arise from correctly modeling the geometry, are discussed.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128944521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"When the Cramér-Rao Inequality Provides No Information","authors":"Steven J. Miller","doi":"10.4310/CIS.2007.V7.N3.A3","DOIUrl":"https://doi.org/10.4310/CIS.2007.V7.N3.A3","url":null,"abstract":"We investigate a one-parameter family of probability densities (related to the Pareto distribution, which describes many natural phenomena) where the Cramer-Rao inequality provides no information.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128084588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximization of the portfolio growth rate under fixed and proportional transaction costs","authors":"Jan Palczewski, L. Stettner","doi":"10.4310/CIS.2007.V7.N1.A3","DOIUrl":"https://doi.org/10.4310/CIS.2007.V7.N1.A3","url":null,"abstract":"This paper considers a discrete-time Markovian model of asset prices with economic factors and transaction costs with proportional and fixed terms. Existence of optimal strategies maximizing average growth rate of portfolio is proved in the case of complete and partial observation of the process modelling the economic factors. The proof is based on a modification of the vanishing discount approach. The main difficulty is the discontinuity of the controlled transition operator of the underlying Markov process.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129287777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle","authors":"P. Caines, Minyi Huang, R. Malhamé","doi":"10.4310/CIS.2006.V6.N3.A5","DOIUrl":"https://doi.org/10.4310/CIS.2006.V6.N3.A5","url":null,"abstract":"Abstract. We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent (or particle) at the microscopic level and the mass of individuals (or particles) at the macroscopic level. The overall game is decomposed into (i) an optimal control problem whose Hamilton-Jacobi-Bellman (HJB) equation determines the optimal control for each individual and which involves a measure corresponding to the mass effect, and (ii) a family of McKean-Vlasov (M-V) equations which also depend upon this measure. We designate the NCE Principle as the property that the resulting scheme is consistent (or soluble), i.e. the prescribed control laws produce sample paths which produce the mass effect measure. By construction, the overall closed-loop behaviour is such that each agent’s behaviour is optimal with respect to all other agents in the game theoretic Nash sense.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133276911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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