A canonical space-time state space model: state and parameter estimation

The maximum likelihood estimation of a dynamic spatiotemporal model is introduced, centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description. The neighborhood description defines a specific parameterization of the state transition matrix, chosen on the basis of prior knowledge about the system. The model used is inspired by the spatiotemporal ARMA (STARMA) model, but the representation used is based on the standard state-space model. The inclusion of the neighborhood into an expectation-maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model. The process of including the neighborhood, and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper

Bounded state space

This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented

State-space Correlations and Stabilities

The state-space pair correlation functions and notion of stability of extremal and non-extremal black holes in string theory and M-theory are considered from the viewpoints of thermodynamic Ruppeiner geometry. From the perspective of intrinsic Riemannian geometry, the stability properties of these black branes are divulged from the positivity of principle minors of the space-state metric tensor. We have explicitly analyzed the state-space configurations for (i) the two and three charge extremal black holes, (ii) the four and six charge non-extremal black branes, which both arise from the string theory solutions. An extension is considered for the $D_6$-$D_4$-$D_2$-$D_0$ multi-centered black branes, fractional small black branes and two charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and nature of stabilities have been investigated for three charged bubbling black brane foams, and thereby the M-theory solutions are brought into the present consideration. In the case of extremal black brane configurations, we have pointed out that the ratio of diagonal space-state correlations varies as inverse square of the chosen parameters, while the off diagonal components vary as inverse of the chosen parameters. We discuss the significance of this observation for the non-extremal black brane configurations, and find similar conclusion that the state-space correlations extenuate as the chosen parameters are increased.Comment: 35 pages, Keywords: Black Hole Physics, Higher-dimensional Black Branes, State-space Correlations and Statistical Configurations. PACS numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.50.Gh Higher-dimensional black holes, black strings, and related object

Wandering in the state space

We analyse the topology of the state space of two systems: i) N Ising spins +/-1 with the antiferromagnetic interactions on a triangular lattice, with the condition of minimum of energy, ii) a roundabout of three access roads and three exit roads, with up to 2 cars on each road. The state space is represented by a network, and states - as nodes; two nodes are linked if an elementary process (spin flip or car shift) transforms the respective states one into another. Information is collected on the number of neighbours of states, what allows to distinguish classes and subclasses of states, and on the cluster structure of the state space. In the Ising systems, the clusters are characterized by anisotropy of the spin-spin correlation functions. In the case of a roundabout, the clusters differ by the number of empty or full roads. The method is general and it provides a basis for applications of the random walk theory

Distributed graph-based state space generation

LTSMIN provides a framework in which state space generation can be distributed easily over many cores on a single compute node, as well as over multiple compute nodes. The tool works on the basis of a vector representation of the states; the individual cores are assigned the task of computing all successors of states that are sent to them. In this paper we show how this framework can be applied in the case where states are essentially graphs interpreted up to isomorphism, such as the ones we have been studying for GROOVE. This involves developing a suitable vector representation for a canonical form of those graphs. The canonical forms are computed using a third tool called BLISS. We combined the three tools to form a system for distributed state space generation based on graph grammars. We show that the time performance of the resulting system scales well (i.e., close to linear) with the number of cores. We also report surprising statistics on the memory\ud consumption, which imply that the vector representation used to store graphs in LTSMIN is more compact than the representation used in GROOVE

State Space Reduction For Parity Automata

Exact minimization of ?-automata is a difficult problem and heuristic algorithms are a subject of current research. We propose several new approaches to reduce the state space of deterministic parity automata. These are based on extracting information from structures within the automaton, such as strongly connected components, coloring of the states, and equivalence classes of given relations, to determine states that can safely be merged. We also establish a framework to generalize the notion of quotient automata and uniformly describe such algorithms. The description of these procedures consists of a theoretical analysis as well as data collected from experiments

Standard State Space Models of Unawareness

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly