Set Of Possible States Research Articles

Measures of success in a class of evolutionary models with fixed population size and structure

We investigate a class of evolutionary models, encompassing many established models of well-mixed and spatially structured populations. Models in this class have fixed population size and structure. Evolution proceeds as a Markov chain, with birth and death probabilities dependent on the current population state. Starting from basic assumptions, we show how the asymptotic (long-term) behavior of the evolutionary process can be characterized by probability distributions over the set of possible states. We then define and compare three quantities characterizing evolutionary success: fixation probability, expected frequency, and expected change due to selection. We show that these quantities yield the same conditions for success in the limit of low mutation rate, but may disagree when mutation is present. As part of our analysis, we derive versions of the Price equation and the replicator equation that describe the asymptotic behavior of the entire evolutionary process, rather than the change from a single state. We illustrate our results using the frequency-dependent Moran process and the birth-death process on graphs as examples. Our broader aim is to spearhead a new approach to evolutionary theory, in which general principles of evolution are proven as mathematical theorems from axioms.

DEVELOPMENT OF THE GUARANTEED ESTIMATION ROBUST ALGORITHM OF LINEAR CONTROLLED SYSTEM STATES

Ellipsoidal approximation of the ellipsoid and hyperlayer crossing has been considered as a basis of the algorithm of states estimation of the linear controlled system whose set of possible states is represented with an ellipsoid, and observations – with a hyperlayer. This representation is considered as an analogue of Kalman filter. The conditions of a priori system state and a posteriori measurement information compatibility and sensitivity of the algorithm to a choice of its parameters have been investigated. Dependence of the system state estimate improvement on a relative width of the hyperlayer of a set of observations has been shown. The obtained algorithm in comparison with the known solutions at minor degradation of accuracy is much easier in realization and stabler in operation from the standpoint of prior guesses violation.

Propositional Dynamic Logic with Storing, Recovering and Parallel Composition

This work extends Propositional Dynamic Logic (PDL) with parallel composition operator and four atomic programs which formalize the storing and recovering of elements in data structures. A generalization of Kripke semantics is proposed that instead of using set of possible states it uses structured sets of possible states. This new semantics allows for representing data structures and using the five new operator one is capable of reasoning about the manipulation of these data structures. The use of the new language (PRSPDL) is illustrated with some examples. We present sound and complete set of axiom schemata and inference rules to prove all the valid formulas for a restricted fragment called RSPDLo.

Multi-parameter fronts of strong discontinuities in continuum mechanics

The strong discontinuities in solutions of hyperbolic systems of equations of continuum mechanics are considered. It is assumed that there is a flow of mass through the discontinuity front. If the number of boundary conditions that must be satisfied at a discontinuity (which follow from conservation laws or from other laws and assumptions) is less than the number of unknowns in the system of equations describing the state and motion of the medium behind the discontinuity, then as the discontinuity propagates along a specified fixed state of the medium, the set of possible states behind the discontinuity (shock adiabat) can depend on more than one parameter (multi-parameter discontinuities). The number of parameters on which a possible state behind a discontinuity depends can be reduced by introducing “additional” boundary conditions, which appear as conditions that ensure the existence of a solution for the discontinuity structure problem. These additional boundary conditions are specified by small-scale processes that occur within the structure, and terms corresponding to these processes must be introduced into the hyperbolic equations to describe them. Two examples of systems of equations related to the mechanics of deformable solids when multi-parameter discontinuities appear are considered, their structure is studied, and problems in which such discontinuities appear are considered. One of these examples is the description of a version of a phase transformation in the form of the formation of a non-linear elastic Kelvin–Voigt medium when a stream of non-interacting particles is compacted. In the other example the very simple case of the formation of a multi-parameter discontinuity as a consequence of the appearance of residual strains in a discontinuity is described.

Online Model Identification for Set-valued State Estimators With Discrete-Time Measurements

AbstractAlthough Kalman Filters provide an optimal solution to the state estimation problem for linear systems, they require knowledge of an accurate description of the model of the system. More robust approaches to Kalman Filtering for systems with uncertain models have been developed, such as set-valued state estimators, which identify the set of possible states that the system may be in, given a description of its uncertainties. The theory behind this class of filters contemplates the possibility of determining if a given system model is feasible with respect to its measurements, but does not explore the possibility of explicitly identifying the system online. This work provides insight into the advantages of performing simultaneous model identification for the class of set-valued estimators, by introducing an Adaptive Set-Valued Estimator, and presenting a practical example of its usage. The results of this robust estimator are then compared to those obtained when using a classical set-valued estimator.

Analysis of quantum walks with time-varying coin on d-dimensional lattices

In this paper, we present a study of discrete time quantum walks whose underlying graph is a d-dimensional lattice. The dynamical behavior of these systems is of current interest because of their applications in quantum information theory as tools to design quantum algorithms. We assume that, at each step of the walk evolution, the coin transformation is allowed to change so that we can use it as a control variable to drive the evolution in a desired manner. We give an exact description of the possible evolutions and of the set of possible states that can be achieved with such a system. In particular, we show that it is possible to go from a state where there is probability 1 for the walker to be found in a vertex to a state where all the vertices have equal probability. We also prove a number of properties of the set of admissible states in terms of the number of steps needed to obtain them. We provide explicit algorithms for state transfer in low dimensional cases as well as results that allow to reduce algorithms on two-dimensional lattices to algorithms on the one-dimensional lattice, the cycle.

Jeffrey conditioning and external Bayesianity

Abstract. Suppose that several individuals who have separately assessed prior probability distributions over a set of possible states of the world wish to pool their individual distributions into a single group distribution, while taking into account jointly perceived new evidence. They have the option of (i) first updating their individual priors and then pooling the resulting posteriors or (ii) first pooling their priors and then updating the resulting group prior. If the pooling method that they employ is such that they arrive at the same final distribution in both cases, the method is said to be externally Bayesian, a property first studied by Madansky (1964). We show that a pooling method for discrete distributions is externally Bayesian if and only if it commutes with Jeffrey conditioning, parameterized in terms of certain ratios of new to old odds, as in Wagner (2002), rather than in terms of the posterior probabilities of members of the disjoint family of events on which such conditioning originates.

A framework for data mining on combinatorial game theory

Combinatorics is the study of discrete, finite spaces. Combinatorial games are games that can be studied through the use of combinatorics. They are typically, but not necessarily, two-player games with a finite set of possible states and a well-defined winning condition. The search space in combinatorial games is typically very large. In this paper, we proposed a framework to apply data mining techniques such as Bayesian classification to the combinatorial game theory, in particular, a game called Audacity. Our experimental results show that the Bayesian classification is effective for discovering classification rules in combinatorial games, such as the Audacity game.

Robust Fault Detection with Unknown-Input Interval Observers using Zonotopes

This paper presents the problem of robust fault detection using unknown-input interval observers. These observers face the robustness problem using two complementary strategies. First, disturbances considered as unknown inputs are decoupled. Second, process/measurement noise and modeling uncertainty are considered unknown but bounded by intervals. Their effect is addressed using an interval state observation method based on zonotope representation of the set of possible states. Finally, an example based on a linearized model of a flight control system is proposed to show the effectiveness of the proposed approach.

LIMITATION ON THE ACCESSIBLE INFORMATION FOR QUANTUM CHANNELS WITH INEFFICIENT MEASUREMENTS

To transmit classical information using a quantum system, the sender prepares the system in one of a set of possible states and sends it to the receiver. The receiver then makes a measurement on the system to obtain information about the senders choice of state. The amount of information which is accessible to the receiver depends upon the encoding and the measurement. Here we derive a bound on this information which generalizes the bound derived by Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] to include inefficient measurements, and thus all quantum operations. This also allows us to obtain a generalization of a bound derived by Hall [Hall, Phys. Rev. A 55, 100 (1997)], and to show that the average reduction in the von Neumann entropy which accompanies a measurement is concave in the initial state, for all quantum operations.

Operations that do not disturb partially known quantum states

Consider a situation in which a quantum system is secretly prepared in a state chosen from the known set of states. We present a principle that gives a definite distinction between the operations that preserve the states of the system and those that disturb the states. The principle is derived by alternately applying a fundamental property of classical signals and a fundamental property of quantum ones. The principle can be cast into a simple form by using a decomposition of the relevant Hilbert space, which is uniquely determined by the set of possible states. The decomposition implies the classification of the degrees of freedom of the system into three parts depending on how they store the information on the initially chosen state: one storing it classically, one storing it nonclassically, and the other one storing no information. Then the principle states that the nonclassical part is inaccessible and the classical part is read-only if we are to preserve the state of the system. From this principle, many types of no-cloning, no-broadcasting, and no-imprinting conditions can easily be derived in general forms including mixed states. It also gives a unified view on how various schemes of quantum cryptography work. The principle helps one to derive optimum amount of resources (bits, qubits, and ebits) required in data compression or in quantum teleportation of mixed-state ensembles.

Quantum Limited State Discrimination

Quantum theory restricts our ability to determine the state of a physical system. This is true even if we know for certain that it was prepared in one of a known set of possible states. I describe two types of optimal strategy for state discrimination. These are (i) state discrimination with minimum probability of error and (ii) unambiguous or error-free state discrimination.

The non-monotonic temperature dependence of the yield stress in TiAl and CuAu alloys

An anomalous temperature dependence of the yield stress in the ordered CuAu alloy was detected. Blocked <101] superdislocations were observed in the region of the anomalous trend from room temperature to 300°C. Blocking of single dislocations was not detected at these temperatures. The comparison with the known data on the TiAl intermetallic was carried on. The causes of the nonmonotonous temperature dependence of the yield stress with two extremum points were analyzed. The set of possible states of dislocations in TiAl was discussed. A unified scheme with account of mutual dislocation transitions was proposed for the description of the deformation behavior over the whole temperature interval. Specific features of the dislocation structure of CuAu and TiAl were explained. The connection between the brittleness of TiAl and dislocation transformations was discussed.

Evaluating policies based on their long term average cost

Many decision problems can be characterized by a set of possible states and a cost associated with each possible state transition, hi this paper we discuss how to select a policy from a set of possible policies in the long term. If the cost matrix is not available the transition matrix can be used to compare expected return times to states. In our setting the transition matrix is defined by use of linguistic terms and as a consequence, the expected return times are fuzzy. In the case where the cost matrix is available, fuzzy average costs are computed. The resulting fuzzy quantities are compared by introducing the concept of minimizing sets. Finally, we look at the case where the transition takes place from a state to a state that is known to be an element of some subset of states, but we do not know which one. We use the Dempster–Shafer theory [Shafer 1976] together with techniques of Norton [Norton 1988] and Smetz [Smetz 1976] to approximate the transition probabilities

Set-valued observers and optimal disturbance rejection

A set-valued observer (also called guaranteed state estimator) produces a set of possible states based on output measurements and models of exogenous signals. We consider the guaranteed state estimation problem for linear time-varying systems with a priori magnitude bounds on exogenous signals. We provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l/sup /spl infin//-induced norm sense. We then consider the utility of set-valued observers for disturbance rejection with output feedback and derive the following general separation structure. An optimal controller can consist of a set-valued observer followed by a static nonlinear function on the observed set of possible states. A general construction of this function is provided in the scalar control case. Furthermore, in the special case of full-control, i.e., the number of control inputs equals the number of states, optimal output feedback controllers can take the form of an optimal estimate of the full-state feedback controller.

Externalités et coordination: La concurrence des standards technologiques

The dynamics of technological adoption are studied in a Markovian industry in which competing firms interact through price and network externalities. Technological complementarities alter firms producti vities, entailing permanent fluctuations in output and equilibrium price. The limit distribution on the set of possible states of the industry is examined and shown to be closely related to the dispersion of firms technological expectations. Standardization and diversity are possible outcomes of the process, depending on the level of firm heterogeneity. Welfare implications are then discussed in contexts of competitive and oligopolistic market inter action.

Approximate set-valued observers for nonlinear systems

A set-valued observer (SVO) produces a set of possible states based on output measurements and a priori models of exogenous disturbances and noises. Previous work considered linear time-varying systems and unknown-but-bounded exogenous signals. In this case, the sets of possible state vectors take the form of polytopes whose centers are optimal state estimates. These polytopic sets can be computed by solving several small linear programs. An SVO can be constructed conceptually for nonlinear systems; however, the set of possible state vectors no longer takes the form of polytopes, which in turn inhibits their explicit computation. This paper considers an "extended SVO". As in the extended Kalman filter, the state equations are linearized about the state estimate, and a linear SVO is designed along the linearization trajectory. Under appropriate observability assumptions, it is shown that the extended SVO provides an exponentially convergent state estimate in the case of sufficiently small initial condition uncertainty and provides a nondivergent state estimate in the case of sufficiently small exogenous signals.

The displacement bound estimation for structures with an interval description of uncertain parameters

A structure subjected to interval parameters and interval loads which are unknown, except for the fact that they belong to given intervals, is studied and the displacement bound estimation is given. These parameters are uncertain, and yet they are not treated as being random since no information is available on their probabilistic characteristics. A set of possible states of the system is described by interval matrices. The perturbation method is employed as a simple analytical tool for determining static responses—interval displacements of finite element equilibrium equations with interval parameters. The numerical results show that the proposed method is extremely effective.

Natural frequencies of structures with uncertain but nonrandom parameters

In this paper, we present a method for computing upper and lower bounds of the natural frequencies of a structure with parameters which are unknown, except for the fact that they belong to given intervals. These parameters are uncertain, yet they are not treated as being random, since no information is available on their probabilistic characteristics. The set of possible states of the system is described by interval matrices. By solving the generalized interval eigenvalue problem, the bounds on the natural frequencies of the structure with interval parameters are evaluated. Numerical results show that the proposed method is extremely effective.

Optimal design of laminated plate with obstacle

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.