Low-Rank Approximation of Integral Operators by Interpolation

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called -admissibility condition min {diam(),diam()} 2dist(,) that ensures that the kernel function is approximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be far enough from the singularity such that the parameter has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any is sufficient if interpolation instead of Taylor expansionisused for the kernel approximation, which paves the way for grey-box panel clustering algorithms.     

Redesign of a Systems Engineering Language: Formalisation of χ

This paper describes the redesign of a systems engineering language called . This is an engineering language designed to specify and analyse industrial systems. The main objective of this redesign was to enable mathematical reasoning about specifications. We discuss the original language, the requirements and design decisions, and the resulting syntax and semantics of the new version of , called . In particular, we elaborate on semantical aspects of s time model.     

Fast Online Q(λ)

Q()-learning uses TD()-methods to accelerate Q-learning. The update complexity of previous online Q() implementations based on lookup tables is bounded by the size of the state/action space. Our faster algorithm's update complexity is bounded by the number of actions. The method is based on the observation that Q-value updates may be postponed until they are needed.     

When Physical Systems Realize Functions...

After briefly discussing the relevance of the notions computation and implementation for cognitive science, I summarize some of the problems that have been found in their most common interpretations. In particular, I argue that standard notions of computation together with a state-to-state correspondence view of implementation cannot overcome difficulties posed by Putnam's Realization Theorem and that, therefore, a different approach to implementation is required. The notion realization of a function, developed out of physical theories, is then introduced as a replacement for the notional pair computation-implementation. After gradual refinement, taking practical constraints into account, this notion gives rise to the notion digital system which singles out physical systems that could be actually used, and possibly even built.     

Coordinating Multiple Agents via Reinforcement Learning

In this paper, we attempt to use reinforcement learning techniques to solve agent coordination problems in task-oriented environments. The Fuzzy Subjective Task Structure model (FSTS) is presented to model the general agent coordination. We show that an agent coordination problem modeled in FSTS is a Decision-Theoretic Planning (DTP) problem, to which reinforcement learning can be applied. Two learning algorithms, coarse-grained and fine-grained, are proposed to address agents coordination behavior at two different levels. The coarse-grained algorithm operates at one level and tackle hard system constraints, and the fine-grained at another level and for soft constraints. We argue that it is important to explicitly model and explore coordination-specific (particularly system constraints) information, which underpins the two algorithms and attributes to the effectiveness of the algorithms. The algorithms are formally proved to converge and experimentally shown to be effective.     

Efficient Solution of Multi-Term Fractional Differential Equations Using P(EC)<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript>E Methods

We investigate strategies for the numerical solution of the initial value problem with initial conditions where 0<₁<₂<<. Here y ⁽ _j ) denotes the derivative of order _j >0 (not necessarily _j ) in the sense of Caputo. The methods are based on numerical integration techniques applied to an equivalent nonlinear and weakly singular Volterra integral equation. The classical approach leads to an algorithm with very high arithmetic complexity. Therefore we derive an alternative that leads to lower complexity without sacrificing too much precision. Mathematics Subject Classification: Primary 65L05; Secondary 65L06, 65L20     

A predicate transformer for the progress property ‘to-always’

The temporal property to-always has been proposed for specifying progress properties of concurrent programs. Although the to-always properties are a subset of the leads-to properties for a given program, to-always has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformerwta, derive some of its properties, and use it to define to-always. Proof rules for to-always are derived from the properties ofwta. We conclude by briefly describing two application areas, nondeterministic data flow networks and self-stabilizing systems where to-always properties are useful.     

Comparative complexity of the representation of languages by probabilistic automata

We analyze the effect of the degree of isolation of a cut point on the number of states P(U, ) of a probabilistic automaton representing the language U. We give an example of a language Uⁿ consisting of words of length n such that there exist numbers < for which P(Uⁿ, )/P(Uⁿ, )0 as n.Translated from Kibernetika, No. 3, pp. 21–25, May–June, 1989.     

A note to the definition of the ŁΠ-algebras

The -algebras are interesting algebraic structures. They were introduced by Esteva, Godo, and Montagna. These algebras are closely related to the well-known MV-algebras and -algebras. They have two sets of operations and reduct to one set is an MV-algebra and to the other one is a -algebra.Other important reducts of -algebras are so-called P-algebras (an MV-algebras enriched with product connective) and -algebras (-algebras with additional involutive negation).The definition of -algebras is based on its MV-algabraic reduct and the additional identities. In this paper we present how to base this definition on the other reducts we mention above. We present minimal sets of conditions which has to be added to the defining conditions of those reducts in order to obtain -algebras.