|Associative reinforcement learning (ARL) tasks de ned originally by Barto and Anandan [1] combine elements of problems involving optimization under uncertainty, studied by learning automata theorists, and supervised learning pattern-classi cation. The stochastic real-valued (SRV) unit algorithm [6] has been designed for an extended version of ARL tasks wherein the learning system's outputs can...

We give a unateness tester for functions of the form f : [n] → R, where n, d ∈ N and R ⊆ R with query complexity O( log(max(d,n)) ). Previously known unateness testers work only for Boolean functions over the domain {0, 1}. We show that every unateness tester for realvalued functions over hypergrid has query complexity Ω(min{d, |R|}). Consequently, our tester is nearly optimal for real-valued f...

We show that for a subanalytic function / on a locally compact subanalytic set X there exists a unique subanalytic triangulation (a simplicial complex K , a subanalytic homeomorphism n: \K\ —► X) such that f o n\a , a 6 K , are linear. Let X be a subanalytic set contained and closed in a Euclidean space. A subanalytic triangulation of X is a pair (K , n) where K isa simplicial complex and n is ...

The paper pursues the definition of a maxitive integral on all real-valued functions (i.e., the integral of the pointwise maximum of two functions must be the maximum of their integrals). This definition is not determined by maxitivity alone: additional requirements on the integral are necessary. The paper studies the consequences of additional requirements of invariance with respect to affine ...

In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Gutiérrez Garćıa, T. Kubiak and J. Picado [Localic real functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. The purpose is to sh...

In the early sixties, Amice ([Am1], [Am2]) studied the space of K-valued, locally analytic functions on Z Z p and formulated a complete description of its dual, the ring of K-valued, locally Q p-analytic distributions on Z Z p , when K is a complete subfield of C p. She found an isomorphism between the ring of distributions and the space of global functions on a rigid variety over K parameteriz...

In this paper, we will be working with rings and ideals of real analytic functions. Given x ∈ R, let Ax be the ring of real-valued functions f : R → R that are analytic at x. When x = 0 is the origin, it is useful to think of A0 as a subring of the formal power series ring R[[ω1, . . . , ωd]] = R[[ω]] which consists of power series which are convergent in some neighborhood of the origin. For al...