T. Parthasarathy

Bio: T. Parthasarathy is an academic researcher from Indian Statistical Institute. The author has contributed to research in topics: Stochastic game & Linear complementarity problem. The author has an hindex of 22, co-authored 64 publications receiving 1876 citations. Previous affiliations of T. Parthasarathy include Case Western Reserve University & Université catholique de Louvain.

On measurable relations

Abstract: The results in this paper supplement those in "Measurable relations" by C. J. Him-melberg [H]. Some results of that paper are extended and examples are given showing the sharpness of earlier results. In particular, examples are given showing (i) that the intersection of two weakly measurable, closed-valued relations may fail to be weakly measurable, and (ii) that Filippov's implicit function theorem may fail without appropriate restrictions either on the domain of the relation or on its values.

On global univalence theorems

Abstract: Preliminaries and statement of the problem.- P-matrices and N-matrices.- Fundamental global univalence results of Gale-Nikaido-Inada.- Global homeomorphisms between finite dimensional spaces.- Scarf's conjecture and its validity.- Global univalent results in R2 and R3.- On the global stability of an autonomous system on the plane.- Univalence for mappings with Leontief type Jacobians.- Assorted applications of univalence mapping results.- Further generalizations and remarks.

Optimal Plans for Dynamic Programming Problems

Abstract: It is proved that there exist stationary optimal plans for discounted dynamic programming problems, and that there exist semi-Markov e-optimal plans for positive dynamic programming problems. The actions are required to be taken in a variable action set Fs, and the reward function rs, a is a Borel measurable function of s, a and an u.s.c. function of a. Our results are related to recent work by Furukawa, Maitra, and Schal. The key tool is a generalization of a selection theorem of Dubins and Savage.

An orderfield property for stochastic games when one player controls transition probabilities

Abstract: When the transition probabilities of a two-person stochastic game do not depend on the actions of a fixed player at all states, the value exists in stationary strategies. Further, the data of the stochastic game, the values at each state, and the components of a pair of optimal stationary strategies all lie in the same Archimedean ordered field. This orderfield property holds also for the nonzero sum case in Nash equilibrium stationary strategies. A finite-step algorithm for the discounted case is given via linear programming.

Equilibria for Discounted Stochastic Games

Abstract: We prove the existence of subgame-perfect equilibria for discounted stochastic games with general state and action sets, using minimal assumptions (measurability as a function of states, and for each fixed state, compactness of action sets and continuity on those)—except for the rather strong assumption that the transition probabilities are norm-continuous functions of the actions.

Enhancing security and privacy in biometrics-based authentication systems

Abstract: Because biometrics-based authentication offers several advantages over other authentication methods, there has been a significant surge in the use of biometrics for user authentication in recent years. It is important that such biometrics-based authentication systems be designed to withstand attacks when employed in security-critical applications, especially in unattended remote applications such as e-commerce. In this paper we outline the inherent strengths of biometrics-based authentication, identify the weak links in systems employing biometrics-based authentication, and present new solutions for eliminating some of these weak links. Although, for illustration purposes, fingerprint authentication is used throughout, our analysis extends to other biometrics-based methods.

Discrete-time controlled Markov processes with average cost criterion: a survey

Abstract: This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.

On the individuality of fingerprints

Abstract: Fingerprint identification is based on two basic premises: (1) persistence and (2) individuality. We address the problem of fingerprint individuality by quantifying the amount of information available in minutiae features to establish a correspondence between two fingerprint images. We derive an expression which estimates the probability of a false correspondence between minutiae-based representations from two arbitrary fingerprints belonging to different fingers. Our results show that (1) contrary to the popular belief, fingerprint matching is not infallible and leads to some false associations, (2) while there is an overwhelming amount of discriminatory information present in the fingerprints, the strength of the evidence degrades drastically with noise in the sensed fingerprint images, (3) the performance of the state-of-the-art automatic fingerprint matchers is not even close to the theoretical limit, and (4) because automatic fingerprint verification systems based on minutia use only a part of the discriminatory information present in the fingerprints, it may be desirable to explore additional complementary representations of fingerprints for automatic matching.

Survey of Measurable Selection Theorems

Abstract: Suppose $(T,\mathcal{M})$ is a measurable space, X is a topological space, and $\emptyset e F(t) \subset X$ for $t \in T$. Denote ${\operatorname {Gr}}F = \{ (t,x):x \in F(t)\} $. The problem surveyed (reviewing work of others) is that of existence off: $f:T \to X$ such that $f(t) \in F(t)$ for $t \in T$ and $f^{ - 1} (U) \in \mathcal{M}$ for open $U \subset X$. The principal conditions that yield such f are (i) X is Polish, each $F(t)$ is closed, and $\{ t:F(t) \cap U e \emptyset \} \in \mathcal{M}$ a .tit whenever $U \subset X$ is open (Kuratowski and Ryll-Nardzewski and, under stronger assumption, Castaing), or (ii) T is a Hausdorff space, ${\operatorname {Gr}}F$ is a continuous image of a Polish space, and M is the $\sigma $-algebra of sets measurable with respect to an outer measure, among which are the open sets of T (primarily von Neumann). The latter result follows from the former by lifting F in a natural way to a map into the closed sets of a Polish space. This procedure leads to the theory ...