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.

Enhancing security and privacy in biometrics-based authentication systems

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.

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

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.

/pdf/on-the-individuality-of-fingerprints-9q3ikds9fa.pdf

On the individuality of fingerprints

Suppose $(T,\mathcal{M})$ is a measurable space, X is a topological space, and $\emptyset \ne F(t) \subset X$ 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 $\{ t:F(t) \cap U \ne \emptyset \} \in \mathcal{M}$ 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 ...

Survey of Measurable Selection Theorems

Methods of Feasible Directions. By G. Zoutendijk. Pp. 126. 30s. 1960. (D. van Nostrand Co. London)

The class of fully semimonotone matrices is well known in the study of the linear complementarity problem. Stone [(1981) Ph.D. thesis, Dept. of Operations Research, Stanford University, Stanford, CA] introduced this class and conjectured that the principal minors of any fully semimonotone Q0-matrix are non-negative. While the problem is still open, Murthy and Parthasarathy [(1998) Math. Program.82, 401–411] introduced the concept of incidence using which they proved that the principal minors of any matrix in the class of fully copositive Q0-matrices, a subclass of fully semimonotone Q0-matrices, are non-negative. In this paper, we study some properties of fully semimonotone matrices in connection with incidence. The main result of the paper shows that Stone's conjecture is true in the special case where the complementary cones have no partial incidence. We also present an interesting characterization of Q0 for matrices with a special structure. This result is very useful in checking whether a given matrix belongs to Q0 provided it has the special structure. Several examples are discussed in connection with incidence and Q0 property.

On fully semimonotone matrices

In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results.

Stationary, completely mixed and symmetric optimal and equilibrium strategies in stochastic games

We define two-person zero-sum and nonzero-sum stochastic games with finite state space and finite action space We discuss the case of β-discounted payoffs as well as that of undiscounted or limiting time average payoffs We look at certain classes of stochastic games that possess the orderfield property, that is, given rational inputs, such games have a rational solution To solve such classes exactly, there is hope for finding finite arithmetic-step algorithms We discuss algorithms for some such classes We also briefly discuss determinacy of stochastic games with countable state space and Borel payoffs Furthermore, we outline some applications of stochastic games as well as some recent work


Keywords:

discounted;
undiscounted;
finite stochastic game;
existence of value;
determinacy;
orderfield property;
perfect information;
one player control;
switching control;
additive reward additive transition;
separable reward-state independent transition;
simple stochastic game;
countable state space and Borel payoffs;
exact algorithms;
applications of stochastic games

Multistage (Stochastic) Games

It is shown that discounted general-sum stochastic games with two players, two states, and one player controlling the rewards have the ordered field property. For the zero-sum case, this result implies that, when starting with rational data, also the value is rational and that the extreme optimal stationary strategies are composed of rational components.

/pdf/a-class-of-stochastic-games-with-ordered-field-property-fg2yc60bct.pdf

A class of stochastic games with ordered field property

Given a linear transformation L on a finite dimensional real inner product space V to itself and an element q ∈ V we consider the general linear complementarity problem LCP(L, K, q) on a proper cone K ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution for LCP(L, K, q), whenever L is strongly monotone. Lipschitz constants of L is vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear complementarity problems. We give a numerical illustration of a closed algorithmic map in the setting of a standard linear complementarity problem. On account of the difficulties in numerically implementing such algorithms for general linear complementarity problems, we give an alternative algorithm for computing the solution for a special class of strongly monotone semidefinite linear complementarity problems along with a numerical example.

T. Parthasarathy

Papers

On fully semimonotone matrices

Stationary, completely mixed and symmetric optimal and equilibrium strategies in stochastic games

Multistage (Stochastic) Games

A class of stochastic games with ordered field property

Solving strongly monotone linear complementarity problems