Role of information in the stochastic zero-sum differential game

In this paper, a linear-quadratic Gaussian zero-sum differential game is studied. Maneuverability is defined to measure players' strength. It is shown that a more maneuverable player would prefer a more observable information system. An example is given to show that a more controllable player might not prefer more observable measurements in the stochastic environment.The research reported in this paper was made possible through support extended to the Division of Engineering and Applied Physics, Harvard University, by the US Office of Naval Research under the Joint Services Electronics Program by Contract No. N00014-75-c-0648 and by the National Science Foundation under Grant No. GK31511.     

A Framework for Evaluating Knowledge-Based Interestingness of Association Rules

In Knowledge Discovery in Databases (KDD)/Data Mining literature, interestingness measures are used to rank rules according to the interest a particular rule is expected to evoke. In this paper, we introduce an aspect of subjective interestingness called item-relatedness. Relatedness is a consequence of relationships that exist between items in a domain. Association rules containing unrelated or weakly related items are interesting since the co-occurrence of such items is unexpected. Item-Relatedness helps in ranking association rules on the basis of one kind of subjective unexpectedness. We identify three types of item-relatedness – captured in the structure of a fuzzy taxonomy (an extension of the classical concept hierarchy tree). An item-relatedness measure for describing relatedness between two items is developed by combining these three types. Efficacy of this measure is illustrated with the help of a sample taxonomy. We discuss three mechanisms for extending this measure from a two-item set to an association rule consisting of a set of more than two items. These mechanisms utilize the relatedness of item-pairs and other aspects of an association rule, namely its structure, distribution of items and item-pairs. We compare our approach with another method from recent literature.     

Averaging of Systems with Slow Variables

We justify the averaging method for systems with delay described by both slow and fast variables. The results obtained are applied to the analysis of one problem in control theory.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

A generalization of hadwiger's transversal theorem to intersecting sets

Given an ordered family of compact convex sets in the plane, if every three sets can be intersected by some directed line consistent with the ordering, then there exists a common transversal of the family. This generalizes Hadwiger's Transversal Theorem to families of compact convex sets which are not necessarily pairwise disjoint. If every six sets can be intersected by some directed line consistent with the ordering, then there exists a common transversal which is consistent with the ordering. If the family is pairwise disjoint and every four sets can be intersected by some directed line consistent with the ordering, then there exists a common transversal which is consistent with the ordering.     

A monte carlo model for simulation of tank battles

A Monte Carlo model for simulation of company-level tank battles is described. The simulation is started with an observation phase. The probability of discovery is dependent upon properties of the terrain etc. Target selection is simulated deterministically with priority rules. Every unit belongs to one of the following states of fight: undamaged, able to shoot only, able to move only, shocked and out of action.It is possible to simulate surprise attacks and battles after a sudden contact if the units are assumed to fight from the same position during the whole battle. In a later version of the model, the units are permitted to show as much of themselves as they wish during the battle. Thus it is possible to simulate (small) changes of position, initiated by the current events.     

A combinatorial characterization of the Klein quadric

We give a combinatorial characterization of the Klein quadric in terms of its incidence structure of points and lines. As an application, we obtain a combinatorial proof of a result of Havlicek.In memoriam Giuseppe TalliniWork supported by National Research Project Strutture Geometriche, Combinatoria e loro applicazioni of the Italian Ministere dell'Università e della Ricerca Scientifica and by G.N.S.A.G.A. of C.N.R.      

Absolut stetige Maße auf lokalkompakten Halbgruppen

LetS be a locally compact semigroup. It is shown that if a measure is absolutely continuous and ifS is cancellative, then the measure concentrated on a Borel subsetB ofS (i. e. =(B.)) is also absolutely continuous. Other properties of absolutely continuous measures will be obtained. Moreover we will answer the question when absolutely continuous probability measures exist. This is the case ifS admits an invariant integral on the space of all continuous functions onS with compact support. Another result is the following: If the compact semigroupS has a connected kernel then there exist absolutely continuous probability measures if and only ifS is amenable.     

On the spectral density and asymptotic normality of weakly dependent random fields

For weakly stationary random fields, conditions on coefficients of linear dependence are given which are, respectively, sufficient for the existence of a continuous spectral density, and necessary and sufficient for the existence of a continuous positive spectral density. For strictly stationary random fields, central limit theorems are proved under the corresponding unrestricted -mixing condition and just finite or barely infinite second moments. No mixing rate is assumed.     

“Solar” properties of sets in Banach spaces

In this article we consider relations between different classes of suns. A sufficient condition for a set to be a sun is given.Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 795–805, June, 1973.     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

On the continuity of midpoint hull convex set-valued functions

Summary The concept of hull convexity (midpoint hull convexity) for set-valued functions in vector spaces is examined. This concept, introduced by A. V. Fiacco and J. Kyparisis (Journal of Optimization Theory and Applications,43 (1986), 95–126), is weaker than one of convexity (midpoint convexity).The main result is a sufficient condition for a midpoint hull convex set-valued function to be continuous. This theorem improves a result obtained by K. Nikodem (Bulletin of the Polish Academy of Sciences, Mathematics,34 (1986), 393–399).     

Positivity and Stability for One-Sided Coupled Operator Matrices

Many evolutionary systems can be described by an abstract Cauchy problem governed by an operator matrix. Assuming this problem to be one-sided coupled and well-posed we study in this paper the positivity and the stability of the associated matrix semigroup. The abstract results are illustrated by several examples.     

Small random perturbations in second-order oscillatory systems

The limit behavior of the solutions of a nonlinear differential equation that describes an oscillatory system with small random perturbations of the type of multidimensional white and shot noises is studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 11–16, January, 1992.     

Minimal indefinite Randomisierungen von Spielen

Summary For games with uncountably many pure strategies there exists in general not only a uniquely determined mixed extension, but a system of different randomizations. A randomization for which the interval between lower and upper value is as small as possible is called minimal indefinite. A minimal indefinite randomization is either definite (strictly determined) or the game is essentially indefinite. The construction of increasing sequences of sets of minimal indefinitely randomized games by means of iterated composition leads to criteria for a randomization to be minimal indefinite. As a by-product we get an arsenal of necessary conditions for the existence of a definite randomization. The notion of randomization is understood here in a rather wide sense: Instead of using a condition adapted to convexity only a much weaker composibility-condition is required; conditions on measurability are reduced to a minimum.     

Computing convolutions by reciprocal search

In this paper we show how certain geometric convolution operations can be computed efficiently. Here efficiently means that our algorithms have running time proportional to the input size plus the output size. Our convolution algorithms rely on new optimal solutions for certain reciprocal search problems, such as finding intersections between blue and green intervals, and overlaying convex planar subdivisions.This research was done while on leave from Cornell at DEC/SRC.     

Computations in choice groupoids

Defining achoice as a mapping of the subsets of a setX into their respective subsets, a one-to-one (and naturally) corresponding binary operation,sequential choice, is identified under which the power set ofX is closed as achoice groupoid. A complete logical diagram is given, exhibiting all the implications between conjunctions of the seven conditions: (1) idempotence, (2) consistency, (3) absorbence, and (4) homomorphism of a choice, and (5) commutativity, (6) associativity, and (7) path-independence of the corresponding sequential choice.     

Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory

According to Maslov, many 2D quasilinear systems of PDE possess only three algebras of singular solutions with properties of structural self-similarity and stability. They are the algebras of shock waves, narrow solitons, and square-root point singularities (solitary vortices). Their propagation is described by infinite chains of ODE (the Hugoniót–Maslov chains). We consider the Hugoniót-Maslov chain for the square-root point singularities of the shallow water equations. We discuss different related mathematical questions (in particular, unexpected integrability effects) as well as their possible application to the problem of typhoon dynamics.     

Model reduction techniques for sampled-data systems

An approximately balanced realization of linear finite-dimensional sampled-data systems is proposed. The theoretical support of the approximately balancing algorithm is represented by a result on the asymptotic expansions with respect to the sampling step of the sampled controllability and observability graminas. Reduced order models obtained as singular perturbational approximations of approximately balanced realizations of sampled-data systems are shown to be acceptable solutions to the sampled-data system model reduction problem in the sense that, enjoying some asymptotic properties, they come close to the exact solutions as the sampling step decreases. An example illustrates the results.     

Construction of Pseudorandom Binary Sequences Using Additive Characters

In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large.