Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With certain restrictions on the metric, we establish that the spectrum is discrete and satisfies Weyl’s asymptotic formula. 1. Discreteness of the Spectrum When...

Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of incomplete information and that this value is uniform, i.e. there are ǫ-optimal strategies for both players that are ǫ-optimal in any long enough prefix of the game. ...

In this paper we focus our attention on the estimation of dynamic discrete systems in which the observed signal is not always related to all components in the state vector, but on the contrary, it can be considered incomplete, since we do not know if a particular observed signal contains information regarding all components or not. We develop a very simple framework to deal with these situation...

1 American options in discrete time 2 1.1 Discrete markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Martingale measure and arbitrage price . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Binomial model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 American options . . . . . . . . . . . . . . . . ....

The discrete multi-way layout is an abstract data-type associated with regression, experimental designs, digital images or videos, spatial statistics, gene or protein chips, and more. The factors influencing response can be nominal or ordinal. The observed factor level combinations are finitely discrete and often incomplete or irregularly spaced. This paper develops low risk biased estimators o...

We address a prediction problem that frequently occurs in practice We wish to predict the value of a function on the basis of discrete obser vational dat a that are incomplete in two senses Only certain arguments of the function ar e observed and the function value is observed only for certain combinations of values of these arguments We solve the problem under a monotonicity condition that is ...

Bayesian networks provide a powerful intelligent information fusion architecture for modeling probabilistic and causal patterns involving multiple random variables. This paper advances a computable theory of learning discrete Bayesian networks from data. The theory is based on the MAP-MDL principles for maximizing the joint probability or interchangeably miniziming the joint description length ...