The limit order book is a device for storing demand and effecting trades that is the primary mechanism for price formation in most modern financial markets. We study the limit order book under a random process model of order flow, using simulations and an analytic treatment based on a master...

One of the many remarkable properties of the brain is the degree to which it is fault and failure tolerant. In many cases even the loss of substantial amounts of brain cells or tissue does not totally abolish brain function, a property known as "graceful degradation". It is therefore not...

In this working document, we report on a new approach to high performance simulation. The main inspiration to this approach is the concept of complex systems: disparate elements with well-defined interactions rules and non nonlinear emergent macroscopic behavior. We provide arguments and...

It has been well-known since the pioneering work of Claude Shannon in the 1940s that a message transmitted with optimal efficiency over a channel of limited bandwidth is indistinguishable from random noise to a receiver who is unfamiliar with the language in which the message is written. In this...

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k1. For the Wiener measure occurring in many applications we have k=2. We want to...

Sheltered from deleterious mutations, genes with overlapping or partially redundant functions may be important sources of novel gene functions. While most partially redundant genes originated in gene duplications, it is much less clear why genes with overlapping functions have been retained, in...

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to stochastic and deterministic processes by using a...

Daily records of atmospheric surface pressure, temperture and geopotential heights of 500 hPa ispbaric level were tested for nonlinearity, the necessary condition for deterministic chaos, using redundancy and surrogate data techniques. While the time series of the temperature and the...

We present a method for calculating the ``noise sensitivity signature'' of a learning algorithm which is based on scrambling the output of classes of various fractions of the training data. This signature can be used to indicate a good (or bad) match between the complexity of the classifier and...

This paper analyzes the evolutionary dynamics of a modified version of Rosenthal's ``centipede,'' whereby the players' strategies are represented by finite-state automata. In the framework considered, the automata required to implement different strategies may differ among them both with respect...