Given an n-ary k-valued function f , gap(f) denotes the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f . We particularly solve a problem concerning the explicit determination of n-ary k-valued functions f with 2 ≤ gap(f) ≤ n ≤ k. Our methods yield new combinatorial results about the number of such functions.

Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric log...

Salisbury and Verzani introduced a class of martingales for the Brownian superprocess related to conditionings of the process to exit the boundary of a bounded domain in Rd in a particular way. The corresponding class of functions, denoted Hg,h1,...,hN , was generalized by Dynkin to more general superprocesses and shown to be X-harmonic. Salisbury and Verzani conjectured that a certain choice o...

Motivated by economic thought, a recent research agenda has suggested the algorithmic study of combinatorial optimization problems under functions which satisfy the property of decreasing marginal cost. A natural first step to model such functions is to consider submodular functions. However, many fundamental problems have turned out to be extremely hard to approximate under general submodular ...

Integrated Circuit manufacturing complexities have resulted in decreasing product yields and reliabilities. This process has been accelerated with the advent of very deep sub-micron technologies coupled with the introduction of newer materials and technologies like copper interconnects, siliconon-insulator and increased wafer sizes. The need to improve product yields has been recognized and cur...

8 What are the psychological functions that could only be performed 9 consciously? People have intuitively assumed that many acts of volition are not 10 influenced by unconscious information. These acts range from simple examples 11 such as making a spontaneous motor movement, to higher cognitive control. 12 However, the available evidence suggests that under suitable conditions, 13 unconscious...

This paper presents a method for transforming a function into a combination of correlated perturbated functions by splitting its input space into sub-spaces, assigning each to a different function in such a way that a majority vote on their outputs will always yield the correct initial functions output. This novel technique allows function obfuscation and implementation diversication. Applicati...

We consider latent structural versions of probit loss and ramp loss. We show that these surrogate loss functions are consistent in the strong sense that for any feature map (finite or infinite dimensional) they yield predictors approaching the infimum task loss achievable by any linear predictor over the given features. We also give finite sample generalization bounds (convergence rates) for th...

The dynamics of discrete mathematical systems can be related to the values of certain ordering parameters. Experiments with the total set of possible structures of a boolean network with six elements and extended sets of two-valued boolean functions show that three simple parameters describing the topology, the bias of boolean functions, and their canalyzing potential yield necessary conditions...