Turing computability with neural nets

This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10⁵ synchronously evolving processors, interconnected linearly. High-order connections are not required.     

A fuzzy approach to cooperative n-person games

The object of this paper is to provide a systematic treatment of bargaining procedures as a basis for negotiation. An innovative fuzzy logic approach to analyze n-person cooperative games is developed. A couple of indices, the Good Deal Index and the Counterpart Convenience Index are proposed to characterize the heuristic of bargaining and to provide a solution concept. The indices are examined theoretically and experimentally by analyzing three case studies. The results verify the validity of the approach.     

Stochastic Accelerated Alternating Direction Method of Multipliers with Importance Sampling

In this paper, we incorporate importance sampling strategy into accelerated framework of stochastic alternating direction method of multipliers for solving a class of stochastic composite problems with linear equality constraint. The rates of convergence for primal residual and feasibility violation are established. Moreover, the estimation of variance of stochastic gradient is improved due to the use of important sampling. The proposed algorithm is capable of dealing with the situation, where the feasible set is unbounded. The experimental results indicate the effectiveness of the proposed method.     

Lower Bounds for the Lp-Norm in Terms of the Mellin Transform

Given a measurable function f on (0, ) with Mellin transformF(s), let |f|_p denote the L^p-norm of f with respect to the measuredx/x. We prove that under certain assumptions, for instanceif f is real and non-negative and F() converges for in an openinterval and F() 0, then wherec_p (2e)^–1. We derive similar inequalities for complex-valuedf, for the L^p-norm of the derivative of f, and for the supremumof real-valued f and of its derivative. The lower bounds areeminently applicable when f is a convolution product.     

Absorption and thermal study of dental enamel when irradiated with Nd:YAG laser with the aim of caries prevention

It is widely recognized that Nd:YAG can increase enamel resistance to demineralization; however, the safe parameters and conditions that enable the application of Nd:YAG laser irradiation in vivo are still unknown. The aim of this study was to determine a dye as a photoabsorber for Nd:YAG laser and to verify in vitro a safe condition of Nd:YAG irradiation for caries prevention. Fifty-eight human teeth were selected. In a first morphological study, four dyes (waterproof India ink., iron oxide, caries indicator and coal paste) were tested before Nd:YAG laser irradiation, under two different irradiation conditions: 60 mJ/pulse and 10 Hz (84.9 J/cm²); 80 mJ/pulse and 10 Hz (113.1 J/cm²). In a second study, the enamel surface and pulp chamber temperatures were evaluated during laser irradiations. All dyes produced enamel surface melting, with the exception of the caries indicator, and coal paste was the only dye that could be completely removed. All irradiation conditions produced temperature increases of up to 615.08°C on the enamel surface. Nd:YAG laser irradiation at 60 mJ/pulse, 10 Hz and 84.9 J/cm² promoted no harmful temperature increase in the pulp chamber (ANOVA, p < 0.05). Among all dyes tested, the coal paste was an efficient photoabsorber for Nd:YAG irradiation, considered feasible for clinical practice. Nd:YAG laser at 84.9 J/cm² can be indicated as a safe parameter for use in caries prevention.     

Virtual parallel computing and a search algorithm using matrix product States

We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product state that encodes multiple inputs. Matrix evolution follows from the sequential application of gates, as in a logical circuit. The action by classical probabilistic one-bit and deterministic two-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions. We argue that if the classical computational cost of testing solutions (witnesses) requires less than O(n^{2}) local two-bit gates acting on n bits, the search problem can be fully solved in subexponential time. Therefore, for this restricted type of search problem, the virtual parallelization scheme is faster than Grover's quantum algorithm.     

Periodic Boundary Value Problems for a Class of Functional Differential Equations

In this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part.     

Attractors in coherent systems of differential equations

Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor, and orbits are nowhere dense. This paper provides characterizations of attractors for the wider class of coherent systems, defined by the property that all directed feedback loops are positive. Several new results for cooperative systems are obtained in the process. Connections with biological models are discussed.