The Complexity of Computations by Networks

We survey the current state of knowledge concerning the computation of Boolean functions by networks, with particular emphasis on the addition and multiplication of binary numbers

Generalizing Binary Operations

Most day to day calculations take place within the field of real numbers with the two binary operations of addition and multiplication. In this field, these two operations are definitionally independent of one another. However, if we approach binary operations from a different point of view, e.g. that of recursive formulae, we can develop multipli cation from addition by use of the concept of repeated addition. Along similar lines, we can develop exponentiation from multiplication by re peated multiplication. The next logical step would be to try to develop another binary operation based on repeated exponentiation

On computing in fine-grained compartmentalised Belousov-Zhabotinsky medium

We introduce results of computer experiments on information processing in a hexagonal array of vesicles filled with Belousov-Zhabotinsky (BZ) solution in a sub-excitable mode. We represent values of Boolean variables by excitation wave-fragments and implement basic logical gates by colliding the wave-fragments. We show that a vesicle filled with BZ mixture can implement a range of basic logical functions. We cascade BZ-vesicle logical gates into arithmetic circuits implementing addition of two one-bit binary numbers. We envisage that our theoretical results will be applied in chemical laboratory designs of massive-parallel computers based on fine-grained compartmentalisation of excitable chemical systems

msBP: An R package to perform Bayesian nonparametric inference using multiscale Bernstein polynomials mixtures

msBP is an R package that implements a new method to perform Bayesian multiscale nonparametric inference introduced by Canale and Dunson (2016). The method, based on mixtures of multiscale beta dictionary densities, overcomes the drawbacks of Pólya trees and inherits many of the advantages of Dirichlet process mixture models. The key idea is that an infinitely-deep binary tree is introduced, with a beta dictionary density assigned to each node of the tree. Using a multiscale stick-breaking characterization, stochastically decreasing weights are assigned to each node. The result is an infinite mixture model. The package msBP implements a series of basic functions to deal with this family of priors such as random densities and numbers generation, creation and manipulation of binary tree objects, and generic functions to plot and print the results. In addition, it implements the Gibbs samplers for posterior computation to perform multiscale density estimation and multiscale testing of group differences described in Canale and Dunson (2016)

Synergistic toxicity of some sulfonamide mixtures on Daphnia magna

In livestock farming, sulfonamides (SAs) are used prophylactically and simultaneously in large numbers of animals. Therefore, traces of these compounds, alone or in combination, have been repeatedly detected in the environment. Synergistic interactions among chemicals in such mixtures represent an area of concern for the regulatory authorities. In this study, the acute toxic effects of binary and ternary mixtures of SAs were evaluated in Daphnia magna, in order to verify whether, based on their individual toxicity, they jointly exert a larger effect than would be predicted by individual actions alone. First, following the Concentration Addition (CA) principle, some preliminary observations were made by testing a number of drug combinations with an expected 50% effect. Then, mixtures more recognised for their synergistic effect (four binary and two ternary) were assayed in a range of reducing concentrations. The data acquired were processed using CompuSyn software, which integrates the different shape of the curves obtained in calculating the Combination Index (CI) for the evaluation of synergistic effects. For binary mixtures, synergy was also evaluated using the curvilinear isobologram method for heterodynamic drugs. Results indicate that most of the selected mixtures exhibit a synergistic effect using the CI methodology. For binary mixtures, these findings were also confirmed by isobologram analysis. Detected synergies indicate that the CA is not always precautionary as a reference model for the evaluation of the aquatic toxicity of SAs mixtures