Two Topics Ahead Membrane Computing

Two topics from the area of probability theory and randomness challenging membrane computing together with open problems and research proposals are discussed

Modeling the overalternating bias with an asymmetric entropy measure

Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin proposed an asymmetric measure of entropy that can be ideal to account for such bias and to quantify subjective randomness. We fitted Marcellin's entropy and Renyi's entropy (a generalized form of uncertainty measure comprising many different kinds of entropies) to experimental data found in the literature with the Differential Evolution algorithm. We observed a better fit for Marcellin's entropy compared to Renyi's entropy. The fitted asymmetric entropy measure also showed good predictive properties when applied to different datasets of randomness-related tasks. We concluded that Marcellin's entropy can be a parsimonious and effective measure of subjective randomness that can be useful in psychological research about randomness perception

Randomness, Determinism and Undecidability in the Economic Cycle Theory

AbstractThe scientific literature that studies the Business cycles contains a historical debate between random and deterministic models. On the one hand, models built with explanatory variables follow a stochastic trajectory and produce, through transmission mechanisms, the studied cycles. Its rationale: the so-called Slutsky-Yule effect. In addition, models in which the system phase at time T fixes, applying the “ceteris paribus condition”, the phase at time t + 1. The cycle would be the product of variables, making it possible to predict and enabling economic policies to combat recessions. The thesis of this work is as follows. The application of the theorems of Chaitin of undecidability shows that it is not possible to conclude such debate. It is impossible to determine with absolute certainty whether the observed cycles follow a deterministic or stochastic model. To reach this result, I outline the fundamental theories of the business cycle, providing a classification and examples of mathematical models. I review the definition of randomness, and I consider the demonstration of Chaitin about the impossibility of deciding whether a data set is stochastic or not. A consequence, he says, of Gödel incompleteness theorems. I conclude considering a string of economic data, aggregated or not, as random or deterministic, depends on the theory. This applies to all cyclical phenomena of any nature. Specific mathematical models have observable consequences. But probabilism and determinism are only heuristic programs that guide the knowledge progress. Key words: Randomness, Business cycle theories, Undecidability, Heuristic.JEL: B40, D50, E32

A meta-analysis of randomness in human behavioral research

This work analyzes the concept of randomness in binary sequences from three different perspectives: mathematically, statistically, and psychologically and examines the research on human perception of randomness and the question of whether or not humans can simulate random behavior. Generally, research shows that human subjects have great difficulty producing random sequences, even when they are instructed and motivated. We survey some of the literature and present some leading theoretical proposals. Finally, we present some basic statistical tests that can be used to evaluate randomness in a given binary sequence

Indices of regularity and indices of randomness for m-ary strings

The notions “regularity index” and “randomness index” previously introduced forbinary strings (2-ary) have been modified slightly and generalized for m-ary strings(m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomyhas been replaced by a gradation of values of regularity and of randomness.With this approach, the more regular an m-ary string, the less random it is, and viceversa. The distributions of frequencies of different length strings —2-ary and 3-arystrings— according to their indices of randomness, are shown by histograms.Keywords: regularity index, randomness index, m-ary strings.Las nociones de ´?ndice de regularidad y de ´?ndice de aleatoriedad previamente introducidaspara cadenas binarias (2-arias) son modificadas ligeramente y generalizadaspara cadenas m-arias (m = 2, 3, 4, . . .). Dichas nociones resultan complementarias y ladicotom´?a regular-aleatorio es sustituida por una gradaci´on de valores de regularidady de aleatoriedad. Con el enfoque utilizado, cuanto m´as regular es una cadena m-ariamenos aleatoria debe ser considerada y viceversa. Las distribuciones de frecuenciasde cadenas —de diversas longitudes— 2-arias y 3-arias en funci´on de sus ´?ndices dealeatoriedad son presentadas mediante histogramas.Palabras clave: ´?ndice de regularidad, ´?ndice de aleatoriedad, cadenas m-arias

On the Application of PSpice for Localised Cloud Security

The work reported in this thesis commenced with a review of methods for creating random binary sequences for encoding data locally by the client before storing in the Cloud. The first method reviewed investigated evolutionary computing software which generated noise-producing functions from natural noise, a highly-speculative novel idea since noise is stochastic. Nevertheless, a function was created which generated noise to seed chaos oscillators which produced random binary sequences and this research led to a circuit-based one-time pad key chaos encoder for encrypting data. Circuit-based delay chaos oscillators, initialised with sampled electronic noise, were simulated in a linear circuit simulator called PSpice. Many simulation problems were encountered because of the nonlinear nature of chaos but were solved by creating new simulation parts, tools and simulation paradigms. Simulation data from a range of chaos sources was exported and analysed using Lyapunov analysis and identified two sources which produced one-time pad sequences with maximum entropy. This led to an encoding system which generated unlimited, infinitely-long period, unique random one-time pad encryption keys for plaintext data length matching. The keys were studied for maximum entropy and passed a suite of stringent internationally-accepted statistical tests for randomness. A prototype containing two delay chaos sources initialised by electronic noise was produced on a double-sided printed circuit board and produced more than 200 Mbits of OTPs. According to Vladimir Kotelnikov in 1941 and Claude Shannon in 1945, one-time pad sequences are theoretically-perfect and unbreakable, provided specific rules are adhered to. Two other techniques for generating random binary sequences were researched; a new circuit element, memristance was incorporated in a Chua chaos oscillator, and a fractional-order Lorenz chaos system with order less than three. Quantum computing will present many problems to cryptographic system security when existing systems are upgraded in the near future. The only existing encoding system that will resist cryptanalysis by this system is the unconditionally-secure one-time pad encryption