A new development cycle of the Statistical Toolkit

The Statistical Toolkit is an open source system specialized in the statistical comparison of distributions. It addresses requirements common to different experimental domains, such as simulation validation (e.g. comparison of experimental and simulated distributions), regression testing in the course of the software development process, and detector performance monitoring. Various sets of statistical tests have been added to the existing collection to deal with the one sample problem (i.e. the comparison of a data distribution to a function, including tests for normality, categorical analysis and the estimate of randomness). Improved algorithms and software design contribute to the robustness of the results. A simple user layer dealing with primitive data types facilitates the use of the toolkit both in standalone analyses and in large scale experiments.Comment: To be published in the Proc. of CHEP (Computing in High Energy Physics) 201

DES Security Enhancement using Genetic Algorithm

In this paper is proposed method for creating Data Encryption Standard (DES) sub-keys. The proposal simplifies the creation and expansion process of the encryption key of the Data Encryption Standard (DES) algorithm, which is considered one of the most important elements in the process of encryption. The sub-keys generation methods is implemented by using a genetic algorithm. The sub-keys generated using this method, based on genetic algorithm; they give a totally different group of pseudorandom sub-keys each time program is executed.Furthermore, comparison analyses between the proposed method sub-keys generation process and the standard technique used in Data Encryption Standard (DES) it give optimum results.The proposed method is also evaluated and subjected to many randomness tests in order to measure it‟s strength after encryption using National Institute of Standards and Technology-Test Suite is a statistical (NIST-STS) for randomness tests. The result shows that the proposed method gives good result and can be used it in many ciphers for sub-keys generation

Understanding Size Effects in Small Scale Deformation: A Statistical Perspective

Recent experimental observations of micro-compression / tension tests indicate that as the size of test specimen decreases the yield strength increases. This raises a fundamental question: Why is smaller stronger? Is there a fundamental relationship between the size of a specimen and its intrinsic strength? This simple question pushes the limit of the current understanding of the physical mechanisms underlying material deformation, especially at small scales. In order to explain the experimental observations of the strength of small specimens containing a limited number of dislocations, a simple statistical model is developed. Two different types of randomness are introduced, viz., randomness in the spatial location of dislocations and randomness in the stress needed to activate them. For convenience, the randomness in the activation stress is modeled by assigning a random Schmid factor to the dislocations. In contrast to the previous stochastic models, the current model not only predicts the yield strength in the presence of dislocations but also in their absence. Furthermore, the model has the capability to predict the scatter in the yield strength in addition to the mean. Monte Carlo simulations are also performed for comparison. Interestingly, the model adds credence to the notion that “smaller is stronger” from a purely statistical point of view. The model is found to quantitatively explain the yield strength and scatter in micro-compression / tension tests of Mo-alloy fibers using dislocation densities and arrangements measured by TEM. Furthermore, the model is extended to spherical indentation pop-in which is an analogous size dependent problem in small scale mechanics. In this case, the model predicts the load and maximum shear stress at pop-in as a function of indenter radius and is found to closely match the experimental results on single crystal molybdenum using a dislocation density estimated by micro-focus x-ray techniques. In summary, the current work provides possible explanations for the strength and scatter in strength of small specimens from a purely statistical perspective

An Evolutionary Approach to the Design of Controllable Cellular Automata Structure for Random Number Generation

Cellular Automata (CA) has been used in pseudorandom number generation over a decade. Recent studies show that two-dimensional (2-d) CA Pseudorandom Number Generators (PRNGs) may generate better random sequences than conventional one-dimensional (1-d) CA PRNGs, but they are more complex to implement in hardware than 1-d CA PRNGs. In this paper, we propose a new class of 1-d CA Controllable Cellular Automata (CCA) without much deviation from the structure simplicity of conventional 1-d CA. We give a general definition of CCA first and then introduce two types of CCA – CCA0 and CCA2. Our initial study on them shows that these two CCA PRNGs have better randomness quality than conventional 1-d CA PRNGs but their randomness is affected by their structures. To find good CCA0/CCA2 structures for pseudorandom number generation, we evolve them using the Evolutionary Multi-Objective Optimization (EMOO) techniques. Three different algorithms are presented in this paper. One makes use of an aggregation function; the other two are based on the Vector Evaluated Genetic Algorithm (VEGA). Evolution results show that these three algorithms all perform well. Applying a set of randomness tests on the evolved CCA PRNGs, we demonstrate that their randomness is better than that of 1-d CA PRNGs and can be comparable to that of two-dimensional CA PRNGs

A Family of Controllable Cellular Automata for Pseudorandom Number Generation

In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) ─ CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1-d CA. Moreover, their randomness can be comparable to that of 2-d CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved compared with any individual CCA PRNG

Quantum Randomness Certified by the Uncertainty Principle

We present an efficient method to extract the amount of true randomness that can be obtained by a Quantum Random Number Generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min- and max- entropies. We tested our method with two different QRNGs, using a train of qubits or ququart, demonstrating the scalability toward practical applications.Comment: 10 page

Pseudorandom number generation based on controllable cellular automata

A novel Cellular Automata (CA) Controllable CA (CCA) is proposed in this paper. Further, CCA are applied in Pseudorandom Number Generation. Randomness test results on CCA Pseudorandom Number Generators (PRNGs) show that they are better than 1-d CA PRNGs and can be comparable to 2-d ones. But they do not lose the structure simplicity of 1-d CA. Further, we develop several different types of CCA PRNGs. Based on the comparison of the randomness of different CCA PRNGs, we find that their properties are decided by the actions of the controllable cells and their neighbors. These novel CCA may be applied in other applications where structure non-uniformity or asymmetry is desired

Testing the randomness in the sky-distribution of gamma-ray bursts

We have studied the complete randomness of the angular distribution of gamma-ray bursts (GRBs) detected by the Burst and Transient Source Experiment (BATSE). Because GRBs seem to be a mixture of objects of different physical nature, we divided the BATSE sample into five subsamples (short1, short2, intermediate, long1, long2) based on their durations and peak fluxes, and we studied the angular distributions separately. We used three methods, Voronoi tesselation, minimal spanning tree and multifractal spectra, to search for non-randomness in the subsamples. To investigate the eventual non-randomness in the subsamples, we defined 13 test variables (nine from the Voronoi tesselation, three from the minimal spanning tree and one from the multifractal spectrum). Assuming that the point patterns obtained from the BATSE subsamples are fully random, we made Monte Carlo simulations taking into account the BATSE's sky-exposure function. The Monte Carlo simulations enabled us to test the null hypothesis (i.e. that the angular distributions are fully random). We tested the randomness using a binomial test and by introducing squared Euclidean distances in the parameter space of the test variables. We concluded that the short1 and short2 groups deviate significantly (99.90 and 99.98 per cent, respectively) from the full randomness in the distribution of the squared Euclidean distances; however, this is not the case for the long samples. For the intermediate group, the squared Euclidean distances also give a significant deviation (98.51 per cent)