Equiprobable Distribution Research Articles

STUDY OF THE INFLUENCE OF MgO DOPING ON THE THERMOPHYSICAL PROPERTIES OF CERAMICS BASED ON LITHIUM METAZIRCONATE

The paper presents the results of studying the effect of doping with magnesium oxide (MgO) of lithium-containing ceramics based on lithium metazirconate (Li2ZrO3) on the change in the thermophysical parameters of ceramics. The method of mechanochemical synthesis followed by high-temperature annealing at a temperature of 1300 °C, used to initiate the processes of phase transformations from structural ordering, was chosen as the main method for obtaining ceramics, as well as for performing MgO doping processes. In the course of the studies, it was found that an increase in the concentration of the MgO dopant above 0.10 mol leads to the formation of impurity inclusions in the structure of ceramics in the form of a tetragonal phase MgLi2ZrO4, the content of which increases with an increase in the concentration of the dopant. In the case of a dopant concentration of 0.25 mol, the phase composition of ceramics is an equiprobable distribution of two phases, monoclinic Li2ZrO3 and tetragonal MgLi2ZrO4. In the course of measuring thermophysical parameters, it was found that the formation of the MgLi2ZrO4 phase in the composition of ceramics leads to an increase in the thermal conductivity by 5–10%, and in the case of an equiprobable distribution of phases in two-phase MgLi2ZrO4– Li2ZrO3 ceramics, the increase in thermal conductivity is more than 25% in comparison with undoped ceramics. An increase in the efficiency of heat-conducting properties for two-phase ceramics is due to an increase in the rate of phonon heat transfer due to additional interfacial boundaries, as well as an increase in the degree of structural ordering and density of ceramics.

Fractal Divergences of Generalized Jacobi Polynomials

The notion of entropy (including macro state entropy and information entropy) is used, among others, to define the fractal dimension. Rényi entropy constitutes the basis for the generalized correlation dimension of multifractals. A motivation for the study of the information measures of orthogonal polynomials is because these polynomials appear in the densities of many quantum mechanical systems with shape-invariant potentials (e.g., the harmonic oscillator and the hydrogenic systems). With the help of a sequence of some generalized Jacobi polynomials, we define a sequence of discrete probability distributions. We introduce fractal Kullback–Leibler divergence, fractal Tsallis divergence, and fractal Rényi divergence between every element of the sequence of probability distributions introduced above and the element of the equiprobability distribution corresponding to the same index. Practically, we obtain three sequences of fractal divergences and show that the first two are convergent and the last is divergent.

Stability of Characteristics of Physical Random Number Generators

The development of technologies leads to the need of revising the methods used to obtain cryptographic keys. The randomness parameters of sequences generated by physical random sequence generators are affected by the physical parameters of the recording equipment and the environment. The requirements for the randomness of the sequence, when passing the binary test, are obtained. It is shown that as the sequence length increases, the requirements for possible deviations from the equiprobable distribution of 0 and 1 increase. The randomness stability of the sequences generated by the generator based on the study of photons is estimated. The oscillator under study consists of an LED and a compact silicon photomultiplier designed to detect low-power light radiation. Possible physical processes leading to the deterioration of the randomness of sequences are shown. The possibility of using a generator of random numerical sequences based on a small-sized silicon photomultiplier for cryptographic purposes is estimated.

A property of extreme entropy values in critical regimes of two-phase flows

In a critical regime of vertical ascending flows, a certain part of solid particles moves with the flow, while another part settles against the flow. Entropy is a key parameter in the analysis of properties of mass systems. It can be considered as consisting of two parts ― internal entropy arising during irreversible processes within the system and external entropy depending on the system correlation with the surroundings. Here a system represents the totality of all solid particles of various sizes simultaneously present in the flow. In thermodynamics, ordinary total entropy consisting of these two components has a tendency to reach the maximum when the entire system reaches equilibrium. In this case, its internal entropy always increases. In contrast to the conventional entropy, the internal entropy in the process under study can decrease due to the peculiarities of the solid phase motion and mass exchange caused by the latter. However, in a critical regime, one can always reveal a narrow size class in a mixture of particles, whose entropy tends to maximum when this class reaches a peculiar equilibrium in the flow. The peculiarity of this equilibrium consists in an equiprobable distribution of particles of this class in both directions – upwards and downwards. For other size classes participating in the process, the internal entropy does not reach the maximum, and these classes are not equally distributed between the directions of motion. The condition of optimal mass exchange of the total granulometric set of particles in specific conditions of critical flow is connected with an equilibrium size class. Ill. 1. Ref. 2.

Generalized de Bruijn graphs

Abstract We study the graphs of transitions between states of nonautonomous automata that provide, with independent equiprobable input signs, an equiprobable distribution on the set of all states in the minimum possible number of cycles, as is the case of the de Bruijn graphs corresponding to shift registers. It is proved that in the case of a binary input alphabet, there are at least 12r−33 pairwise nonisomorphic directed graphs with 2 r vertices that have this property. All graphs of this type with 8 and 9 vertices are found.

Random number generation with arrays of coupled quantumdot micropillar lasers

The paper investigates the results of random number generation with arrays of coupled quantum-dot micropillar lasers. The micropillars array laser generation is modeled based on the rate equations for quantum dot lasers. The numerical simulation of the dynamics for the arrays of coupled quantum-dot micropillar lasers is carried out utilizing the semi-implicit Euler method, implemented in Julia programming language. The algorithm of random bit sequence generation consists of the following steps: sampling the values of the total field intensity for coupled micropillar lasers; normalizing and discretizing the obtained values per resolution of the 8-bit analog-to-digital converter; extracting the four least significant bits from the bit representation of the sampled values; concatenating the bit values in a single sequence. The possibility of the bit sequences generation having an equiprobable distribution of zeros and ones with a performance of up to 400 Gbit/s was shown utilizing a random number generator based on an array of coupled quantum-dot micropillar lasers for sequences with a length of 14285716 bits at a sampling rate of 100 gigasamples per second and four least significant bits extraction. The resulting bit sequences successfully passed 14 NIST 800-22 statistical tests for the p-value equal to 0.01. The proposed method can be applied to develop random number generators based on larger arrays of coupled quantum-dot micropillar lasers. The results can be utilized in the experimental implementation of random number generators based on arrays of coupled quantum-dot micropillar lasers.

Study of the regularities of resistance to deformation and damage accumulation under irregular low cycle loading

The results of computation and experimental studies of changes in the regularities of the strain resistance and damage accumulation in conditions of the irregular low cycle loading are presented and compared with similar data for a regular cyclic elastoplastic deformation at the same loading. The irregular mode of low cycle loading implemented in the study is adopted in the form of an equiprobable distribution of changes in the stress amplitudes within a given range between maximum and minimum levels at the symmetric form of the cycles. This mode was reproduced on test equipment through introduction of the corresponding functional dependence of changes in the stress amplitude in the cycles into the control program. The data on a cycle-by-cycle kinetics of both cyclic and unilaterally accumulated strains obtained under irregular mode of loading were recorded in a databank and then compared with the data for a regular loading. This provided the possibility of their analytical description by the corresponding equations of state with the correction of the parameters of the diagrams of cyclic elastoplastic deformation taking into account the conditions of irregularity of loading modes. The results of the experiments are presented in the form of diagrams of the tests modes, curves of a low cycle fatigue of the studied material at the soft and hard loading modes, diagrams of a cycle-by-cycle kinetics of the cyclic and accumulated strains at the regular and irregular modes, and also as kinetic diagrams of damages accumulation for these conditions. Using the summation criteria expressed through the deformation characteristics of accumulated damage, it is shown that taking into account change in the character of the strain development under irregular low-cycle loading, the criterion dependences can be used to assess the durability and compare it with the similar data under regular modes when accepting the condition of attaining the limiting state.

On the number of ones in outcome sequence of extended Pohl generator

Abstract Formulas for distributions of number of ones (non-zeroes) in the cycle of the output sequence of generalized binary Pohl generator are obtained. Limit theorems for these distributions are derived in the case when the lengths of registers are coprime and tend to infinity, the contents of different registers are independent, but cell contents within each register may be dependent. The consequences of these theorems are given for the case when the contents of cells are independent random variables having equiprobable distribution on {0, 1}.

Effect of Ni doping on stabilization of Sm(Co1−xFex)5 compound: thermodynamic calculation and experiment

The calculation of the heat of formation of Sm(Co1−x−yFexNiy)5 compound using homemade software in the framework of Miedema’s model was carried out. In addition we investigated the influence of the probability of occupation the transition metals sites by 3d-ions, in particular, equiprobable distribution of 3d-ions among 2c and 3g sites and selective distribution Co/Ni-(2c), Fe-(3g). The maximal Fe and Ni doping ranges, where Sm(Co1−x−yFexNiy)5 phase with the CaCu5-type crystal structure stable, were estimated for both types of distribution. The corresponding values of the number of 3d-electrons per atom were 7.23 (Fe/Co/Ni-(2c, 3g)) and 7.3 (Co/Ni-(2c), Fe-(3g)). Based on calculation the Sm(Co1−x−yFexNiy)5 (x = 0.15, 0.3, 0.45; y = 0.05, 0.1, 0.15) melt-spun ribbons were synthesized. The maximal doping level of x = 0.5 and y = 0.2 was experimentally determined for Fe and Ni atoms, respectively. These values are in good agreement with the theoretical prediction, assumed equiprobable distribution of 3d-ions among transition metal sites. The best among the series in terms of energy product Sm(Co0.6Fe0.3Ni0.1)5 sample possesses a coercivity of 10.9 kOe and remanent magnetization of 51 emu g−1.

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

This paper is focused on the derivation of data-processing and majorization inequalities for f-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first introduced without proofs, followed by exemplifications of the theorems with further related analytical results, interpretations, and information-theoretic applications. One application refers to the performance analysis of list decoding with either fixed or variable list sizes; some earlier bounds on the list decoding error probability are reproduced in a unified way, and new bounds are obtained and exemplified numerically. Another application is related to a study of the quality of approximating a probability mass function, induced by the leaves of a Tunstall tree, by an equiprobable distribution. The compression rates of finite-length Tunstall codes are further analyzed for asserting their closeness to the Shannon entropy of a memoryless and stationary discrete source. Almost all the analysis is relegated to the appendices, which form the major part of this manuscript.

Three-dimensional stochastic assimilation of gravity data in Lalor volcanogenic massive sulphide, Manitoba, Canada

We propose a new numerical workflow based on stochastic data integration where we merge a conceptual geological model, drillhole geophysical and geological logs, and surface geophysical data to compute a unified numerical model of a volcanogenic massive sulphide (VMS) deposit. The first step of the workflow consists in building a three-dimensional (3D) numerical conceptual model of the geology. This conceptual model, as well as geological logs, is then used to generate multiple equiprobable scenarios of the geology by means of multiple-point simulation (MPS). The MPS method studies high-order statistics in the space of a numerical conceptual model, making it possible to reproduce complex geological structures. We then use conventional conditional sequential Gaussian simulation, which is a method based on a node-by-node sequential process, to stochastically populate the geological grid with densities. For this purpose we use available density logs to simulate multiple equiprobable spatial distributions of the density at high spatial resolution within each geological unit separately. The stochastic high-resolution density models are iteratively combined by the gradual deformation method to minimize the difference between measured Bouguer anomaly data and the data computed on the combined realizations of density. Application of the proposed method to the Lalor deposit, a VMS deposit in Manitoba, Canada, produces a density model that honours the geology of the deposit and the Bouguer anomaly data. This unified model has the advantage to include all the available information (geological and density logs and surface geophysics) at scales appropriate for mining applications.

Learning Automaton-Based Neighbor Discovery for Wireless Networks Using Directional Antennas

This letter studies the problem of neighbor discovery (i.e., finding 1-hop neighbor nodes) in a wireless adhoc network, with exclusive use of directional antennas. We model the neighbor discovery process as a learning automaton, operating in a non-stationary learning environment with unknown dynamics. The node learns about its environment from its past observations and adjusts its strategy to achieve a faster discovery rate. The asymptotic behavior of the proposed learning scheme is analyzed and is shown to converge to an equi-probable probability distribution. The proposed scheme achieves significantly faster network-wide neighbor discovery in densely populated networks.

The Cluster Variation Method: A Primer for Neuroscientists.

Effective Brain–Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables, is defined in terms of a single interaction enthalpy parameter (h) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found.

An investigation of the bus headways and the passenger waiting time on the urban routes

Waiting time at stop for boarding in shuttle vehicles is most unwanted part of passenger transportation difficulty using public transport. The value of average waiting time at bus stop directly affects the degree of traveling satisfaction and is an indicator that determines the quality of transport services. The article made a statistical analysis of bus headway at stops, located at the joint area of several routes in the city Zaporozhye (Ukraine) during the period of morning peak hours. The presence of significant linear correlation between expectation of network headway of different groups of buses, each of which corresponds to the selection of passenger variant, and its standard deviation. It is established that the headway at bus stop for various groups of routes having inconsistent schedules with sufficient accuracy for practical calculations can be described by the law of the gamma distribution with shape parameter that, subject to the random passenger arrival at stop and equiprobable passenger distribution for groups of routes increases the average passenger waiting time at bus stop by 15-25 % in comparison with the case of regular bus traffic.

Investigating the Relationship Between the Diversity Index and Frequency of Offending

Recent work has suggested that specialization is correlated with frequency of offending, but this observed relationship may actually depend on the measuring instrument used. The diversity index is a common method of measuring specialization in such studies, and this paper investigates whether this observed correlation is due in part to the mathematical form of the diversity index itself. The criminological question as to whether specialization increases or decreases with offense frequency cannot be answered until the behavior of the diversity index is better understood. We use simulations to investigate the behavior of the diversity index where the number of crimes is small (the small sample problem), simulating from known distributions of offending. Two of the distributions used in the simulation are defined to be unspecialized. The first uses an equiprobable distribution of offenses across offense categories. The second uses the distribution of offenses in the British population. The third distribution is from a specialist distribution and assumes that different offenders have different probabilities of choosing particular offenses.We report these simulations for both three and ten crime categories. To set the simulated results in context, we use an extract from the UK Police National Computer to investigate the criminological question as to whether specialization increases with offense frequency. For all three simulation schemes, the diversity index D increases steeply with the frequency of offending N at low frequencies, with the increase slowing around N = 20, and becoming flat when the number of offenses N reaches 500. This relationship is observed for both three crime categories and ten crime categories. The observed relationship of D with N can be used to correct the diversity index to allow the true relationship of specialization with offense frequency to be investigated. We recommend that the diversity index be used with caution when there are small numbers of crimes over fixed time periods. Any increase or decrease of the diversity index over the criminal career life course may reflect the behavior of the measurement tool with the number of offenses, rather than any change in specialization itself. Applying one of the suggested suitable correction methods to D will mitigate this problem.

Orientational bistability and magneto-optical response in compensated ferronematic liquid crystals

In the framework of continuum theory we consider magnetic field induced transitions in soft compensated ferronematic liquid crystals, i.e., suspensions of ferromagnetic nanoparticles in nematic solvents with equiprobable distribution of the particles parallel and antiparallel to the director. Such systems are liquid-crystalline analogs of antiferromagnetics. We study the sequence of re-entrant transitions (uniform compensated phase – non-uniform phase – uniform saturation phase – non-uniform phase) between phases with different orientations of the director and magnetization. These transitions take place under the magnetic field action in the case of weak coupling between disperse magnetic phase and nematic matrix. We show that these transitions can be first or second order, and obtain the expressions for determining the order of orientational transitions. For the case of first order transitions, when the ferronematic shows orientational bistability, we study magnetic field influence on the orientational behavior of the director and magnetization, redistribution of magnetic impurity, and magneto-optical response.

Optical modeling of volcanic ash particles using ellipsoids

AbstractThe single‐scattering properties of volcanic ash particles are modeled here by using ellipsoidal shapes. Ellipsoids are expected to improve the accuracy of the retrieval of aerosol properties using remote sensing techniques, which are currently often based on oversimplified assumptions of spherical ash particles. Measurements of the single‐scattering optical properties of ash particles from several volcanoes across the globe, including previously unpublished measurements from the Eyjafjallajökull and Puyehue volcanoes, are used to assess the performance of the ellipsoidal particle models. These comparisons between the measurements and the ellipsoidal particle model include consideration of the whole scattering matrix, as well as sensitivity studies on the point of view of the Advanced Along Track Scanning Radiometer (AATSR) instrument. AATSR, which flew on the ENVISAT satellite, offers two viewing directions but no information on polarization, so usually only the phase function is relevant for interpreting its measurements. As expected, ensembles of ellipsoids are able to reproduce the observed scattering matrix more faithfully than spheres. Performance of ellipsoid ensembles depends on the distribution of particle shapes, which we tried to optimize. No single specific shape distribution could be found that would perform superiorly in all situations, but all of the best‐fit ellipsoidal distributions, as well as the additionally tested equiprobable distribution, improved greatly over the performance of spheres. We conclude that an equiprobable shape distribution of ellipsoidal model particles is a relatively good, yet enticingly simple, approach for modeling volcanic ash single‐scattering optical properties.

Statistical Complexity. Applications in Electronic Systems

In this review, a statistical measure of complexity is introduced and its properties are discussed. This measure is based on the interplay between the Shannon information, or a function of it, and the separation of the set of accessible states to a system from the equiprobability distribution, i.e. the disequilibrium. Different applications concerning with quantum systems are shown, from prototypical systems such as the H-atom, to other ones such as the periodic table, the metal clusters, the crystalline bands or the traveling densities. In all of them, this type of statistical indicators shows an interesting behavior able to discern and highlight some conformational properties of those systems.

Multiple-Antenna Fading Channels With Arbitrary Inputs: Characterization and Optimization of the Information Rate

We investigate the high-SNR capacity of multiple-antenna fading coherent channels driven by inputs that are constrained to obey a certain equiprobable discrete distribution rather than the optimal capacity-achieving Gaussian one. In particular, we capitalize on the machinery of asymptotic analysis, most notably the asymptotic expansion of integrals, in order to construct high-SNR expansions to the average minimum-mean squared error (MMSE) and—via the relation between MMSE and mutual information—high-SNR expansions to the average mutual information, thereby providing immediately a high-SNR expansion to the so-called constrained capacity. We use the expansions to characterize the constrained capacity of various multiple-antenna fading coherent channels, including Rayleigh fading models, Ricean fading models, and antenna-correlated models. The analysis unveils in detail the impact of the number of transmit and receive antennas, transmit and receive antenna correlation, line-of-sight components, and the geometry of the signaling scheme on the reliable information transmission rate. We also use the expansions to optimize the constrained capacity of multiple-antenna fading coherent channels, as an example, we focus on the derivation of design criteria for space-time signaling schemes.

Multiserver systems with rejections and the equiprobable distribution of customers

The queueing systems with rejections, arbitrary service time distributions, and two ways of the distributions of customers over heterogeneous servers (the equiprobable customer distribution over all (idle and busy) servers and the equiprobable customer distribution over idle servers) are discussed and used to find the stationary distributions of the number of customers. Their invariance with respect to service time distribution functions is proved. For an MX/M/n/0 system with homogeneous servers and the equiprobable customer distribution over all servers, the algorithm is proposed for determining the stationary distributions of the number of customers when their number in the batch is less than six. MX/M/2/0 and MX/M/3/0 systems with the equiprobable customer distribution over all servers and the arbitrary distribution of the number of arriving customers are studied. The results are checked using simulation models based on GPSS World software.