Narrow Results

The mixed spin-1/2 and spin-1 Blume–Capel model is studied with randomly alternated coordination numbers (CN) on the Bethe lattice (BL) by utilizing the exact recursion relations. Two different CNs are randomly distributed on the BL by using the standard–random (SR) approach. It is observed that this model presents first-order phase transitions and tricritical points for variations of CNs 3 and 4, even if these behaviors are not displayed for the regular mixed-spin on the BL. The phase diagrams are mapped by obtaining the phase transition temperatures of the first- and second-order on several planes.

We obtain analytically a universal expression of the resonant energies for any one-dimensional (1D) models with the defects having symmetric internal structures. In a 1D periodic system with the on-site energy ε₀=0 and a nearest-neighbor matrix element t₀=1.0, two classes of the most interesting and simplest wavefunction behaviors are numerically obtained for the resonant energies around (a) 0, ±1, (b) , respectively. We show that similar wavefunction behaviors can be found widely in many quasiperiodic and random systems where the delocalization phenomena are predicted. We suggest that the envelope of these wavefunctions can be generally used as a criterion of delocalization of electronic states in 1D random and quasiperiodic lattices.

In this paper, theoretical analysis and extensive simulations are used to investigate asymmetric simple exclusion processes (ASEPs) with zoned inhomogeneity and on-ramp in a single-lane system. There are five possible phase diagrams with different hopping rate p and on-ramp rate q. Interestingly, the MC/MC, MC/LD and MC/HD phase can exist in the phase diagram with different hopping rate p and on-ramp rate q. When the on-ramp rate is fixed, with the decreasing of hopping rate, the HD/HD phase shrinks, it implies the heavy traffic in the system.

Critical constituent gates are first detected and graded based on their individual impact of an error in the outputs. This brings in the idea of practical reliability analysis metric. Then, the approximation of arithmetic circuits by random logic applied to least significant gates is introduced. The 74283 fast adder is used as an example to illustrate the feasibility of the proposed methods. Simulation results show the potential efficient application of the proposed reliability analysis metric and approximation method.

The probability that a linear embedding of a regular polygon in R³ is knotted should increase as a function of the number of sides. This assertion is investigated by means of an exploration of the compact variety of based oriented linear maps of regular polygons into R³. Asymptotically, an estimation of the probability of knotting is made by means of the HOMFLY polynomial.

This work discusses the random self-similar tree generation by employing multiple basic patterns, and investigates the character code and standardization algorithm for multiple basic patterns. With reference to the wide range of various basic patterns in natural shapes, the general coding method and the corresponding algorithm to calculate the topological distance is developed for random self-similar tree with multiple basic patterns. To assess the adaptability of the process, the general coding method is applied to transfer the generated river network to a code series and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. Finally, the width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results reveal that the random self-similar tree with multiple basic patterns proposed in this study can be implemented successfully to calculate hydrologic responses.

The safety evaluations of structures are usually performed by assuming uncertain 18 input parameters either as probabilistic or possibilistic in nature. Safety evaluations of structural systems characterized by some of the input parameters as possibilistic and others that are sufficient enough to model as probabilistic are unsuitable and restricted to gross assumption at early stages of modeling. The present paper deals with the safety analysis of such a hybrid uncertain system. Relying on the fundamental concept of entropy-based transformation; the feasibility of reliability analysis of a hybrid uncertain system in a possibilistic format is demonstrated in the present study. This will enable the designers to model the structural parameter uncertainty probabilistically as well possibilistically depending on the nature and quality of the input data. The bounds on the probability of failure based on the evidence theory are also computed to study the consistency of the possibility of failure results obtained by the transformation-based algorithm. A numerical example illustrates the capability of the proposed possibilistic approach of safety evaluation of hybrid uncertain system.

A short review is presented of a recently developed computational approach which allows the study of the resistance noise over the full range of bias values, from the linear regime up to electrical breakdown. Resistance noise is described in terms of two competing processes in a random resistor network. The two processes are thermally activated and driven by an electrical bias. In the linear regime, a scaling relation has been found between the relative variance of resistance fluctuations and the average resistance. The value of the critical exponent is significantly higher than that associated with 1/f noise. In the nonlinear regime, occurring when the bias overcomes the threshold value, the relative variance of resistance fluctuations scales with the bias. Two regions can be identified in this regime: a moderate bias region and a pre-breakdown one. In the first region, the scaling exponent has been found independent of the values of the model parameters and of the bias conditions. A strong nonlinearity emerges in the pre-breakdown region which is also characterized by non-Gaussian noise. The results compare well with measurements of electrical breakdown in composites and with electromigration experiments in metallic lines.

In this work we are interested in the self-affine fractals studied by Gatzouras and Lalley [5] and by the author [11] who generalize the famous general Sierpinski carpets studied by Bedford [1] and McMullen [13]. We give a formula for the Hausdorff dimension of sets which are randomly generated using a finite number of self-affine transformations each generating a fractal set as mentioned before. The choice of the transformation is random according to a Bernoulli measure. The formula is given in terms of the variational principle for the dimension.

This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove the existence and uniqueness of non-negative global solution as well as the existence of compact absorbing and attracting sets for the solutions of the corresponding random system. After that, we study the internal structure of the attracting set to obtain more detailed information about the long-time behavior of the state variables. In such a way, we provide conditions under which the extinction of the species cannot be avoided and conditions to ensure the persistence of the species, which is often the main goal pursued by practitioners. In addition, we illustrate the theoretical results with several numerical simulations.

The long time behavior of random KPP equations with nonlocal diffusion is investigated in this paper. The stability of the positive constant equilibrium solution is established for random KPP equations, and the spreading speed property is obtained for the random KPP equation with nonlocal diffusion by means of the comparison principle and auxiliary systems. Our theoretical results can be applied to two generalized KPP models, in which the take-over property of the lattice KPP with a random coefficient is obtained.

Let ${(F_n)}_{n\ge 1}$ be the sequence of Fibonacci numbers. Guy and Matiyasevich proved that

We prove that for every periodic sequence $s={(s_n)}_{n\ge 1}$ in $\{-1,+1\}$ there exists an effectively computable rational number $C_s>0$ such that

Assume that $n$ mobile sensors are thrown uniformly and independently at random with the uniform distribution on the unit interval. We study the expected sum over all sensors $i$ from $1$ to $n,$ where the contribution of the $i^{\mathrm{\text{th}}}$ sensor is its displacement from the current location to the anchor equidistant point $t_i=\frac{i}{n}-\frac{1}{2n},$ raised to the $a^{\mathrm{\text{th}}}$ power, when $a$ is an odd natural number.

As a consequence, we derive the following asymptotic identity. Fix $a$ positive integer. Let $X_{i:n}$ denote the $i^{\mathrm{\text{th}}}$ order statistic from a random sample of size $n$ from the Uniform$(0,1)$ population. Then

A smart grid consists of two networks: the power network and the communication network, which are interconnected by edges spanning across the networks. We model smart grids as complex interdependent networks, and study targeted and adaptive attacks on smart grids for the first time. Due to an attack on one network, nodes in the other network might get isolated, which in turn will disconnect nodes in the first network. Such cascading failures can result in disintegration of either or both of the networks. Earlier works considered only random failures. In real life, an attacker is more likely to compromise nodes selectively.

We study cascading failures in smart grids, where an attacker selectively compromises the nodes with probabilities proportional to their degrees, betweenness, or clustering coefficient. We mathematically and experimentally analyze the sizes of the giant components of the networks under different types of targeted attacks, and compare the results with the corresponding sizes under random attacks. We show that networks disintegrate faster for targeted attacks compared to random attacks. We next study adaptive attacks, where an attacker compromises nodes in rounds. Here, some nodes are compromised in each round based on their degree, betweenness or clustering coefficients, instead of compromising all nodes together. We show experimentally that an adversary has an advantage in this adaptive approach, compared to compromising the same number of nodes all at once.

We compare different actual forms of democracy and analyse in which way they are variations of a “natural consensus decision process”. We analyse how a “pure consensus procedure” is open to boycott of a minority, and how a “consensus decision followed by majority voting” is open to “false play” by a majority. We introduce a “random consensus procedure” in order to come closer to a natural decision process, and investigate how for such decision procedure false play of a minority is plausible to happen. We introduce the combined notion of “quantum parliament” and “quantum decision procedure”, and prove it to be the only one, when applied after consensus decision, that is immune to false play. We define a new form of democracy applying a quantum consensus system for its decision procedures.

This paper proposes a new numerical optimization technique, Search via Probability (SP) algorithm, for single-objective optimization problems. The SP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each iteration, and on the performance of SP algorithm we create good conditions for its appearance. We test this approach by implementing the SP algorithm on some test single-objective optimization problems, and we find very stable results.

No abstract received.

The probability that a linear embedding of a regular polygon in R³ is knotted should increase as a function of the number of sides . This assertion is investigated by means of an exploration of the compact variety of based oriented linear maps of regular polygons into R³. Asymptotically, an estimation of the probability of knotting is made by means of the HOMFLY polynomial.

This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl asymptotics for the eigenvalues of non-self-adjoint operators with small random perturbations. In the introduction we also review the notion of pseudo-spectrum and its relation to non-self-adjoint spectral problems.

In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.