Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites

Variable-range hopping conductivity has long been understood in terms of a canonical prescription for relating the single-particle density of states to the temperature-dependent conductivity. Here we demonstrate that this prescription breaks down in situations where a large and long-ranged random potential develops. In particular, we examine a canonical model of a completely compensated semiconductor, and we show that at low temperatures hopping proceeds along self-organized, low-dimensional subspaces having fractal dimension $d = 2$. We derive and study numerically the spatial structure of these subspaces, as well as the conductivity and density of states that result from them. One of our prominent findings is that fractal ordering of low energy sites greatly enhances the hopping conductivity, and allows Efros-Shklovskii type conductivity to persist up to unexpectedly high temperatures.Comment: 9 pages, 6 figures; published version with added references and discussio

Analysis on accrual-based models in detecting earnings management

This paper analyzes the problems with the alternative accrual-based models in detecting earnings management. The researcher will focus on comparing the Jones Model and the Modified Jones Model, which are the two most frequently used model in empirical analysis nowadays. Earnings management is a kind of management which uses accounting techniques to meet the executives‟ needs for earnings; it is a widely debated topic, hence it is worth looking at. Experts and professionals in this area found many approaches to detect the earnings management; within these approaches are the accrual-based models which include the modified Jones model, which currently is a favourite model to many researchers. Using OLS model, the author found that sometimes using the Jones models alone cannot solve the problems. The samples used in this paper are the China‟s ST companies (listed companies which made a loss for two years and thus clearly have the motive to manipulate their earnings). This paper also provides some examples of situations which the Jones models cannot handle

Echo Phenomena in Populations of Chemical Oscillators

The emergence of collective behavior has been observed in all levels of biological systems, for example, the aggregation of slime mold, swarm motion of insects and the collective motion in schools of sh. Synchronization is one of the most important collective behaviors and can play a pivotal role in maintaining the normal function of a living system, such as pacemaker cells in the heart, circadian rhythms, and insulin release from pancreatic cells. Synchronization typically arises as a result of the interaction of large ensembles of oscillators. Studies of the Belousov-Zhabotinsky (BZ) chemical oscillators have shown a variety of collective dynamical behaviors, such as phase clusters, dynamical quorum sensing and chimera states. The discovery of echo phenomena in large populations of coupled Kuramoto oscillators motivates us to study this dynamical behavior using photosensitive BZ oscillators.;In this thesis, we examine echo behavior experimentally and mathematically. The experiments are carried out with a BZ micro-oscillator system. A large system of micro-oscillators is achieved by the design of a large oscillator array (LOA), which permits coupling of over 1000 oscillators. The dimensionless Zhabotinsky, Buchholtz, Kiyatkin and Epstein (ZBKE) mathematical model is used to investigate the behavior. The experiment and numerical results illustrate that if a BZ system of oscillators is subject to two perturbations, separated by time tau, then at the time tau after second perturbation, the oscillators show a measurable response in their collective signal. Factors such as noise and size of the perturbation impacting the magnitude of the echo are examined and a theoretical calculation of the magnitude of the echo as a function of the size of the perturbation exhibits good agreement with simulation results using the ZBKE model

On the equality of BKK bound and birationally invariant intersection index

The Bernshtein-Kushnirenko-Khovanskii theorem provides a generic root count for system of Laurent polynomials in terms of the mixed volume of their Newton polytopes which has since been known as the BKK bound. A recent and far-reaching generalization of this theorem is the study of birationally invariant intersection index by Kaveh and Khovanskii. In this paper we generalize the BKK bound in the direction of the birationally invariant intersection index, and the main result allows the application of BKK bound to Laurent polynomial systems that has algebraic relations among the coefficients. Applying this result, we establish the birationally invariant intersection index for a well-studied algebraic Kuramoto equations

A stratified polyhedral homotopy method for sampling positive dimensional zero sets of polynomial systems

Numerical algebraic geometry revolves around the study of solutions to polynomial systems via numerical method. The polyhedral homotopy of Huber and Sturmfels for computing isolated solutions and the concept of witness sets for as numerical representations of non-isolated solution components, put forth by Sommese and Wampler, are two of the fundamental tools in this field. In this paper, we show that a modified polyhedral homotopy can reveal sample sets of non-isolated solution components, akin to witness sets, as by-products from the process of computing isolated solutions