For the coupled stochastic dynamical system, we study the functional relation between noisy fluctuation and node degree. We extend the approaches for obtaining functional relation in Wang et al. (2009) to the weighted network whose link weight is dependent on the node degree. For the network with strong heterogeneity in degree distribution, we find that the theoretical result derived from the approaches in Wang et al. (2009) shows disagreement with numerical results. Here, we propose novel approaches using the average of higher order moments and improve the accuracy of functional relation between noisy fluctuation and node degree. Also, we investigate the functional relation of noisy fluctuation versus node input strength.

Novelty seeking (NS) and harm avoidance (HA) are two major dimensions of temperament in Cloninger's neurobiological model of personality. Previous neurofunctional and biological studies on temperament dimensions of HA and NS suggested that the temperamental traits have significant correlations with cortical and subcortical brain regions. However, no study to date has investigated the functional network modular organization as a function of the temperament dimension. The temperament dimensions were originally proposed to be independent of one another. However, a meta-analysis based on 16 published articles found a significant negative correlation between HA and NS (Miettunen et al., 2008). Based on this negative correlation, the current study revealed the whole-brain connectivity modular archi- tecture for two contrasting temperament groups. The k-means clustering algorithm, with the temperamental traits of HA and NS as an input, was applied to divide the 40 subjects into two temperament groups: ‘high HA and low NS’ versus ‘low HA and high NS’. Using the graph theoretical framework, we found a functional segregation of whole brain network architectures derived from resting-state functional MRI. In the ‘high HA and low NS’ group, the regulatory brain regions, such as the prefrontal cortex (PFC), are clustered together with the limbic system. In the ‘low HA and high NS’ group, however, brain regions lying on the dopaminergic pathways, such as the PFC and basal ganglia, are partitioned together. These findings suggest that the neural basis of inhibited, passive, and inactive behaviors in the ‘high HA and low NS’ group was derived from the increased network associations between the PFC and limbic clusters. In addition, supporting evidence of topological differences between the two temperament groups was found by analyzing the functional connectivity density and gray matter volume, and by computing the relationships between the morphometry and function of the brain.

We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications.？

In 1958, L.J. Mordell provided the formula for the integral of the product of two Bernoulli polynomials, he also remarked: The integrals containing the product of more than two Bernoulli polynomials do not appear to lead to simple results. In this paper, we provide explicit formulas for the integral of the product of $r$ Bernoulli polynomials, where $r$ is any positive integer. Many authors’ results in this direction, including Norlund, Mordell,Carlitz, Agoh and Dilcher are special cases of the formulas given in this paper.

It is known that certain combinatorial convolution sums involving two divisor functions product formulae of arbitrary level can be explicitly expressed as a linear combination of divisor functions. In this article we deal with cases for certain combinatorial convolution sums involving three, four, six and twelve divisor functions product formula and obtain explicit expressions.

In this article, we study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials, and obtain identities. As applications of these identities, we give several concrete interpretations in terms of the procedural modelling method.？

It is known that certain convolution sums using Liouville identity can be expressed as a combination of divisor functions and Bernoulli numbers. In this article we find seven combinatorial convolution sums derived from divisor functions and Bernoulli numbers

The topological derivative-based non-iterative imaging algorithm has demonstrated its applicability in limited-aperture inverse scattering problems. However, this has been confirmed through many experimental simulation results, and the reason behind this applicability has not been satisfactorily explained. In this paper, we identify the mathematical structure and certain properties of topological derivatives for the imaging of two-dimensional crack-like thin penetrable electromagnetic inhomogeneities that are completely embedded in a homogeneous material. To this end, we establish a relationship with an infinite series of Bessel functions of integer order of the first kind. Based on the derived structure, we discover a necessary condition for applying topological derivatives in limited-aperture inverse scattering problems, and thus confirm why topological derivatives can be applied. Furthermore, we analyze the structure of multi-frequency topological derivative, and identify why this improves the single-frequency topological derivative in limited-aperture inverse scattering problems. Various numerical simulations are conducted with noisy data, and the results support the derived structure and exhibit certain properties of single- and multi-frequency topological derivatives.

A localized axial Green's function method(LAGM) is proposed for the convection-diffusion equation. The axial Green's function method(AGM) enables us to calculate the numerical solutionof a multi-dimensional problem using only one-dimensional Green's functions for the axially split differential operators. This AGM has been developed not only for the elliptic boundary value problems but also for the steady Stokes flows,however, this paper is concerned with the localization of the AGM.This localization of the method is needed for practical purpose when computing the axial Green's function, specifically for the convection-diffusion equation on a line segment that we call the local axial line. Although our focus is mainly on the convection-dominated cases in arbitrary domains, this method can solve other cases in a unified way.Numerical results show that, despite irregular types of discretization on an arbitrary domain,we can calculate the numerical solutions using the LAGM without loss of accuracy even in cases of large convection. In particular, it is also shown that randomly distributed axial lines are available in our LAGM andcomplicated domains are not a burden.

We investigate the information flow among 22 industry sectors in the Korean stock market by using the symbolic transfer entropy (STE) method. We consider the daily index of 22 industry sectors in the Korean Composite Stock Price Index (KOSPI) from January 3, 2000 to March 30, 2012. We measure the degree of asymmetry in the information flow and the amount of information flow among the industry sectors before, during, and after the subprime crisis in order to analyze how to relate them to the market crisis. We find that the amount of information flow and the number of connectedness during the financial crisis in the Korean stock market are higher than those before and after the market crisis. In addition, we find the role of the insurance sector, which is related to risk management, increases as information source after the crisis