Stochastic Data Clustering

In 1961 Herbert Simon and Albert Ando published the theory behind the long-term behavior of a dynamical system that can be described by a nearly uncoupled matrix. Over the past fifty years this theory has been used in a variety of contexts, including queueing theory, brain organization, and ecology. In all these applications, the structure of the system is known and the point of interest is the various stages the system passes through on its way to some long-term equilibrium. This paper looks at this problem from the other direction. That is, we develop a technique for using the evolution of the system to tell us about its initial structure, and we use this technique to develop a new algorithm for data clustering.Comment: 23 page

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms

Vibrational density of states of silicon nanoparticles

The vibrational density of states of silicon nanoparticles in the range from 2.3 to 10.3 nm is studied with the help of molecular-dynamics simulations. From these simulations the vibrational density of states and frequencies of bulk-like vibrational modes at high-symmetry points of the Brillouin-zone have been derived. The results show an increase of the density of states at low frequencies and a transfer of modes from the high-frequency end of the spectrum to the intermediate range. At the same time the peak of transverse optical modes is shifted to higher frequencies. These observations are in line with previous simulation studies of metallic nanoparticles and they provide an explanation for a previously observed discrepancy between experimental and theoretical data [C. Meier et al., Physica E, 32, 155 (2006)].Comment: 7 pages, 5 figure; accepted for publication in Phys. Rev.

Numerical methods for problems involving the Drazin inverse

The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success

Social working memory: neurocognitive networks and directions for future research.

Navigating the social world requires the ability to maintain and manipulate information about people's beliefs, traits, and mental states. We characterize this capacity as social working memory (SWM). To date, very little research has explored this phenomenon, in part because of the assumption that general working memory systems would support working memory for social information. Various lines of research, however, suggest that social cognitive processing relies on a neurocognitive network (i.e., the "mentalizing network") that is functionally distinct from, and considered antagonistic with, the canonical working memory network. Here, we review evidence suggesting that demanding social cognition requires SWM and that both the mentalizing and canonical working memory neurocognitive networks support SWM. The neural data run counter to the common finding of parametric decreases in mentalizing regions as a function of working memory demand and suggest that the mentalizing network can support demanding cognition, when it is demanding social cognition. Implications for individual differences in social cognition and pathologies of social cognition are discussed