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.

Phase diagram and dynamic response functions of the Holstein-Hubbard model

We present the phase diagram and dynamical correlation functions for the Holstein-Hubbard model at half filling and at zero temperature. The calculations are based on the Dynamical Mean Field Theory. The effective impurity model is solved using Exact Diagonalization and the Numerical Renormalization Group. Excluding long-range order, we find three different paramagnetic phases, metallic, bipolaronic and Mott insulating, depending on the Hubbard interaction U and the electron-phonon coupling g. We present the behaviour of the one-electron spectral functions and phonon spectra close to the metal insulator transitions.Comment: contribution to the SCES04 conferenc

Cross Calibration of Imaging Air Cherenkov Telescopes with Fermi

An updated model for the synchrotron and inverse Compton emission from a population of high energy electrons of the Crab Nebula is used to reproduce the measured spectral energy distribution from radio to high energy gamma-rays. By comparing the predicted inverse Compton component with recent Fermi measurements of the nebula's emission, it is possible to determine the average magnetic field in the nebula and to derive the underlying electron energy distribution. The model calculation can then be used to cross calibrate the Fermi observations with ground based air shower measurements. The resulting energy calibration factors are derived and can be used for combining broad energy measurements taken with Fermi in conjunction with ground based measurements.Comment: 2009 Fermi Symposium, eConf Proceedings C091122, 5 pages, 5 figures, 3 table