Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map

Whileas the Kohonen Self Organizing Map shows an asymptotic level density following a power law with a magnification exponent 2/3, it would be desired to have an exponent 1 in order to provide optimal mapping in the sense of information theory. In this paper, we study analytically and numerically the magnification behaviour of the Elastic Net algorithm as a model for self-organizing feature maps. In contrast to the Kohonen map the Elastic Net shows no power law, but for onedimensional maps nevertheless the density follows an universal magnification law, i.e. depends on the local stimulus density only and is independent on position and decouples from the stimulus density at other positions.Comment: 8 pages, 10 figures. Link to publisher under http://link.springer.de/link/service/series/0558/bibs/2415/24150939.ht

Parameter estimation in pair hidden Markov models

This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some restrictions with respect to the full parameter space naturally occur. Existence of two different Information divergence rates is established and divergence property (namely positivity at values different from the true one) is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.Comment: corrected typo

A New Simulated Annealing Algorithm for the Multiple Sequence Alignment Problem: The approach of Polymers in a Random Media

We proposed a probabilistic algorithm to solve the Multiple Sequence Alignment problem. The algorithm is a Simulated Annealing (SA) that exploits the representation of the Multiple Alignment between $D$ sequences as a directed polymer in $D$ dimensions. Within this representation we can easily track the evolution in the configuration space of the alignment through local moves of low computational cost. At variance with other probabilistic algorithms proposed to solve this problem, our approach allows for the creation and deletion of gaps without extra computational cost. The algorithm was tested aligning proteins from the kinases family. When D=3 the results are consistent with those obtained using a complete algorithm. For $D>3$ where the complete algorithm fails, we show that our algorithm still converges to reasonable alignments. Moreover, we study the space of solutions obtained and show that depending on the number of sequences aligned the solutions are organized in different ways, suggesting a possible source of errors for progressive algorithms.Comment: 7 pages and 11 figure

Haplotype-aware graph indexes

The variation graph toolkit (VG) represents genetic variation as a graph. Each path in the graph is a potential haplotype, though most paths are unlikely recombinations of true haplotypes. We augment the VG model with haplotype information to identify which paths are more likely to be correct. For this purpose, we develop a scalable implementation of the graph extension of the positional Burrows-Wheeler transform. We demonstrate the scalability of the new implementation by indexing the 1000 Genomes Project haplotypes. We also develop an algorithm for simplifying variation graphs for k-mer indexing without losing any k-mers in the haplotypes

Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent $\alpha$ estimated from the data. We treat $\alpha$ as an unknown parameter, but for theoretical simplicity we also consider the case that $\alpha$ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions

X-Ray Synchrotron White Beam Excitation of Auger Electrons

Auger electron spectra have been measured at the Cornell High Energy Synchrotron Source (CHESS), using the full white beam x-ray spectrum as the excitation source. Ordinary Auger spectra obtained in the laboratory with an electron beam source must employ derivative techniques to distinguish the Auger structures from the large background due to the excitation beam. The synchrotron white beam eliminates this source of background and produces signal rates as high as 107 cps. Superior signal-to-background ratios are found for Auger peaks above a few hundred eV, and count rates are large enough to suggest microprobe applications. X-ray induced Auger satellite peaks were observed with intensities much greater than the electron-induced counterpart; this anomaly is not completely understood

Empirical 2MASS-WFC3/IR filter transformations from synthetic photometry

Near-infrared bandpasses on spaceborne observatories diverge from their ground-based counterparts as they are free of atmospheric telluric absorption. Available transformations between respective filter systems in the literature rely on theoretical stellar atmospheres, which are known to have difficulties reproducing observed spectral energy distributions of cool giants. We present new transformations between the 2MASS $JHK_S$ and HST WFC3/IR F110W, F125W, & F160W photometric systems based on synthetic photometry of empirical stellar spectra from four spectral libraries. This sample comprises over 1000 individual stars, which together span nearly the full HR diagram and sample stellar populations from the solar neighborhood out to the Magellanic Clouds, covering a broad range of ages, metallicities, and other relevant stellar properties. In addition to global color-dependent transformations, we examine band-to-band differences for cool, luminous giant stars in particular, including multiple types of primary distance indicators.Comment: 24 pages, 15 figures, accepted to A

Reorientation of Spin Density Waves in Cr(001) Films induced by Fe(001) Cap Layers

Proximity effects of 20 \AA thin Fe layers on the spin density waves (SDWs) in epitaxial Cr(001) films are revealed by neutron scattering. Unlike in bulk Cr we observe a SDW with its wave vector Q pointing along only one {100} direction which depends dramatically on the film thickness t_{Cr}. For t_{Cr} < 250 \AA the SDW propagates out-of-plane with the spins in the film plane. For t_{Cr} > 1000 \AA the SDW propagates in the film plane with the spins out-of-plane perpendicular to the in-plane Fe moments. This reorientation transition is explained by frustration effects in the antiferromagnetic interaction between Fe and Cr across the Fe/Cr interface due to steps at the interface.Comment: 4 pages (RevTeX), 3 figures (EPS