27,531 research outputs found
Planar diagrams from optimization
We propose a new toy model of a heteropolymer chain capable of forming planar
secondary structures typical for RNA molecules. In this model the sequential
intervals between neighboring monomers along a chain are considered as quenched
random variables. Using the optimization procedure for a special class of
concave--type potentials, borrowed from optimal transport analysis, we derive
the local difference equation for the ground state free energy of the chain
with the planar (RNA--like) architecture of paired links. We consider various
distribution functions of intervals between neighboring monomers (truncated
Gaussian and scale--free) and demonstrate the existence of a topological
crossover from sequential to essentially embedded (nested) configurations of
paired links.Comment: 10 pages, 10 figures, the proof is added. arXiv admin note: text
overlap with arXiv:1102.155
Zero Temperature Insulator-Metal Transition in Doped Manganites
We study the transition at T=0 from a ferromagnetic insulating to a
ferromagnetic metallic phase in manganites as a function of hole doping using
an effective low-energy model Hamiltonian proposed by us recently. The model
incorporates the quantum nature of the dynamic Jahn-Teller(JT) phonons strongly
coupled to orbitally degenerate electrons as well as strong Coulomb correlation
effects and leads naturally to the coexistence of localized (JT polaronic) and
band-like electronic states. We study the insulator-metal transition as a
function of doping as well as of the correlation strength U and JT gain in
energy E_{JT}, and find, for realistic values of parameters, a ground state
phase diagram in agreement with experiments. We also discuss how several other
features of manganites as well as differences in behaviour among manganites can
be understood in terms of our model.Comment: To be published in Europhysics Letter
Dynamics of Barred Galaxies
Some 30% of disc galaxies have a pronounced central bar feature in the disc
plane and many more have weaker features of a similar kind. Kinematic data
indicate that the bar constitutes a major non-axisymmetric component of the
mass distribution and that the bar pattern tumbles rapidly about the axis
normal to the disc plane. The observed motions are consistent with material
within the bar streaming along highly elongated orbits aligned with the
rotating major axis. A barred galaxy may also contain a spheroidal bulge at its
centre, spirals in the outer disc and, less commonly, other features such as a
ring or lens. Mild asymmetries in both the light and kinematics are quite
common. We review the main problems presented by these complicated dynamical
systems and summarize the effort so far made towards their solution,
emphasizing results which appear secure. (Truncated)Comment: This old review appeared in 1993. Plain tex with macro file. 82 pages
18 figures. A pdf version with figures at full resolution (3.24MB) is
available at http://www.physics.rutgers.edu/~sellwood/bar_review.pd
Detecting event-related recurrences by symbolic analysis: Applications to human language processing
Quasistationarity is ubiquitous in complex dynamical systems. In brain
dynamics there is ample evidence that event-related potentials reflect such
quasistationary states. In order to detect them from time series, several
segmentation techniques have been proposed. In this study we elaborate a recent
approach for detecting quasistationary states as recurrence domains by means of
recurrence analysis and subsequent symbolisation methods. As a result,
recurrence domains are obtained as partition cells that can be further aligned
and unified for different realisations. We address two pertinent problems of
contemporary recurrence analysis and present possible solutions for them.Comment: 24 pages, 6 figures. Draft version to appear in Proc Royal Soc
Functional organization of human sensorimotor cortex for speech articulation.
Speaking is one of the most complex actions that we perform, but nearly all of us learn to do it effortlessly. Production of fluent speech requires the precise, coordinated movement of multiple articulators (for example, the lips, jaw, tongue and larynx) over rapid time scales. Here we used high-resolution, multi-electrode cortical recordings during the production of consonant-vowel syllables to determine the organization of speech sensorimotor cortex in humans. We found speech-articulator representations that are arranged somatotopically on ventral pre- and post-central gyri, and that partially overlap at individual electrodes. These representations were coordinated temporally as sequences during syllable production. Spatial patterns of cortical activity showed an emergent, population-level representation, which was organized by phonetic features. Over tens of milliseconds, the spatial patterns transitioned between distinct representations for different consonants and vowels. These results reveal the dynamic organization of speech sensorimotor cortex during the generation of multi-articulator movements that underlies our ability to speak
Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail
<p>Abstract</p> <p>Background</p> <p>The optimal score for ungapped local alignments of infinitely long random sequences is known to follow a Gumbel extreme value distribution. Less is known about the important case, where gaps are allowed. For this case, the distribution is only known empirically in the high-probability region, which is biologically less relevant.</p> <p>Results</p> <p>We provide a method to obtain numerically the biologically relevant rare-event tail of the distribution. The method, which has been outlined in an earlier work, is based on generating the sequences with a parametrized probability distribution, which is biased with respect to the original biological one, in the framework of Metropolis Coupled Markov Chain Monte Carlo. Here, we first present the approach in detail and evaluate the convergence of the algorithm by considering a simple test case. In the earlier work, the method was just applied to one single example case. Therefore, we consider here a large set of parameters:</p> <p>We study the distributions for protein alignment with different substitution matrices (BLOSUM62 and PAM250) and affine gap costs with different parameter values. In the logarithmic phase (large gap costs) it was previously assumed that the Gumbel form still holds, hence the Gumbel distribution is usually used when evaluating p-values in databases. Here we show that for all cases, provided that the sequences are not too long (<it>L </it>> 400), a "modified" Gumbel distribution, i.e. a Gumbel distribution with an additional Gaussian factor is suitable to describe the data. We also provide a "scaling analysis" of the parameters used in the modified Gumbel distribution. Furthermore, via a comparison with BLAST parameters, we show that significance estimations change considerably when using the true distributions as presented here. Finally, we study also the distribution of the sum statistics of the <it>k </it>best alignments.</p> <p>Conclusion</p> <p>Our results show that the statistics of gapped and ungapped local alignments deviates significantly from Gumbel in the rare-event tail. We provide a Gaussian correction to the distribution and an analysis of its scaling behavior for several different scoring parameter sets, which are commonly used to search protein data bases. The case of sum statistics of <it>k </it>best alignments is included.</p
- …