On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision

Stationary phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.Comment: 6 pages, 7 figures, RevTex 4.0 styl

A simple solution of the critical Kauffman model with connectivity one

The Kauffman model is a model of genetic computation that highlights the importance of criticality at the border of order and chaos. But our understanding of its behavior is incomplete, and much of what we do know relies on intricate arguments. We give a simple proof that the number of attractors for the critical Kauffman model with connectivity one grows faster than previously believed. Our approach relies on a link between the critical dynamics and number theory.Comment: 2 page

A Multinational Analysis of Mutations and Heterogeneity in PZase, RpsA, and PanD Associated with Pyrazinamide Resistance in M/XDR Mycobacterium tuberculosis.

Pyrazinamide (PZA) is an important first-line drug in all existing and new tuberculosis (TB) treatment regimens. PZA-resistance in M. tuberculosis is increasing, especially among M/XDR cases. Noted issues with PZA Drug Susceptibility Testing (DST) have driven the search for alternative tests. This study provides a comprehensive assessment of PZA molecular diagnostics in M/XDR TB cases. A set of 296, mostly XDR, clinical M. tuberculosis isolates from four countries were subjected to DST for eight drugs, confirmatory Wayne's assay, and whole-genome sequencing. Three genes implicated in PZA resistance, pncA, rpsA, and panD were investigated. Assuming all non-synonymous mutations cause resistance, we report 90% sensitivity and 65% specificity for a pncA-based molecular test. The addition of rpsA and panD potentially provides 2% increase in sensitivity. Molecular heterogeneity in pncA was associated with resistance and should be evaluated as a diagnostic tool. Mutations near the N-terminus and C-terminus of PZase were associated with East-Asian and Euro-American lineages, respectively. Finally, Euro-American isolates are most likely to have a wild-type PZase and escape molecular detection. Overall, the 8-10% resistance without markers may point to alternative mechanisms of resistance. Confirmatory mutagenesis may improve the disconcertingly low specificity but reduce sensitivity since not all mutations may cause resistance

Paramagnetic Meissner effect in superconductors from self-consistent solutions of Ginzburg-Landau equations

The paramagnetic Meissner effect (PME) is observed in small superconducting samples, and a number of controversial explanations of this effect are proposed, but there is as yet no clear understanding of its nature. In the present paper PME is considered on the base of the Ginzburg-Landau theory (GL). The one-dimensional solutions are obtained in a model case of a long superconducting cylinder for different cylinder radii R, the GL-parameters \kappa and vorticities m. Acording to GL-theory, PME is caused by the presence of vortices inside the sample. The superconducting current flows around the vortex to screeen the vortex own field from the bulk of the sample. Another current flows at the boundary to screen the external field H from entering the sample. These screening currents flow in opposite directions and contribute with opposite signs to the total magnetic moment (or magnetization) of the sample. Depending on H, the total magnetization M may be either negative (diamagnetism), or positive (paramagnetism). A very complicated saw-like dependence M(H) (and other characteristics), which are obtained on the base of self-consistent solutions of the GL-equations, are discussed.Comment: 6 pages, 5 figures, RevTex, submitted to Phys. Rev.

Multi-Modal Human-Machine Communication for Instructing Robot Grasping Tasks

A major challenge for the realization of intelligent robots is to supply them with cognitive abilities in order to allow ordinary users to program them easily and intuitively. One way of such programming is teaching work tasks by interactive demonstration. To make this effective and convenient for the user, the machine must be capable to establish a common focus of attention and be able to use and integrate spoken instructions, visual perceptions, and non-verbal clues like gestural commands. We report progress in building a hybrid architecture that combines statistical methods, neural networks, and finite state machines into an integrated system for instructing grasping tasks by man-machine interaction. The system combines the GRAVIS-robot for visual attention and gestural instruction with an intelligent interface for speech recognition and linguistic interpretation, and an modality fusion module to allow multi-modal task-oriented man-machine communication with respect to dextrous robot manipulation of objects.Comment: 7 pages, 8 figure