Rotor interaction in the annulus billiard

Introducing the rotor interaction in the integrable system of the annulus billiard produces a variety of dynamical phenomena, from integrability to ergodicity

Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case

Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let \k be a primitive multiplicative character of order $N$ over finite field \fq. This paper studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2 case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2 case with order $N$ being general even integer (i.e. N=2^{r}\cd N_0 where $r,N_0$ are positive integers and $N_03$ is odd.) is obtained. Thus, the problem of explicit evaluation of Gauss sums in index 2 case is completely solved

Sibling Rivalry among Paralogs Promotes Evolution of the Human Brain

Geneticists have long sought to identify the genetic changes that made us human, but pinpointing the functionally relevant changes has been challenging. Two papers in this issue suggest that partial duplication of SRGAP2, producing an incomplete protein that antagonizes the original, contributed to human brain evolution

Degeneracy Algorithm for Random Magnets

It has been known for a long time that the ground state problem of random magnets, e.g. random field Ising model (RFIM), can be mapped onto the max-flow/min-cut problem of transportation networks. I build on this approach, relying on the concept of residual graph, and design an algorithm that I prove to be exact for finding all the minimum cuts, i.e. the ground state degeneracy of these systems. I demonstrate that this algorithm is also relevant for the study of the ground state properties of the dilute Ising antiferromagnet in a constant field (DAFF) and interfaces in random bond magnets.Comment: 17 pages(Revtex), 8 Postscript figures(5color) to appear in Phys. Rev. E 58, December 1st (1998

A unified approach to combinatorial key predistribution schemes for sensor networks

There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified framework to study these kinds of schemes. To do so, we define a new, general class of designs, termed “partially balanced t-designs”, that is sufficiently general that it encompasses almost all of the designs that have been proposed for combinatorial key predistribution schemes. However, this new class of designs still has sufficient structure that we are able to derive general formulas for the metrics of the resulting key predistribution schemes. These metrics can be evaluated for a particular scheme simply by substituting appropriate parameters of the underlying combinatorial structure into our general formulas. We also compare various classes of schemes based on different designs, and point out that some existing proposed schemes are in fact identical, even though their descriptions may seem different. We believe that our general framework should facilitate the analysis of proposals for combinatorial key predistribution schemes and their comparison with existing schemes, and also allow researchers to easily evaluate which scheme or schemes present the best combination of performance metrics for a given application scenario

Electron beam charging of insulators: A self-consistent flight-drift model

International audienceElectron beam irradiation and the self-consistent charge transport in bulk insulating samples are described by means of a new flight-drift model and an iterative computer simulation. Ballistic secondary electron and hole transport is followed by electron and hole drifts, their possible recombination and/or trapping in shallow and deep traps. The trap capture cross sections are the Poole-Frenkel-type temperature and field dependent. As a main result the spatial distributions of currents j(x,t), charges, the field F(x,t) and the potential slope V(x,t) are obtained in a self-consistent procedure as well as the time-dependent secondary electron emission rate sigma(t) and the surface potential V0(t) For bulk insulating samples the time-dependent distributions approach the final stationary state with j(x,t)=const=0 and sigma=1. Especially for low electron beam energies E0=4 keV the incorporation of mainly positive charges can be controlled by the potential VG of a vacuum grid in front of the target surface. For high beam energies E0=10, 20, and 30 keV high negative surface potentials V0=−4, −14, and −24 kV are obtained, respectively. Besides open nonconductive samples also positive ion-covered samples and targets with a conducting and grounded layer (metal or carbon) on the surface have been considered as used in environmental scanning electron microscopy and common SEM in order to prevent charging. Indeed, the potential distributions V(x) are considerably small in magnitude and do not affect the incident electron beam neither by retarding field effects in front of the surface nor within the bulk insulating sample. Thus the spatial scattering and excitation distributions are almost not affected

Information-theoretic interpretation of quantum error-correcting codes

Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that "redundant" information can be distributed over quantum bits even though this does not violate the quantum "no-cloning" theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analogue of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev.

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199

Integrating Exercise Into Personalized Ventricular Arrhythmia Risk Prediction in Arrhythmogenic Right Ventricular Cardiomyopathy

BACKGROUND: Exercise is associated with sustained ventricular arrhythmias (VA) in Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC) but is not included in the ARVC risk calculator (arvcrisk.com). The objective of this study is to quantify the influence of exercise at diagnosis on incident VA risk and evaluate whether the risk calculator needs adjustment for exercise. METHODS: We interviewed ARVC patients without sustained VA at diagnosis about their exercise history. The relationship between exercise dose 3 years preceding diagnosis (average METh/wk) and incident VA during follow-up was analyzed with time-to-event analysis. The incremental prognostic value of exercise to the risk calculator was evaluated by Cox models. RESULTS: We included 176 patients (male, 43.2%; age, 37.6±16.1 years) from 3 ARVC centers, of whom 53 (30.1%) developed sustained VA during 5.4 (2.7-9.7) years of follow-up. Exercise at diagnosis showed a dose-dependent nonlinear relationship with VA, with no significant risk increase 18, >24, and >36 METh/wk), was significantly associated with VA (hazard ratios, 2.53-2.91) but was also correlated with risk factors currently in the risk calculator model. Thus, adding athlete status to the model did not change the C index of 0.77 (0.71-0.84) and showed no significant improvement (Akaike information criterion change, <2). CONCLUSIONS: Exercise at diagnosis was dose dependently associated with risk of sustained VA in ARVC patients but only above 15 to 30 METh/wk. Exercise does not appear to have incremental prognostic value over the risk calculator. The ARVC risk calculator can be used accurately in athletic patients without modification