Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

We study the growth with time of (the coefficients of the asymptoticexpansion of) the error in the numerical integration with linearmultistep methods of periodic solutions of systems of ordinarydifferential equations. Particular attention is devoted to reversiblesystems. It turns out that symmetric linear multistep methodscannot be recommended in spite of the fact that they mimic thereversibility of the true flow. For reversible second-ordersystems, linear multistep methods without parasitic double rootsare useful.     

Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems

In this paper we present a new algorithm for solving polynomial equations based on the Taylor series of the inverse function of a polynomial, f _P (y). The foundations of the computing of such series have been previously developed by the authors in some recent papers, proceeding as follows: given a polynomial function \(y=P(x)=a_0+a_1x+\cdots+a_mx^m\), with \(a_i \in \mathcal{R}, 0 \leq i \leq m\), and a real number u so that P′(u)?≠?0, we have got an analytic function f _P (y) that satisfies x?=?f _P (P(x)) around x?=?u. Besides, we also introduce a new proof (completely different) of the theorems involves in the construction of f _P (y), which provide a better radius of convergence of its Taylor series, and a more general perspective that could allow its application to other kinds of equations, not only polynomials. Finally, we illustrate with some examples how f _P (y) could be used for solving polynomial systems. This question has been already treated by the authors in preceding works in a very complex and hard way, that we want to overcome by using the introduced algorithm in this paper.     

A multiscale simulation system for the prediction of drug-induced cardiotoxicity

The preclinical assessment of drug-induced ventricular arrhythmia, a major concern for regulators, is typically based on experimental or computational models focused on the potassium channel hERG (human ether-a-go-go-related gene, K(v)11.1). Even if the role of this ion channel in the ventricular repolarization is of critical importance, the complexity of the events involved make the cardiac safety assessment based only on hERG has a high risk of producing either false positive or negative results. We introduce a multiscale simulation system aiming to produce a better cardiotoxicity assessment. At the molecular scale, the proposed system uses a combination of docking simulations on two potassium channels, hERG and KCNQ1, plus three-dimensional quantitative structure-activity relationship modeling for predicting how the tested compound will block the potassium currents IK(r) and IK(s). The obtained results have been introduced in electrophysiological models of the cardiomyocytes and the ventricular tissue, allowing the direct prediction of the drug effects on electrocardiogram simulations. The usefulness of the whole method is illustrated by predicting the cardiotoxic effect of several compounds, including some examples in which classic hERG-based models produce false positive or negative results, yielding correct predictions for all of them. These results can be considered a proof of concept, suggesting that multiscale prediction systems can be suitable for being used for preliminary screening in lead discovery, before the compound is physically available, or in early preclinical development when they can be fed with experimentally obtained data.     

Asymmetrical hippocampal connectivity in mesial temporal lobe epilepsy: evidence from resting state fMRI

Background

Recent studies have shown that the human right-hemispheric auditory cortex is particularly sensitive to reduction in sound quality, with an increase in distortion resulting in an amplification of the auditory N1m response measured in the magnetoencephalography (MEG). Here, we examined whether this sensitivity is specific to the processing of acoustic properties of speech or whether it can be observed also in the processing of sounds with a simple spectral structure. We degraded speech stimuli (vowel /a/), complex non-speech stimuli (a composite of five sinusoidals), and sinusoidal tones by decreasing the amplitude resolution of the signal waveform. The amplitude resolution was impoverished by reducing the number of bits to represent the signal samples. Auditory evoked magnetic fields (AEFs) were measured in the left and right hemisphere of sixteen healthy subjects.

Results

We found that the AEF amplitudes increased significantly with stimulus distortion for all stimulus types, which indicates that the right-hemispheric N1m sensitivity is not related exclusively to degradation of acoustic properties of speech. In addition, the P1m and P2m responses were amplified with increasing distortion similarly in both hemispheres. The AEF latencies were not systematically affected by the distortion.

Conclusions

We propose that the increased activity of AEFs reflects cortical processing of acoustic properties common to both speech and non-speech stimuli. More specifically, the enhancement is most likely caused by spectral changes brought about by the decrease of amplitude resolution, in particular the introduction of periodic, signal-dependent distortion to the original sound. Converging evidence suggests that the observed AEF amplification could reflect cortical sensitivity to periodic sounds.     

连续波锁模P_r~（3＋）：YLF激光器

本文报导了采用氩离子激光器来泵浦Ｒｒ￣（３＋）：ＹＬＦ晶体，应用声光调制器实现了主动锁模；同时应用振动─高反射平面镜也实现了被动锁模，两种锁模均得到了ｐｓ光脉冲。据作者了解这是这种晶体材料的第一次锁模运转。