A Comparative Study of Reservoir Computing for Temporal Signal Processing

Reservoir computing (RC) is a novel approach to time series prediction using recurrent neural networks. In RC, an input signal perturbs the intrinsic dynamics of a medium called a reservoir. A readout layer is then trained to reconstruct a target output from the reservoir's state. The multitude of RC architectures and evaluation metrics poses a challenge to both practitioners and theorists who study the task-solving performance and computational power of RC. In addition, in contrast to traditional computation models, the reservoir is a dynamical system in which computation and memory are inseparable, and therefore hard to analyze. Here, we compare echo state networks (ESN), a popular RC architecture, with tapped-delay lines (DL) and nonlinear autoregressive exogenous (NARX) networks, which we use to model systems with limited computation and limited memory respectively. We compare the performance of the three systems while computing three common benchmark time series: H{\'e}non Map, NARMA10, and NARMA20. We find that the role of the reservoir in the reservoir computing paradigm goes beyond providing a memory of the past inputs. The DL and the NARX network have higher memorization capability, but fall short of the generalization power of the ESN

Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Method of making a piezoelectric shear wave resonator

An acoustic shear wave resonator comprising a piezoelectric film having its C-axis substantially inclined from the film normal such that the shear wave coupling coefficient significantly exceeds the longitudinal wave coupling coefficient, whereby the film is capable of shear wave resonance, and means for exciting said film to resonate. The film is prepared by deposition in a dc planar magnetron sputtering system to which a supplemental electric field is applied. The resonator structure may also include a semiconductor material having a positive temperature coefficient of resonance such that the resonator has a temperature coefficient of resonance approaching 0 ppm

Binning for IC Quality: Experimental Studies on the SEMATECH Data

The earlier smaller bipolar study did not provide a high enough bin 0 population to directly observe test escapes and thereby estimate defect levels for the best bin. Results presented here indicate that the best bin can be reasonably expected to show a 2 - 5 factor improvement in defect levels over the average for the lot for moderate to high yields (the overall yield for these experiments was approximately 65%). The experiments also confirm the dependence of the best bin quality on test transparency. The defect level improvement is poorer for the case Of IDDQ escapes where the tests applied had a much higher escape rate. Overall experimental results are consistent with analytical projections for typical values of the clustering parameter in [9]. The final version of this paper will include extensive analysis to validate the analytical models based on this data

Mexico's Health System: More Comprehensive Reform Needed

Jason Lakin discusses and critiques a Policy Forum that reviews 25 years of reform to the Mexican health system and argues that more comprehensive reform is needed

Observables in the Decays of B to Two Vector Mesons

In general there are nine observables in the decay of a B meson to two vector mesons defined in terms of polarization correlations of these mesons. Only six of these can be detected via the subsequent decay angular distributions because of parity conservation in those decays. The remaining three require the measurement of the spin polarization of one of the decay products.Comment: 12 pages, no figur

High resolution optothermal spectroscopy of pyridine in the S-1 state

The optothermal technique has been utilized to obtain the first high resolution spectrum of pyridine in the region of the S1←S0 electronic transition. Rotational profiles for several vibronic bands (000,6a10,16b206a10,6a20,1210) were measured and found to be severely homogeneously broadened with linewidths of the order of 3–5 GHz, in agreement with previous lifetime measurements. Rotational constants of pyridine in the excited S1 vibronic levels were extracted by a band contour analysis. The values obtained are in good agreement with results from ab initio calculations, also presented here

Evolution and dispersal of snakes across the Cretaceous-Paleogene mass extinction.

Mass extinctions have repeatedly shaped global biodiversity. The Cretaceous-Paleogene (K-Pg) mass extinction caused the demise of numerous vertebrate groups, and its aftermath saw the rapid diversification of surviving mammals, birds, frogs, and teleost fishes. However, the effects of the K-Pg extinction on the evolution of snakes-a major clade of predators comprising over 3,700 living species-remains poorly understood. Here, we combine an extensive molecular dataset with phylogenetically and stratigraphically constrained fossil calibrations to infer an evolutionary timescale for Serpentes. We reveal a potential diversification among crown snakes associated with the K-Pg mass extinction, led by the successful colonisation of Asia by the major extant clade Afrophidia. Vertebral morphometrics suggest increasing morphological specialisation among marine snakes through the Paleogene. The dispersal patterns of snakes following the K-Pg underscore the importance of this mass extinction event in shaping Earth's extant vertebrate faunas