Echo State Networks (ESN) are reservoir networks that satisfy well-established criteria for stability when constructed as feedforward networks. Recent evidence suggests that stability criteria are altered in the presence of reservoir substructures, such as clusters. Understanding how the reservoir architecture affects stability is thus important for the appropriate design of any ESN. To quantit...

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

We have carried out a series of small scale collisional N-body calculations of single-mass star clusters to investigate the dependence of the lifetime of star clusters on their initial parameters. Our models move through an external galaxy potential with a logarithmic density profile and they are limited by a cut-off radius. In order to find scaling relations between the lifetime of star cluste...

The objective of this research is to design an approach for selecting appropriate raw materials for facial tissues in Iran. There are three possibilities to maintain raw materials: (1) imported virgin pulp; (2) bagasse (sugar cane residue) plus some imported raw materials; and (3) recycled paper plus some imported raw materials. Owing to the shortage of raw materials as well as the high rate of...

As an important long-term incentive mode, the equity incentive promotes the managers to contribute to the interest uniformity of managers and shareholders. By using Paired-Samples T test methods and regression analysis method and choosing companies that issued the equity incentive plan in 2007 as the sample, this paper comparatively analyzes the differences in the performance of companies befor...

The covering radius R of a code is the maximal distance of any vector from the code. This work gives a number of new results concerning t[ n, k], the minimal covering radius of any binary code of length n and dimension k. For example r[ n, 41 and t [ n, 51 are determined exactly, and reasonably tight bounds on t[ n, k] are obtained for any k when n is large. These results are found by using sev...

The standard radius of curvature at a point q(s) on a smooth curve can be defined as the limiting radius of circles through three points that all coalesce to q(s). In the study of ideal knot shapes it has recently proven useful to consider a global radius of curvature of the curve at q(s) defined as the smallest possible radius amongst all circles passing through this point and any two other po...

The measurement of spherical surface radii exceeding few meters presents a challenge, because the familiar radius-bench method requires large part displacements. Dual-focus zone plates can extend the radius-bench method to measurements of large radii. OCIS codes: (220.4840) Testing, (050.1965) Diffractive lenses

Potassium Channels allow potassium flux and are essential for the generation of electric current acrossexcitable membranes. Potassium Channels are also the targets of various intracellular controlmechanisms; such that the suboptimal regulation of channel function might be related to pathologicalconditions. Realistic studies of ion current in biologic channels present a major challenge for compu...