On controllability of neuronal networks with constraints on the average of control gains

Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently

Universal conductance fluctuation of mesoscopic systems in the metal-insulator crossover regime

We report a theoretical investigation on conductance fluctuation of mesoscopic systems. Extensive numerical simulations on quasi-one-dimensional, two-dimensional, and quantum dot systems with different symmetriescircular orthogonal ensemble, circular unitary ensemble (CUE), and 〔circular symplectic ensemble (CSE)〕indicate that the conductance fluctuation can reach a universal value in the crossover regime for systems with CUE and CSE symmetries. The conductance distribution is found to be a universal function from diffusive to localized regimes that depends only on the average conductance, dimensionality, and symmetry of the system. The numerical solution of DMPK equation agrees with our result in quasi-one dimension. Our numerical results in two dimensions suggest that this universal conductance fluctuation is related to the metal-insulator transition. In the localized regime with average conductance <0.3, the conductance distribution seems to be superuniversal independent of dimensionality and symmetry.published_or_final_versio

State estimation for discrete-time neural networks with Markov-mode-dependent lower and upper bounds on the distributed delays

Copyright @ 2012 Springer VerlagThis paper is concerned with the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters and mixed time-delays. The parameters of the neural networks under consideration switch over time subject to a Markov chain. The networks involve both the discrete-time-varying delay and the mode-dependent distributed time-delay characterized by the upper and lower boundaries dependent on the Markov chain. By constructing novel Lyapunov-Krasovskii functionals, sufficient conditions are firstly established to guarantee the exponential stability in mean square for the addressed discrete-time neural networks with Markovian jumping parameters and mixed time-delays. Then, the state estimation problem is coped with for the same neural network where the goal is to design a desired state estimator such that the estimation error approaches zero exponentially in mean square. The derived conditions for both the stability and the existence of desired estimators are expressed in the form of matrix inequalities that can be solved by the semi-definite programme method. A numerical simulation example is exploited to demonstrate the usefulness of the main results obtained.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60774073 and 61074129, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2010313

Catalytic Activities of Transition Metal Phosphides for NO Dissociation and Reduction With CO

A series of metal phosphides (MoP, WP, Co2P, Fe2P and Ni2P) were synthesized byH2-temperature-programmed reduction method. Amongst these phosphides, Fe2P was found to show a considerably higher activity for NO dissociation than other phosphides. Herein, it was firstly used as a catalyst for NO reduction with CO. Although the Fe2P catalyst showed an excellent activity for NO conversion to N2, there was a competition between NO reduction by CO and Fe2P oxidation by oxygen originated from NO dissociation. A complete equality of NO conversion and NO reduction degree can be obtained after increasing CO concentration in the system, which demonstrated that a catalytic redox cycle can be established on Fe2P catalyst, and hence in-situ oxidation of bulk Fe2P was avoided

An improved diameter bound for finite simple groups of Lie type

© 2019 London Mathematical Society For a finite group (Formula presented.), let (Formula presented.) denote the maximum diameter of a connected Cayley graph of (Formula presented.). A well-known conjecture of Babai states that (Formula presented.) is bounded by (Formula presented.) in case (Formula presented.) is a non-abelian finite simple group. Let (Formula presented.) be a finite simple group of Lie type of Lie rank (Formula presented.) over the field (Formula presented.). Babai's conjecture has been verified in case (Formula presented.) is bounded, but it is wide open in case (Formula presented.) is unbounded. Recently, Biswas and Yang proved that (Formula presented.) is bounded by (Formula presented.). We show that in fact (Formula presented.) holds. Note that our bound is significantly smaller than the order of (Formula presented.) for (Formula presented.) large, even if (Formula presented.) is large. As an application, we show that more generally (Formula presented.) holds for any subgroup (Formula presented.) of (Formula presented.), where (Formula presented.) is a vector space of dimension (Formula presented.) defined over the field (Formula presented.)

Singular Effects of Spin-Flip Scattering on Gapped Dirac Fermions

We investigate the effects of spin-flip scattering on the Hall transport and spectral properties of gapped Dirac fermions. We find that in the weak scattering regime, the Berry curvature distribution is dramatically compressed in the electronic energy spectrum, becoming singular at band edges. As a result the Hall conductivity has a sudden jump (or drop) of $e^2/2h$ when the Fermi energy sweeps across the band edges, and otherwise is a constant quantized in units of $e^2/2h$. In parallel, spectral properties such as the density of states and spin polarization are also greatly enhanced at band edges. Possible experimental methods to detect these effects are discussed

A Hessenberg Markov chain for fast fibre delay line length optimization

In this paper we present an approach to compute the invariant vector of the N + 1 state Markov chain P presented in (Rogiest et al., Lecture Notes in Computer Science, NET-COOP 2007 Special Issue, pp. 4465:185-194) to determine the loss rate of an FDL buffer consisting of N lines, by solving a related Hessenberg system (i.e., a Markov chain skip-free in one direction). This system is obtained by inserting additional time instants in the sample paths of P and allows us to compute the loss rate for various FDL lengths by solving a single system. This is shown to be especially effective in reducing the computation time of the heuristic LRA algorithm presented in (Lambert et al., Proc. NAEC 2005, pp. 545-555) to optimize the FDL lengths, where improvements of several orders of magnitude can be realized

Key region of laminin receptor 1 for interaction with human period 1

The 67 kDa laminin receptor 1 (Lamr1) is a novel protein that interacts with human circadian clock protein period 1 (hPer1). We confirmed the interaction between hPer1 and complete Lamr1 (295 amino acids) through yeast two-hybrid system in the present study. And we identified the interaction between hPer1 and hLamr11-190/hLamr1201-295 with yeast two-hybrid system. The results showed that hPer1 could interact with two partial Lamr1, which each contained a laminin-binding region, suggesting that both two partial sequences contained the binding region for hPer1. To define the key region of Lamr1 to interact with hPer1, pGADT7-Rec/hLamr11-190 was mutated with the palindromic sequence LMWWML, part LMW and WML, respectively. With yeast two-hybrid system, we found that hPer1 could not interact with Lamr1 mutated with LMWWML and LMW, but could interact with Lamr1 mutated with WML. It suggested that the palindromic sequence LMWWML in peptide G of Lamr1, especially LMW of it, was necessary for the interaction. Although, the palindromic sequence LMWWML is just the actual binding site for laminin. Together, these findings suggested that hPer1 might interact with Lamr1 by occupying the laminin-binding sites. It will be beneficial for studying the mechanism of hPer1 interaction with Lamr1.Key words: Laminin receptor 1 (Lamr1), human circadian clock protein period 1 (hPer1), interaction, yeast twohybrid, key region