Drive network to a desired orbit by pinning control

summary:The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology

Asymptotic Behavior for Radially Symmetric Solutions of a Logistic Equation with a Free Boundary

In this paper we investigate a logistic equation with a new free boundary condition appearing in ecology, we aim to describe the spreading of a new or invasive species by studying the asymptotic behavior of the radially symmetric solutions of the problem. We will obtain a trichotomy result: spreading (the solution converges to a stationary solution defined on the half–line), transition (the solution converges to a stationary solution with compact support) and vanishing (the solution converges to 0 within a finite time). Besides we can also obtain a dichotomy result (either spreading or vanishing happens). Moreover, in the spreading case, we give the sharp estimate of the asymptotic spreading speed of the free boundary

Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term

We study the asymptotic behavior of solutions of a Fisher equation with free boundaries and the nonlocal term (an integral convolution in space). This problem can model the spreading of a biological or chemical species, where free boundaries represent the spreading fronts of the species. We give a dichotomy result, that is, the solution either converges to 1 locally uniformly in R, or to 0 uniformly in the occupying domain. Moreover, we give the sharp threshold when the initial data u0 = σφ, that is, there exists σ ∗ > 0 such that spreading happens when σ > σ , and vanishing happens when σ ≤

Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term

We study the asymptotic behavior of solutions of a Fisher equation with free boundaries and the nonlocal term (an integral convolution in space). This problem can model the spreading of a biological or chemical species, where free boundaries represent the spreading fronts of the species. We give a dichotomy result, that is, the solution either converges to $1$ locally uniformly in $\mathbb{R}$, or to $0$ uniformly in the occupying domain. Moreover, we give the sharp threshold when the initial data $u_0=\sigma \phi$, that is, there exists $\sigma^*>0$ such that spreading happens when $\sigma>\sigma^*$, and vanishing happens when $\sigma\leq \sigma^*$

Regulatory role of excitatory interneurons by combining electrical stimulation for absence seizures in the coupled thalamocortical model

The role of excitatory interneurons (EINs) in the cortical has received increasing attention in the discussion of absence seizures. Numerous physiological experiments have confirmed the correlation between EIN and absence seizures. However, the dynamic mechanisms underlying this relationship are not well understood, and there are some challenges in selecting appropriate stimulation strategies for pyramidal clusters. In this study, we incorporated EIN into the previous Taylor model and developed an improved thalamocortical coupled model consisting of ten neuronal populations. Initially, we investigated the excitatory induction effect of EIN to pyramidal clusters and the external input of EIN. Then, four different targeted treatment approaches (deep brain stimulation (DBS), current balanced biphasic pulse (CBBP), 1:0 coordinated resetting stimulation (1:0 CRS), and 3:2 CRS) were applied to the pyramidal clusters. Moreover, we established two quantitative indices to evaluate the stimulation effects. The results showed that modifying the external input of EIN and the coupling strength projected onto the pyramidal clusters can effectively transition the system from an absence seizure state to other normal states. Additionally, inputs from the left compartment were found to reduce the generation of abnormal discharge regions in the right compartment. Furthermore, considering the treatment effects and current consumption, the 3:2 CRS stimulation strategy appeared to be the most suitable treatment approach for the pyramidal clusters. This work introduces a novel coupled model containing EIN, which contributes new theoretical foundations and insights for the future treatment of absence seizures

Single Nanoparticle Translocation Through Chemically Modified Solid Nanopore

The nanopore sensor as a high-throughput and low-cost technology can detect single nanoparticle in solution. In the present study, the silicon nitride nanopores were fabricated by focused Ga ion beam (FIB), and the surface was functionalized with 3-aminopropyltriethoxysilane to change its surface charge density. The positively charged nanopore surface attracted negatively charged nanoparticles when they were in the vicinity of the nanopore. And, nanoparticle translocation speed was slowed down to obtain a clear and deterministic signal. Compared with previous studied small nanoparticles, the electrophoretic translocation of negatively charged polystyrene (PS) nanoparticles (diameter ~100 nm) was investigated in solution using the Coulter counter principle in which the time-dependent nanopore current was recorded as the nanoparticles were driven across the nanopore. A linear dependence was found between current drop and biased voltage. An exponentially decaying function (t(d)  ~ e(−v/v0)) was found between the duration time and biased voltage. The interaction between the amine-functionalized nanopore wall and PS microspheres was discussed while translating PS microspheres. We explored also translocations of PS microspheres through amine-functionalized solid-state nanopores by varying the solution pH (5.4, 7.0, and 10.0) with 0.02 M potassium chloride (KCl). Surface functionalization showed to provide a useful step to fine-tune the surface property, which can selectively transport molecules or particles. This approach is likely to be applied to gene sequencing. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s11671-016-1255-6) contains supplementary material, which is available to authorized users

Electrically facilitated translocation of protein through solid nanopore

Abstract Nanopores have been proven as versatile single-molecule sensors for individual unlabeled biopolymer detection and characterization. In the present work, a relative large nanopore with a diameter of about 60 nm has been used to detect protein translocation driven by a series of applied voltages. Compared with previous studied small nanopores, a distinct profile of protein translocation through a larger nanopore has been characterized. First, a higher threshold voltage is required to drive proteins into the large nanopore. With the increase of voltages, the capture frequency of protein into the nanopore has been markedly enhanced. And the distribution of current blockage events is characterized as a function of biased voltages. Due to the large dimension of the nanopore, the adsorption and desorption phenomenon of proteins observed with a prolonged dwell time has been weakened in our work. Nevertheless, the protein can still be stretched into an unfolded state by increased electric forces at high voltages. In consideration of the high throughput of the large nanopore, a couple of proteins passing through the nanopore simultaneously occur at high voltage. As a new feature, the feasibility and specificity of a nanopore with distinct geometry have been demonstrated for sensing protein translocation, which broadly expand the application of nanopore devices.</jats:p

Pervasive hybridization during evolutionary radiation of Rhododendron subgenus Hymenanthes in mountains of southwest China

Radiations are especially important for generating species biodiversity in mountainous ecosystems. The contribution of hybridization to such radiations has rarely been examined. Here, we use extensive genomic data to test whether hybridization was involved in evolutionary radiation within Rhododendron subgenus Hymenanthes, whose members show strong geographic isolation in the mountains of southwest China. We sequenced genomes for 143 species of this subgenus and 93 species of four other subgenera, and found that Hymenanthes was monophyletic and radiated during the late Oligocene to middle Miocene. Widespread hybridization events were inferred within and between the identified clades and subclades. This suggests that hybridization occurred both early and late during diversification of subgenus Hymenanthes, although the extent to which hybridization, speciation through mixing-isolation-mixing or hybrid speciation, accelerated the diversification needs further exploration. Cycles of isolation and contact in such and other montane ecosystems may have together promoted species radiation through hybridization between diverging populations and species. Similar radiation processes may apply to other montane floras in this region and elsewhere

Hierarchical bismuth vanadate/reduced graphene oxide composite photocatalyst for hydrogen evolution and bisphenol A degradation

Bismuth vanadate (BiVO4) is a widely studied photocatalyst for the depollution of contaminated wastewater, production of hydrogen by water splitting, and organic synthesis. The photophysical properties of BiVO4 are sensitive to morphology and quantum confinement effects, and can exhibit enhanced photocatalytic performance in nanocomposites with graphene. Synthesis of hierarchical BiVO4 plates decorated by nanoparticles (h-BiVO4) in contact with reduced graphene oxide (RGO) is reported via a facile one-pot solution phase approach using ethanolamine and a polyethylene glycol stabilizer. The resulting h-BiVO4/RGO photocatalyst exhibited superior photoactivity for bisphenol A (BPA) degradation and hydrogen evolution under visible light irradiation compared to single component h-BiVO4 or a μm-sized block-like BiVO4 morphology. Rates of BPA photocatalytic degradation and apparent quantum efficiency (AQE) decreased in the order h-BiVO4/RGO (4.5 × 10−2 mmol.g−1.min−1; 15.1% AQE) > h-BiVO4 (3.5 × 10−2 mmol.g−1.min−1; 11.7% AQE) > BiVO4 (1 × 10−2 mmol.g−1.min−1; 3.4% AQE), representing a 4.5 fold enhancement for h-BiVO4/RGO versus BiVO4. Liquid phase photodegradation products included benzene-1,4-diol, cyclohexa-2,5-diene-1,4-dione and (2Z)-but-2-enedioic acid. The rate of photocatalytic hydrogen production under visible light was 11.5 µmol.g−1.h−1 for h-BiVO4/RGO, ~383.3 times greater than for BiVO4 (0.03µmol.g−1.h−1). The superior photocatalytic performance of h-BiVO4/RGO is largely attributed to its higher surface area, aided by enhanced visible light absorption and charge separation across the semiconductor-RGO interface, which together confer a higher density and lifetime of photoexcited charge carriers