Dynamics and synchronization of neural models with memristive membranes under energy coupling

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms.The electrophysiological environment inside and outside of the nerve cell is different.Due to the continuous and periodical properties of electromagnetic fields in the cell during its operation,electronic components involving two capacitors and a memristor are effective in mimicking these physical features.In this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance.It is found that the memristive neural circuit can present abundant firing patterns without stimulus.The Hamilton energy function is deduced using the Helmholtz theorem.Further,a neuronal network consisting of memristive neurons is proposed by introducing energy coupling.The controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Optimal Control for Age Distribution and Weighted Size Competitive Species in a Polluted Environment

In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.

THE(p,q)-ANALOG OF MULTIVALENT BAZILEVIC FUNCTIONS ASSOCIATED WITH A LIMACON

This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-analog of a class of multivalently Bazilevic functions as-sociated with a limacon function,and obtains the corresponding coefficient estimates and the Fekete-Szego inequality,which extend and improve the related results for starlike functions,even q-starlike functions.

Partial wetting of the soft elastic graded substrate due to elastocapillary deformation

Surface tension plays a central role in the mechanical behavior of soft materials such as gels.Elastocapillary deformation of elastic graded substrates is ubiquitous in soft materials.In this work,the effect of a partially wetting sessile liquid droplet on the elastocapillary deformation of a soft elastic graded substrate is studied.The modulus is assumed to have an exponential form along the thickness direction.By applying the Fourier transformation,a mixed boundary-value problem is reduced into a dual integral equation.The numerical results show that the surface displacement is strongly affected by the inhomogeneity of the material.The study of the wetting properties of gel substrates is essential for both understanding the wetting phenomena of gels and developing gels for applications as soft actuators and sensors that can be used in wearable electronics and soft robotics.

A review of the influencing factors on teleseismic traveltime tomography

Teleseismic traveltime tomography is an important tool for investigating the crust and mantle structure of the Earth.The imaging quality of teleseismic traveltime tomography is affected by many factors,such as mantle heterogeneities,source uncertainties and random noise.Many previous studies have investigated these factors separately.An integral study of these factors is absent.To provide some guidelines for teleseismic traveltime tomography,we discussed four main influencing factors:the method for measuring relative traveltime differences,the presence of mantle heterogeneities outside the imaging domain,station spacing and uncertainties in teleseismic event hypocenters.Four conclusions can be drawn based on our analysis.(1)Comparing two methods,i.e.,measuring the traveltime difference between two adjacent stations(M1)and subtracting the average traveltime of all stations from the traveltime of one station(M2),reveals that both M1 and M2 can well image the main structures;while M1 is able to achieve a slightly higher resolution than M2;M2 has the advantage of imaging long wavelength structures.In practical teleseismic traveltime tomography,better tomography results can be achieved by a two-step inversion method.(2)Global mantle heterogeneities can cause large traveltime residuals(up to about 0.55 s),which leads to evident imaging artifacts.(3)The tomographic accuracy and resolution of M1 decrease with increasing station spacing when measuring the relative traveltime difference between two adjacent stations.(4)The traveltime anomalies caused by the source uncertainties are generally less than 0.2 s,and the impact of source uncertainties is negligible.

A Multi-Layered Model for Heat Conduction Analysis of Thermoelectric Material Strip

A multi-layered model for heat conduction analysis of a thermoelectric material strip(TEMs)with a Griffith crack under the electric flux and energy flux load has been developed.The materials parameters of the TEMs vary continuously in an arbitrary manner.To derive the solution,the TEMs is divided into several sub-layers with different material properties.The mixed boundary problem is reduced to a system of singular integral equations,which are solved numerically.The effect of strip width on the electric flux intensity factor and thermal flux intensity factor are studied.

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

The contact problem for thermoelectric materials with functionally graded properties is considered.The material properties,such as the electric conductivity,the thermal conductivity,the shear modulus,and the thermal expansion coefficient,vary in an exponential function.Using the Fourier transform technique,the electro-thermoelastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density,the normal energy flux,and the contact pressure.Meanwhile,the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s formula.After addressing the non-linearity excited by thermoelectric effects,the particular solutions of the displacement fields can be assessed.The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented.The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials(FGTEMs).

Majorization and Fekete-Szegö Problems for Multivalent Meromorphic Functions Associated with the Mittag-Leffler Function

The main object of this present paper is to investigate the problem of majorization of certain class of multivalent meromorphic functions of complex order involving Mittag-Leffler function. Meanwhile, for this subclass the corresponding coefficient estimates and some Fekete-Szegö type inequalities are obtained. Moreover we point out some new or known consequences of our main results.

Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems

This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.

An eikonal equation-based earthquake location method by inversion of multiple phase arrivals

The precise determination of earthquake location is the fundamental basis in seismological community,and is crucial for analyzing seismic activity and performing seismic tomography.First arrivals are generally used to practically determine earthquake locations.However,first-arrival traveltimes are not sensitive to focal depths.Moreover,they cannot accurately constrain focal depths.To improve the accuracy,researchers have analyzed the depth phases of earthquake locations.The traveltimes of depth phases are sensitive to focal depths,and the joint inversion of depth phases and direct phases can be implemented to potentially obtain accurate earthquake locations.Generally,researchers can determine earthquake locations in layered models.Because layered models can only represent the first-order feature of subsurface structures,the advantages of joint inversion are not fully explored if layered models are used.To resolve the issue of current joint inversions,we use the traveltimes of three seismic phases to determine earthquake locations in heterogeneous models.The three seismic phases used in this study are the first P-,sPg-and PmP-waves.We calculate the traveltimes of the three seismic phases by solving an eikonal equation with an upwind difference scheme and use the traveltimes to determine earthquake locations.To verify the accuracy of the earthquake location method by the inversion of three seismic phases,we take the 2021 M_(S)6.4 Yangbi,Yunnan earthquake as an example and locate this earthquake using synthetic and real seismic data.Numerical tests demonstrate that the eikonal equation-based earthquake location method,which involves the inversion of multiple phase arrivals,can effectively improve earthquake location accuracy.

Reliability and control of strongly nonlinear vibro-impact system under external and parametric Gaussian noises

This paper mainly focuses on reliability and the optimal bounded control for maximizing system reliability of a strongly nonlinear vibro-impact system. Firstly, the new stochastic averaging in which the impact condition is converted to the system energy is applied to obtain the averaged It? stochastic differential equation, by which the associated Backward Kolmogorov(BK)equation and Generalized Pontryagin(GP) equation are derived. Then, the dynamical programming equations are obtained based on the dynamical programming principle, by which the optimal bounded control for maximizing system reliability is devised.Finally, the effects of the bounded control and noise intensity on the reliability of the vibro-impact system are discussed in detail;meanwhile, the influence of impact conditions on the system's reliability is also studied. The feasibility and effectiveness of the proposed analytical method are substantiated by numerical results obtained from Monte-Carlo simulation.

Fracture analysis of cortical bone under the condition of cement line debonding and osteon pullout

Cortical bone consists of osteons embedded in interstitial bone tissue and there is a thin amorphous interface, named cement line, between osteon and interstitial bone. Due to fatigue and cyclic loading, the pullout or debonding phenomenon often occurs in osteonal and interstitial tissue bone. The study aims to construct a fiber-reinforced composite material debonding model for cortical bone, in which the bonding condition along the osteon, cement line and interstitial tissue bone are assumed to be imperfect. In the study, we used the complex variable method to obtain series representations for stress fields in the osteon, cement line and the interstitial tissue bone with a radial crack. The effects of material properties of osteon and cement line, crack position, and varying degrees of debonding on the fracture behavior were investigated by computing the stress intensity factor （SIF） in the vicinity of the microcrack tips. The investigation results indicated that the cement line was important for controlling the fracture toughening mechanisms and that the level of imperfect bonding among osteon, cement line and interstitial tissue bone had a pronounced effect on the crack behavior and should not be ignored.

Energy flow accounts for the adaptive property of functional synapses

In the presence of external stimuli and electromagnetic radiation(EMR),biological neurons can exhibit different firing patterns and switch to appropriate firing modes because of intrinsic self-adaption.Coupling to memristive synapses can discern the EMR effect,and memristive synapses connecting to neurons can be effectively regulated by external physical fields.From a dynamical viewpoint,the appropriate setting for memristive synapse intensity can trigger changes in neural activities;however,the biophysical mechanism of adaptive regulation in the memristive biophysical neuron has not been clarified.Herein,a memristor is used to control a simple neural circuit by generating a memristive current,and an equivalent memristive neuron model is obtained.A single firing mode can be stabilized in the absence of EMR,while multiple firing modes occur in the neuron under EMR.The gain of the memristive synaptic current is dependent on the energy flow,and the shunted energy flow in the memristive channel can control the energy ratio between the electric field and magnetic field.The growth and enhancement of the memristive synapse depend on the energy flow across the memristive channel.The memristive synapse is enhanced when its field energy is below the threshold,and it is suppressed when its field energy is above the threshold.These results explain why and how multiple firing modes are induced and controlled in biological neurons.Furthermore,the self-adaption property of memristive neurons was also clarified.Thus,the control of energy flow in the memristive synapse can effectively regulate the membrane potentials,and neural activities can be effectively controlled to select suitable body gaits.

Dynamics of a stochastic delayed avian influenza model with mutation and temporary immunity

In this paper,the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity.First,we prove the existence and uniqueness of the global positive solution for the stochastic model.Second,we give two different thresholds R_(01)^(s) and,R_(02)^(s) and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system,respectively.Compared with the corresponding deterministic model,the thresholds affected by the white noises are smaller than the ones of the deterministic system.Finally,numerical simulations are carried out to support our theoretical results.It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations,while prompt the spread of mutant avian influenza in human population.

An Augmented IB Method&Analysis for Elliptic BVP on Irregular Domains

The immersed boundary method is well-known,popular,and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface.In this paper,an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains(exterior or interior)with a Dirichlet boundary condition.The new method inherits the simplicity,robustness,and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives.Numerical examples are provided to confirm the analysis.

Perpetual cutoff method and CDE′(K, N) condition on graphs

By using the perpetual cutoff method,we prove two discrete versions of gradient estimates for bounded Laplacian on locally finite graphs with exception sets under the condition of CDE′(K,N).This generalizes a main result of F.Münch who considers the case of CD(K,∞)curvature.Hence,we answer a question raised by Münch.For that purpose,we characterize some basic properties of radical form of the perpetual cutoff semigroup and give a weak commutation relation between bounded LaplacianΔand perpetual cutoff semigroup P w t in our setting.

On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights

Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs,for continuous function defined on bounded intervals.In the present paper,we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in[16].By using new methods,we also give right approximation rate estimations of the approximation by Li’s neural networks.

A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

Velocity structure and radial anisotropy beneath the northeastern Tibetan Plateau revealed by eikonal equation-based teleseismic P-wave traveltime tomography

The northeastern Tibetan Plateau serves as the frontier for the northeastward expansion of the plateau.In this area,the Tibetan Plateau interacts with the surrounding blocks,such as the Alxa Block,the Ordos Block,the Kunlun-West Qinling belt and the Sichuan Basin.Because of this expansion and interaction,this area suffers from intense deformation.At present,the evolution and deformation mechanisms of the northeastern Tibetan Plateau remain controversial.To provide new insights into these mechanisms,in this study,we conduct tomography of the P-wave velocity and radial anisotropy structures beneath the northeastern Tibetan Plateau.We choose a total of 667 teleseismic earthquakes from August 2006 to October 2020.Waveforms of these earthquakes were recorded by 921 broadband seismic stations in the northeastern Tibetan Plateau and surrounding areas.We first perform cross-correlation on waveforms of each station pair and obtain 770,749 P-wave traveltime differences.Then,we invert the differential traveltime data by applying eikonal equation-based teleseismic tomography.Finally,the P-wave velocity and radial anisotropy structures at depths from 30 to 800 km below the northeastern Tibetan Plateau are obtained.Our tomographic model shows clear low-velocity anomalies and positive radial anisotropy in the lower crust under the northeastern Qilian orogen,the northeastern Songpan-Ganzi belt and the western Qinling fold zone.These features are integrated to demonstrate the existence of lower crustal flow in the study area.Prominent low-velocity anomalies and positive radial anisotropy are found in the uppermost mantle beneath the Qilian orogen,the northeastern Songpan-Ganzi belt and western Qinling fold zone.These characteristics are combined to infer a weak lithosphere and horizontal asthenospheric flow under these tectonic units.Both the Ordos Block and the Sichuan Basin exhibit clear high-velocity anomalies and negative radial anisotropy in the uppermost mantle,thereby reflecting the high mechanical strength of the lithosphere beneath these blocks.High-velocity anomalies are also present in the upper mantle under the northern Chuandian block,potentially implying the northward subduction of the Indian plate.Furthermore,the front of the subducted Indian plate is imaged close to the Xianshuihe fault rather than the Kunlun fault.