We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation with a homogeneous kernel. The constructed m...
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We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation with a homogeneous kernel. The constructed model naturally encodes the heterogeneous energy dissipation by jointly learning a set of state features and the non-Markovian coupling among the features. Numerical results demonstrate the limitation of the standard generalized Langevin equation and the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition.
Different from the common delayed synchronization(DS)in which response appears after stimulation,anticipated synchronization(AS)in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which respon...
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Different from the common delayed synchronization(DS)in which response appears after stimulation,anticipated synchronization(AS)in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which response of the receiver neuron appears before stimulation of the sender neuron,showing an interesting function of brain to anticipate the *** dynamical mechanism for the AS remains unclear due to complex dynamics of inhibitory and excitatory *** this article,the paradoxical roles of excitatory synapse and inhibitory autapse in the formation of AS are ***,in addition to the common roles such that inhibitory modulation delays and excitatory modulation advances spike,paradoxical roles of excitatory stimulation to delay spike via type-II phase response and of inhibitory autapse to advance spike are obtained in suitable parameter regions,extending the dynamics and functions of the excitatory and inhibitory ***,AS is related to the paradoxical roles of the excitatory and inhibitory modulations,presenting deep understandings to the *** autapse induces spike of the receiver neuron advanced to appear before that of the sender neuron at first,and then excitatory synapse plays a delay role to prevent the spike further advanced,resulting in the AS as the advance and delay effects realize a dynamic ***,inhibitory autapse with strong advance,middle advance,and weak advance and delay effects induce phase drift(spike of the receiver neuron advances continuously),AS,and DS,respectively,presenting comprehensive relationships between AS and other *** results present potential measures to modulate AS related to brain function.
The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the Levenberg...
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The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation(LMB)neural networks(NNs),i.e.,*** FO-HBV-DIS with the response of antibody immune is categorized into five dynamics,healthy hepatocytes(H),capsids(D),infected hepatocytes(I),free virus(V)and antibodies(W).The investigations for three different FO variants have been tested numerically to solve the nonlinear *** data magnitudes are implemented 75%for training,10%for certification and 15%for testing to solve the FO-HBV-DIS with the response of antibody *** numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton *** authenticate the validity,competence,consistency,capability and exactness of the LMBNNs,the numerical presentations using the mean square error(MSE),error histograms(EHs),state transitions(STs),correlation and regression are accomplished.
The current investigations present a novel prevention dynamic in the Human immunodeficiency virus (HIV) system, which is one of the deathly, convertible and unsafe viruses that arise almost the entire world. Since the...
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We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynami...
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We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematica...
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In the evolving era of social robots, managing a swarm of autonomous agents to perform particular tasks has become essential for numerous industries. The task becomes more challenging for large-scale swarms and comple...
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This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching *** nanoparticles of silver and alumina have mixed i...
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This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching *** nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal *** that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate *** analysis method is used for the solution of the resultant *** this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness *** of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin *** distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.
With the increasing use of mobile phones and messaging services, SMS spam has become a significant issue for users. In this paper, we propose a novel approach1 to tackle this problem by using Sine-Cosine Algorithm (SC...
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When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary *** homogeneou...
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When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary *** homogeneous Dirichlet boundary conditions,u(±1)=0,popular choices include the "Chebyshev difference basis" ζn(x)≡Tn+2(x)-Tn(x) with coefficients here denoted by bnand the "quadratic factor basis" Qn(x)≡(1-x2)Tn(x) with coefficients *** u(x) is weakly singular at the boundary,then the coefficients andecrease proportionally to O(A(n)/nκ) for some positive constant κ,where A(n) is a logarithm or a *** prove that the Chebyshev difference coefficients bndecrease more slowly by a factor of 1/n while the quadratic factor coefficients cndecrease more slowly still as O(A(n)/nκ-2).The error for the unconstrained Chebyshev series,truncated at degree n=N,is O(|A(N)|/Nκ) in the interior,but is worse by one power of N in narrow boundary layers near each of the *** having nearly identical error norms in interpolation,the error in the Chebyshev basis is concentrated in boundary layers near both endpoints,whereas the error in the quadratic factor and difference basis sets is nearly uniformly oscillating over the entire interval in ***,for Chebyshev polynomials,the values of their derivatives at the endpoints are O(n2),but only O(n) for the difference ***,we give the asymptotic coefficients and rigorous error estimates of the approximations in these three bases,solved by the least squares *** also find an interesting fact that on the face of it,the aliasing error is regarded as a bad thing;actually,the error norm associated with the downward curving spectral coefficients decreases even faster than the error norm of infinite *** the premise is under the same basis,and when involving different bases,it may not be established yet.
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