Baldwinhildebrandt3635

Totally asymmetric exclusion processes (TASEPs) with open boundaries are known to exhibit moving shocks or delocalized domain walls (DDWs) for sufficiently small equal injection and extraction rates. In contrast, TASEPs in a ring with a single inhomogeneity display pinned shocks or localized domain walls (LDWs) under equivalent conditions [see, e.g., H. Hinsch and E. Frey, Phys. Rev. Lett. 97, 095701 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.095701]. By studying periodic exclusion processes composed of a driven (TASEP) and a diffusive segment, we discuss gradual fluctuation-induced depinning of the LDW, leading to its delocalization and formation of a DDW-like domain wall, similar to the DDWs in open TASEPs in some limiting cases under long-time averaging. This smooth crossover is controlled essentially by the fluctuations in the diffusive segment. Our studies provide an explicit route to control the quantitative extent of domain-wall fluctuations in driven periodic inhomogeneous systems, and should be relevant in any quasi-one-dimensional transport processes where the availability of carriers is the rate-limiting constraint.We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems.Multiple species in the ecosystem are believed to compete cyclically for maintaining balance in nature. The evolutionary dynamics of cyclic interaction crucially depends on different interactions representing different natural habits. Based on a rock-paper-scissors model of cyclic competition, we explore the role of mortality of individual organisms in the collective survival of a species. For this purpose a parameter called "natural death" is introduced. It is meant for bringing about the decease of an individual irrespective of any intra- and interspecific interaction. We perform a Monte Carlo simulation followed by a stability analysis of different fixed points of defined rate equations and observe that the natural death rate is surprisingly one of the most significant factors in deciding whether an ecosystem would come up with a coexistence or a single-species survival.The gradient-based optimization method for deep machine learning models suffers from gradient vanishing and exploding problems, particularly when the computational graph becomes deep. In this work, we propose the tangent-space gradient optimization (TSGO) for probabilistic models to keep the gradients from vanishing or exploding. The central idea is to guarantee the orthogonality between variational parameters and gradients. selleck kinase inhibitor The optimization is then implemented by rotating the parameter vector towards the direction of gradient. We explain and test TSGO in tensor network (TN) machine learning, where TN describes the joint probability distribution as a normalized state |ψ〉 in Hilbert space. We show that the gradient can be restricted in tangent space of 〈ψ|ψ〉=1 hypersphere. Instead of additional adaptive methods to control the learning rate η in deep learning, the learning rate of TSGO is naturally determined by rotation angle θ as η=tanθ. Our numerical results reveal better convergence of TSGO in comparison to the off-the-shelf Adam.Periodic pulse train stimulation is generically used to study the function of the nervous system and to counteract disease-related neuronal activity, e.g., collective periodic neuronal oscillations. The efficient control of neuronal dynamics without compromising brain tissue is key to research and clinical purposes. We here adapt the minimum charge control theory, recently developed for a single neuron, to a network of interacting neurons exhibiting collective periodic oscillations. We present a general expression for the optimal waveform, which provides an entrainment of a neural network to the stimulation frequency with a minimum absolute value of the stimulating current. As in the case of a single neuron, the optimal waveform is of bang-off-bang type, but its parameters are now determined by the parameters of the effective phase response curve of the entire network, rather than of a single neuron. The theoretical results are confirmed by three specific examples two small-scale networks of FitzHugh-Nagumo neurons with synaptic and electric couplings, as well as a large-scale network of synaptically coupled quadratic integrate-and-fire neurons.We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates with the particle distance and allows for the existence of stable bound states, despite the purely repulsive character of the Coulomb interaction. We design an order parameter to classify these bound states and use it to identify a structural crossover of the particle order, occurring when the electric field strength is varied. Amorphous particle configurations for a vanishing electric field and crystalline order in the regime of a strong electric field are observed. We study the impact of parameter variations on the particle order and conclude that the crossover occurs for a wide range of parameter values and even holds for different helical systems.