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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. 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. #link# 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. Akti-1/2 datasheet 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.Plasmas, as well as several other many-body systems of technological interest, have been studied mostly as a purely classical subject. However, in dense plasmas, and in some semiconductor devices, metallic nanostructures and thin metal films, when the de Broglie wavelength of the charge carriers is comparable to the interparticle distance, quantum effects come into play. Because the classical kinetic equations are phase-space equations with positions and momenta as variables, which variables are noncommuting in quantum mechanics, kinetic equations are not directly applicable to quantum plasmas. Therefore, most treatments consider a full quantum many-body problem in Hilbert space and then, by reduction, obtain the quantum version of the kinetic equations. However, quantum mechanics may also be directly formulated in phase space by modifying the Poisson algebra into a new deformed algebra, hence the classical kinetic equations may also be deformed into their corresponding quantum versions. link2 This is the approach followed here and applied to derive the quantum corrections to the Vlasov-Poisson, Vlasov-Maxwell, and Boltzmann equations (in the latter case also within the relaxation-time approximation).We focus on the asymmetry of the interaction in the optimal velocity (OV) model, which is a model of self-driven particles, and analytically investigate the effects of the asymmetry on the fluctuation-response relation, which is one of the remarkable relationships in statistical physics. By linearizing a modified OV model, i.e., the backward-looking optimal velocity model, which can easily control the magnitude of asymmetry in the interaction, we derive n coupled linear oscillators with asymmetric interactions. We analytically solve the equations of the n coupled linear oscillators and calculate the response and correlation functions. We find that the fluctuation response relation does not hold in the n coupled linear oscillators with asymmetric interactions. Moreover, as the magnitude of the asymmetry increases, the difference between the response and correlation functions increases .We present a first-principles thermodynamic approach to provide an alternative to the Langevin equation by identifying the deterministic (no stochastic component) microforce F_k,BP acting on a nonequilibrium Brownian particle (BP) in its kth microstate m_k. (The prefix "micro" refers to microstate quantities and carry a suffix k.) The deterministic new equation is easier to solve using basic calculus. Being oblivious to the second law, F_k,BP does not always oppose motion but viscous dissipation emerges upon ensemble averaging. The equipartition theorem is always satisfied. We reproduce well-known results of the BP in equilibrium. We explain how the microforce is obtained directly from the mutual potential energy of interaction beween the BP and the medium after we average it over the medium so we only have to consider the particles in the BP. Our approach goes beyond the phenomenological and equilibrium approach of Langevin and unifies nonequilibrium viscous dissipation from mesoscopic to macroscopic scales and provides new insight into Brownian motion beyond Langevin's and Einstein's formulation.It has recently been reported that statistical signatures of brain criticality, obtained from distributions of neuronal avalanches, can depend on the cortical state. We revisit these claims with a completely different and independent approach, employing a maximum entropy model to test whether signatures of criticality appear in urethane-anesthetized rats. To account for the spontaneous variation of cortical states, we parse the time series and perform the maximum entropy analysis as a function of the variability of the population spiking activity. To compare data sets with different numbers of neurons, we define a normalized distance to criticality that takes into account the peak and width of the specific heat curve. We found a universal collapse of the normalized distance to criticality dependence on the cortical state, on an animal by animal basis. This indicates a universal dynamics and a critical point at an intermediate value of spiking variability.An intense radiation field can modify plasma properties and the corresponding refractive index and lead to nonlinear propagation effects such as self-focusing. We estimate the corresponding effects in pair plasmas for circularly polarized waves, in both unmagnetized and strongly magnetically dominated cases. First, in the unmagnetized pair plasma the ponderomotive force does not lead to charge separation but to density depletion. Second, for astrophysically relevant plasmas of pulsar magnetospheres [and possible loci of fast radio bursts (FRBs)], where the cyclotron frequency ω_B dominates over the plasma frequency ω_p and the frequency of the electromagnetic wave ω_B≫ω_p,ω, we show that (i) there is virtually no nonlinearity due to changing effective mass in the field of the wave; (ii) the ponderomotive force is F_p^(B)=-m_ec^2/4B_0^2∇E^2, which is reduced by a factor (ω/ω_B)^2 if compared to the unmagnetized case (B_0 is the external magnetic field and E is the electric field of the wave); and (iii) for a radiation beam propagating along a constant magnetic field in the pair plasma with density n_±, the ponderomotive force leads to the appearance of circular currents that lead to a decrease of the field within the beam by a factor ΔB/B_0=2πn_±m_ec^2E^2/B_0^4. Applications to the physics of FRBs are discussed; we conclude that for the parameters of FRBs, the dominant magnetic field completely suppresses nonlinear self-focusing or filamentation.Reckoning of pairwise dynamical correlations significantly improves the accuracy of mean-field theories and plays an important role in the investigation of dynamical processes in complex networks. In this work, we perform a nonperturbative numerical analysis of the quenched mean-field theory (QMF) and the inclusion of dynamical correlations by means of the pair quenched mean-field (PQMF) theory for the susceptible-infected-susceptible model on synthetic and real networks. link3 We show that the PQMF considerably outperforms the standard QMF theory on synthetic networks of distinct levels of heterogeneity and degree correlations, providing extremely accurate predictions when the system is not too close to the epidemic threshold, while the QMF theory deviates substantially from simulations for networks with a degree exponent γ>2.5. The scenario for real networks is more complicated, still with PQMF significantly outperforming the QMF theory. However, despite its high accuracy for most investigated networks, in a few cases PQMF deviations from simulations are not negligible. We found correlations between accuracy and average shortest path, while other basic network metrics seem to be uncorrelated with the theory accuracy. Our results show the viability of the PQMF theory to investigate the high-prevalence regimes of recurrent-state epidemic processes in networks, a regime of high applicability.Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of straight semirigid rods adsorbed on two-dimensional square lattices. The depositing objects can be adsorbed on the surface forming two layers. The filling of the lattice is carried out following a generalized random sequential adsorption (RSA) mechanism. In each elementary step, (i) a set of k consecutive nearest-neighbor sites (aligned along one of two lattice axes) is randomly chosen and (ii) if each selected site is either empty or occupied by a k-mer unit in the first layer, then a new k-mer is then deposited onto the lattice. Otherwise, the attempt is rejected. The process starts with an initially empty lattice and continues until the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. A wide range of values of k (2≤k≤64) is investigated. The study of the kinetic properties of the system shows that (1) the jamming coverage θ_j,k is a decreasing function with increasing k, with θ_j,k→∞=0.
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