Oneillmalmberg8863

In this paper, we investigated the possibility of using the magnetic Laplacian to characterize directed networks. We address the problem of characterization of network models and perform the inference of the parameters used to generate these networks under analysis. Many interesting results are obtained, including the finding that the community structure is related to rotational symmetry in the spectral measurements for a type of stochastic block model. Due the hermiticity property of the magnetic Laplacian we show here how to scale our approach to larger networks containing hundreds of thousands of nodes using the Kernel Polynomial Method (KPM), a method commonly used in condensed matter physics. Using a combination of KPM with the Wasserstein metric, we show how we can measure distances between networks, even when these networks are directed, large, and have different sizes, a hard problem that cannot be tackled by previous methods presented in the literature.Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law parameters with the requirement of using momental points for the characteristic function, but the selection of points is only poorly explained and has not been elaborated. We propose a new characteristic function-based approach by introducing a technique of selecting plausible points, which could bring the method of moments available for practical use. Our method outperforms other state-of-art methods that exhibit a closed-form expression of all four parameters of stable laws. Finally, the applicability of the method is illustrated by using several data of financial assets. Numerical results reveal that our approach is advantageous when modeling empirical data with stable distributions.We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-Huxley type [Wojcik et al., PLoS One 9, e92918 (2014)]. The computational reduction to return maps for the phase-lags between neurons reveals a rich multiplicity of rhythmic patterns in such circuits. this website We perform a detailed bifurcation analysis to show how such rhythms can emerge, disappear, and gain or lose stability, as the parameters of the individual cells and the synapses are varied.We study a discrete-time model for a population subject to harvesting. A maximum annual catch H is fixed, but a minimum biomass level T must remain after harvesting. This leads to a mathematical model governed by a continuous piecewise smooth map, whose dynamics depend on two relevant parameters H and T. We combine analytical and numerical results to provide a comprehensive overview of the dynamics with special attention to discontinuity-induced (border-collision) bifurcations. link2 We also discuss our findings in the context of harvest control rules.In this paper, a fixed-time terminal synergetic observer for synchronization of fractional-order nonlinear chaotic systems is proposed. First, fixed-time terminal attractors for fractional-order nonlinear systems are introduced on the basis of fixed-time stability of integer-order nonlinear differential equations and on defining particular fractional-order macro-variables. Second, a new synergetic observer dedicated to the synchronization of fractional-order chaotic systems is developed. The proposed observer converges in a predefined fixed-time uniformly bounded with respect to initial conditions. Thanks to the step-by-step procedure, only one communication channel is used to achieve the synchronization. Third, a fixed-time synergetic extended observer with unknown input is constructed to simultaneously estimate the state variables and to recover the unknown input. Finally, computer simulations are performed to illustrate the efficiency of the proposed synchronization method and its application in a secure communication scheme.This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g., for an infinite number of delays), the non-asymptotic setting is not well-understood. First, we show that the minimal time-delays required for perfect signal recovery are solely determined by the sparsity in the Fourier spectrum for scalar systems. For the vector case, we provide a rank test and a geometric interpretation for the necessary and sufficient conditions for the existence of an accurate linear time delayed model. Furthermore, we prove that the output controllability index of a linear system induced by the Fourier spectrum serves as a tight upper bound on the minimal number of time delays required. An explicit expression for the exact linear model in the spectral domain is also provided. From a numerical perspective, the effect of the sampling rate and the number of time delays on numerical conditioning is examined. An upper bound on the condition number is derived, with the implication that conditioning can be improved with additional time delays and/or decreasing sampling rates. Moreover, it is explicitly shown that the underlying dynamics can be accurately recovered using only a partial period of the attractor. Our analysis is first validated in simple periodic and quasiperiodic systems, and sensitivity to noise is also investigated. Finally, issues and practical strategies of choosing time delays in large-scale chaotic systems are discussed and demonstrated on 3D turbulent Rayleigh-Bénard convection.In this paper, we derive a four-mode model for the Kolmogorov flow by employing Galerkin truncation and the Craya-Herring basis for the decomposition of velocity field. After this, we perform a bifurcation analysis of the model. Though our low-dimensional model has fewer modes than past models, it captures the essential features of the primary bifurcation of the Kolmogorov flow. For example, it reproduces the critical Reynolds number for the supercritical pitchfork bifurcation and the flow structures of past works. We also demonstrate energy transfers from intermediate scales to large scales. We perform direct numerical simulations of the Kolmogorov flow and show that our model predictions match the numerical simulations very well.Following the idea that dissipation in turbulence at high Reynolds number is dominated by singular events in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows, scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the drag law deduced by Newton for a projectile moving quickly in a fluid at rest. Inspired by this Newton's drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between the Reynolds stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space). This model takes the form of an integrodifferential equation for the velocity which is eventually solved for a Poiseuille flow in a circular pipe.Detrended fluctuation analysis (DFA) is widely used to characterize long-range power-law correlations in complex signals. However, it has restrictions when nonstationarity is not limited only to slow variations in the mean value. To improve the characterization of inhomogeneous datasets, we have proposed the extended DFA (EDFA), which is a modification of the conventional method that evaluates an additional scaling exponent to take into account the features of time-varying nonstationary behavior. Based on EDFA, here, we analyze rat electroencephalograms to identify specific changes in the slow-wave dynamics of brain electrical activity associated with two different conditions, such as the opening of the blood-brain barrier and sleep, which are both characterized by the activation of the brain drainage function. We show that these conditions cause a similar reduction in the scaling exponents of EDFA. Such a similarity may represent an informative marker of fluid homeostasis of the central nervous system.We analyze the 2019 Chilean social unrest episode, consisting of a sequence of events, through the lens of an epidemic-like model that considers global contagious dynamics. We adjust the parameters to the Chilean social unrest aggregated public data available from the Undersecretary of Human Rights and observe that the number of violent events follows a well-defined pattern already observed in various public disorder episodes in other countries since the 1960s. Although the epidemic-like models display a single event that reaches a peak followed by an exponential decay, we add standard perturbation schemes that may produce a rich temporal behavior as observed in the 2019 Chilean social turmoil. Although we only have access to aggregated data, we are still able to fit it to our model quite well, providing interesting insights on social unrest dynamics.The key to the survival of a species lies in understanding its evolution in an ever-changing environment. We report a theoretical model that integrates frequency-dependent selection, mutation, and asexual reproduction for understanding the biological evolution of a host species in the presence of parasites. We study the host-parasite coevolution in a one-dimensional genotypic space by considering a dynamic and heterogeneous environment modeled using a fitness landscape. It is observed that the presence of parasites facilitates a faster evolution of the host population toward its fitness maximum. We also find that the time required to reach the maximum fitness (optimization time) decreases with increased infection from the parasites. However, the overall fitness of the host population declines due to the parasitic infection. In the limit where parasites are considered to evolve much faster than the hosts, the optimization time reduces even further. link3 Our findings indicate that parasites can play a crucial role in the survival of its host in a rapidly changing environment.The development of 2D and 3D structures on the nanoscale containing viral nanoparticles (VNPs) as interesting nanobuilding blocks has come into focus for a bottom-up approach as an alternative to the top-down approach in nanobiotechnology. Our research has focused on the plant Tomato Bushy Stunt Virus (TBSV). In a previous study, we reported the impact of the pH value on the 2D assembly of viral monolayers. Here, we extend these studies into the third dimension by using specific interactions between the layers in combination with selective side chains on the viral capsid. The virus bilayer structure is prepared by an alternating deposition of His-tagged TBSV (4D6H-TBSV, first layer), Ni-NTA nanogold (second layer) complexes and 4D6H-TBSV, respectively, and 6D-TBSV (6xaspartic acid TBSV) as the third layer, i.e., the second layer of VNPs. The formed layer structures were imaged by using scanning force and scanning electron microscopy. The data show that a virus bilayer structure was successfully built up by means of the interaction between Ni-NTA nanogold and histidine.