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Interlayer antisynchronization in degree-biased duplex networks

Physical Review E 2023年第3期107卷 034313-034313页

作者： Sayantan Nag Chowdhury Sarbendu Rakshit Chittaranjan Hens Dibakar Ghosh Department of Environmental Science and Policy University of California Davis California 95616 USA Technology Innovation Hub (TIH) IDEAS (Institute of Data Engineering Analytics and Science Foundation) Indian Statistical Institute 203 B. T. Road Kolkata 700108 India Department of Mechanical Engineering University of California Riverside California 92521 USA Center for Computational Natural Sciences and Bioinformatics International Institute of Information Technology Gachibowli Hyderabad 500032 India Physics and Applied Mathematics Unit Indian Statistical Institute 203 B. T. Road Kolkata 700108 India

With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.

关键词： Coupled oscillators Dynamics of networks Synchronization

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Identifying the impact of local connectivity patterns on dynamics in excitatory-inhibitory networks

arXiv

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arXiv 2024年

作者： Shao, Yuxiu Dahmen, David Recanatesi, Stefano Shea-Brown, Eric Ostojic, Srdjan School of Systems Science Beijing Normal University Beijing China Laboratoire de Neurosciences Cognitives et Computationnelles INSERM U960 Ecole Normale Superieure - PSL Research University Paris France Computational and Systems Neuroscience Jülich Research Center Jülich Germany Technion Israel Institute of Technology Haifa Israel Department of Applied Mathematics and Computational Neuroscience Center University of Washington SeattleWA United States Allen Institute for Brain Science SeattleWA United States

Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Seminal theoretical results on dynamics of such networks are based on the assumption that synaptic strengths depend on the type of neurons they connect, but are otherwise statistically independent. Recent synaptic physiology datasets however highlight the prominence of specific connectivity patterns that go well beyond what is expected from independent connections. While decades of influential research have demonstrated the strong role of the basic EI cell type structure, to which extent additional connectivity features influence dynamics remains to be fully determined. Here we examine the effects of pair-wise connectivity motifs on the linear dynamics in excitatory-inhibitory networks using an analytical framework that approximates the connectivity in terms of low-rank structures. This low-rank approximation is based on a mathematical derivation of the dominant eigenvalues of the connectivity matrix, and predicts the impact on responses to external inputs of connectivity motifs and their interactions with cell-type structure. Our results reveal that a particular pattern of connectivity, chain motifs, have a much stronger impact on dominant eigenmodes than other pairwise motifs. In particular, an over-representation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks and generates a potential instability that requires revisiting the classical excitation-inhibition balance criteria. Examining effects of external inputs, we show that chain motifs can on their own induce paradoxical responses, where an increased input to inhibitory neurons leads to a decrease in their activity due to the recurrent feedback. These findings have direct implications for the interpretation of experiments in which responses to optogenetic perturbations are measured and used to infer the dynamical regime of cortical circuits. © 2024, CC BY-NC-ND.

关键词： Neurons

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Ab Initio Generalized Langevin Equation

arXiv

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arXiv 2022年

作者： Xie, Pinchen Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency. © 2022, CC BY.

关键词： Molecular dynamics

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Age of Information in Multi-Source Updating Systems: An M/G/1 Vacation Queueing Model

Age of Information in Multi-Source Updating Systems: An M/G/...

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IEEE International Conference on Communications (ICC)

作者： Muthukrishnan Senthil Kumar Aresh Dadlani Masoumeh Moradian Behrouz Maham Theodoros A. Tsiftsis Department of Applied Mathematics and Computational Sciences PSG College of Technology Coimbatore India Department of Electrical and Computer Engineering Nazarbayev University Astana Kazakhstan School of Computer Science Institute for Research in Fundamental Sciences Tehran Iran Department of Informatics and Telecommunications University of Thessaly Lamia Greece

Concurrent with the rise of real-time wireless systems enabled by the Internet of Things, the age of information (AoI) has been widely perceived as a crucial destination-centric performance metric to quantify the timeliness of data delivery. This paper deals with the analysis of information freshness in a multi-source M/G/1 queueing system with utilization of idle server time, referred to as server vacation, in an effective manner. In particular, the status update packets in our model are generated independently by a finite set of source nodes and according to a Poisson process, while their service time follows a general random variable. Using stochastic decomposition and the Laplace-Stieltjes transform, we derive the average AoI (AAoI) expression for the multi-source M/G/1 queueing model with generally-distributed vacation time in closed form. Our numerical simulations validate the accuracy of the derived AAoI expression and assess the impact of different parameters on the system performance.

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Multiple scales analysis of a nonlinear timestepping instability in simulations of solitons

arXiv

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arXiv 2024年

作者： Hyatt, Benjamin A. Lecoanet, Daniel Anders, Evan H. Burns, Keaton J. Department of Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL60208 United States Center for Interdisciplinary Exploration and Research in Astrophysics Northwestern University EvanstonIL60201 United States Kavli Institute for Theoretical Physics University of California Santa Barbara Santa BarbaraCA93106 United States Department of Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States

The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in pseudospectral simulations of nonlinear wave propagation resulting in finite-time blow-up. The blow-up time scale is independent of the spatial resolution and spectral basis but sensitive to the timestepping scheme and the timestep size. The instability appears in multi-step and multi-stage implicit-explicit (IMEX) timestepping schemes of different orders of accuracy and has been found to manifest in simulations of soliton solutions of the Korteweg-de Vries (KdV) equation and traveling wave solutions of a nonlinear generalized Klein-Gordon equation. Focusing on the case of KdV solitons, we show that modal predictions from linear stability theory are unable to explain the instability because the spurious growth from linear dispersion is small and nonlinear sources of error growth converge too slowly in the limit of small timestep size. We then develop a novel multi-scale asymptotic framework that captures the slow, nonlinear accumulation of timestepping errors. The framework allows the solution to vary with respect to multiple time scales related to the timestep size and thus recovers the instability as a function of a slow time scale dictated by the order of accuracy of the timestepping scheme. We show that this approach correctly describes our simulations of solitons by making accurate predictions of the blow-up time scale and transient features of the instability. Our work demonstrates that studies of long-time simulations of nonlinear waves should exercise caution when validating their timestepping schemes. © 2024, CC BY-NC-ND.

关键词： Solitons

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Phonon-mediated Migdal effect in semiconductor detectors

arXiv

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arXiv 2022年

作者： Liang, Zheng-Liang Mo, Chongjie Zheng, Fawei Zhang, Ping College of Mathematics and Physics Beijing University of Chemical Technology Beijing100029 China Beijing Computational Science Research Center Beijing100193 China School of Physics Beijing Institute of Technology Beijing100081 China School of Physics and Physical Engineering Qufu Normal University Qufu273165 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

The Migdal effect inside detectors provides a new possibility of probing the sub-GeV dark matter (DM) particles. While there has been well-established methods treating the Migdal effect in isolated atoms, a coherent and complete description of the valence electrons in semiconductor is still absent. The bremstrahlung-like approach is a promising attempt, but it turns invalid for DM masses below a few tens of MeV. In this paper, we lay out a framework where phonon is chosen as an effective degree of freedom to describe the Migdal effect in semiconductors. In this picture, a valence electron is excited to the conduction state via exchange of a virtual phonon, accompanied by a multi-phonon process triggered by an incident DM particle. Under the incoherent approximation, it turns out that this approach can effectively push the sensitivities of the semiconductor targets further down to the MeV DM mass region. Copyright © 2022, The Authors. All rights reserved.

关键词： Excited states

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Dynamic stabilization and heat transport characteristics of monolayer SnSe at finite temperature: A study by phonon quasiparticle approach

引用

Physical Review B 2021年第1期103卷 014304-014304页

作者： Yong Lu Fa-wei Zheng Yu Yang Ping Zhang Dong-Bo Zhang College of Mathematics and Physics Beijing University of Chemical Technology Beijing 100029 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China College of Nuclear Science and Technology Beijing Normal University Beijing 100875 China Beijing Computational Science Research Center Beijing 100193 China

The structural stability of monolayer SnSe at finite temperature is investigated by the phonon quasiparticle approach that combines first-principles molecular dynamics and lattice dynamics. At 300 K, we witness the dynamic stability of monolayer Pmmn SnSe that is originated from the Cmcm bulk phase. The pair correlation and atomic displacement distribution functions of Sn and Se atoms confirm the lattice stability at high temperature. The hardening of Raman activated Ag2 and B2g modes at the Γ(0,0,0) point and normal modes at the boundary M(0,12,12) point of the Brillouin zone is observed with giant frequency shifts, revealing the heavy anharmonicity in monolayer SnSe. The calculated anharmonic phonon dispersions and density of states show significant temperature dependence and some medium-frequency phonon modes adopt giant frequency shifts. Due to the lattice anharmonicity, the predicted lattice thermal conductivity within the framework of a phonon gas model is very low for monolayer SnSe, close to the value of the bulk phase along the out-of-plane direction. As temperature increases, the characteristic of covalent bonds between Sn and Se atoms in plane and the normal direction of monolayer SnSe becomes isotropic. This results in a high degeneracy of the electronic band structure, beneficial to the electronic transport properties. A thermoelectric ZT of ∼0.52 for n doping is predicted at 300 K, hinting that the monolayer SnSe is a fairly good thermoelectric material suitable for application at room temperature.

关键词： First-principles calculations Lattice dynamics Phonons Thermal conductivity Thermoelectric effects

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MAXIMALITY AND COMPLETENESS OF ORTHOGONAL EXPONENTIALS ON THE CUBE

arXiv

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arXiv 2024年

作者： Kolountzakis, Mihail N. Lev, Nir Matolcsi, Máté Department of Mathematics and Applied Mathematics University of Crete Voutes Campus Heraklion70013 Greece Institute of Computer Science Foundation of Research and Technology Hellas N. Plastira 100 Vassilika Vouton Heraklion700 13 Greece Department of Mathematics Bar-Ilan University Ramat-Gan5290002 Israel HUN-REN Alfréd Rényi Mathematical Institute Department of Analysis Reáltanoda utca 13-15 BudapestH-1053 Hungary Institute of Mathematics Budapest University of Technology and Economics Műegyetem rkp. 3. BudapestH-1111 Hungary

It is possible to have a packing by translates of a cube that is maximal (i.e. no other cube can be added without overlapping) but does not form a tiling. In the long running analogy of packing and tiling to orthogonality and completeness of exponentials on a domain, we pursue the question whether one can have maximal orthogonal sets of exponentials for a cube without them being complete. We prove that this is not possible in dimensions 1 and 2, but is possible in dimensions 3 and higher. We provide several examples of such maximal incomplete sets of exponentials, differing in size, and we raise relevant questions. We also show that even in dimension 1 there are sets which are spectral (i.e. have a complete set of orthogonal exponentials) and yet they also possess maximal incomplete sets of orthogonal *** Codes 42B10, 42C05, 52C22 © 2024, CC BY.

关键词： Geometry

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Inverted pin beams for robust long-range propagation through atmospheric turbulence

arXiv

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arXiv 2023年

作者： Droulias, Sotiris Loulakis, Michalis Papazoglou, Dimitris G. Tzortzakis, Stelios Chen, Zhigang Efremidis, Nikolaos K. Institute of Applied and Computational Mathematics FORTH Crete Heraklion70013 Greece Department of Digital Systems University of Piraeus Piraeus18534 Greece Institute of Electronic Structure and Laser Foundation for Research and Technology - Hellas P.O. Box 1527 Crete Heraklion71110 Greece Department of Materials Science and Technology University of Crete Crete Heraklion700 13 Greece MOE Key Laboratory of Weak-Light Nonlinear Photonics TEDA Applied Physics Institute School of Physics Nankai University Tianjin300457 China Collaborative Innovation Center of Extreme Optics Shanxi University Shanxi Taiyuan030006 China Department of Applied Mathematics University of Crete Heraklion71409 Greece

We introduce a new class of optical beams, which feature a spatial profile akin to an "inverted pin". In particular, we asymptotically find that close to the axis the transverse amplitude profile of such beams takes the form of a Bessel function with width that gradually increases during propagation. We examine numerically the behavior of such inverted pin beams in turbulent environments as measured via the scintillation index, and show that they outperform Gaussian beams (collimated and focused) as well as Bessel beams and regular pin beams, which are all optimized, especially in the moderate and strong fluctuation regimes. Copyright © 2023, The Authors. All rights reserved.

关键词： Gaussian beams

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From order to disorder of alkanethiol SAMs on complex Au (211), (221) and (311) surfaces: Impact of the substrate

arXiv

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arXiv 2021年

作者： Stefanakis, Dimitrios Harmandaris, Vagelis Kopidakis, Georgios Remediakis, Ioannis Department of Materials Science & Technology University of Crete Vassilika Voutes Heraklion700 13 Greece Department of Mathematics & Applied Mathematics - University of Crete Vassilika Voutes Heraklion700 13 Greece Institute of Applied & Computational Mathematics Foundation for Research and Technology-Hellas 711 10 Heraklion Greece Computation-Based Science and Technology Research Center The Cyprus Institute Nicosia2121 Cyprus Institute of Electronic Structure and Laser Foundation for Research and Technology-Hellas 711 10 Heraklion Greece

We investigate the impact of the substrate on the structural properties and the morphology of alkanethiol self-assembled monolayers (SAMs) on gold, using first principles calculations and atomistic molecular dynamics simulations. We consider hexadecanethiols on Au(211), Au(221) and Au(311) surfaces which contain few-atom wide terraces separated by monoatomic steps similar to the complex Au surfaces used in experiments. The structure of the SAMs is probed via several structural properties including tilt angles, mean C atom heights from the surface, precession angles, gauche defects, gyration tensors and relative shape anisotropy. Comparing these properties to those of the well-studied SAMs on Au(111), we observe similarities but also striking differences. A clear order to disorder transition is observed by changing the substrate: well-ordered SAMs on (111) and (211) surfaces become mixed ordered-disordered structures on (311) and fully disordered on (221). The presence of steps on the Au surfaces also results in preferential tilt orientations with long-range order. Our results show that in addition to the expected grafting density dependence, the transition from order to disorder crucially depends on substrate morphology. The onset of ordering behavior is related to the atomic structure of the surface. The key parameter that affects long-range order is the energy for changing the dihedral angle between Au-S-C(1) − C(2) of the adsorbed alkanethiol. © 2021, CC BY.

关键词： Molecular dynamics

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