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Nonlinear dynamics

Moritz Augustin, Josef Ladenbauer, Fabian Baumann, Klaus Obermayer
The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated...
June 23, 2017: PLoS Computational Biology
Gabriel Koch Ocker, Krešimir Josić, Eric Shea-Brown, Michael A Buice
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing...
June 23, 2017: PLoS Computational Biology
Hoda S Hashemi, Hassan Rivaz
A critical step in quasi-static ultrasound elastography is estimation of time-delay between two frames of radiofrequency (RF) data that are obtained while the tissue is undergoing deformation. This paper presents a novel technique for timedelay estimation (TDE) of all samples of RF data simultaneously, thereby exploiting all the information in RF data for TDE. A nonlinear cost function that incorporates similarity of RF data intensity and prior information of displacement continuity is formulated. Optimization of this function involves searching for TDE of all samples of the RF data, rendering the optimization intractable with conventional techniques given that the number of variables can be approximately one million...
June 21, 2017: IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Simone Pezzotti, Daria Ruth Galimberti, Marie-Pierre Gaigeot
We provide a detailed description of the structure of water at the interface with the air (liquid-vapor LV interface) from state-of-the-art DFT-based molecular dynamics simulations. For the first time, a two-dimensional (2D) H-bond extended network has been identified and fully characterized, demonstrating that interfacial water is organized into a 2D sheet with H-bonds oriented parallel to the instantaneous surface and following its spatial and temporal oscillations. By analyzing the nonlinear vSFG (vibrational sum frequency generation) spectrum of the LV interface in terms of layer-by-layer signal, we demonstrate that the 2D water sheet is solely responsible for the spectral signatures, hence providing the interfacial 3...
June 23, 2017: Journal of Physical Chemistry Letters
Fan Wu, Tycho Heimbach, Panos Hatsis, Hai-Ming Tang, Raviprakash Dugyala, Qin Yue, Tao Wang, Handan He
Drug-induced cardiotoxicity, including tachycardia and QT prolongation, remains a major safety concern that needs to be identified and its risk mitigated in early stages of drug development. In the present study, an integrated toxicokinetic-toxicodynamic (TK-TD) modeling approach within a nonlinear mixed-effect modeling framework is applied to investigate concurrent abnormal heart rate and QT changes in three beagle dogs, using a Novartis internal compound (NVS001) as the case example. By accounting for saturable drug absorption, circadian rhythms, drug-effect tolerance, and nonlinear rate-dependency of QT interval, the dynamic TK-TD model captures the experimentally observed drug effects on heart rate and QT interval across a wide dosing range of NVS001 in beagle dogs...
June 22, 2017: Journal of Pharmacokinetics and Pharmacodynamics
Nguyen Viet Hung, Krzysztof Zegadlo, Aliaksandr Ramaniuk, Vladimir V Konotop, Marek Trippenbach
We consider a nanostructure of two coupled ring waveguides with constant linear gain and nonlinear absorption - the system that can be implemented in various settings including polariton condensates, optical waveguides or atomic Bose-Einstein condensates. It is found that, depending on the parameters, this simple configuration allows for observing several complex nonlinear phenomena, which include spontaneous symmetry breaking, modulational instability leading to generation of stable circular flows with various vorticities, stable inhomogeneous states with interesting structure of currents flowing between rings, as well as dynamical regimes having signatures of chaotic behavior...
June 22, 2017: Scientific Reports
S A M Saddam Chowdhury, Javid Atai
The existence, stability and collision dynamics of moving Bragg grating solitons in a semilinear dual-core system where one core has the Kerr nonlinearity and is equipped with a Bragg grating with dispersive reflectivity, and the other core is linear are investigated. It is found that moving soliton solutions exist as a continuous family of solutions in the upper and lower gaps of the system's linear spectrum. The stability of the moving solitons are investigated by means of systematic numerical stability analysis, and the effect and interplay of various parameters on soliton stability are analyzed...
June 22, 2017: Scientific Reports
Steven A Yamada, Ward H Thompson, Michael D Fayer
Many of water's remarkable properties arise from its tendency to form an intricate and robust hydrogen bond network. Understanding the dynamics that govern this network is fundamental to elucidating the behavior of pure water and water in biological and physical systems. In ultrafast nonlinear infrared experiments, the accessible time scales are limited by water's rapid vibrational relaxation (1.8 ps for dilute HOD in H2O), precluding interrogation of slow hydrogen bond evolution in non-bulk systems. Here, hydrogen bonding dynamics in bulk D2O were studied from the perspective of the much longer lived (36...
June 21, 2017: Journal of Chemical Physics
Liliana Ironi, Ettore Lanzarone
Computational and mathematical models have significantly contributed to the rapid progress in the study of gene regulatory networks (GRN), but researchers still lack a reliable model-based framework for computer-aided analysis and design. Such tool should both reveal the relation between network structure and dynamics and find parameter values and/or constraints that enable the simulated dynamics to reproduce specific behaviors. This paper addresses these issues and proposes a computational framework that facilitates network analysis or design...
June 19, 2017: IEEE/ACM Transactions on Computational Biology and Bioinformatics
Manukumara Manjappa, Yogesh Kumar Srivastava, Ankur Solanki, Abhishek Kumar, Tze Chien Sum, Ranjan Singh
The recent meteoric rise in the field of photovoltaics with the discovery of highly efficient solar-cell devices is inspired by solution-processed organic-inorganic lead halide perovskites that exhibit unprecedented light-to-electricity conversion efficiencies. The stunning performance of perovskites is attributed to their strong photoresponsive properties that are thoroughly utilized in designing excellent perovskite solar cells, light-emitting diodes, infrared lasers, and ultrafast photodetectors. However, optoelectronic application of halide perovskites in realizing highly efficient subwavelength photonic devices has remained a challenge...
June 22, 2017: Advanced Materials
John M Felt, Sarah Depaoli, Jitske Tiemensma
Objective: The stress response is a dynamic process that can be characterized by predictable biochemical and psychological changes. Biomarkers of the stress response are typically measured over time and require statistical methods that can model change over time. One flexible method of evaluating change over time is the latent growth curve model (LGCM). However, stress researchers seldom use the LGCM when studying biomarkers, despite their benefits. Stress researchers may be unaware of how these methods can be useful...
2017: Frontiers in Neuroscience
Eliodoro Chiavazzo, Roberto Covino, Ronald R Coifman, C William Gear, Anastasia S Georgiou, Gerhard Hummer, Ioannis G Kevrekidis
We describe and implement a computer-assisted approach for accelerating the exploration of uncharted effective free-energy surfaces (FESs). More generally, the aim is the extraction of coarse-grained, macroscopic information from stochastic or atomistic simulations, such as molecular dynamics (MD). The approach functionally links the MD simulator with nonlinear manifold learning techniques. The added value comes from biasing the simulator toward unexplored phase-space regions by exploiting the smoothness of the gradually revealed intrinsic low-dimensional geometry of the FES...
June 20, 2017: Proceedings of the National Academy of Sciences of the United States of America
Jeffrey B Wagman, Alex Dayer, Alen Hajnal
Possibilities for behavior (i.e., affordances) can be perceived with units spanning anatomical components and external objects. For example, affordances for standing on an inclined surface can be perceived with an object held in the hand or attached to the head. We investigated whether these two person-plus-object perceptual systems exhibit the same pattern of nonlinear phase transitions in perception of this affordance. Blindfolded participants explored an inclined surface with a rod held in the hand or attached to the head and reported whether they could stand on that surface...
May 2017: Experimental Psychology
Chao Mei, Feng Li, Jinhui Yuan, Zhe Kang, Xianting Zhang, Binbin Yan, Xinzhu Sang, Qiang Wu, Xian Zhou, Kangping Zhong, Liang Wang, Kuiru Wang, Chongxiu Yu, P K A Wai
Parabolic pulses have important applications in both basic and applied sciences, such as high power optical amplification, optical communications, all-optical signal processing, etc. The generation of parabolic similaritons in tapered hydrogenated amorphous silicon photonic wires at telecom (λ ~ 1550 nm) and mid-IR (λ ≥ 2100 nm) wavelengths is demonstrated and analyzed. The self-similar theory of parabolic pulse generation in passive waveguides with increasing nonlinearity is presented. A generalized nonlinear Schrödinger equation is used to describe the coupled dynamics of optical field in the tapered hydrogenated amorphous silicon photonic wires with either decreasing dispersion or increasing nonlinearity...
June 19, 2017: Scientific Reports
Alexandra M Tayar, Shirley S Daube, Roy H Bar-Ziv
Building biological systems outside the cell is an emerging interdisciplinary research field aimed to study design principles, and to emulate biological functions for technology. Reconstructing programmable cellular functions, from assembly of protein/nucleic-acid machines to spatially distributed systems, requires implementing minimal systems of molecular interactions encoded in genes, source-sink protein expression dynamics, and materials platforms for reaction-diffusion scenarios. Here, we first review how molecular turnover mechanisms, combined with nonlinear interactions and feedback in cell-free gene networks enable programmable dynamic expression patterns in various compartments...
June 16, 2017: Current Opinion in Chemical Biology
Christoph Schmidt-Hieber, Gabija Toleikyte, Laurence Aitchison, Arnd Roth, Beverley A Clark, Tiago Branco, Michael Häusser
Understanding how active dendrites are exploited for behaviorally relevant computations is a fundamental challenge in neuroscience. Grid cells in medial entorhinal cortex are an attractive model system for addressing this question, as the computation they perform is clear: they convert synaptic inputs into spatially modulated, periodic firing. Whether active dendrites contribute to the generation of the dual temporal and rate codes characteristic of grid cell output is unknown. We show that dendrites of medial entorhinal cortex neurons are highly excitable and exhibit a supralinear input-output function in vitro, while in vivo recordings reveal membrane potential signatures consistent with recruitment of active dendritic conductances...
June 19, 2017: Nature Neuroscience
Alexander B Boyd, Dibyendu Mandal, Paul M Riechers, James P Crutchfield
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the information-processing second law (IPSL): the physical entropy of the Universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delineates the thermodynamic functioning of autonomous Maxwellian demons and information engines. How do these systems begin to function as engines, Landauer erasers, and error correctors? We identify a minimal, and thus inescapable, transient dissipation of physical information processing, which is not captured by asymptotic rates, but is critical to adaptive thermodynamic processes such as those found in biological systems...
June 2, 2017: Physical Review Letters
B B L Witte, L B Fletcher, E Galtier, E Gamboa, H J Lee, U Zastrau, R Redmer, S H Glenzer, P Sperling
We present simulations using finite-temperature density-functional-theory molecular dynamics to calculate the dynamic electrical conductivity in warm dense aluminum. The comparison between exchange-correlation functionals in the Perdew-Burke-Enzerhof and Heyd-Scuseria-Enzerhof (HSE) approximation indicates evident differences in the density of states and the dc conductivity. The HSE calculations show excellent agreement with experimental Linac Coherent Light Source x-ray plasmon scattering spectra revealing plasmon damping below the widely used random phase approximation...
June 2, 2017: Physical Review Letters
Yiwei Li, Osman Kahraman, Christoph A Haselwandter
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments...
May 2017: Physical Review. E
P Buonsante, R Franzosi, A Smerzi
The notion of negative absolute temperature emerges naturally from Boltzmann's definition of "surface" microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of such construct has been challenged, on account that only the Gibbs "volume" entropy-and the strictly positive temperature thereof-would give rise to a consistent thermodynamics. Here we present analytical and numerical evidence that Boltzmann microcanonical entropy provides a consistent thermometry for both signs of the temperature...
May 2017: Physical Review. E
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