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Stochastic modeling

Haram Kim, Emre Brookes, Weiming Cao, Borries Demeler
Sedimentation velocity experiments performed in the analytical ultracentrifuge are modeled using finite-element solutions of the Lamm equation. During modeling, three fundamental parameters are optimized: the sedimentation coefficients, the diffusion coefficients, and the partial concentrations of all solutes present in a mixture. A general modeling approach consists of fitting the partial concentrations of solutes defined in a two-dimensional grid of sedimentation and diffusion coefficient combinations that cover the range of possible solutes for a given mixture...
May 17, 2018: European Biophysics Journal: EBJ
David J Jörg, Luis G Morelli, Frank Jülicher
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker...
March 2018: Physical Review. E
Hanqing Nan, Long Liang, Guo Chen, Liyu Liu, Ruchuan Liu, Yang Jiao
Three-dimensional (3D) collective cell migration in a collagen-based extracellular matrix (ECM) is among one of the most significant topics in developmental biology, cancer progression, tissue regeneration, and immune response. Recent studies have suggested that collagen-fiber mediated force transmission in cellularized ECM plays an important role in stress homeostasis and regulation of collective cellular behaviors. Motivated by the recent in vitro observation that oriented collagen can significantly enhance the penetration of migrating breast cancer cells into dense Matrigel which mimics the intravasation process in vivo [Han et al...
March 2018: Physical Review. E
Han Kheng Teoh, Ee Hou Yong
We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p=0, the dynamics remain invariant in each renormalization-group (RG) transformation. Two fully attractive fixed points, ρ_{c}^{*}=0 and 1, and one unstable fixed point, ρ_{c}^{*}=1/(v_{max}+1), are obtained. The critical exponent ν which is related to the correlation length is calculated for various v_{max}...
March 2018: Physical Review. E
David Darmon
In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed...
March 2018: Physical Review. E
Shanshan Qin, Chao Tang
Complex dynamical systems often have tipping points and exhibit catastrophic regime shift. Despite the notorious difficulty of predicting such transitions, accumulating studies have suggested the existence of generic early-warning signals (EWSs) preceding upcoming transitions. However, previous theories and models were based on the effect of the intrinsic noise (IN) when a system is approaching a critical point, and did not consider the pervasive environmental fluctuations or the extrinsic noise (EN). Here, we extend previous theory to investigate how the interplay of EN and IN affects EWSs...
March 2018: Physical Review. E
Guillermo Rodrigo
Gene expression programs in living cells are highly dynamic due to spatiotemporal molecular signaling and inherent biochemical stochasticity. Here we study a mechanism based on molecule-to-molecule variability at the RNA level for the generation of bursts of protein production, which can lead to heterogeneity in a cell population. We develop a mathematical framework to show numerically and analytically that genes regulated post transcriptionally by small RNA molecules can exhibit such bursts due to different states of translation activity (on or off), mostly revealed in a regime of few molecules...
March 2018: Physical Review. E
Jordi Baró, Jörn Davidsen
The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation. Avalanche models involving critical failure have determined common universality classes for stick-slip processes and fracture. However, not all empirical failure processes exhibit the trademarks of criticality. The rheological properties of materials introduce dissipation, usually reproduced in conceptual models as a hardening of the coarse grained elements of the system...
March 2018: Physical Review. E
Diamantino C da Silva, Ginestra Bianconi, Rui A da Costa, Sergey N Dorogovtsev, José F F Mendes
We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by the condition that at each step, all the faces must be triangles. Stochastic application of these operations leads to random networks with different architectures. We perform extensive numerical simulations and explore the geometries of growing and equilibrium complex networks generated by these transformations and their local structural properties...
March 2018: Physical Review. E
Subrata Dev, Sakuntala Chatterjee
In response to a concentration gradient of chemoattractant, E. coli bacterium modulates the rotational bias of flagellar motors which control its run-and-tumble motion, to migrate towards regions of high chemoattractant concentration. Presence of stochastic noise in the biochemical pathway of the cell has important consequences on the switching mechanism of motor bias, which in turn affects the runs and tumbles of the cell in a significant way. We model the intracellular reaction network in terms of coupled time evolution of three stochastic variables-kinase activity, methylation level, and CheY-P protein level-and study the effect of methylation noise on the chemotactic performance of the cell...
March 2018: Physical Review. E
Tatsuro Kawamoto
The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation-maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold...
March 2018: Physical Review. E
Juliane Weber, Christopher Zachow, Dirk Witthaut
Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation. The only input parameter for this model is the empirical autocorrelation function...
March 2018: Physical Review. E
S I Denisov, T V Lyutyy, V V Reva, A S Yermolenko
We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models...
March 2018: Physical Review. E
Markus Nyberg, Ludvig Lizana, Tobias Ambjörnsson
In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process...
March 2018: Physical Review. E
Julian Lee
Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition...
March 2018: Physical Review. E
N V Antonov, N M Gulitskiy, M M Kostenko, A V Malyshev
In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time...
March 2018: Physical Review. E
A Tamm, M Caro, A Caro, G Samolyuk, M Klintenberg, A A Correa
Stochastic Langevin dynamics has been traditionally used as a tool to describe nonequilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their wavelength. We propose a generalization of Langevin dynamics that can capture a differential coupling between collective modes and the bath, by introducing spatial correlations in the random forces. This allows modeling the electronic subsystem in a metal as a generalized Langevin bath endowed with a concept of locality, greatly improving the capabilities of the two-temperature model...
May 4, 2018: Physical Review Letters
Raimund M Kovacevic
In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker-Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour...
2018: Central European Journal of Operations Research
Dor Hirsh Bar Gai, Zachary Graybill, Paule Voevodsky, Ekundayo Shittu
Many developing countries still face the prevalence of preventable childhood diseases because their vaccine supply chain systems are inadequate by design or structure to meet the needs of their populations. Currently, Nigeria is evaluating options in the redesign of the country's vaccine supply chain. Using Nigeria as a case study, the objective is to evaluate different regional supply chain scenarios to identify the cost minimizing optimal hub locations and storage capacities for doses of different vaccines to achieve a 100% fill rate...
May 14, 2018: Vaccine
Yifan Zhang, Xunzhang Gao, Xuan Peng, Jiaqi Ye, Xiang Li
The High Resolution Range Profile (HRRP) recognition has attracted great concern in the field of Radar Automatic Target Recognition (RATR). However, traditional HRRP recognition methods failed to model high dimensional sequential data efficiently and have a poor anti-noise ability. To deal with these problems, a novel stochastic neural network model named Attention-based Recurrent Temporal Restricted Boltzmann Machine (ARTRBM) is proposed in this paper. RTRBM is utilized to extract discriminative features and the attention mechanism is adopted to select major features...
May 16, 2018: Sensors
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