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This article presents Namazu, a low-cost tunable shaking table framework for uniaxial vibration experiments in engineering education and research. All components and corresponding assembly are detailed. The design is easy to use and requires minimum maintenance. Open-source software covering signal generation and microcontroller programming is proposed to prescribe the motion of the table. There is no restriction in the programming language used to interface with the table. Communication with the microcontroller is performed via a serial interface, which eliminates the need for additional software. Besides, any displacement signals, including random ones, can be chosen. Due to the open-source nature of the Namazu table, users can also implement custom methods for signal generation and modify the table hardware. Suggestions are given in the paper. Accuracy is analyzed through displacement measurements. In addition, the Shinozuka benchmark is proposed and applied to test the table accuracy in the frequency domain. The results show good consistency of the signals obtained with the setpoints. Thus, Namazu, including the shaking table and a software suite, offers a versatile, accessible, and accurate solution for vibration experiments. [ABSTRACT FROM AUTHOR]

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players' strategies and realized payoffs using Bayes' rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games and enable us to characterize conditions under which learning leads to a complete information equilibrium. Funding: Financial support from the Air Force Office of Scientific Research [Project Building Attack Resilience into Complex Networks], the Simons Institute [research fellowship], and a Michael Hammer Fellowship is gratefully acknowledged. [ABSTRACT FROM AUTHOR]

We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional, and the rates are equal to the absolute value of the velocity vector field associate to the deterministic motion. From the stochastic dynamics, we determine the entropy production and the entropy flux. This last quantity is found to be the negative of the divergence of the velocity vector field. In the case of a Hamiltonian dynamics, it vanishes identically. [ABSTRACT FROM AUTHOR]

We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension 2n into a Hilbert space of dimension n which is obtained by a peculiar canonical transformation that changes a pair of real canonical variables into a pair of complex canonical variables which are complex conjugate of each other. The probabilistic character of quantum mechanics is devised by treating the wave function as a stochastic variable. The dynamics of the underlying system is chosen so as to preserve the norm of the state vector. [ABSTRACT FROM AUTHOR]

The suspension system is an important part of a vehicle and directly affects the vehicle's comfort and stability during driving. There are various nonlinearities and uncertainties in the vehicle suspension system, and even small changes can have a significant impact on the suspension performance. This paper provides an in-depth study of quarter- and half-vehicle suspensions modeled with nonlinear springs and dampers, considering the stochastic uncertainty of various parameters. A mathematical model of a nonlinear vehicle suspension was developed to more accurately simulate the increased stiffness of suspension springs with travel and the energy consumption of dampers. The sparse grid-based polynomial chaos expansion is employed to construct the metamodels of the system response in both the frequency and time domains. This approach effectively captures the stochastic characteristics of the system response, reducing computational cost while improving accuracy. Based on polynomial metamodels, various performance indicators of the nonlinear suspension were analyzed, including statistical moments, probability distributions, and parameter sensitivities. The results are then compared and discussed, revealing that uncertainties in the nonlinear spring, sprung mass, and tire stiffness significantly impact the frequency response, time response, ride comfort, and safety. These findings contribute to a deeper understanding of the dynamic characteristics and behaviors of nonlinear vehicle suspensions under complex parameter uncertainties and provide a reference for enhancing suspension performance. [ABSTRACT FROM AUTHOR]

The transport of molecules and particles through single pores is the basis of biological processes, including DNA and protein sequencing. As individual objects pass through a pore, they cause a transient change in the current that can be correlated with the object size, surface charge, and even chemical properties. The majority of experiments and modeling have been performed with spherical objects, while much less is known about the transport characteristics of aspherical particles, which would act as a model system, for example, for proteins and bacteria. The transport kinetics of aspherical objects is an especially important, yet understudied, problem in nanopore analytics. Here, using the Wiener process, we present a simplified model of the diffusion of rod-shaped particles through a cylindrical pore, and apply it to understand the translation and rotation of the particles as they pass through the pore. Specifically, we analyze the influence of the particles' geometrical characteristics on the effective diffusion type, the first passage time distribution, and the particles' orientation in the pore. Our model shows that thicker particles pass through the channel slower than thinner ones, while their lengths do not affect the passage time. We also demonstrate that both spherical and rod-shaped particles undergo normal diffusion, and the first passage time distribution follows an exponential asymptotics. The model provides guidance on how the shape of the particle can be modified to achieve an optimal passage time. [ABSTRACT FROM AUTHOR]

The SOS/ERK cascades are key signaling pathways that regulate cellular processes ranging from cellular proliferation, differentiation and apoptosis to tumor formation. However, the properties of these signaling pathways are not well understood. More importantly, how stochastic perturbations of internal and external cellular environment affect these pathways remains unanswered. To answer these questions, we, in this paper, propose a stochastic model according to the biochemical reaction processes of the SOS/ERK pathways, and, respectively, research the dynamical behaviors of this model under the four kinds of noises: Gaussian noise, colored noise, Lévy noise and fraction Brown noise. Some important results are found that Gaussian and colored noises have less effect on the stability of the system when the strength of the noise is small; Lévy and fractional Brownian noises significantly change the trajectories of the system. Power spectrum analysis shows that Lévy noise induces a system with quasi-periodic trajectories. Our results not only provide an understanding of the SOS/ERK pathway, but also show generalized rules for stochastic dynamical systems. [ABSTRACT FROM AUTHOR]

We present a novel probabilistic deep learning approach, the "stochastic latent transformer" (SLT), designed for the efficient reduced‐order modeling of stochastic partial differential equations. Stochastically driven flow models are pertinent to a diverse range of natural phenomena, including jets on giant planets, ocean circulation, and the variability of midlatitude weather. However, much of the recent progress in deep learning has predominantly focused on deterministic systems. The SLT comprises a stochastically‐forced transformer paired with a translation‐equivariant autoencoder, trained toward the Continuous Ranked Probability Score. We showcase its effectiveness by applying it to a well‐researched zonal jet system, where the interaction between stochastically forced eddies and the zonal mean flow results in a rich low‐frequency variability. The SLT accurately reproduces system dynamics across various integration periods, validated through quantitative diagnostics that include spectral properties and the rate of transitions between distinct states. The SLT achieves a five‐order‐of‐magnitude speedup in emulating the zonally‐averaged flow compared to direct numerical simulations. This acceleration facilitates the cost‐effective generation of large ensembles, enabling the exploration of statistical questions concerning the probabilities of spontaneous transition events. Plain Language Summary: Stochastically driven systems are widespread in nature, from jets on giant planets to ocean circulation and the variability of weather. We describe a novel machine learning (ML) approach to the time evolving behavior of a well‐studied stochastically‐driven zonal jet system, serving as an analog for mid‐latitude weather. Our approach involves constructing a probabilistic ML model of our stochastic system, in contrast to existing research that predominantly focuses on ML techniques for deterministic systems or apply deterministic models to systems that are inherently probabilistic. The model is evaluated using various metrics, confirming its ability to accurately capture the statistical properties of the original system. Our approach significantly speeds up simulations compared to traditional methods, enabling the creation of large data sets highlighting specific events of interest, such as spontaneous transitions between different states characterized by varying numbers of observed jets, shedding light on aspects of the system's behavior and predictability. We demonstrate advantages of the proposed method over existing techniques and expect that these methods are highly transferable to other systems that exhibit stochasticity and inherent uncertainties. Key Points: We present a probabilistic machine learning approach for modeling the time evolution of stochastically driven systemsApplying this approach to a well‐researched zonal jet system, we achieve a five‐order‐of‐magnitude speedup in emulating the zonally‐averaged flowThis enables us to efficiently generate large ensembles, facilitating the process of establishing accurate probabilities of rare events, such as transition rates between different long‐lived states [ABSTRACT FROM AUTHOR]

In this article, to study the heat flow behavior, we perform analytical investigations in a rotor chain type model (involving inner stochastic noises) with next and next-nearest-neighbor (NN) interactions. It is known in the literature that the chain rotor model with long range interactions presents an insulating phase for the heat conductivity. But we show, in contrast with such a behavior, that the addition of a next-NN potential increases the thermal conductivity, at least in the low temperature regime, indicating that the insulating property is a genuine long range interaction effect. We still establish, now by numerical computations, the existence of a thermal rectification in systems with graded structures. [ABSTRACT FROM AUTHOR]

The interior of a living cell is an active, fluctuating, and crowded environment, yet it maintains a high level of coherent organization. This dichotomy is readily apparent in the intracellular transport system of the cell. Membrane-bound compartments called endosomes play a key role in carrying cargo, in conjunction with myriad components including cargo adaptor proteins, membrane sculptors, motor proteins, and the cytoskeleton. These components coordinate to effectively navigate the crowded cell interior and transport cargo to specific intracellular locations, even though the underlying protein interactions and enzymatic reactions exhibit stochastic behavior. A major challenge is to measure, analyze, and understand how, despite the inherent stochasticity of the constituent processes, the collective outcomes show an emergent spatiotemporal order that is precise and robust. This review focuses on this intriguing dichotomy, providing insights into the known mechanisms of noise suppression and noise utilization in intracellular transport processes, and also identifies opportunities for future inquiry. [ABSTRACT FROM AUTHOR]

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description. [ABSTRACT FROM AUTHOR]

The interplay of host–parasite and predator–prey interactions is critical in ecological dynamics because both predators and parasites can regulate communities. But what is the prevalence of infected prey and predators when a parasite is transmitted through trophic interactions considering stochastic demographic changes? Here, we modelled and analysed a complex predator–prey–parasite system, where parasites are transmitted from prey to predators. We varied parasite virulence and infection probabilities to investigate how those evolutionary factors determine species' coexistence and populations' composition. Our results show that parasite species go extinct when the infection probabilities of either host are small and that success in infecting the final host is more critical for the survival of the parasite. While our stochastic simulations are consistent with deterministic predictions, stochasticity plays an important role in the border regions between coexistence and extinction. As expected, the proportion of infected individuals increases with the infection probabilities. Interestingly, the relative abundances of infected and uninfected individuals can have opposite orders in the intermediate and final host populations. This counterintuitive observation shows that the interplay of direct and indirect parasite effects is a common driver of the prevalence of infection in a complex system. [ABSTRACT FROM AUTHOR]

This paper introduces a multidisciplinary conceptual perspective encompassing artificial intelligence (AI), artificial general intelligence (AGI), and cybernetics, framed within what we call the formalism of generalized neuromorphism. Drawing from recent advancements in computing, such as neuromorphic computing and spiking neural networks, as well as principles from the theory of open dynamical systems and stochastic classical and quantum dynamics, this formalism is tailored to model generic networks comprising abstract processing events. A pivotal aspect of our approach is the incorporation of the memory space and the intrinsic non-Markovian nature of the abstract generalized neuromorphic system. We envision future computations taking place within an expanded space (memory space) and leveraging memory states. Positioned at a high abstract level, generalized neuromorphism facilitates multidisciplinary applications across various approaches within the AI community. [ABSTRACT FROM AUTHOR]

From classical stochastic equations of motion, we derive the quantum Schrödinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function ϕ are proportional to the coordinates and momenta associated with the degrees of freedom of an underlying classical system. The wave function ϕ is assumed to be a complex time-dependent random variable that obeys a stochastic equation of motion that preserves the norm of ϕ . The quantum Liouville equation is obtained by considering that the stochastic part of the equation of motion changes the phase of ϕ but not its absolute value. The Schrödinger equation follows from the Liouville equation. The wave function ψ obeying the Schrödinger equation is related to the stochastic wave function by | ψ | 2 = ⟨ | ϕ | 2 ⟩ . [ABSTRACT FROM AUTHOR]

In the proposed approach, a 3D response of the guy line treated as a small-sag cable is considered. The strong dynamic wind action leads to the base motion excitation of the guy line. Longitudinal cable displacements are coupled with lateral ones. Hamilton's principle and Galerkin method are used to obtain the set of differential equations of motion. The cable excitation is assumed as a narrow-band stochastic process modelled as a response of an auxiliary linear filter to a Gaussian white noise process. The equivalent linearization technique is applied to obtain approximate analytical results verified against the numerical Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

We investigate two different types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The first model is obtained by analytically 'integrating out' the oscillators and the second is based on a derivation using projection operator techniques. We observe that these two models behave very differently when the tagged particle is exposed to external harmonic potentials or pulling forces. Most importantly, we find that the analytic model has a well defined friction kernel and can be used to extract work, consistent with the microscopic system, while the projection model corresponds to an effective equilibrium model, which cannot be used to extract work. We apply the analysis to two popular non-equilibrium systems, time-delay feedback control and the active Ornstein–Uhlenbeck process. Finally, we highlight that our study could have important consequences for dynamic coarse-graining of non-equilibrium systems going far beyond the linear systems investigated in this manuscript. [ABSTRACT FROM AUTHOR]

This paper introduces a Lyapunov-based control strategy alongside two filtering methods for controlling and estimating the evolution of coherence vector elements from sequential homodyne measurements. The methods include traditional quantum filtering and a novel extended Kalman filter, which explicitly addresses the dynamics of a stochastic master equation with correlated noise, thereby ensuring the quantum properties of the estimated state variable by design. We also explore scenarios where the system’s Hamiltonian is unknown, demonstrating that both filters exhibit reduced performance with increased estimation errors. To address this, we propose a multiple model estimation scheme applicable to either filter. The estimated density operator is then controlled using the proposed switching-based Lyapunov scheme, which guarantees noise-to-state practical stability in probability. We demonstrate the effectiveness of our approach in stabilizing a qubit coupled to a leaky cavity under homodyne detection, even with uncertainty in the resonance frequency.

• A data-driven model identification method is devised to extract the non-Gaussian governing laws of the multistable VEH. • The Lévy, drift and diffusion terms can be approximately expressed by the sample trajectories of system. • The data-driven identified results agree well with the original system. • The dynamics of VEH can be further explored based on the data-driven stochastic differential equation. In engineering, due to the complex structural characteristics of system and the non-Gaussian properties of random excitation, it is difficult to establish an accurate stochastic dynamic model for the strongly nonlinear multistable vibration energy harvester (VEH), especially for these driven by non-Gaussian Lévy noise. From the view of machine learning, a data-driven model identification method is devised to extract the non-Gaussian governing laws of the multistable VEH with the aid of the observed sample trajectory data. Based on the Nonlocal Kramers-Moyal formulas, the Lévy, drift and diffusion terms can be approximately expressed by the sample trajectories of the system. By implementing the least square method and the stepwise sparse regressor algorithm, the optimal drift and diffusion coefficients can be identified, and then the non-Gaussian stochastic differential equation of VEH is extracted. Two examples are utilized to verify the feasibility and effectiveness of the data-driven modelling method in VEH, which indicates that the identified results agree well with the original system. Finally, the stochastic dynamic behaviors induced by non-Gaussian Lévy noise are explored based on the data-driven penta-stable VEH. The proposed method can provide the theoretical guidance for the modelling and dynamics research of VEH in engineering. [ABSTRACT FROM AUTHOR]

In their pioneering study on dopamine release, Romo and Schultz speculated "...that the amount of dopamine released by unmodulated spontaneous impulse activity exerts a tonic, permissive influence on neuronal processes more actively engaged in preparation of self-initiated movements...."1 Motivated by the suggestion of "spontaneous impulses," as well as by the "ramp up" of dopaminergic neuronal activity that occurs when rodents navigate to a reward,2-5 we asked two questions. First, are there spontaneous impulses of dopamine that are released in cortex? Using cell-based optical sensors of extrasynaptic dopamine, [DA]ex,6 we found that spontaneous dopamine impulses in cortex of naive mice occur at a rate of ∼0.01 per second. Next, can mice be trained to change the amplitude and/or timing of dopamine events triggered by internal brain dynamics, much as they can change the amplitude and timing of dopamine impulses based on an external cue?7-9 Using a reinforcement learning paradigm based solely on rewards that were gated by feedback from real-time measurements of [DA]ex, we found that mice can volitionally modulate their spontaneous [DA]ex. In particular, by only the second session of daily, hour-long training, mice increased the rate of impulses of [DA]ex, increased the amplitude of the impulses, and increased their tonic level of [DA]ex for a reward. Critically, mice learned to reliably elicit [DA]ex impulses prior to receiving a reward. These effects reversed when the reward was removed. We posit that spontaneous dopamine impulses may serve as a salient cognitive event in behavioral planning.

Stochastic processes on graphs can describe a great variety of phenomena ranging from neural activity to epidemic spreading. While many existing methods can accurately describe typical realizations of such processes, computing properties of extremely rare events is a hard task, particularly so in the case of recurrent models, in which variables may return to a previously visited state. Here, we build on the matrix product cavity method, extending it fundamentally in two directions: First, we show how it can be applied to Markov processes biased by arbitrary reweighting factors that concentrate most of the probability mass on rare events. Second, we introduce an efficient scheme to reduce the computational cost of a single node update from exponential to polynomial in the node degree. Two applications are considered: inference of infection probabilities from sparse observations within the SIRS epidemic model and the computation of both typical observables and large deviations of several kinetic Ising models. [ABSTRACT FROM AUTHOR]

The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature. While many such applications utilize frequency or time domain formulations, relatively few consider stochastic dynamic excitations. This paper presents an efficient and compact code called TopSTO for structural topology optimization considering stationary stochastic dynamic loading using a method derived from random vibration theory. The theory, described in conjunction with the implementation in the provided code, is illustrated for a seismically excited building. This work demonstrates the efficiency of the approach in terms of both the computational resources and minimal amount of code required. This code is intended to serve as a baseline for understanding the theory and implementation of this topology optimization approach and as a foundation for additional applications and developments. [ABSTRACT FROM AUTHOR]

Abstract The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral (WPI) technique. The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators, and relates to an experiment performed by Buks and Roukes. Compared to alternative modeling and solution treatments in the literature, the paper exhibits the following novelties. First, typically adopted linear, or higher‐order polynomial, approximations of the nonlinear electrostatic forces are circumvented. Second, for the first time, stochastic modeling is employed by considering a random excitation component representing the effect of diverse noise sources on the system dynamics. Third, the resulting high‐dimensional, nonlinear system of coupled stochastic differential equations governing the dynamics of the micromechanical array is solved based on the WPI technique for determining the response joint probability density function. Comparisons with pertinent Monte Carlo simulation data demonstrate a quite high degree of accuracy and computational efficiency exhibited by the WPI technique. Further, it is shown that the proposed model can capture, at least in a qualitative manner, the salient aspects of the frequency domain response of the associated experimental setup.

Abstract Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example. Noise‐induced phenomena, such as noise‐induced quasi‐cycle, three‐state intermittency, and chaos, are observed. In the intermittency process, the optimal path used to describe the transition mechanism is calculated and confirmed to pass through an unstable periodic orbit, a chaotic saddle, a saddle point, and a heteroclinic trajectory in an orderly sequence using generalized cell mapping with a digraph method constructively. The corresponding optimal fluctuation forces are delineated to uncover the effects of noise during the transition process. Then the process will switch frequently between the attractors and the chaotic saddle as noise intensity increased further, that is, noise induced chaos emerging. A threshold noise intensity is defined by stochastic sensitivity analysis when a confidence ellipsoid is tangent to the stable manifold of the periodic orbit, which agrees with the simulation results. It is finally reported that these results and methods can be generalized to analyze the stochastic dynamics of other nonlinear mechanical systems with similar structures.

Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio, (b / c) ∗ , which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that (b / c) ∗ decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes (b / c) ∗ small to facilitate cooperation. In contrast, (b / c) ∗ tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes (b / c) ∗ by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery. [ABSTRACT FROM AUTHOR]

In this paper, a computationally efficient approach is proposed for the determination of the nonstationary response statistics of hysteretic oscillators endowed with fractional derivative elements. This problem is of particular practical significance since many important engineering systems exhibit hysteretic/inelastic behavior optimally captured only through the concept of fractional derivative, and many natural excitations as seismic waves and atmospheric turbulence are both stochastic and nonstationary in time. Specifically, the approach is based on a statistical linearization scheme involving an equivalent system of augmented dimension. First, relying on a transformation scheme, the fractional derivative term is represented by a set of coupled linear ordinary differential equations. Next, the evolution of the system response statistics is captured by incorporating the statistical linearization technique in a nonstationary sense. This involves integrating in time a set of ordinary differential equations. Several numerical applications pertaining to classical hysteretic oscillators are considered, and the versatility of the proposed method is assessed via comparison with pertinent Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Chemotaxis, the directional motility of cells in response to spatial gradients of chemical cues, is a fundamental process behind a wide range of biological events, including the innate immune response and cancer metastasis. Recent advances in cell biology have shown that the protrusions that enable amoeboid cells to move are driven by the stochastic threshold crossings of an underlying excitable system. As a cell encounters a chemoattractant gradient, the size of this threshold is regulated spatially so that the crossings are biased toward the front of the cell. For efficient directional migration, cells must limit undesirable lateral and rear‐directed protrusions. The inclusion of a control mechanism to suppress these unwanted firings would enhance chemotactic efficiency. It is known that absolute concentration robustness (ACR) exerts tight control over the mean and variance of species concentration. Here, we demonstrate how the coupling of the ACR mechanism to the cellular signaling machinery reduces the likelihood of threshold crossings in the excitable system. Moreover, we show that using the cell's innate gradient sensing apparatus to direct the action of ACR to the rear suppresses the lateral movement of the cells and that this results in improved chemotactic performance. [ABSTRACT FROM AUTHOR]

Constructing a microstructure of red clay is an important part of studying the physical and mechanical properties of red clay. The study of red clay microstructure is generalized. The red clay matrix and pores are regarded as two types of randomly moving particles, and the microstructure model of three-dimensional red clay random porous media is established from the Langevin equation of the phase separation process in stochastic dynamics, using the separation and aggregation of the two particles. The model controls the evolution process of the porous medium by artificially controlling the particle placement. Here, the trends of porosity, average pore length, Euler’s number, and the fractal dimension of the porous medium during the evolution process under different parameter conditions (smooth length Δ and rise and fall term η) are calculated, and a feasible method for surviving the microstructure of red clay is summarized. Due to the consideration of the interaction forces between the solid- and void-phase particles, the porous media generated by this model are more similar to the real porous media in nature, with connected and unconnected pore structures and tortuous pore channels. Finally, the red clay of Bijie, Guizhou, is modeled as an example to prove the feasibility of the method.

In this paper, we consider stochastic dynamics of a two-dimensional stochastic differential equation with additive noise. When the strength of the noise is zero, this equation undergoes a Bautin bifurcation. We obtain the main conclusions including the existence and uniqueness of the solution, synchronization of system and property of the random equilibrium, where going through some processes like deducing the stationary probability density of the equation and calculating the Lyapunov exponent. For better understanding of the effect under noise, we make a clear comparison between the stochastic system and the deterministic one and make precise numerical simulations to show the slight changes at Bautin bifurcation point. Furthermore, we take a real model as an example to present the application of our theoretical results.

In this paper, the discrete-time version of a continuous-time model with fundamentalists and momentum traders is presented. Our aim consists of studying the impact of cross-sectional momentum traders on the dynamics of the model. To this end, the continuous-time deterministic skeleton of the benchmark model is transformed using sophisticated discretization techniques. It is worth noting that the model does not always maintain the same characteristics after moving from continuous to discrete time. In spite of this, our discrete-time system preserves the dynamic properties of the continuous-time original model. Moreover, heterogeneity introduces an important non-linearity into the market dynamics, causing our deterministic financial model to generate erratic time series similar to the patterns observed in real markets. In particular, we show that the time series originated by the perturbed deterministic system capture some of the main stylized facts of the U.S. financial market. Converting the benchmark model from continuous time to discrete time allows the use of financial data available in discrete time. [ABSTRACT FROM AUTHOR]

Mass spectrometric innovations in analytical instrumentation tend to be accompanied by the development of a data-processing methodology, expecting to gain molecular-level insights into real-life objects. Qualitative and semi-quantitative methods have been replaced routinely by precise, accurate, selective, and sensitive quantitative ones. Currently, mass spectrometric 3D molecular structural methods are attractive. As an attempt to establish a reliable link between quantitative and 3D structural analyses, there has been developed an innovative formula [ D S D ″ , t o t = ∑ i n D S D ″ , i = ∑ i n 2.6388.10 − 17 × I i 2 ¯ − I i ¯ 2 ] capable of the exact determination of the analyte amount and its 3D structure. It processed, herein, ultra-high resolution mass spectrometric variables of paracetamol, atenolol, propranolol, and benzalkonium chlorides in biota, using mussel tissue and sewage sludge. Quantum chemistry and chemometrics were also used. Results: Data on mixtures of antibiotics and surfactants in biota and the linear dynamic range of concentrations 2–80 ng.(mL)−1 and collision energy CE = 5–60 V are provided. Quantitative analysis of surfactants in biota via calibration equation ln[D″SD] = f(conc.) yields the exact parameter |r| = 0.99991, examining the peaks of BAC-C12 at m/z 212.209 ± 0.1 and 211.75 ± 0.15 for tautomers of fragmentation ions. Exact parameter |r| = 1 has been obtained, correlating the theory and experiments in determining the 3D molecular structures of ions of paracetamol at m/z 152, 158, 174, 301, and 325 in biota. [ABSTRACT FROM AUTHOR]

We analyze a stochastic approach to population dynamics in which the number of individuals in each class is treated as a stochastic variable. The description of the dynamics is based on the Fokker-Planck equation from which we show that the time evolution of the average number of individuals are identified as the differential equations of the deterministic approach. We also show by calculating the time correlation function that the stochastic fluctuations as well as the stochastic oscillations in the number of individuals are proportional to the square root of the whole size of the population. We have applied the present approach to predator-prey or food chain models with three and four biological species and shown that both models display stochastic oscillations depending on the constant rates. The stochastic approach predicts extinction of species by the stochastic fluctuations in populations with small number of individuals. [ABSTRACT FROM AUTHOR]

The simple model of an ionic current flowing through a single channel in a biological membrane is used to depict the complexity of the corresponding empirical data underlying different internal constraints and thermal fluctuations. The residence times of the channel in the open and closed states are drawn from the exponential distributions to mimic the characteristics of the real channel system. In the selected state, the dynamics are modeled by the overdamped Brownian particle moving in the quadratic potential. The simulated data allow us to directly track the effects of temperature (signal-to-noise ratio) and the channel's energetic landscape for conformational changes on the ionic currents' complexity, which are hardly controllable in the experimental case. To accurately describe the randomness, we employed four quantifiers, i.e., Shannon, spectral, sample, and slope entropies. We have found that the Shannon entropy predicts the anticipated reaction to the imposed modification of randomness by raising the temperature (an increase of entropy) or strengthening the localization (reduction of entropy). Other complexity quantifiers behave unpredictably, sometimes resulting in non-monotonic behaviour. Thus, their applicability in the analysis of the experimental time series of single-channel currents can be limited. [ABSTRACT FROM AUTHOR]