Narrow Results

Quantitative models may exhibit sophisticated behaviour that includes having multiple steady states, bistability, limit cycles, and period-doubling bifurcation. Such behaviour is typically driven by the numerical dynamics of the model, where the values of various numerical parameters play the crucial role. We introduce in this paper natural correspondents of these concepts to reaction systems modelling, a framework based on elementary set theoretical, forbidding/enforcing-based mechanisms. We construct several reaction systems models exhibiting these properties.

This paper presents a neural system-based technique for segmenting short impaired speech utterances into silent, unvoiced, and voiced sections. Moreover, the proposed technique identifies those points of the (voiced) speech where the spectrum becomes steady. The resulting technique thus aims at detecting that limited section of the speech which contains the information about the potential impairment of the speech. This section is of interest to the speech therapist as it corresponds to the possibly incorrect movements of speech organs (lower lip and tongue with respect to the vocal tract). Two segmentation models to detect and identify the various sections of the disordered (impaired) speech signals have been developed and compared. The first makes use of a combination of four artificial neural networks. The second is based on a support vector machine (SVM). The SVM has been trained by means of an ad hoc nested algorithm whose outer layer is a metaheuristic while the inner layer is a convex optimization algorithm. Several metaheuristics have been tested and compared leading to the conclusion that some variants of the compact differential evolution (CDE) algorithm appears to be well-suited to address this problem. Numerical results show that the SVM model with a radial basis function is capable of effective detection of the portion of speech that is of interest to a therapist. The best performance has been achieved when the system is trained by the nested algorithm whose outer layer is hybrid-population-based/CDE. A population-based approach displays the best performance for the isolation of silence/noise sections, and the detection of unvoiced sections. On the other hand, a compact approach appears to be clearly well-suited to detect the beginning of the steady state of the voiced signal. Both the proposed segmentation models display outperformed two modern segmentation techniques based on Gaussian mixture model and deep learning.

Rumor, as a form of information, can be widely spread in a short time. A host of researchers focus on the spread of rumor, aiming to explore the rules of rumor spreading and put forward effective measures to help control the spread of rumor. In real life, when the individual is not interested in the rumor spread or feels that the rumor is not related to him, it is easy to trigger the individual’s vigilance awareness. On the contrary, if the rumor is more closely related to the individual’s life, the individual will usually be less alert and have great motivation to share it with friends. Based on the typical Susceptible–Infected–Recovered (SIR) model, a new vigilant state is added to describe the above phenomenon and a Susceptible–Vigilant–Infectious–Recovered (SVIR) rumor model is proposed. In addition, considering the fact that the infectious with high emotion may cause emotional resonance among individuals, this model adds a connection edge from the recovered to the infectious triggered by emotional infection. Based on the obtained dynamic equations, the steady state of the model is analyzed by utilizing basic reproduction number method and verified on the generated homogeneous network as well as Facebook network. Simulation results reveal that the improvement of individual vigilance awareness can reduce the influence of rumor. Although high emotional infectious can promote the spread of rumor, appealing them to clarify the fact for curbing rumor spreading is a forceful measure.

As an important area of social networks, rumor spread has attracted the attention of many scholars. It aims to explore the rumor propagation, and to propose effective measures to curb the further spread of rumors. Different from some existing works, this paper believes that susceptible persons affected by rumor-refuting information will first enter the critical state, while ones who related to rumors will directly turn into the spread state. Therefore, this paper proposes a Susceptible-Infectious-Critical-Recovered (SICR) rumor model. In addition, considering that infectious persons with high levels of refuting rumors may cause emotional resonance among individuals, this model adds a connecting edge from the recovered to the infectious who are triggered by the information of refuting the rumors. First, the basic regeneration number $R(0)$ is obtained by using the next generation matrix method. Then, the global stability of the rumor-free equilibrium $E(0)$ and the persistence of rumor propagation are proved in detail in theoretical analysis. The simulation results show that the existence of a critical state can reduce the influence of rumors. Rumor refutation mechanism, as soon as possible to curb the spread of rumors, is an effective measure.

In computational fluid dynamics (CFD), there is a transformation of methods over the years for building commercially coded software. Each method has predicted its own set of importance, but the exportation and prediction of data are some of the crucial elements for post-processing and validating results. In the present investigation, a detailed comparative analysis is performed over finite difference method (FDM) and finite volume method (FVM) method for the 1D steady-state heat conduction problem over a 1-m-long plate. The comparison was made between solution creation and validation between FDM and FVM for the analytical and computational scheme. The convergence-dependent study is performed as multi-objective optimization to predict how artificial neural network (ANN) can be used to verify and validate the solution of CFD.

Rumor, as an important form of information dissemination, has always been a research hotspot in the field of complex networks. How to better understand the rules of rumor propagation and establish a practical dissemination model is a significant challenge. To further study the state transfer in information transmission, this paper established the Ignorant-Spreader-Stifler-Transition (ISRT) model, introduced different influence mechanisms and calculate the influence rate accurately by function. Specifically, (1) Based on SIR model, this paper introduces the transition state, considering that transition may awaken spontaneously to spread rumors due to individual cognition. In this paper, the ratio of the current communicator and the degree of doubt of the transition are introduced into the spontaneous arousal function. (2) This paper redefines the propagation probability function and the forgetting probability function, and introduces the time function to describe the rate from the propagator to the restorer. (3) Due to the presence of highly emotional leader propagators in the network who would awaken the immune to spread rumors again, the model added a link from the recovering person to the infected person. Finally, the nonpropagation equilibrium point $E_0$ and propagation equilibrium point $E_1$ are obtained by establishing the mean field equation. The experimental results show that different influencing mechanisms can more accurately locate the stage change of rumor transmission, which provides theoretical support for more effective control of information transmission.

Rumors can bring about a seriously negative impact on all respects of society in this information era. More targeted control strategies can be acquired through the research of rumor propagation. When receiving rumors, individuals may keep imperturbable according to their rationality or bygone experience, and then choose not to propagate rumors provisionally. Oppositely, others may ask people around them about the realness of rumors due to bewilderment, which may further lead to the propagation of rumors. Therefore, an Ignorant–Conservative–Disseminator–Restorer–Ignorant (ICDRI) rumor dissemination model is proposed, which comprehensively considers users’ various probable actions under rumor and anti-rumor information. Furthermore, new links are added among nodes in accordance with the individual discrepancy theory and the influencing factors of rumor spreading including negation factor, authority factor, exhaustion factor, etc. According to the calculated basic regeneration number, simulation analysis and model comparison, the steady state and superiority of the ICDRI model is proved. Finally, strategies to control the spread of rumors are obtained through the sensitivity analysis of parameters. The simulation results demonstrate that the ICDRI model can more realistically reflect the dissemination of rumors, and the official rumor refutation or circular can efficaciously curb the spreading of rumors.

The two-temperature description of the RNA-like molecule is invented. Instead of equilibrium treatment of the polymer state, the steady state viewpoint is proposed. The molecule is considered as being in an adiabatic steady state, which is a non-equilibrium one. The general approach to the molecule in such a steady state is discussed and the simple model with saturating bonds is considered. The relation between mean square end-to-end distance and the number of monomers is derived for the simple system under condition T>Θ. The obtained relation depends on additional so-called disorder temperature.

We propose and analyze an efficient scheme for suppressing the absorption of a weak probe field based on intersubband transitions in a four-level asymmetric coupled quantum well (CQW) driven coherently by a probe laser field and a control laser field. We study the steady-state process analytically and numerically, and our results show that the probe absorption can be completely eliminated under the condition of Raman resonance (i.e. two-photon detuning is zero). Besides, we can observe one transparency window without requiring one- or two-photon detuning to exactly vanish. This investigation may provide a possible scheme for EIT in solids by using the CQW.

The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general cannot describe the steady state of an open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.

We show that in an artificial dynamic neural network that depends on a real parameter μ, steady states do not exist for μ ≤ -2, and positive and negative steady states exist for μ > -2. We hope that such a bifurcation phenomenon in our network model may explain some of the real observations in nature.

A nonlinear three-term recurrence relation arising from seeking the steady states of a cellular neural network with bang bang control is studied. A complete analysis of its periodic behavior is given. In particular, we show that each solution is periodic and its prime period can be determined by two of its consecutive terms. By means of our periodicity analysis, we may then solve the steady state problem which to our knowledge is not solved by other means.

Memristors have attracted considerable attention since their physical realization was reported by Hewlett-Packard (HP) Lab in 2008. Their distinctive properties like nonvolatility, re-configurability and analog processing capability have found promising potential in developing future neuromorphic computing systems, next-generation nonvolatile memories, etc. However, the device characteristics of memristors and their utilizations have not been fully studied. Particularly, predicting the composite behaviors in memristor series and parallel circuits is challenging because of the polarity- and state-dependent electric property of individual memristors. In this paper, the composite characteristics of multiple memristor circuits in series and parallel, respectively, are investigated comprehensively. Specifically, the transient behaviors are revealed in terms of the changes of charge or flux thresholds of the memristors and the conditions to achieve the steady state through transient state are also studied. Furthermore, their composite electric properties in the steady state are presented. Finally, the impact of unavoidable process variations of memristors on composite behaviors is analyzed based on massive Monte-Carlo simulations.

In this paper, we investigate pattern formation in Keller–Segel chemotaxis models over a multidimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as chemoattraction rate $\chi$ increases. Then using Crandall–Rabinowitz local theory with $\chi$ being the bifurcation parameter, we obtain the existence of nonhomogeneous steady states of the system which bifurcate from this homogeneous steady state. Stability of the bifurcating solutions is also established through rigorous and detailed calculations. Our results provide a selection mechanism of stable wavemode which states that the only stable bifurcation branch must have a wavemode number that minimizes the bifurcation value. Finally, we perform extensive numerical simulations on the formation of stable steady states with striking structures such as boundary spikes, interior spikes, stripes, etc. These nontrivial patterns can model cellular aggregation that develop through chemotactic movements in biological systems.

We consider three connected populations with strong Allee effect, and give a complete classification of the steady state structure of the system with respect to the Allee threshold and the dispersal rate, describing the bifurcations at each critical point where the number of steady states change. One may expect that by increasing the dispersal rate between the patches, the system would become more well-mixed, hence simpler. However, we show that it is not always the case, and the number of steady states may (temporarily) go up by increasing the dispersal rate. Besides sequences of pitchfork and saddle-node bifurcations, we find triple-transcritical bifurcations and also a sun-ray shaped bifurcation where twelve steady states meet at a single point then disappear. The major tool of our investigations is a novel algorithm that decomposes the parameter space with respect to the number of steady states and finds the bifurcation values using cylindrical algebraic decomposition with respect to the discriminant variety of the polynomial system.

We consider the cell division equation which describes the continuous growth of cells and their division in two pieces. Growth conserves the total number of cells while division conserves the total mass of the system but increases the number of cells. We give general assumptions on the coefficient so that we can prove the existence of a solution (λ, N, ϕ) to the related eigenproblem. We also prove that the solution can be obtained as the sum of an explicit series. Our motivation, besides its applications to the biology and fragmentation, is that the eigenelements allow to prove a priori estimates and long-time asymptotics through the General Relative Entropy.¹⁶.

Two models of receptor-mediated morphogen transport in a biological tissue are proposed to investigate morphogen gradient formation. The first model concerns intracellular transport of morphogen molecules, while the second describes transport along the cell surface. Both models couple via diffusivity a quasilinear degenerate parabolic equation describing the transport of the morphogens with an ordinary differential equation describing reversible binding kinetics of receptors. A detailed study of the steady states is provided, together with numerical tests which compare the models with experimental data.

We study the dynamical stability of nontrivial steady states to a multidimensional parabolic–parabolic chemotaxis-consumption model in a bounded domain, where the physical zero-flux boundary condition for the bacteria and the nonhomogeneous Dirichlet boundary condition for the oxygen are prescribed. We first prove that the spectrum set of the linearized operator at the steady state only consists of eigenvalues with finite algebraic multiplicity. Then we show that all eigenvalues have negative real part if the concentration of the oxygen at boundary is small, or the diffusive coefficient $𝜖$ of the oxygen is large, or $𝜖$ is small. In the radial setting, we further show that all eigenvalues have negative real part without any assumption on the parameters. This result of spectral analysis implies the local asymptotic stability of the nontrivial steady states to the chemotaxis-consumption model under the above assumptions.

A simple model of particle creation and annihilation in an isolated assembly of particles with conserved energy and fixed volume, the Cell Model (CM), is formulated. With increasing time, particle number distribution, obtained by averaging over many systems, approaches a time-independent, steady state (SS) distribution. Dependence of the SS distribution on creation and annihilation conditional reaction probabilities is studied. The results obtained for the SS are compared with predictions of statistical mechanics within the microcanonical ensemble (MCE). In general, the predictions of both models are different. They agree only if the creation and annihilation conditional reaction probabilities are equal. This condition also results in the detailed balance in the SS.

The Notch–Delta signaling pathway is a highly conserved signaling system that partakes in a diverse process of growth, patterns and differentiation. Experiments have shown that Delta from different cells activates this pathway (trans-activation) while Delta from the same cell inhibits this pathway (cis-inhibition). The Notch–Delta interactions could switch a cell to one of the two opposite fates: either Sender (high Delta/low Notch) or Receiver (low Delta/high Notch). We studied a Notch–Delta signaling model from Sprinzak et al., (2010), to investigate the cell fate through steady state analysis. The focus was placed on a fundamental case of one single cell with fixed external Delta and Notch supplies. First, we proved there exists a unique steady state which is asymptotically stable. Second, we derived the increasing/decreasing and asymptotic properties of the steady state with respect to all the parameters. Third, we studied the sensitivity and discovered the cell fate is only sensitive to the production rates of Notch and Delta under strong cis-inhibition. Finally, we applied this model to multi-cellular cases and found that the lateral inhibition pattern could be created with the spatially varied Delta production rate. The Hopf bifurcation is not observed in the current model.