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Haplotype-resolved genome assembly plays a crucial role in understanding allele-specific functions. However, obtaining haplotype-resolved assembly for auto-polyploid genomes remains challenging. Existing methods can be classified into reference-based phasing, assembly-based phasing, and gamete binning. Nevertheless, there is a lack of cost-effective and efficient methods for haplotyping auto-polyploid genomes. In this study, we propose a novel phasing algorithm called PolyGH, which combines Hi-C and gametic data. We conducted experiments on tetraploid potato cultivars and divided the method into three steps. Firstly, gametic data was utilized to bin non-collapsed contigs, followed by merging adjacent fragments of the same type within the same contig. Secondly, accurate Hi-C signals related to differential genomic regions were acquired using unique k-mers. Finally, collapsed fragments were assigned to haplotigs based on combined Hi-C and gametic signals. Comparing PolyGH with Hi-C-based and gametic data-based methods, we found that PolyGH exhibited superior performance in haplotyping auto-polyploid genomes when integrating both data types. This approach has the potential to enhance haplotype-resolved assembly for auto-polyploid genomes. [ABSTRACT FROM AUTHOR]

We mainly investigate the multiple inverse stochastic resonance (ISR) induced by electrical autapse and chemical autapse under different types of input current. It is found that average firing rate is shown as a decaying oscillation process with time delay for both electrical autapse and chemical autapse under noise and input current. Furthermore, we find that average firing rate has several minimums as a function of time delay of autapse, which is called multiple ISR. As a consequence, our work suggests that, autapse can regulate and control the neuronal activities and induce multiple ISR. Compared with signal current, the multiple ISR phenomenon driven by constant current is more apparent. [ABSTRACT FROM AUTHOR]

This paper primarily investigates the inverse stochastic resonance (ISR) of neuron network driven by Lévy noise with electrical autapse and chemical autapse, respectively. Firstly, the discharge of Hodgkin–Huxley (HH) neuron network under different noise parameters, autapse parameters and network coupling strength is shown. Then, the variation of average firing rate with Lévy noise in the case of electrical autapse and chemical autapse is presented. We find that there exists a minimum value of the average firing rate curve caused by stability index and noise intensity of Lévy noise across the whole network, which is the phenomenon of ISR. With the increase of autaptic intensity and coupling strength, the ISR inhibitory effect of neuron discharge is weakened. In addition, with the increase of coupling strength, the neuron discharge of neural network is more intense and regular. As a consequence, our work suggests that autaptic intensity and coupling efficient of neuronal network can regulate the neuronal firing activities and suppress the effect of ISR, and Lévy noise can induce ISR phenomenon in Newman–Watts neuronal network. [ABSTRACT FROM AUTHOR]

In this paper, a competition model between tumor cells and immune system with random switching environment is proposed and investigated. The stochastic switching environment is assumed to be telegraph noise expressed as multi-state Markov chain. The theoretical threshold for extinction and persistence of tumor cells are obtained. Besides, stochastic simulations are performed to substantiate and interpret the conclusions. It is found that stochastic switching environment plays an important part in the process of tumor evolution. The simple model proposed in our paper is conducive to understand the theoretical mechanism between tumor cells and immune system under random environment. [ABSTRACT FROM AUTHOR]

In this paper, the phenomenon of inverse stochastic resonance (ISR) induced by Levy noise is investigated in a single neuron. Firstly, the discharge of Hodgkin–Huxley neuron at different current strengths without noise is studied. Then we cite the concept of average spiking rate and use it as a scale to measure the discharge of neuron. Under the influence of Levy noise, it is found that the average firing rate can reach a minimum caused by stability index and a scale parameter of Levy noise. The conclusion is that ISR could be induced by Levy noise when the input current strength reaches the critical threshold. Besides, in order to further prove that Levy noise can produce ISR, interspike intervals (ISIs) histogram is used for studying discharge patterns in voltage. Finally, we find that with the increase of stability index and scale parameter of Levy noise, the total number of ISIs decreases first and then increases, which implies the appearance of ISR. [ABSTRACT FROM AUTHOR]

We investigate a stochastic model for single species population growth with strong and weak Allee effects subjected to coupling between non-Gaussian and Gaussian colored noise as well as nonzero cross-correlation in between. Stationary probability distribution of population model is obtained depending on the Fokker–Planck equation. The mean first-passage time is also calculated in order to quantify the time of transition between survival state and extinction state with Allee effect in population. The intensity of non-Gaussian colored noise can induce phase transition, and population may be vulnerable to extinction due to the increase in the intensity of non-Gaussian colored noise. Whether Allee effect is strong or weak, the increase in Allee threshold will not contribute to the survival and stability of the population. Further, the phenomenon of resonant activation is firstly discovered in the study of population dynamics with Allee effect. These behaviors can be interpreted on the basis of a biological model of population evolution. [ABSTRACT FROM AUTHOR]

This paper mainly studies the phenomenon of inverse stochastic resonance induced by non-Gaussian noise in a representative Hodgkin–Huxley model. Firstly, spiking manners of neurons under different input currents are investigated and different current thresholds and bifurcation diagram are given. Besides, the limit cycle with different input current are plotted. Then, taking the average firing rate as a measurement, the result shows that a minimum exists in the curve corresponding to the intensity, correlation time and deviation coefficient of non-Gaussian noise, which is named inverse stochastic resonance(ISR). More important, it is found that the mean firing rate will remain unchanged with noise intensity and deviation coefficient when correlation time is sufficiently large and finally trends toward a constant value which is completely determined by input current. Further, the present results will be benefit to investigate the functional roles of randomness in neural spiking. [ABSTRACT FROM AUTHOR]

Based on the two-dimensional (2D) neural map, we investigate the impacts of non-Gaussian colored noise on the firing activity of discrete system. Taking the coherence parameter R to measure the regularity of firing behavior, it is demonstrated that coherence parameter R has a pronounced minimum value with the noise intensity and the correlation time of non-Gaussian colored noise, which is the so-called phenomenon of coherence resonance (CR). Besides, the firing activity is not sensitive to the non-Gaussian parameter which determines the departure from the Gaussian distribution when the correlation time is large enough. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the phenomenon that stochastic fluctuation induced the competition between tumor extinction and recurrence in the model of tumor growth derived from the catalytic Michaelis–Menten reaction. We analyze the probability transitions between the extinction state and the state of the stable tumor by the Mean First Extinction Time (MFET) and Mean First Return Time (MFRT). It is found that the positional fluctuations hinder the transition, but the environmental fluctuations, to a certain level, facilitate the tumor extinction. The observed behavior could be used as prior information for the treatment of cancer. [Copyright &y& Elsevier]

Abstract: We investigate a stochastic model of tumor growth derived from the catalytic Michaelis–Menten reaction with positional and environmental fluctuations under subthreshold periodic treatment. Firstly, the influences of environmental fluctuations on the treatable stage are analyzed numerically. Applying the standard theory of stochastic resonance derived from the two-state approach, we derive the signal-to-noise ratio (SNR) analytically, which is used to measure the stochastic resonance phenomenon. It is found that the weak environmental fluctuations could induce the extinction of tumor cells in the subthreshold periodic treatment. The positional stability is better in favor of the treatment of the tumor cells. Besides, the appropriate and feasible treatment intensity and the treatment cycle should be highlighted considered in the treatment of tumor cells. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the dynamic behavior of virus infection model with delay effect influenced by external noise. First, a mathematical model describing the evolution of virus under the influences of stochastic noise and delay effect is developed. And necessary conditions for extinction and weak persistence are derived by Ito's formula. A new basic reproduction number R ˜ 0 for virus infection model with delay effect to determine whether extinction or persistence is given. It is found that the delay parameter τ affects the new basic reproduction number R ˜ 0 , and the behavior of extinction and survival of virus. Besides, the threshold for extinction of stochastic model is smaller than the one of deterministic model. In the end, stochastic simulations are applied to illustrate and test the theoretical conclusions. • The effect of delay and stochastic noise on virus infection model is investigated. • Sufficient conditions for extinction and weak persistence of virus are derived. • A new basic reproduction number for stochastic virus infection model is given. • The theoretical results we obtain are verified by stochastic simulation. [ABSTRACT FROM AUTHOR]

Motivation Constructing a phylogenetic tree requires calculating the evolutionary distance between samples or species via large-scale resequencing data, a process that is both time-consuming and computationally demanding. Striking the right balance between accuracy and efficiency is a significant challenge. Results To address this, we introduce a new algorithm, MIKE (MinHash-based k -mer algorithm). This algorithm is designed for the swift calculation of the Jaccard coefficient directly from raw sequencing reads and enables the construction of phylogenetic trees based on the resultant Jaccard coefficient. Simulation results highlight the superior speed of MIKE compared to existing state-of-the-art methods. We used MIKE to reconstruct a phylogenetic tree, incorporating 238 yeast, 303 Zea , 141 Ficus , 67 Oryza , and 43 Saccharum spontaneum samples. MIKE demonstrated accurate performance across varying evolutionary scales, reproductive modes, and ploidy levels, proving itself as a powerful tool for phylogenetic tree construction. Availability and implementation MIKE is publicly available on Github at https://github.com/Argonum-Clever2/mike.git. [ABSTRACT FROM AUTHOR]

We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method. [ABSTRACT FROM AUTHOR]

We investigate coherence resonance (CR) in the FitzHugh-Nagumo (FHN) neurons models driven by bounded noise. By considering the coefficient of coherence resonance as a ratio, it is numerically demonstrated that bounded noise can cause CR by adjusting either the intensity of bounded noise or its frequency. When the intensity and frequency of bounded noise take certain limited values respectively, the strongest CR phenomenon is produced. [ABSTRACT FROM AUTHOR]

In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a class of stochastic time-delayed systems driven by correlated Gaussian white noises are considered. Novikov’s theorem is used to derive delay Fokker–Planck equations. In the case of small time delays, approximate stationary solutions are obtained. As a special case, the delay Fokker–Planck equation and the approximate stationary probability density function is obtained for a bistable system. Numerical simulations show that the small-delay approximation is a good approximation in the case of small delay. Furthermore, the effects of the correlated noises and the feedback are investigated. The critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by (the degree of the correlation of the noises) and (the strength of the feedback). Both and can change the curve of the stationary probability density function from a bimodal to a unimodal structure. [Copyright &y& Elsevier]