Stochastic Growth Research Articles

Stochastic behaviors of an improved Gompertz tumor growth model with coupled two types noise

In this work, an improved Gompertz tumor growth model has been introduced. The expressions of steady probability distributions (SPD) of stochastic Gompertz tumor growth models are studied by using the technique of Fokker-Planck equation (FPE), and their dynamic behaviors are also further investigated. Moreover, the expressions for mean, variance, skewness, as well as the mean first-passage time (MFPT) also have been derived. And the influence of noise intensity, correlation coefficient, and noise correlation time of SPD are further analyzed. It is worthy noting that the colored noise intensity has an important impact on SPD. Furthermore, adjusting birth and death parameters also significantly impact SPD, MFPT, mean, variance as well as skewness.

A data-driven framework to manage uncertainty due to limited transferability in urban growth models

The processes of urban growth vary in space and time. There is a lack of model transferability, which means that models estimated for a particular study area and period are not necessarily applicable for other periods and areas. This problem is often addressed through scenario analysis, where scenarios reflect different plausible model realisations based typically on expert consultation. This study proposes a novel framework for data-driven scenario development which, consists of three components - (i) multi-area, multi-period calibration, (ii) growth mode clustering, and (iii) cross-application. The framework finds clusters of parameters, referred to as growth modes: within the clusters, parameters represent similar spatial development trajectories; between the clusters, parameters represent substantially different spatial development trajectories. The framework is tested with a stochastic dynamic urban growth model across European functional urban areas over multiple time periods, estimated using a Bayesian method on an open global urban settlement dataset covering the period 1975–2014.The results confirm a lack of transferability, with reduced confidence in the model over the validation period, compared to the calibration period. Over the calibration period the probability that parameters estimated specifically for an area outperforms those for other areas is 96%. However, over an independent validation period, this probability drops to 72%.Four growth modes are identified along a gradient from compact to dispersed spatial developments. For most training areas, spatial development in the later period is better characterized by one of the four modes than their own historical parameters. The results provide strong support for using identified parameter clusters as a tool for data-driven and quantitative scenario development, to reflect part of the uncertainty of future spatial development trajectories.A promising further application is to use the growth modes to characterize past spatial development patterns. A trend of increasingly dispersed patterns could be identified over the studied functional urban areas which calls for more detailed explorations.

Asymptotic Behavior of Three Connected Stochastic Delay Neoclassical Growth Systems Using Spectral Technique

In this study, we consider a nonlinear system of three connected delay differential neoclassical growth models along with stochastic effect and additive white noise, which is influenced by stochastic perturbation. We derived the conditions for positive equilibria, stability and positive solutions of the stochastic system. It is observed that when a constant delay reaches a certain threshold for the steady state, the asymptotic stability is lost, and the Hopf bifurcation occurs. In the case of the finite domain, the three connected, delayed systems will not collapse to infinity but will be bounded ultimately. A Legendre spectral collocation method is used for the numerical simulations. Moreover, a comparison of a stochastic delayed system with a deterministic delayed system is also provided. Some numerical test problems are presented to illustrate the effectiveness of the theoretical results. Numerical results further illustrate the obtained stability regions and behavior of stable and unstable solutions of the proposed system.

Are genetic variation and demographic performance linked?

Quantifying relationships between genetic variation and population viability is important from both basic biological and applied conservation perspectives, yet few populations have been monitored with both long-term demographic and population genetics approaches. To empirically test whether and how genetic variation and population dynamics are related, we present one such paired approach. First, we use eight years of historical demographic data from five populations of Boechera fecunda (Brassicaceae), a rare, self-compatible perennial plant endemic to Montana, USA, and use integral projection models to estimate the stochastic population growth rate (λ S) and extinction risk of each population. We then combine these demographic estimates with previously published metrics of genetic variation in the same populations to test whether genetic diversity within populations is linked to demographic performance. Our results show that in this predominantly inbred species, standing genetic variation and demography are weakly positively correlated. However, the inbreeding coefficient was not strongly correlated with demographic performance, suggesting that more inbred populations are not necessarily less viable or at higher extinction risk than less inbred populations. A contemporary re-census of these populations revealed that neither genetic nor demographic parameters were consistently strong predictors of current population density, although populations showing lower probabilities of extinction in demographic models had larger population sizes at present. In the absence of evidence for inbreeding depression decreasing population viability in this species, we recommend conservation of distinct, potentially locally adapted populations of B. fecunda rather than alternatives such as translocations or reintroductions.

Stochastic growth, conservation of capital and convergence to a positive steady state

Stochastic growth, conservation of capital and convergence to a positive steady state

The magnitude of heterogeneity in individual-cell growth dynamics is an inherent characteristic of Salmonella enterica ser. Typhimurium strains

Individual-cell heterogeneity is a major source of variability in biological systems affecting importantly, among others, microbial behavior. Characterization of cell populations of pathogenic bacterial strains in their entirety, ignoring the phenotypic variability of single cells, may result in erroneous safety risk estimates. The objective of the present study was the evaluation and comparison of the heterogeneity in the individual-cell growth dynamics of different strains of Salmonella enterica. The stochasticity in the growth of single cells of five S. enterica ser. Typhimurium strains was quantitatively described using time-lapse microscopy, and the existence of a strain effect was statistically assessed. In total, 831 growing microcolonies originating from single cells were monitored and analyzed, and the growth kinetic parameters of lag time (λ) and maximum specific growth rate (μmax) for each one of them were estimated. An extensive heterogeneity in individual-cell growth kinetics was recorded, while significant inter-strain differences in their heterogeneity were evident based on simultaneous Bonferroni confidence intervals and Levene’s tests. The Logistic and LogLogistic probability distribution provided the best fitting for μmax and λ data, respectively for all the tested strains. The strain effect on the above distributions was also demonstrated with pairwise comparisons of the decile differences. The impact of strain-dependent heterogeneity on microbial growth was visualized by comparing stochastic growth curves of different strains using Monte Carlo simulation. In conclusion, the individual-cell growth dynamics of S. enterica are heterogeneous, with the magnitude of the observed heterogeneity appearing to be an inherent characteristic of bacterial strains.

Existence and uniqueness of solutions for stochastic urban-population growth model

Urban-population growth model has attracted attention over the last few decades due to its usefulness in representing population dynamics, virus dynamics, and epidemics. Researchers have included stochastic perturbation in the urban-population growth model to improve the model, attempting to capture the random nature of real-time dynamics. When doing so, researchers have presented conditions to ensure that the corresponding stochastic solution is both positive and unique (in probability). This paper advances that knowledge by showing that the stochastic diffusion constant can be both positive and negative—previous results in the literature have required that such a constant be positive only. A numerical simulation illustrates the paper's findings.

A compressed logistic equation on bacteria growth: inferring time-dependent growth rate

We propose a compressed logistic model for bacterial growth by invoking a time-dependent rate instead of the intrinsic growth rate (constant), which was adopted in traditional logistic models. The new model may have a better physiological basis than the traditional ones, and it replicates experimental observations, such as the case example for E. coli, Salmonella, and Staphylococcus aureus. Stochastic colonial growth at a different rate may have a fractal-like nature, which should be an origin of the time-dependent reaction rate. The present model, from a stochastic viewpoint, is approximated as a Gaussian time evolution of bacteria (error function).

Formation Mechanism of Microbial Diversity in Artificial Intelligence Devices due to Intermediate Disturbance by Low-Dose UV Radiation for Complementary Medicine.

The development of artificial intelligence devices in the complementary medicine field is rapid and the surface microbial diversity pollution was found with periodic low-dose ultraviolet radiation (LDUVR). Since artificial intelligence devices do not have enough different types of substrates for microbial communities, it is unclear how the great microbial diversity can emerge and persist, as this clearly defies the competitive exclusion principle of ecology. In this study, the 5 most common genera in the artificial intelligence devices, Escherichia, Pseudomonas, Streptococcus, Staphylococcus and Aeromonas have been sampled without and with periodic LDUVR, respectively. A new hypothesis was put up to clarify the construction and maintenance process of high microbiological diversity in artificial intelligence devices by comparing and evaluating the variations between the dynamic response characteristics of their relative abundances in the two scenarios as follows: the periodic LDUVR can be regarded as an adverse factor with intermediate disturbance, causing stronger microbial stochastic growth responses (SGR) which would inevitably give rise to stronger random variation of the other important processes tightly correlated with SGR, such as intra- and interspecific competition process, and substrates production and consumption process, which could effectively diminish the auto- and cross-correlation of stochastic processes of microbial populations, alleviating the intra- and inter-specific competitions. In artificial intelligence devices with LDUVR, these crucial succession processes can propel the microbial communities to generate and sustain a high species diversity. Finally, thorough Monte Carlo simulations were used to thoroughly confirm the idea. This research can build the theoretical groundwork, offer fresh viewpoints, and suggest potential microbial prevention strategies for the succession of microbial communities in LDUVR.

Interval neutrosophic stochastic dynamical systems driven by Brownian motion

Stochastic and neutrosophic theory are effective tools for modeling real-world phenomena and natural dynamical systems, where inputs are often affected by stochastic noises and outputs often contain both randomness and indeterminacy. In this work, we present a new type of stochastic differential equations (SDE) driven by an one-dimensional Brownian motion that can be considered as an efficient tool to describe the uncertain behavior of dynamical systems operating in interval neutrosophic environments with stochastic noises. After introducing some basic foundations on neutrosophic arithmetic, neutrosophic calculus and neutrosophic stochastic process, we define the new form of interval neutrosophic stochastic differential equations taking values in neutrosophic environment. Under some suitable conditions, the unique existence result of stochastic solution is obtained based on the use of Picard successive approximation. We also introduce an efficient numerical algorithm, namely Euler–Maruyama method, to solve the numerical solution of proposed problem and further demonstrate the effectiveness of the numerical method by solving some examples in stochastic biological systems such as stochastic logistic growth model, stochastic Lotka–Volterra predator–prey model, and stochastic SARS model, respectively.

Approximating Nash Equilibrium for Optimal Consumption in Stochastic Growth Model with Jumps

Approximating Nash Equilibrium for Optimal Consumption in Stochastic Growth Model with Jumps

Stretching of a Fractal Polymer around a Disc Reveals Kardar-Parisi-Zhang Scaling.

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. We use scaling analysis and computer simulations to examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. We reveal that the typical excursions of the polymer away from the surface and curvature-induced correlation length scale as Δ∼R^{β} and S^{*}∼R^{1/z}, respectively, with the Kardar-Parisi-Zhang (KPZ) growth β=1/3 and dynamic exponents z=3/2. Although probability distribution of excursions does not belong to KPZ universality class, the KPZ scaling is independent of the fractal dimension of the polymer and, thus, is universal across classical polymer models, e.g., SAW, randomly branching polymers, crumpled unknotted rings. Additionally, our Letter establishes a mapping between stretched polymers in curved geometry and the Balagurov-Vaks model of random walks among traps.

Stochastic line integrals and stream functions as metrics of irreversibility and heat transfer

Stochastic line integrals are presented as a useful metric for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled electrical circuits. Here we provide a general framework for understanding properties of stochastic line integrals and clarify their implementation for experiments and simulations. For two-dimensional systems, stochastic line integrals can be expressed in terms of a stream function, the sign of which determines the orientation of nonequilibrium steady-state probability currents. Theoretical results are supported by numerical studies of an overdamped two-dimensional mass-spring system driven out of equilibrium. Additionally, the stream function permits analytical understanding of the scaling dependence of stochastic area growth rate on key parameters such as the noise strength for both linear and nonlinear springs.

Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate

Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces1 and of interfaces in bacterial colonies2, and spin transport in quantum magnets3-6 all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space-time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar-Parisi-Zhang (KPZ) equation7. Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence8-17. Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space-time scaling laws18,19, combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantumsystems.

Growth rate of a stochastic growth process driven by an exponential Ornstein–Uhlenbeck process

We study the stochastic growth process in discrete time xi+1 = (1 + μi)xi with the growth rate μi=ρeZi−12Var(Zi) proportional to the exponential of an Ornstein–Uhlenbeck (O–U) process dZt = −γZtdt + σdWt sampled on a grid of uniformly spaced times with time step τ. Using large deviation theory, we compute the asymptotic growth rate (Lyapunov exponent) λ=limn→∞1nlogE[xn]. We show that this limit exists, under appropriate scaling of the O–U parameters, and is expressed as the solution of a variational problem. The asymptotic growth rate is equal to the thermodynamical pressure of a one-dimensional lattice gas with attractive exponential potentials. For Zt, a stationary O–U process of the lattice gas coincides with a model considered previously by Kac and Helfand. We derive upper and lower bounds on λ. In the large mean-reversion limit γnτ ≫ 1, the two bounds converge and the growth rate is given by a lattice version of the van der Waals equation of state. The predictions are tested against numerical simulations of the stochastic growth model.

A cytoskeletal vortex drives phage nucleus rotation during jumbo phage replication in E.coli.

Nucleus-forming jumbo phages establish an intricate subcellular organization, enclosing phage genomes within a proteinaceous shell called the phage nucleus. During infection in Pseudomonas, some jumbo phages assemble a bipolar spindle of tubulin-like PhuZ filaments that positions the phage nucleus at midcell and drives its intracellular rotation. This facilitates the distribution of capsids on its surface for genome packaging. Here we show that the Escherichia coli jumbo phage Goslar assembles a phage nucleus surrounded by an array of PhuZ filaments resembling a vortex instead of a bipolar spindle. Expression of a mutant PhuZ protein strongly reduces Goslar phage nucleus rotation, demonstrating that the PhuZ cytoskeletal vortex is necessary for rotating the phage nucleus. While vortex-like cytoskeletal arrays are important in eukaryotes for cytoplasmic streaming and nucleus alignment, this work identifies a coherent assembly of filaments into a vortex-like structure driving intracellular rotation within the prokaryotic cytoplasm.

Demography of cape petrels in response to environmental changes

AbstractPredicting the responses of populations in changing environments is an important task for ecologists. Understanding the population dynamics of high‐latitude breeding species is critical given the particularly rapid environmental changes that occur in these regions. Using long‐term mark–resighting data acquired over 53‐years in Pointe Géologie, Terre Adélie, Antarctica, we estimated age‐specific demographic parameters and evaluated the effect of the environment on survival of a poorly known species, the cape petrel Daption capense. We then modeled the dynamics of this population using a life‐history model and performed prospective and retrospective analyses to estimate the sensitivity of the population growth rate to demographic parameters, and to quantify their relative contribution. Survival of cape petrel increased with age, being 0.610 (±0.193) for juveniles, 0.739 (±0.158) for individuals from 2 to 4, and 0.920 (±0.031) for older individuals. Minimum age at first reproduction was 3 years old, the age at which all birds were recruited was 14 years, and mean age at first reproduction was 9.05 (±2.06) years. Adult survival increased over time and was positively correlated with the southern annular mode (SAM). The stochastic population growth rate was estimated at 1.019, and adult survival over age 5 made the largest contribution to variance of the population growth rate. Sensitivity analyses revealed that population regulation was mainly driven by the SAM. Our results suggest that despite the decrease in breeding success, the population of cape petrels at Pointe Géologie increased due to the increase in immature and adult survival.

(Digital Presentation) Finite Element Modeling of Thermoelectric Effects in Phase Change Memory Cells

Phase change memory (PCM) is a high-speed high-endurance non-volatile electronic memory technology which utilizes the electrical resistivity difference between the amorphous and the crystalline phases of phase change materials, such as Ge2Sb2Te5 (GST), to store information [1]. PCM cells are switched by short duration electrical pulses by melting a small volume to transition to dielectric amorphous phase (reset) or heating above glass-transition temperature to crystallize (set). The cells experience extremely large thermal gradients (~ 50 K/nm) and high current densities (~50 MA/cm2) during reset. Hence thermoelectric (TE) contributions are very significant both in bulk and at the material and solid-liquid interfaces [2]. In this work, we performed finite element simulations of mushroom PCM cells and analyzed contributions of Joule heating (symmetric) and thermoelectric heat (asymmetric) during reset and set operations using COMSOL Multiphysics. A field effect transistor (FET), modeled using a circuit model, is used as an access device. We self-consistently solve for current continuity, heat transport (Fig. 1) and phase changes in the materials, including temperature, electric-field and phase-dependent electrical and thermal conductivity, thermal boundary resistances and latent heat of fusion, along with temperature dependent stochastic nucleation, growth and grain-boundary amorphization, accounting for all energy exchanges [3-6].Thermoelectric heat exchanges are due to generation and recombination of electrons and holes as well as the kinetic energy absorbed or released by the transported free charge carriers [7]. These energy exchanges can take place at material interfaces (Peltier heat) or in bulk material (Thomson heat). Discontinuity of Seebeck coefficient and temperature (due to thermal boundary resistances) make TE contributions very significant in PCM devices.Our simulation results show the significance of the TE contributions on the reset behavior of PCM devices (Fig. 2). Self-heating at the bottom TiN-GST interface is substantially higher for one of the current polarities, giving rise to an over-sized mushroom in the case of negative polarity, for the same reset pulse amplitude. The negative polarity case (over-reset cell) cannot be set with the same set pulse as the positive polarity case. From the power consumption and peak current requirement point of view, it is advantageous to have higher TE heating inside the mushroom and its interfaces. TE cooling away from the mushroom interfaces is advantageous for reduced thermal cross-talk and write-disturb on the neighboring cells. However, thermal gradients also need to be kept under consideration for reliability perspective.Acknowledgement: Md Tashfiq Bin Kashem acknowledges support from General Electric through a Graduate Fellowship for Innovation. This work is supported through US National Science Foundation (NSF) award # 1710468.

Forecast disagreement about long-run macroeconomic relationships

Using survey forecast data, this paper studies whether professional forecasters utilize long-run cointegration relationships among macroeconomic variables to forecast the future, as postulated in stochastic growth models. Significant heterogeneity exists among forecasters. The majority of the forecasters do not use these long-run relationships. The results are robust across different groups, to addressing the multiple testing problem and to allowing for structural break.

Stochastic growth tree networks with an identical fractal dimension: Construction and mean hitting time for random walks.

There is little attention paid to stochastic tree networks in comparison with the corresponding deterministic analogs in the current study of fractal trees. In this paper, we propose a principled framework for producing a family of stochastic growth tree networks T possessing fractal characteristic, where t represents the time step and parameter m is the number of vertices newly created for each existing vertex at generation. To this end, we introduce two types of generative ways, i.e., Edge-Operation and Edge-Vertex-Operation. More interestingly, the resulting stochastic trees turn out to have an identical fractal dimension d = ln ⁡ 2 ( m + 1 ) / ln ⁡ 2 regardless of the introduction of randomness in the growth process. At the same time, we also study many other structural parameters including diameter and degree distribution. In both extreme cases, our tree networks are deterministic and follow multiple-point degree distribution and power-law degree distribution, respectively. Additionally, we consider random walks on stochastic growth tree networks T and derive an expectation estimation for mean hitting time ⟨ H ⟩ in an effective combinatorial manner instead of commonly used spectral methods. The result shows that on average, the scaling of mean hitting time ⟨ H ⟩ obeys ⟨ H ⟩ = | T |, where | T | represents vertex number and exponent λ is equivalent to 1 + ln ⁡ 2 / ln ⁡ 2 ( m + 1 ). In the meantime, we conduct extensive experimental simulations and observe that empirical analysis is in strong agreement with theoretical results.