We review studies of an evolution operator ℒ for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of ℒ yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator ℒ in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape (...) rate up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ℒn. Using an integral representation of the evolution operator ℒ, we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula. (shrink)

This paper explores the functional role of noise in synthetic biology and its relation to the concept of randomness. Ongoing developments in the field of synthetic biology are pursuing the re-organisation and control of biological components to make functional devices. This paper addresses the distinction between noise and randomness in reference to the functional relationships that each may play in the evolution of living and/or synthetic systems. The differentiation between noise and randomness in its constructive role, that (...) is, between noise as a perturbation in routine behaviours and noise as a source of variability that cells may exploit, indicates the need for a clarification and rectification of the conflicting uses of the notion of noise in the studies of the so-called noise biology. (shrink)

This paper proposes a new system whose potential function is with three types of asymmetric potential wells, driven by trichotomous noise. Firstly, the three types of asymmetric bistable system are described in detail, and the changes of asymmetric bistable system potential function under different asymmetric factors are analyzed. Secondly, the effect of potential function parameters, asymmetric factorα, noise intensity D, and the probability of particle transition q is discussed, using numerical simulation. The detection effects of traditional symmetric SR (...) and three types of asymmetric SR are observed and compared under the driving of trichotomous noise and periodic signals. The mean of signal-to-noise ratio gain is the indicator of the system's effectiveness on enhancing weak signal. The results indicate that it can make the detection effect of the asymmetric system better than that of the traditional bistable system by adjusting the parameters of the asymmetric stochastic resonance system and trichotomous noise. (shrink)

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results.

Recent evidence indicates that transcriptional bursts are intrinsically amplified by messenger RNA cytoplasmic processing to generate large stochastic fluctuations in protein levels. These fluctuations can be exploited by cells to enable probabilistic bet‐hedging decisions. But large fluctuations in gene expression can also destabilize cell‐fate commitment. Thus, it is unclear if cells temporally switch from high to low noise, and what mechanisms enable this switch. Here, the discovery of a post‐transcriptional mechanism that attenuates noise in HIV is reviewed. (...) Early in its life cycle, HIV amplifies transcriptional fluctuations to probabilistically select alternate fates, whereas at late times, HIV utilizes a post‐transcriptional feedback mechanism to commit to a specific fate. Reanalyzing various reported post‐transcriptional negative feedback architectures reveals that they attenuate noise more efficiently than classic transcriptional autorepression, leading to the derivation of an assay to detect post‐transcriptional motifs. It is hypothesized that coupling transcriptional and post‐transcriptional autoregulation enables efficient temporal noise control to benefit developmental bet‐hedging decisions. (shrink)

We describe a recent approach for distinguishing between stochastic and deterministic sources of variability, focusing on the mammalian cell cycle. Variability between cells is often attributed to stochastic noise, although it may be generated by deterministic components. Interestingly, lineage information can be used to distinguish between variability and determinism. Analysis of correlations within a lineage of the mammalian cell cycle duration revealed its deterministic nature. Here, we discuss the sources of such variability and the possibility that the (...) underlying deterministic process is due to the circadian clock. Finally, we discuss the “kicked cell cycle” model and its implication on the study of the cell cycle in healthy and cancerous tissues. (shrink)

No two individuals with the autism diagnosis are ever the same—yet many practitioners and parents can recognize signs of ASD very rapidly with the naked eye. What, then, is this phenotype of autism that shows itself across such distinct clinical presentations and heterogeneous developments? The “signs” seem notoriously slippery and resistant to the behavioral threshold categories that make up current assessment tools. Part of the problem is that cognitive and behavioral “abilities” typically are theorized as high-level disembodied and modular functions—that (...) are assessed discretely (impaired, normal, enhanced) to define a spectral syndrome. Even as biology reminds us that organic developing bodies are not made up of independent switches, we remain often seduced by the simplicity of mechanistic and cognitive models. Developmental disorders such as autism have accordingly been theorized as due to different modular dysfunctions—typically of cortical origin, i.e., failures of “theory of mind” (Baron-Cohen et al., 1985), of the “mirror neuron system” (Ramachandran and Oberman, 2006), of “weak central coherence” (Happe and Frith, 2006) or of the balance of “empathizing” and “systemizing” (Baron-Cohen, 2009), just to list a few. -/- The broad array of autonomic (Ming et al., 2005; Cheshire, 2012) and sensorimotor (Damasio and Maurer, 1978; Maurer and Damasio, 1982; Donnellan and Leary, 1995; Leary and Hill, 1996; Donnellan and Leary, 2012; Donnellan et al., 2012) differences experienced and reported by people with autism have by such theories typically been sidelined as “co-morbidities,” possibly sharing genetic causes, but rendered as incidental and decisively behaviorally irrelevant symptoms—surely disconnected from cognition. But what if the development of cortically based mental processes and autonomous control relies on the complexities and proper function of the peripheral nervous systems? Through such an “embodied” lens the heterogeneous symptoms of autism invites new interpretations. We propose here that many behavioral-level findings can be re-defined as downstream effects of how developing nervous systems attempt to cope and adapt to the challenges of having various noisy, unpredictable, and unreliable peripheral inputs. (shrink)

Objective: This study aimed to investigate whether galvanic vestibular stimulation with stochastic noise modulates the body sway and muscle activity of the lower limbs, depending on visual and somatosensory information from the foot using rubber-foam.Methods: Seventeen healthy young adults participated in the study. Each subject maintained an upright standing position on a force plate with/without rubber-foam, with their eyes open/closed, to measure the position of their foot center of pressure. Thirty minutes after baseline measurements under four possible conditions (...) performed without nGVS, the stimulation trials were conducted under the same conditions in random order, which were then repeated a week or more later. The total center of pressure path length movement and COP movement velocity in the mediolateral and anteroposterior directions were recorded for 30 s during nGVS. Furthermore, electromyography activity of the right tibial anterior muscle and soleus muscle was recorded for the same time and analyzed.Results: Three-way analysis of variance and post-hoc multiple comparison revealed a significant increment in COP-related parameters by nGVS, and a significant increment in soleus muscle activity on rubber. There was no significant effect of eye condition on any parameter.Conclusions: During nGVS, body sway and muscle activity in the lower limb may be increased depending not on the visual condition, but on the foot somatosensory condition. (shrink)

There is a widespread attitude in epistemology that, if you know on the basis of perception, then you couldn't have been wrong as a matter of chance. Despite the apparent intuitive plausibility of this attitude, which I'll refer to here as “stochastic infallibilism”, it fundamentally misunderstands the way that human perceptual systems actually work. Perhaps the most important lesson of signal detection theory (SDT) is that our percepts are inherently subject to random error, and here I'll highlight some key (...) empirical research that underscores this point. In doing so, it becomes clear that we are in fact quite willing to attribute knowledge to S that p even when S's perceptual belief that p could have been randomly false. In short, perceptual processes can randomly fail, and perceptual knowledge is stochastically fallible. The narrow implication here is that any epistemological account that entails stochastic infallibilism, like safety, is simply untenable. More broadly, this myth of stochastic infallibilism provides a valuable illustration of the importance of integrating empirical findings into epistemological thinking. (shrink)

Graphical AbstractRecent waves of controversies surrounding genetic engineering have spilled into popular science in Twitter battles between reputable scientists and their followers. Here, a cautionary perspective on the possible blind spots and risks of CRISPR and related biotechnologies is presented, focusing in particular on the stochastic nature of cellular control processes.

Stochastic developmental variation is an additional important source of variance – beyond genes and environment – that should be included in considering how our innate psychological predispositions may interact with environment and experience, in a culture-dependent manner, to ultimately shape patterns of human behaviour.

Random-excitation granule cells are likely to overwhelm spatiotemporal sequences described as in Braitenberg et al.'s target article. A mechanism is proposed involving the Golgi cells to reinforce tidal waves against noise. The recurrent inhibition by the Golgi calls can recruit random excitations of granule cells in phase with sequences of mossy fiber input.

The astonishing efficiency and accuracy of DNA replication has long suggested that refined rules enforce a single highly reproducible sequence of molecular events during the process. This view was solidified by early demonstrations that DNA unwinding and synthesis are coupled within a stable molecular factory, known as the replisome, which consists of conserved components that each play unique and complementary roles. However, recent single-molecule observations of replisome dynamics have begun to challenge this view, revealing that replication may not be defined (...) by a uniform sequence of events. Instead, multiple exchange pathways, pauses, and DNA loop types appear to dominate replisome function. These observations suggest we must rethink our fundamental assumptions and acknowledge that each replication cycle may involve sampling of alternative, sometimes parallel, pathways. Here, we review our current mechanistic understanding of DNA replication while highlighting findings that exemplify multi-pathway aspects of replisome function and considering the broader implications. Recent single-molecule studies have revealed that replisome function is dominated by stochastic sampling of multiple molecular pathways. In the context of these new findings, we re-examine the foundational assumptions and seminal experiments that have guided our understanding of replication mechanism and reconcile several long-debated coordination models. (shrink)

We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein–Langevin equation. Once (...) the thermal Green's function in a Schwarzschild background becomes available to the required accuracy, the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories. (shrink)

The poor denoising effect for noisy grayscale images with traditional processing methods would be obtained under strong noise condition, and some image details would be lost. In this paper, a parallel array model of Fitzhugh–Nagumo neurons was proposed, which can restore noisy grayscale images well with low peak signal-to-noise ratio conditions and the image details are better preserved. Firstly, the row-column scanning method was used to convert the 2D grayscale image into a 1D signal, and then the 1D (...) signal was converted into a binary pulse amplitude modulation signal by signal modulation. The modulated signal was input to an FHN parallel array for stochastic resonance. Finally, the array output signal was restored to a 2D gray image, and the image restoration effect was analyzed based on the PSNR and Structural SIMilarity index. It is shown that the SR effect can be exhibited in an array of FHN neuron nonlinearities by increasing the array size, and the image restoration effect is significantly better than the traditional image restoration method, and larger PSNR and SSIM can be obtained. It provides a new idea for grayscale image restoration in a low PSNR environment. (shrink)

A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such (...) system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results. (shrink)

Binaural pitch fusion is the perceptual integration of stimuli that evoke different pitches between the ears into a single auditory image. This study was designed to investigate how steady background noise can influence binaural pitch fusion. The binaural fusion ranges, the frequency ranges over which binaural pitch fusion occurred, were measured with three signal-to-noise ratios of the pink noise and compared with those measured in quiet. The preliminary results show that addition of an appropriate amount of (...) class='Hi'>noise can reduce binaural fusion ranges, an effect called stochastic resonance. This finding increases the understanding of how specific noise levels can sharpen binaural pitch fusion in normal hearing individuals. Furthermore, it elicits more pathways for research to explore how this benefit can practically be used to help improve binaural auditory perception. (shrink)

Sex‐determining factors are usually assumed to be either genetic or environmental. The present paper aims at drawing attention to the potential contribution of developmental noise, an important but often‐neglected component of phenotypic variance. Mutual inhibitions between male and female pathways make sex a bistable equilibrium, such that random fluctuations in the expression of genes at the top of the cascade are sufficient to drive individual development toward one or the other stable state. Evolutionary modeling shows that stochastic sex (...) determinants should resist elimination by genetic or environmental sex determinants under ecologically meaningful settings. On the empirical side, many sex‐determination systems traditionally considered as environmental or polygenic actually provide evidence for large components of stochasticity. In reviewing the field, I argue that sex‐determination systems should be considered within a three‐ends continuum, rather than the classical two‐ends continuum. (shrink)

Stochastic dynamical reduction for the case of spin-z measurement of a spin-1/2 particle describes a random walk on the spin-z axis. The measurement’s result depends on which of the two points: spin-z=±ħ/2 is reached first. Born’s rule is recovered as long as the expected step size in spin-z is independent of proximity to endpoints. Here, we address the questions raised by this description: (1) When is collapse triggered, and what triggers it? (2) Why is the expected step size in (...) spin-z (as opposed to polar angle) independent of proximity to endpoints? (3) Why does spin “lock” in the vertical directions? The difficulties associated with (1) are rooted, as is Bell’s theorem, in the time-asymmetric assumption that the present distribution over hidden variables is independent of future settings. We believe, a priori of any of the experiments of modern physics, that such a time-asymmetric assumption is dubious when probing the microscopic scale. As for (2) and (3), they are simultaneously resolved by abandoning the fundamental distinction drawn between spin and spatial angular momentum, and by appealing to very tiny (in both magnitude and spatial extent) but numerous patches of magnetic noise in the Stern-Gerlach’s field. (shrink)

In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability (...) of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations. (shrink)

Industry sustainability plays a vital role in shaping the environment for cultural and creative business development. However, considering the influence of the external environment and random factors on the technical efficiency of cultural and creative industries with the inherent defects of the traditional data envelopment analysis model; this manuscript analyzed the operating efficiency of 56 cultural and creative enterprises using the three-stage DEA model from 2012 to 2018. An analysis of the results shows that differences in efficiency exist between stage (...) one and stage three DEA. Furthermore, the environmental elements and statistical noise measured by the stochastic frontier analysis in stage two reveal positive and negative influences on the creative cultural enterprises at different stages. As a result, the overall efficiency of the listed cultural and creative industries was revealed to be low in China. Finally, this study suggested effective countermeasures and recommendations for better-operating efficiency systems for cultural and creative enterprises. (shrink)

This paper, using the author's decomposition method and recent generalizations, presents algorithms for an analytic solution of the stochastic Navier-Stokes system without linearization, perturbation, discretization, or restrictive assumptions on the nature of stochasticity. The pressure, forces, velocities, and initial/boundary conditions can be stochastic processes and are not limited to white noise. Solutions obtained are physically realistic because of the avoidance of assumptions made purely for mathematical tractability by usual methods. Certain extensions and further generalizations of the decomposition (...) method have provided the basis for the solution. (shrink)

In this paper, we study the asymptotic behavior of solutions to the Kirchhoff type stochastic plate equation driven by additive noise defined on unbounded domains. We first prove the uniform estimates of solutions and then establish the existence and upper semicontinuity of random attractors.

By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of subsystems. We explain how probabilities enter into this process, what quantum and classical probabilities have in common and where exactly their difference lies.

Recent work suggests that people predict how objects interact in a manner consistent with Newtonian physics, but with additional uncertainty. However, the sources of uncertainty have not been examined. In this study, we measure perceptual noise in initial conditions and stochasticity in the physical model used to make predictions. Participants predicted the trajectory of a moving object through occluded motion and bounces, and we compared their behavior to an ideal observer model. We found that human judgments cannot be captured (...) by simple heuristics and must incorporate noisy dynamics. Moreover, these judgments are biased consistently with a prior expectation on object destinations, suggesting that people use simple expectations about outcomes to compensate for uncertainty about their physical models. (shrink)

Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) that persists at zero temperature. The presence of thermal noise, however, could destabilize the protein soliton and dissipate its energy within a finite lifetime. In this work, we have computationally solved the system of (...) stochastic differential equations that govern the quantum dynamics of protein solitons at physiological temperature, T=310 K, for either a single isolated α-helix spine of hydrogen bonded peptide groups or the full protein α-helix comprised of three parallel α-helix spines. The simulated stochastic dynamics revealed that although the thermal noise is detrimental for the single isolated α-helix spine, the cooperative action of three amide I exciton quanta in the full protein α-helix ensures soliton lifetime of over 30 ps, during which the amide I energy could be transported along the entire extent of an 18-nm-long α-helix. Thus, macromolecular protein complexes, which are built up of protein α-helices could harness soliton-assisted energy transport at physiological temperature. Because the hydrolysis of a single adenosine triphosphate molecule is able to initiate three amide I exciton quanta, it is feasible that multiquantal protein solitons subserve a variety of specialized physiological functions in living systems. (shrink)

The Neo‐Darwinian concept of natural selection is plausible when one assumes a straightforward causation of phenotype by genotype. However, such simple 1:1 mapping must now give place to the modern concepts of gene regulatory networks and gene expression noise. Both can, in the absence of genetic mutations, jointly generate a diversity of inheritable randomly occupied phenotypic states that could also serve as a substrate for natural selection. This form of epigenetic dynamics challenges Neo‐Darwinism. It needs to incorporate the non‐linear, (...) stochastic dynamics of gene networks. A first step is to consider the mathematical correspondence between gene regulatory networks and Waddington's metaphoric ‘epigenetic landscape’, which actually represents the quasi‐potential function of global network dynamics. It explains the coexistence of multiple stable phenotypes within one genotype. The landscape's topography with its attractors is shaped by evolution through mutational re‐wiring of regulatory interactions – offering a link between genetic mutation and sudden, broad evolutionary changes. (shrink)

Signalling games are popular models for studying the evolution of meaning, but typical approaches do not incorporate vagueness as a feature of successful signalling. Complementing recent like-minded models, we describe an aggregate population-level dynamic that describes a process of imitation of successful behaviour under imprecise perception and realization of similar stimuli. Applying this new dynamic to a generalization of Lewis’s signalling games, we show that stochastic imprecision leads to vague, yet by-and-large efficient signal use, and, moreover, that it unifies (...) evolutionary outcomes and helps avoid sub-optimal categorization. The upshot of this is that we see ‘as-if’-generalization at an aggregate level, without agents actually generalizing. _1_ Introduction _2_ Background _2.1_ Sim-max games and conceptual spaces _2.2_ Vagueness in sim-max games and conceptual spaces _2.3_ Vagueness, functional pressure, and transmission biases _3_ Imprecise Imitation _3.1_ Replicator dynamic in behavioural strategies _3.2_ Noise-perturbed conditional imitation _4_ Exploring Imprecise Imitation _4.1_ Setting the stage _4.2_ Simulation set-up _4.3_ Measures of interest _4.4_ Results _5_ Discussion _5.1_ Levels of vagueness _5.2_ Evolutionary benefits of imprecision _5.3_ Related work _6_ Conclusion Appendix. (shrink)

Phenotypic plasticity is a crucial feature of aggressive cancer, providing the means for cancer progression. Stochastic changes in tumor cell transcriptional programs increase the chances of survival under any condition. I hypothesize that unstable chromatin permits stochastic transitions between transcriptional programs in aggressive cancers and supports non‐genetic heterogeneity of tumor cells as a basis for their adaptability. I present a mechanistic model for unstable chromatin which includes destabilized nucleosomes, mobile chromatin fibers and random enhancer‐promoter contacts, resulting in (...) class='Hi'>stochastic transcription. I suggest potential markers for “unsettled” chromatin in tumors associated with poor prognosis. Although many of the characteristics of unstable chromatin have been described, they were mostly used to explain changes in the transcription of individual genes. I discuss approaches to evaluate the role of unstable chromatin in non‐genetic tumor cell heterogeneity and suggest using the degree of chromatin instability and transcriptional noise in tumor cells to predict cancer aggressiveness. (shrink)

The suspension system is referred to as the set of springs, shock absorbers, and linkages that connect the car to the wheel system. The main purpose of the suspension system is to provide comfort for the passengers, which is created by reducing the effects of road bumpiness. It is worth noting that reducing the effects of such vibrations also diminishes the noise and undesirable sound as well as the effects of fatigue on mechanical parts of the vehicle. Due to (...) the importance of the abovementioned issues, the objective of this article is to reduce such vibrations on the car by implementing an active control method on the suspension system. For this purpose, a conventional first-order sliding mode controller has been designed for stochastic control of the quarter-car model. It is noteworthy that this controller has a significant ability to overcome the stochastic effects, uncertainty, and deal with nonlinear factors. To design a controller, the governing dynamical equation of the quarter-car system has been presented by considering the nonlinear terms in the springs and shock absorber, as well as taking into account the uncertainty factors in the system and the actuator. The design process of the sliding mode controller has been presented and its stability has been investigated in terms of the Lyapunov stability. In the current research, road surface variations are considered as Gaussian white noise. The dynamical system behavior for controlled and uncontrolled situations has been simulated and the extracted results have been presented. Besides, the effects of existing uncertainty in the suspension system and actuator have been evaluated and controller robustness has been checked. Also, the obtained quantitative and qualitative compressions have been presented. Moreover, the effect of controller parameters on the basin of attraction set and its extensiveness has been assessed. The achieved results have indicated the good performance and significant robustness of the designed controller to stabilize the suspension system and mitigate the effects of road bumpiness in the presence of uncertainty and noise factors. (shrink)

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur, for example, when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study, we investigate how learners handle such situations. We focus on the setting where a learner receives and processes a sequence of utterances to master associations between objects and their (...) labels, where the source is inconsistent by design: It uses both “correct” and “incorrect” object‐label pairings. We hypothesize that depending on the order of presentation, the result of the learning may be different. To this end, we consider two types of symbolic learning procedures: the Object‐Label (OL) and the Label‐Object (LO) process. In the OL process, the learner is first exposed to the object, and then the label. In the LO process, this order is reversed. We perform experiments with human subjects, and also construct a computational model that is based on a nonlinear stochastic reinforcement learning algorithm. It is observed experimentally that OL learners are generally better at processing inconsistent input compared to LO learners. We show that the patterns observed in the learning experiments can be reproduced in the simulations if the model includes (a) an ability to regularize the input (and also to do the opposite, i.e., undermatch) and (b) an ability to take account of implicit negative evidence (i.e., interactions among different objects/labels). The model suggests that while both types of learners utilize implicit negative evidence in a similar way, there is a difference in regularization patterns: OL learners regularize the input, whereas LO learners undermatch. As a result, OL learners are able to form a more consistent system of image‐utterance associations, despite the ambiguous learning task. (shrink)

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor’s power law relationship. We showed that the combined effects of environmental/demographic noises and the scaling (...) of population size variability interact with the population dynamics and affect the mean time to extinction. (shrink)

The process of gene expression is affected by many extracellular stimulus signals, and the stochasticity of these signals reshapes gene expression. To adapt the fluctuation of the extracellular environment, genes have many strategies for augmenting their survival probability, frequency modulation, and amplitude modulation. However, it is unclear how genes utilize the stochasticity of signals to regulate gene expression and which strategy will be chosen to maximize cellular function. Here, we analyze a simple mechanistic model to clarify the effect of extracellular (...) random input on gene expression and burst kinetics at different timescales. We can see that in different contexts, extracellular noise has different effects on downstream gene expression, effects which include the following: extracellular noise will make the ON-OFF-state dwell time drift, which will influence the burst frequency and burst size of downstream gene expression under different modulation paradigms; comparing the burst parameter or gene expression products under different modulation paradigms, we can see that the amplitude signal is more sensitive in the case of extracellular noise input, whereas the signal in noiseless conditions is more sensitive when the random input is a fast process, which indicates that the amplitude signal is a superior and common signal in gene expression; and extracellular random input will change the bimodality for gene expression, but its influence is different for gene expression products under different modulation paradigms. These qualitative results reveal that extracellular random input can prompt the gene to achieve its function quickly under different modulation paradigms. (shrink)

The current rise of neurodevelopmental disorders poses a critical need to detect risk early in order to rapidly intervene. One of the tools pediatricians use to track development is the standard growth chart. The growth charts are somewhat limited in predicting possible neurodevelopmental issues. They rely on linear models and assumptions of normality for physical growth data – obscuring key statistical information about possible neurodevelopmental risk in growth data that actually has accelerated, non-linear rates-of-change and variability encompassing skewed distributions. Here, (...) we use new analytics to profile growth data from 36 newborn babies that were tracked longitudinally for 5 months. By switching to incremental (velocity-based) growth charts and combining these dynamic changes with underlying fluctuations in motor performance – as the transition from spontaneous random noise to a systematic signal – we demonstrate a method to detect very early stunting in the development of voluntary neuromotor control and to flag risk of neurodevelopmental derail. (shrink)

Fluorescence microscopy is the primary tool for studying complex processes inside individual living cells. Technical advances in both molecular biology and microscopy have made it possible to image cells from many genetic and environmental backgrounds. These images contain a vast amount of information, which is often hidden behind various sources of noise, convoluted with other information and stochastic in nature. Accessing the desired biological information therefore requires new tools of computational image analysis and modeling. Here, we review some (...) of the recent advances in computational analysis of images obtained from fluorescence microscopy, focusing on bacterial systems. We emphasize techniques that are readily available to molecular and cell biologists but also point out examples where problem‐specific image analyses are necessary. Thus, image analysis is not only a toolkit to be applied to new images but also an integral part of the design and implementation of a microscopy experiment. (shrink)

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and Uncertainty 5:297–323, (...) 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects. (shrink)

A new realislic local model of light propagation and detection is described. The authors propose a novel stochastic model of low-intensity photon detection in which background noise is added to a part of the photon prior to absorption. In this model, in agreement with Planck, there is no quantization of the propagating field. The model has some similarities to theories advanced by E. Santos and T. Marshall in the last decade, but also has substantial deviations from these. A (...) mechanism, conserving energy and momentum, is proposed by which a sudden collapse of the wave-packet is avoided. The experimental Bell inequality violation of Aspect. Grangier and Roger [Phys. Rev. Lett.47, 460 (1981)]is discussed. The authors have carried out a computer simulation of a radio frequency (RF) analogue of the Einstein-Podolsky-Rosen thought experiment to illustrate how the manipulation of certain factors, especially signal to noise ratio, detector threshold and characteristics of the noise, enables the same Bell inequality to be either satisfied or violated by a realistic local model. Building on arguments by Santos. [Phys. Rev. A46. 3646 (1992)],the appropriateness of this Bell lest is discussed. Neither the authors' stochastic-optical model, nor their RF analogue, involves an enhancement assumption of the type defined by Clauser and Horne [Phys. Rev. D10, 526 (1974)]. (shrink)

We give a partial answer to the question whether the Schrödinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrödinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of Nelson’s (...) stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables. The main motivation of this paper is to provide a step for constructing a Newtonian theory which would approximately reproduce quantum mechanics both in unitary evolution and measurement regimes. (shrink)

This paper considers observer design for discrete-time descriptor systems with packet losses. By taking packet loss into consideration, the error dynamic of the proposed observer becomes a stochastic switched system. Consequently, the proposed observer is synthesized in a stochastic switched system framework. Sufficient conditions for the stochastic stability with a prescribed robust performance of the error dynamic system are derived and converted into linear matrix inequalities. Not only can the proposed observer deal with packet losses, but it (...) also attenuates the effect of process disturbance and measurement noise. A numerical simulation of a truck-trailer is given to demonstrate the effectiveness of the proposed method. (shrink)