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Many natural phenomena exhibit a stochastic nature that one attempts at modeling by using stochastic processes of different types. In this context, often one is interested in investigating the memory properties of the natural phenomenon at hand. This is usually accomplished by computing the autocorrelation function of the numerical series describing the considered phenomenon. Often, especially when considering real world data, the autocorrelation function must be computed starting from a single numerical series: i.e. with a time-average approach. Hereafter, we will propose a novel way of evaluating the time-average autocorrelation function, based on the preliminary evaluation of the quantity N({\tau},g{\mu},g{\nu}), that, apart from normalization factors, represents a numerical estimate, based on a single realization of the process, of the 2-point joint probability density function P(x2,{\tau};x1,0). The main advantage of the proposed method is that it allows to quantitatively assess what is the error that one makes when numerically evaluating the autocorrelation function due to the fact that any simulated time series is necessarily bounded. In fact, we show that, for a wide class of stochastic processes admitting a nonlinear Langevin equation with white noise and that can be described by using a Fokker-Planck equation, the way the numerical estimate of the autocorrelation function converges to its theoretical prediction depends on the pdf tails. Moreover, the knowledge of N({\tau},g{\mu},g{\nu}) allows to easily compute the process histogram and to characterize processes with multiple timescales. We will show the effectiveness of our new methodology by considering three stochastic processes whose autocorrelation function and two-point probability density function are both known in an analytical or numerical form, thus allowing direct comparisons., Comment: 15 ages, 3 tables, 4 figures

Drug resistance mediated by clonal evolution is arguably the biggest problem in cancer therapy today. However, evolving resistance to one drug may come at a cost of decreased fecundity or increased sensitivity to another drug. These evolutionary trade-offs can be exploited using ‘evolutionary steering’ to control the tumour population and delay resistance. However, recapitulating cancer evolutionary dynamics experimentally remains challenging. Here, we present an approach for evolutionary steering based on a combination of single-cell barcoding, large populations of 108–109 cells grown without re-plating, longitudinal non-destructive monitoring of cancer clones, and mathematical modelling of tumour evolution. We demonstrate evolutionary steering in a lung cancer model, showing that it shifts the clonal composition of the tumour in our favour, leading to collateral sensitivity and proliferative costs. Genomic profiling revealed some of the mechanisms that drive evolved sensitivity. This approach allows modelling evolutionary steering strategies that can potentially control treatment resistance., Evolutionary steering uses therapies to control tumour evolution by exploiting trade-offs. Here, using a barcoding approach applied to large cell populations, the authors explore evolutionary steering in lung cancer cells treated with EGFR inhibitors.

In recent years complex networks have been identified as powerful mathematical frameworks for the adequate modeling of many applied problems in disparate research fields. Assuming a Master Equation (ME) modeling the exchange of information within the network, we set up a perturbative approach in order to investigate how node alterations impact on the network information flow. The main assumption of the perturbed ME (pME) model is that the simultaneous presence of multiple node alterations causes more or less intense network frailties depending on the specific features of the perturbation. In this perspective the collective behavior of a set of molecular alterations on a gene network is a particularly adapt scenario for a first application of the proposed method, since most diseases are neither related to a single mutation nor to an established set of molecular alterations. Therefore, after characterizing the method numerically, we applied as a proof of principle the pME approach to breast cancer (BC) somatic mutation data downloaded from Cancer Genome Atlas (TCGA) database. For each patient we measured the network frailness of over 90 significant subnetworks of the protein-protein interaction network, where each perturbation was defined by patient-specific somatic mutations. Interestingly the frailness measures depend on the position of the alterations on the gene network more than on their amount, unlike most traditional enrichment scores. In particular low-degree mutations play an important role in causing high frailness measures. The potential applicability of the proposed method is wide and suggests future development in the control theory context.

This paper focuses on the control of microgrids where both gas and electricity are provided to the final customer, i.e., multi-carrier microgrids. Hence, these microgrids include thermal and electrical loads, renewable energy sources, energy storage systems, heat pumps, and combined heat and power units. The parameters characterizing the multi-carrier microgrid are subject to several disturbances, such as fluctuations in the provision of renewable energy, variability in the electrical and thermal demand, and uncertainties in the electricity and gas pricing. With the aim of accounting for the data uncertainties in the microgrid, we propose a Robust Model Predictive Control (RMPC) approach whose goal is to minimize the total economical cost, while satisfying comfort and energy requests of the final users. In the related literature various RMPC approaches have been proposed, focusing either on electrical or on thermal microgrids. Only a few contributions have addressed the robust control of multi-carrier microgrids. Consequently, we propose an innovative RMPC algorithm that employs on an uncertainty set-based method and that can provide better performance compared with deterministic model predictive controllers applied to multi-carrier microgrids. With the aim of mitigating the conservativeness of the approach, we define suitable robustness factors and we investigate the effects of such factors on the robustness of the solution against variations of the uncertain parameters. We show the effectiveness of the proposed RMPC approach by applying it to a realistic residential multi-carrier microgrid and comparing the obtained results with the ones of a baseline robust method. Postprint accepted for publication in IEEE Transactions on Automation Science and Engineering (T-ASE). How to cite: R. Carli, G. Cavone, T. Pippia, B. De Schutter, and M. Dotoli, ”Robust Optimal Control for Demand Side Management of Multi-Carrier Microgrids,” IEEE Transactions on Automation Science and Engineering, vol. 19, no. 3, pp. 1338-1351, July 2022. DOI: https://doi.org/10.1109/TASE.2022.3148856

This article deals with distributed control of microgrids composed of storages, generators, renewable energy sources, and critical and controllable loads. We consider a stochastic formulation of the optimal control problem associated with the microgrid that appropriately takes into account the unpredictable nature of the power generated by renewables. The resulting problem is a mixed-integer linear program and is NP-hard and nonconvex. Moreover, the peculiarity of the considered framework is that no central unit can be used to perform the optimization, but rather the units must cooperate with each other by means of neighboring communication. To solve the problem, we resort to a distributed methodology based on a primal decomposition approach. The resulting algorithm is able to compute high-quality feasible solutions to a two-stage stochastic optimization problem, for which we also provide a theoretical upper bound on the constraint violation. Finally, a Monte Carlo numerical computation on a scenario with a large number of devices shows the efficacy of the proposed distributed control approach. The numerical experiments are performed on realistic scenarios obtained from Generative Adversarial Networks (GANs) trained an open-source historical dataset of the EU.

This article proposes a stochastic nonlinear model predictive controller to support policymakers in determining robust optimal nonpharmaceutical strategies to tackle the COVID-19 pandemic waves. First, a time-varying SIRCQTHE epidemiological model is defined to get predictions on the pandemic dynamics. A stochastic model predictive control problem is then formulated to select the necessary control actions (i.e., restrictions on the mobility for different socioeconomic categories) to minimize the socioeconomic costs. In particular, considering the uncertainty characterizing this decision-making process, we ensure that the capacity of the healthcare system is not violated in accordance with a chance constraint approach. The effectiveness of the presented method in properly supporting the definition of diversified nonpharmaceutical strategies for tackling the COVID-19 spread is tested on the network of Italian regions using real data. The proposed approach can be easily extended to cope with other countries' characteristics and different levels of the spatial scale. IEEE

Background and objectives: Epidemiological models of epidemic spread are an essential tool for optimizing decision-making. The current literature is very extensive and covers a wide variety of deterministic and stochastic models. However, with the increase in computing resources, new, more general, and flexible procedures based on simulation models can assess the effectiveness of measures and quantify the current state of the epidemic. This paper illustrates the potential of this approach to build a new dynamic probabilistic model to estimate the prevalence of SARS-CoV-2 infections in different compartments. Methods: We propose a new probabilistic model in which, for the first time in the epidemic literature, parameter learning is carried out using gradient-free stochastic black-box optimization techniques simulating multiple trajectories of the infection dynamics in a general way, solving an inverse problem that is defined employing the daily information from mortality records. Results: After the application of the new proposal in Spain in the first and successive waves, the result of the model confirms the accuracy to estimate the seroprevalence and allows us to know the real dynamics of the pandemic a posteriori to assess the impact of epidemiological measures by the Spanish government and to plan more efficiently the subsequent decisions with the prior knowledge obtained. Conclusions:The model results allow us to estimate the daily patterns of COVID-19 infections in Spain retrospectively and examine the population’s exposure to the virus dynamically in contrast to seroprevalence surveys. Furthermore, given the flexibility of our simulation framework, we can model situations —even using non-parametric distributions between the different compartments in the model— that other models in the existing literature cannot. Our general optimization strategy remains valid in these cases, and we can easily create other non-standard simulation epidemic models that incorporate more complex and dynamic structures This work has received financial support from the Spanish Ministry of Science, Innovation, and Universities under Grant RTI2018-099646-B-I00, the Consellería de Educación, Universidade e Formación Profesional and the European Regional Development Fund under Grant ED431G-2019/04 SI

We investigate the constructive role of an external noise signal, in the form of a low-rate Poisson sequence of pulses supplied to all inputs of a spiking neural network, consisting in maintaining for a long time or even recovering a memory trace (engram) of the image without its direct renewal (or rewriting). In particular, this unique dynamic property is demonstrated in a single-layer spiking neural network consisting of simple integrate-and-fire neurons and memristive synaptic weights. This is carried out by preserving and even fine-tuning the conductance values of memristors in terms of dynamic plasticity, specifically spike-timing-dependent plasticity-type, driven by overlapping pre- and postsynaptic voltage spikes. It has been shown that the weights can be to a certain extent unreliable, due to such characteristics as the limited retention time of resistive state or the variation of switching voltages. Such a noise-assisted persistence of memory, on one hand, could be a prototypical mechanism in a biological nervous system and, on the other hand, brings one step closer to the possibility of building reliable spiking neural networks composed of unreliable analog elements.

The paper deals with the evaluation of the Expected Shortfall or the Conditional Value-at-Risk for the makespan in scheduling problems represented as temporal activity networks where we assume that only a type-1 fuzzy representation for the activity integer valued durations is known to the scheduler. More precisely, we address the evaluation of the Expected Shortfall associated to a feasible schedule, and we extend the approach recently proposed for the case of interval valued durations. We develop and analyze a suitable computational method to obtain the fuzzy evaluation of the Expected Shortfall of the makespan of a given schedule. The proposed method enables to use the Expected Shortfall as quality criterion for wide classes of scheduling approaches considering risk-aversion in different practical contexts when only a fuzzy representation of activity durations is known.

In this article, we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and the objective function can be nonsmooth. The general algorithm consists of two main steps: a consensus step and an update on a single block of the optimization variable, which is then broadcast to neighbors. Three special instances of the proposed method, involving particular problem structures, are then presented. In the general case, the convergence of a dynamic consensus algorithm over random row stochastic matrices is shown. Then, the convergence of the proposed algorithm to the optimal cost is proven in expected value. Exact convergence is achieved when using diminishing (local) stepsizes, whereas approximate convergence is attained when constant stepsizes are employed. The convergence rate is shown to be sublinear and an explicit rate is provided in the case of constant stepsizes. Finally, the algorithm is tested on a distributed classification problem, first on synthetic data and, then, on a real, high-dimensional, text dataset.

In this work we propose an index to estimate the gut microbiota biodiversity using a modeling approach with the aim of describing its relationship with health and aging. The gut microbiota, a complex ecosystem that links nutrition and metabolism, has a pervasive effect on all body organs and systems, undergoes profound changes with age and life-style, and substantially contributes to the pathogenesis of age-related diseases. For these reasons, the gut microbiota is a suitable candidate for assessing and quantifying healthy aging, i.e. the capability of individuals to reach an advanced age, avoiding or postponing major age-related diseases. The importance of the gut microbiota in health and aging has been proven to be related not only to its taxonomic composition, but also to its ecological properties, namely its biodiversity. Following an ecological approach, here we intended to characterize the relationship between the gut microbiota biodiversity and healthy aging through the development a parsimonious model of gut microbiota from which biodiversity can be estimated. We analysed publicly available metagenomic data relative to subjects of different ages, countries, nutritional habits and health status and we showed that a hybrid niche-neutral model well describes the observed patterns of bacterial relative abundance. Moreover, starting from such ecological modeling, we derived an estimate of the gut microbiota biodiversity that is consistent with classical indices, while having a higher statistical power. This allowed us to unveil an increase of the gut microbiota biodiversity during aging and to provide a good predictor of health status in old age, dependent on life-style and aging disorders.

The spatial organization of chromosomes has key functional roles, yet how chromosomes fold remains poorly understood at the single-molecule level. Here, we employ models of polymer physics to investigate DNA loci in human HCT116 and IMR90 wild-type and cohesin depleted cells. Model predictions on single-molecule structures are validated against single-cell imaging data, providing evidence that chromosomal architecture is controlled by a thermodynamics mechanism of polymer phase separation whereby chromatin self-assembles in segregated globules by combinatorial interactions of chromatin factors that include CTCF and cohesin. The thermodynamics degeneracy of single-molecule conformations results in broad structural and temporal variability of TAD-like contact patterns. Globules establish stable environments where specific contacts are highly favored over stochastic encounters. Cohesin depletion reverses phase separation into randomly folded states, erasing average interaction patterns. Overall, globule phase separation appears to be a robust yet reversible mechanism of chromatin organization where stochasticity and specificity coexist., The molecular and physical mechanisms underlying chromatin folding at the single DNA molecule level remain poorly understood. Here, the authors use polymer modeling to investigate the conformations of two 2Mb-wide DNA loci in normal and cohesin depleted cells, and provide evidence that the architecture of the studied loci is controlled by a thermodynamics mechanism of polymer phase separation whereby chromatin self-assembles in segregated globules.

The statistical properties of human mobility have been studied in the framework of complex systems physics. Taking advantage of the new datasets made available by the information and communication technologies, the distributions of mobility path lengths and of trip durations have been considered to discover the fingerprints of complexity characters, but the role of the different transportation means on the statistical properties of urban mobility has not been studied in depth. In this paper, we cope with the problem of the existence of universal features for pedestrian, bike and vehicular urban mobility. In particular, we propose the use of travel time as the universal energy for the mobility and we define a simple survival model that explains the travel time distribution of the different mobility types. The analysis is performed in the metropolitan area of Bologna (Italy), where GPS datasets were available on individual trips using different transport means. Our results could be helpful for the realization of multimodal sustainable mobility in future cities, compatible with the citizen’s propensities to use different transport means.

Background High-frequency transcranial random noise stimulation (hf-tRNS) is a neuromodulatory technique consisting of the application of alternating current at random intensities and frequencies. hf-tRNS induces random neural activity in the system that may boost the sensitivity of neurons to weak inputs. Stochastic resonance is a nonlinear phenomenon whereby the addition of an optimal amount of noise results in performance enhancement, whereas further noise increments impair signal detection or discrimination. Objective The aim of the study was to assess whether modulatory effects of hf-tRNS rely on the stochastic resonance phenomenon, and what is the specific neural mechanism producing stochastic resonance. Method Observers performed a two-interval forced choice motion direction discrimination task in which they had to report whether two moving patches presented in two temporal intervals had the same or different motion directions. hf-tRNS was administered at five intensity levels (0.5, 0.75, 1.0, 1.5, and 2.25 mA). Results The results showed a significant improvement in performance when hf-tRNS was applied at 1.5 mA, representing the optimal level of external noise. However, stimulation intensity at 2.25 mA significantly impaired direction discrimination performance. An equivalent noise (EN) analysis, used to assess how hf-tRNS modulates the mechanisms underlying global motion processing, showed an increment in motion signal integration with the optimal current intensity, but reduced motion signal integration at 2.25 mA. Conclusion These results indicate that hf-tRNS-induced noise modulates neural signal-to-noise ratio in a way that is compatible with the stochastic resonance phenomenon.

Battery energy storage systems are widely recognized as viable means for providing frequency regulation in electrical systems characterized by the massive deployment of renewable resources. In this case, the estimation of the battery lifetime is very complex since its response depends strongly on the stochastic nature of various contingencies. By starting from the characterization of the power system frequency in terms of the stochastic process, in this paper, tools needed for the battery lifetime estimation are detailed. On the basis of a realistic dynamic model, the state of charge profile requested to a battery providing primary frequency regulation is derived, with the aim of characterizing statistically its degradation. In this way, it is expected to obtain an efficient battery lifetime estimation compared to the heuristic methods. Numerical simulations are carried out in the last part of the paper, illustrating a simulation tool for the estimation of the battery working cycle. © 2018 IEEE.

Given the relevance of stochastic modelling in supply chain analysis and the advances in queuing theory in different subject fields (such as in-plant manufacturing systems), the present paper deals with the application of a Bernoulli model to the simple but representative (and frequently cited) case of a single-vendor single-buyer supply chain with (s, S)-inventory policy, where the maximum capacity S has to be restored in the intermediate warehouse whenever the inventory position reaches or drops below the reorder point s. An analytical stochastic model is presented which considers two two sources of uncertainty, supply uncertainty and demand uncertainty. The model is analytically formulated and solved in closed-form in order to compute some significant performance measures and, consequently, support tactical decisions (such as the definition of the design parameters s and S). Then, the model setting up is discussed. Specifically, the problem of relating demand and supply probabilities to the behaviour exhibited by the buyer and (particularly) the vendor is addressed. Finally, some numerical results are provided for illustration.

The Gamma process with random scale parameter is often used to describe independent increments degradation phenomena in the presence of random effects. In this paper, a new Markovian degradation process, the Transformed Beta process, is proposed, where the degradation growth depends on both the current age and degradation level. It is also shown that the Transformed Beta process shares the same stochastic properties of the Gamma process whose scale parameter is Gamma-distributed, and that the likelihood functions relative to a given set of degradation data under these two models coincide. Due to this circumstance, it is not possible to choose between these two models on the basis of degradation data alone, even though they rely on quite different assumptions. On the other hand, although these models are stochastically equivalent, there are situations in which selecting the wrong model can produce real practical consequences. In fact, it is shown that, if the considered degrading unit is subjected to a so-called “virtual age imperfect maintenance”, where the current degradation level is assumed to be lowered through an age reduction maintenance model, then these two alternative models provide different condition-based distributions of the degradation growth. Hence, in this latter case, a model misidentification can produce wrong predictions of the degradation growth and wrong estimates of the residual reliability. The discussed issue is illustrated via a numerical application based on a real set of degradation data.

Calibrating parameters is a crucial problem within quantitative modeling approaches to reaction networks. Existing methods for stochastic models rely either on statistical sampling or can only be applied to small systems. Here, we present an inference procedure for stochastic models in equilibrium that is based on a moment matching scheme with optimal weighting and that can be used with high-throughput data like the one collected by flow cytometry. Our method does not require an approximation of the underlying equilibrium probability distribution and, if reaction rate constants have to be learned, the optimal values can be computed by solving a linear system of equations. We discuss important practical issues such as the selection of the moments and evaluate the effectiveness of the proposed approach on three case studies.

Numerical modeling of random magnetization dynamics driven by a jump-noise process is discussed. In the important case of weak thermal effects, random magnetization dynamics is reduced to stochastic processes on graphs and numerical analysis of these processes are outlined.

In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic approaches to the multiscale analysis of complex dynamics are being increasingly used, the theoretical properties of the applied measures are poorly understood. This study introduces for the first time a framework for the analytical computation of information dynamics for linear multivariate stochastic processes explored at different time scales. After showing that the multiscale processing of a vector autoregressive (VAR) process introduces a moving average (MA) component, we describe how to represent the resulting VARMA process using state-space (SS) models and how to exploit the SS model parameters to compute analytical measures of information storage and information transfer for the original and rescaled processes. The framework is then used to quantify multiscale information dynamics for simulated unidirectionally and bidirectionally coupled VAR processes, showing that rescaling may lead to insightful patterns of information storage and transfer but also to potentially misleading behaviors.

The Langevin equation used to model Brownian motion includes a stochastic process that is routinely assumed to be a Gaussian white noise. Spatial correlations of the noise are usually ruled out, and the paths traced by the random walkers are statistically independent. In this study, I consider instead noise which is white in time and has a Gaussian correlation in space, and by means of numerical simulation, I show how the spatial correlation determines the time evolution of the spatial separation of random walkers.

Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic) dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications., In Proceedings HSB 2013, arXiv:1308.5724

Internetworking often requires a large amount of users to share a common gateway to obtain connectivity to the Internet. Congestion avoidance mechanisms are used to prevent the saturation of the gateway which represents a bottleneck of the system. The most popular congestion avoidance mechanisms are the Explicit Congestion Notification (ECN) and the Random Early Detection (RED). Recently, a new method for the congestion avoidance has been proposed: the Smart Access Point with Limited Advertised Window (SAP-LAW). The main idea is to hijack the acknowledge packets in the TCP connections in order to artificially reduce the advertised destination window according to some bandwidth allocation policy. Therefore, the flux control mechanism is artificially exploited to control the congestion at the bottleneck. The advantage of this approach is that it does not require any modification in the TCP implementations at the clients. In this paper, we propose stochastic models for the ECN/RED and SAP-LAW mechanisms in order to compare their performances under different scenarios. The models are studied in mean field regime, i.e., under a great number of TCP connections and UDP based transmissions. Augmenting previous work on ECN/RED, we consider the presence of UDP traffic with bursts, and short lived TCP connections. The models for SAP-LAW are totally new. The comparison is performed in terms of different performance indices including average queue length, system throughput and expected queuing time.

We perform a statistical study of the distances between successive occurrencies of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the dinucleotide CG distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g., fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between dinucleotides CG provides useful insights in characterizing and classifying organisms in terms of methylation functionalities., 13 pages, 5 figures. To be published in the Philosophical Transactions A theme issue "DNA as information"

We investigate the potential impact of accounting for seasonal variations in the climatic forcing and using different methods to parameterize the soil water content at field capacity on the water balance components computed by a bucket model (BM). The single-layer BM of Guswa et al. (2002) is employed, whereas the Richards equation (RE) based Soil Water Atmosphere Plant (SWAP) model is used as a benchmark model. The results are analyzed for two differently-textured soils and for some synthetic runs under real-like seasonal weather conditions, using stochastically-generated daily rainfall data for a period of 100 years. Since transient soil-moisture dynamics and climatic seasonality play a key role in certain zones of the World, such as in Mediterranean land areas, a specific feature of this study is to test the prediction capability of the bucket model under a condition where seasonal variations in rainfall are not in phase with the variations in plant transpiration. Reference is made to a hydrologic year in which we have a rainy period (starting 1 November and lasting 151 days) where vegetation is basically assumed in a dormant stage, followed by a drier and rainless period with a vegetation regrowth phase. Better agreement between BM and RE-SWAP intercomparison results are obtained when BM is parameterized by a field capacity value determined through the drainage method proposed by Romano and Santini (2002). Depending on the vegetation regrowth or dormant seasons, rainfall variability within a season results in transpiration regimes and soil moisture fluctuations with distinctive features. During the vegetation regrowth season, transpiration exerts a key control on soil water budget with respect to rainfall. During the dormant season of vegetation, the precipitation regime becomes an important climate forcing. Simulations also highlight the occurrence of bimodality in the probability distribution of soil moisture during the season when plants are dormant, reflecting that soil, it being of coarser or finer texture, can be preferentially in either wetter or drier states over this period.

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algorithm outperforms the original one for regime switching models of compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one. © 2010 EDP Sciences, Società Italiana di Fisica, Springer-Verlag.

In this paper we study some dynamical features of electricity markets modelling demand and supply by means of a nonlinear cobweb model. We consider a demand function periodically perturbed to take into account the real world seasonalities (daily, weekly and yearly) while supply function can include a stochastic term that is able to encompass possible shocks like outages and plants unavailability. Using adaptive expectations we investigate the effects on equilibrium prices in a perturbed and in an unperturbed model considering peak and off-peak market configurations. The model we propose is based on a well known partial equilibrium model which is used to describe price dynamics of non-storable goods. The novelty we introduce is a sigmoid supply function and a periodically perturbed demand function. Our simulative investigations confirm that the model is able to reproduce several effects observed in real price dynamics. We also focus on how the dynamics can be influenced by altering some market rules set by regulators, like price caps and floors. In particular, we show that taking into account periodical perturbations in the demand function can lead to the anticipation, with respect to the classical model, of chaotic dynamics. Moreover, we study how the dynamic is influenced if negative prices are allowed.

We introduce a variational approximation to the microscopic dynamics of rare conformational transitions of macromolecules. Within this framework it is possible to simulate on a small computer cluster reactions as complex as protein folding, using state of the art all-atom force fields in explicit solvent. We test this method against molecular dynamics (MD) simulations of the folding of an alpha- and a beta-protein performed with the same all-atom force field on the Anton supercomputer. We find that our approach yields results consistent with those of MD simulations, at a computational cost orders of magnitude smaller., Accepted for publication on Phys. Rev. Lett

In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep.

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances., Comment: 21 pages, LaTeX, 3 figures, 6 tables

The analysis of repeated measurements on a biomarker, either alone or jointly with the analysis of time to the event of interest, is an area of active research. Nevertheless, we are not yet able to deal in complete generality with these complex data, which frequently consist of error-prone, sparse and intermittent values. In many cancer studies, they arise in the framework of clinical trials and thus their relationship with prognosis is a primary focus. In such a setting, the Cox model is regarded as the standard technique for analysis. The aim of this work is to illustrate an alternative approach to the analysis of studies in which the biomarker values are complicated by interval censoring and an event occurs when the biomarker itself passes a certain threshold. We propose a linear mixed model with a Gaussian stochastic process that allows for interval-censored data and can be used both to track the biomarker trajectory and to estimate the probability of event occurrence. It is developed within the classic approach to longitudinal data analysis that was previously adapted for left-censored data, only. We apply this method to a study on the minimal residual disease (MRD) in childhood leukaemia. MRD is an interval-censored measurement of residual leukaemic cells that was scheduled at 9 time-points during treatment. The aim is to investigate the relationship between MRD and the disease process. Relapse, the event of interest, may conveniently be represented as MRD over a pre-defined threshold. Our focus is on modelling the probability of relapse conditional on MRD observed prior to it. Results show that the approach is promising as it allows proper description of the data, while maintaining flexibility of modelling, feasibility of computations and interpretability of results.

The amount of cellular proteins is a crucial parameter that is known to vary between cells as a function of the replicative passages, and can be important during physiological aging. The process of protein degradation is known to be performed by a series of enzymatic reactions, ranging from an initial step of protein ubiquitination to their final fragmentation by the protea- some. In this paper we propose a stochastic dynamical model of nuclear proteins concen- tration resulting from a balance between a constant production of proteins and their degradation by a cooperative enzymatic reaction. The predictions of this model are com- pared with experimental data obtained by fluorescence measurements of the amount of nuclear proteins in murine tail fibroblast (MTF) undergoing cellular senescence. Our model provides a three-parameter stationary distribution that is in good agreement with the experi- mental data even during the transition to the senescent state, where the nuclear protein concentration changes abruptly. The estimation of three parameters (cooperativity, satura- tion threshold, and maximal velocity of the reaction), and their evolution during replicative passages shows that only the maximal velocity varies significantly. Based on our modeling we speculate the reduction of functionality of the protein degradation mechanism as a possi- ble competitive inhibition of the proteasome.

The present paper focuses on the analysis of impact pressure registrations from repeated model scale sloshing experiments under harmonic rotational excitation. A series of more than 100 experiments, each one encompassing more than 100 impact events, has been conducted seeking the highest feasible repeatability. Different excitation periods, that cover the main features of the impact dynamics, have been considered in a preliminary screening, describing the main features of the impact dynamics. Since, even under a nominally deterministic excitation, the pressure at each impact is characterized by a high variability, a statistical approach is used treating the impact pressure as a stochastic process. For one selected excitation period, the statistical analysis focuses on the ensemble distribution of the maximum pressure during each impact event. Particular attention is given to the evolution of such distributions, in order to detect the variations in the statistical characteristics of the process. This is achieved by, first, identifying the presence and the length of the transient phase and, second, by characterizing the process at stationary state. The statistics of impact pressure for different peaks are discussed mostly in the ensemble domain. Linking the latter with the time domain analysis is made by checking that the problem can be considered “practically ergodic.” The “practical ergodicity” of the process is dealt with by checking to what extent steady state ensemble statistical information can be obtained from a single long run experiment. Statistical checks for correlation and independence of maximum impact pressures are also carried out to test the hypothesis of independent identically distributed random variables. The method of analysis presented in this paper through the considered example case is general in nature and is considered to be highly portable. In particular, it is considered to allow for a more thorough understanding of non-deterministic events such as those considered herein, by looking at them from a sound statistical perspective. The thorough description of the whole experimental setup makes the presented data suitable for comparison purposes and for validation of theoretical/numerical approaches.

A stochastic modelling of electrochemical battery for their lifetime assessment is proposed and numerically evaluated in smart grids context. The method uses a proper battery model, characterized by stochastic current demand, for deducing the battery lifetime. In particular, a stochastic process for describing the current load is adopted, which is namely described by a proper Poisson stochastic process, appearing suitable to describe random smart grid operations. Extensive numerical experiments have been performed by means of this battery model, in order to fit a proper reliability model to numerical lifetime data. Extensive numerical simulations have been performed by adopting, as model parameter values, those obtained after numerous laboratory tests. Hence, it is shown that the Inverse Gaussian model is the best fitting reliability model.

In a significant proportion of individuals, the expected increase of body sway upon eye closure is not actually observed. This result prefigures different visual contributions to the fine regulation of body sway. The present paper documents a method to classify healthy subjects into one visual or non-visual group according to the fractal properties of center of pressure (COP) profiles. The recognition of the sensory strategy consists of several phases: first, stabilogram diffusion analysis is carried out on the time-series of COP; then, stochastic features are extracted by two models of different complexity. In particular, a new technique is proposed which describes with continuity the transition among different scaling regimes. Finally, a linear classifier is designed. The method gave very high performance classifying, with the best set of features, provided by the two parameters of the new model, 93.3% of the examined subjects in agreement with the preclassification, provided by percentage difference of sway between eyes open and eyes closed conditions and computed over the area of the 95% confidence ellipse. © 2000 Elsevier Science B.V.

The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model.

Self-directed lymphocytes may evade clonal deletion at ontogenesis but still remain harmless due to a mechanism called clonal anergy. For B-lymphocytes, two major explanations for anergy developed over the last decades: according to Varela theory, anergy stems from a proper orchestration of the whole B-repertoire, such that self-reactive clones, due to intensive feed-back from other clones, display strong inertia when mounting a response. Conversely, according to the model of cognate response, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. Through statistical mechanics we show that helpers do not prompt activation of a sub-group of B-cells: remarkably, the latter are just those broadly interacting in the idiotypic network. Hence Varela theory can finally be reabsorbed into the prevailing framework of the cognate response model. Further, we show how the B-repertoire architecture may emerge, where highly connected clones are self-directed as a natural consequence of ontogenetic learning. QC 20150430

Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regime of typical fluctuations by a phase transition where the symmetry between the points in the sample is spontaneously broken. For stochastic processes with a fat tailed microscopic noise, this implies that while typical realizations are well described by a diffusion process with continuous sample paths, large deviation paths are typically discontinuous. For eigenvalues of random matrices with fat tailed distributed elements, a large deviation where the trace of the matrix is anomalously large concentrates on just a single eigenvalue, whereas in the thin tailed world the large deviation affects the whole distribution. These results find a natural application to finance. Since the price dynamics of financial stocks is characterized by fat tailed increments, large fluctuations of stock prices are expected to be realized by discrete jumps. Interestingly, we find that large excursions of prices are more likely realized by continuous drifts rather than by discontinuous jumps. Indeed, auto-correlations suppress the concentration of large deviations. Financial covariance matrices also exhibit an anomalously large eigenvalue, the market mode, as compared to the prediction of random matrix theory. We show that this is explained by a large deviation with excess covariance rather than by one with excess volatility., 38 pages, 12 figures

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch), Autocatalytic cycles are rather widespread in nature and in several theoretical models of catalytic reaction networks their emergence is hypothesized to be inevitable when the network is or becomes sufficiently complex. Nevertheless, the emergence of autocatalytic cycles has been never observed in wet laboratory experiments. Here, we present a novel model of catalytic reaction networks with the explicit goal of filling the gap between theoretical predictions and experimental findings. The model is based on previous study of Kauffman, with new features in the introduction of a stochastic algorithm to describe the dynamics and in the possibility to increase the number of elements and reactions according to the dynamical evolution of the system. Furthermore, the introduction of a temporal threshold allows the detection of cycles even in our context of a stochastic model with asynchronous update. In this study, we describe the model and present results concerning the effect on the overall dynamics of varying (a) the average residence time of the elements in the reactor, (b) both the composition of the firing disk and the concentration of the molecules belonging to it, (c) the composition of the incoming flux.

In the paper some considerations are performed with respect to reliability and quality methodologies applied to transportation systems. These systems have to be considered as large complex systems in which the two aspects are closely related, and which experience fast variations in time, so that a satisfactory description must not disregard dynamic aspects. According to this philosophy, the authors propose an index, also directly oriented to customer satisfaction, which in a global way measures the quality of the system (here meant as “service” quality). This index is defined in a probabilistic way in terms of delay with respect to the scheduled timetable, by properly linking this aspect to the faults occurring in the system under investigation. Such approach allows to connect service quality with system reliability. The advantages of the proposed index are discussed and a numerical application is reported in order to demonstrate the main features of the proposed index, which can be expressed analytically under reasonable hypotheses, and also coincides in one case with an Extreme Value distribution function. Finally, hints at possible adoption of a Bayesian method for its estimation are provided. In the course of the paper, some misconception are highlighted which exist in literature about the interpretation and evaluation of common performance indexes such as failure (or hazard) rate and failure intensity.

Erratum: A Generalized Fourier Transform Approach to Risk Measures

Background Anti-tumor therapies aim at reducing to zero the number of tumor cells in a host within their end or, at least, aim at leaving the patient with a sufficiently small number of tumor cells so that the residual tumor can be eradicated by the immune system. Besides severe side-effects, a key problem of such therapies is finding a suitable scheduling of their administration to the patients. In this paper we study the effect of varying therapy-related parameters on the final outcome of the interplay between a tumor and the immune system. Results This work generalizes our previous study on hybrid models of such an interplay where interleukins are modeled as a continuous variable, and the tumor and the immune system as a discrete-state continuous-time stochastic process. The hybrid model we use is obtained by modifying the corresponding deterministic model, originally proposed by Kirschner and Panetta. We consider Adoptive Cellular Immunotherapies and Interleukin-based therapies, as well as their combination. By asymptotic and transitory analyses of the corresponding deterministic model we find conditions guaranteeing tumor eradication, and we tune the parameters of the hybrid model accordingly. We then perform stochastic simulations of the hybrid model under various therapeutic settings: constant, piece-wise constant or impulsive infusion and daily or weekly delivery schedules. Conclusions Results suggest that, in some cases, the delivery schedule may deeply impact on the therapy-induced tumor eradication time. Indeed, our model suggests that Interleukin-based therapies may not be effective for every patient, and that the piece-wise constant is the most effective delivery to stimulate the immune-response. For Adoptive Cellular Immunotherapies a metronomic delivery seems more effective, as it happens for other anti-angiogenesis therapies and chemotherapies, and the impulsive delivery seems more effective than the piece-wise constant. The expected synergistic effects have been observed when the therapies are combined.

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production \Delta s_tot. One is the entropy production of the medium \Delta s_m, which is equal to the energy exchanged with the scatterers, divided by a parameter \theta, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by \theta. At small E, a good collapse of the two distributions is found: in this case the two quantities also verify the Fluctuation Relation (FR), indicating that both are good approximations of \Delta s_tot. Differently, for large values of E, the fluctuations of W violate the FR, while \Delta s_m still verifies it., Comment: 6 pages, 4 figures

In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at arbitrary time, and we applied it successfully to quadratic and piecewise linear diffusion processes. The ability in reproducing statistical features of financial return time series, such as thickness of the tails and scaling properties, makes this processes appealing for option pricing. Since exact analytical results are missing, we exploit the fast convolution as a numerical method alternative to the Monte Carlo simulation both in objective and risk neutral settings. In numerical sections we document how fast convolution outperforms Monte Carlo both in velocity and efficiency terms., 19 pages, 16 figures

We study the distribution of first return times at a given level L in stationary correlated signals. Our approach makes use of the relation between the characteristic function of the first return probability density function (PDF) and the occupation probability of the state L. In this work we consider a discrete in time and space Ornstein-Uhlenbeck (OU) process with exponential decaying correlation function and then, by a subordination approach, we treat the case of a process with power-law tail correlation function and diverging correlation time. In the first case, by inverting the Laplace transforms we write down an exact analytical expression for the first return time PDF as a function of the level L, while in the second case we obtain the expressions for the first two asymptotic behaviors. In both cases no simple form of the return time statistics like stretched-exponential is obtained.

7 páginas, 8 figuras.-- PACS number(s): 05.40.−a, 05.45.−a, 02.50.Ey, This work analyzes numerically the role played by the asymmetry of a piecewise linear potential, in the presence of both a Gaussian white noise and a dichotomous noise, on the resonant activation phenomenon. The features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum, from the initial well to the bottom of the adjacent potential well. Because of the asymmetry of the potential profile together with the random external force uniform in space, we find, for the different asymmetries: (1) an inversion of the curves of the mean first passage time in the resonant region of the correlation time τ of the dichotomous noise, for low thermal noise intensities; (2) a maximum of the mean velocity of the Brownian particle as a function of τ; and (3) an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated. An inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise, behavior confirmed by recent experiments., The authors acknowledge financial support from Spanish MICINN through Project No. FIS2008- 01240, cofunded by FEDER funds, and the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR).

We present an analytical expression for the first return time (FRT) probability density function of a stationary correlated signal. Precisely, we start by considering a stationary discrete-time Ornstein-Uhlenbeck (OU) process with exponential decaying correlation function. The first return time distribution for this process is derived by adopting a well-known formalism typically used in the study of the FRT statistics for nonstationary diffusive processes. Then, by a subordination approach, we treat the case of a stationary process with power-law tail correlation function and diverging correlation time. We numerically test our findings, obtaining in both cases a good agreement with the analytical results. We notice that neither in the standard OU nor in the subordinated case a simple form of waiting time statistics, like stretched-exponential or similar, can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior.

A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to learn efficiently a generative model of the observed data. We study a "hybrid" version of RBM's, in which hidden units are analog and visible units are binary, and we show that thermodynamics of visible units are equivalent to those of a Hopfield network, in which the N visible units are the neurons and the P hidden units are the learned patterns. We apply the method of stochastic stability to derive the thermodynamics of the model, by considering a formal extension of this technique to the case of multiple sets of stored patterns, which may act as a benchmark for the study of correlated sets. Our results imply that simulating the dynamics of a Hopfield network, requiring the update of N neurons and the storage of N(N-1)/2 synapses, can be accomplished by a hybrid Boltzmann Machine, requiring the update of N+P neurons but the storage of only NP synapses. In addition, the well known glass transition of the Hopfield network has a counterpart in the Boltzmann Machine: It corresponds to an optimum criterion for selecting the relative sizes of the hidden and visible layers, resolving the trade-off between flexibility and generality of the model. The low storage phase of the Hopfield model corresponds to few hidden units and hence a overly constrained RBM, while the spin-glass phase (too many hidden units) corresponds to unconstrained RBM prone to overfitting of the observed data., Comment: 15 pages, 2 figures