Search

SummaryWe propose a new method to estimate the ratio between the basic reproduction numbers of a newly emerged variant and the one currently dominating. We use public data of two kinds: the proportions of the daily infected from each strain obtained from a random sample that has been sequenced, and the epidemic curves of total infections and recoveries. Our method is based on a new discrete-time SIR model with two strains, considered both in the deterministic and stochastic versions. In the deterministic case we use maximum likelihood, while in the stochastic setting, since we need to reconstruct the missing incidence and prevalence information of the new variant, we decided to use a hierarchical Bayesian hidden Markov model. This new methodology is applied to data from the Piedmont Italian region in December-January 2022, when the Omicron variant started to be observed and quickly became prevalent. With both approaches, we obtain an estimate of the contagiousness ratio that is consistent with other studies specifically designed for the aim.

SummaryWe here propose a hierarchical Bayesian model to infer RNA synthesis, processing, and degradation rates from sequencing data, based on an ordinary differential equation system that models the RNA life cycle. We parametrize the latent kinetic rates, that rule the system, with a novel functional form, and estimate their parameters through 6 Dirichlet process mixture models. Owing to the complexity of this approach, we are able to simultaneously perform inference, clustering and model selection. We apply our method to investigate transcriptional and post-transcriptional responses of murine fibroblasts to the activation of proto-oncogene Myc. Our approach uncovers simultaneous regulations of the rates, which had not previously been observed in this biological system.

We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments.

Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior. ¶ In this work, we propose a new model for interpreting the animal movent as a mixture of characteristic patterns, that we interpret as different behaviors. The probability that the animal is behaving according to a specific pattern, at each time instant, is nonparametrically estimated using the Logistic-Gaussian process. Owing to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, our model is invariant with respect to the choice of the reference element and of the ordering of the probability vector components. We fit the model under a Bayesian framework, and show that the Markov chain Monte Carlo algorithm we propose is straightforward to implement. ¶ We perform a simulation study with the aim of showing the ability of the estimation procedure to retrieve the model parameters. We also test the performance of the information criterion we used to select the number of behaviors. The model is then applied to a real dataset where a wolf has been observed before and after procreation. The results are easy to interpret, and clear differences emerge in the two phases.

Several tests that can be used to determine dust explosibility parameters have been presented in the technical and scientific literature to assess the characteristics of a dust sample. Some parameters are countable variables that can be defined by a numerical value (e.g. Pmax, kst), while others define a threshold above (or below) which an explosion should not occur (MIE, LOC, autoignition temperature). The latter parameters should be regarded as limit values at which the probability of occurrence of ignition (or explosion propagation, when LOC or LEL are considered) is low enough to be considered negligible. Technical standards describe the procedures that should be adopted to measure different parameters. The Cloud Autoignition Temperature (AIT) is defined, according to the EN 50281 European standard, as the temperature at which 10 consecutive ignition attempts are negative (no ignition). A similar assumption is made in UNI 13821, where MIE is considered. However, these technical standards do not state what the confidence of the threshold value, as determined by standard procedures, is. The ignition probability at such a threshold is assumed to be zero, but this is considered just an assumption, since the relationship between the probability of occurrence of a studied phenomenon (ignition for example) and the independent variable (the temperature, in the case of AIT) has not yet been established. It is known however that the ignition probability does not change abruptly from 0 to 1 as a step function, but through a smooth slope over a temperature interval (Bibbona et al., 2016). The aim of this work has been to propose a new definition of the autoignition temperature that is based on the ignition probability concept. AIT is defined as the temperature at which the ignition probability is lower than a given threshold. In order to arrive at this definition, the dependence of the cloud Autoignition probability on the temperature in the temperature interval close to AIT needs to be investigated. In the present experiment, Lycopodium and Wood Char were used to carry out the tests. The Ignition probability vs temperature relationship in the range in which the probability varies from zero to one (we have called such a range probability escalation interval, PEI) has been determined and the resulting experimental data have been interpreted by means of an appropriate statistical model. Experimental data can, in fact, be used to identify the threshold below which the ignition probability is lower than a suitably predefined level with prescribed confidence, thus providing a more solid ground on which the definition of the AIT could be based.

COGARCH models are continuous time version of the well known GARCH models of nancial returns. They are solution of a stochastic dierential

In clinical research and in more general classification problems, a frequent concern is the reliability of a rating system. In the absence of a gold standard, agreement may be considered as an indication of reliability. When dealing with categorical data, the well-known kappa statistic is often used to measure agreement. The aim of this paper is to obtain a theoretical result about the asymptotic distribution of the kappa statistic with multiple items, multiple raters, multiple conditions, and multiple rating categories (more than two), based on recent work. The result settles a long lasting quest for the asymptotic variance of the kappa statistic in this situation and allows for the construction of asymptotic confidence intervals. A recent application to clinical endoscopy and to the diagnosis of inflammatory bowel diseases (IBDs) is shortly presented to complement the theoretical perspective.

Parameter estimation in diffusion processes from discrete observations up to a first- passage time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modelled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on a misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein- Uhlenbeck model for biological relevant parameters can be up to 25-100 per cent. We compute or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymp- totic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the mem- brane potential of a motoneuron is analysed

The Ornstein–Uhlenbeck process is presented with its main mathematical properties and with original results on the first crossing times in the case of two threshold barriers. The interpretation of filtered white noise, its stationary spectrum and Allan variance are also presented for ease of use in the time and frequency metrology field. An improved simulation scheme for the evaluation of first passage times between two barriers is also introduced.

Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and the parametrization are gauge covariant and some further conditions are satisfied in order to formulate a Nöther theorem that links horizontal and gauge symmetries to the relative conservation laws (generalizing what Fernández, García and Rodrigo did in some recent papers). The case of vakonomic constraints in field theory is also studied within the framework of parametrized variational problems, defining and comparing two different concepts of criticality of a section, one arising directly from the vakonomic schema, the other making use of an adapted parametrization. The general theory is then applied to the case of hydrodynamics of a charged fluid coupled with its gravitational and electromagnetic field. A variational formulation including conserved currents and superpotentials is given that turns out to be computationally much easier than the standard one.

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process.

Book review of Stochastic Chemical Kinetics. Theory and (Mostly) Systems Biological Applications, P. Erdi, G. Lente. Springer (2014)

In this paper we consider large state space continuous time Markov chains arising in the field of systems biology. For a class of such models, namely, for density dependent families of Markov chains that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations and provides a deterministic approximation, while the other uses a diffusion process with which the resulting approximation is stochastic. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior that cannot be captured by a single deterministic quantity.In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation in order to cover the case when the process reaches the boundary with non-negligible probability. In this paper we generalize the method so that it can be applied to any density dependent Markov chains. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the jump-diffusion approximation only to those components of the model that are in density dependent form and are associated with high population levels. The remaining components are treated as discrete quantities. The resulting process is a hybrid switching jump diffusion, i.e., a diffusion with hybrid state space and jumps where the discrete state changes can be seen as switches that take the diffusion from one condition to another. We show that the stochastic differential equations that characterize this process can be derived automatically both from the description of the original Markov chains or starting from a higher level description language, like stochastic Petri nets. The proposed approach is illustrated on three models: one modeling the so-called crazy clock reaction, one describing viral infection kinetics and the last considering transcription regulation.

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial random walks that are observed until they reach a boundary. Clinical trials are shown to be representable within this scheme and an application to the estimation of the multinomial probabilities following multinomial clinical trials is presented.

We study the estimation of the input parameters in a Feller neuronal model from a trajectory of the membrane potential sampled at discrete times. These input parameters are identified with the drift and the infinitesimal variance of the underlying stochastic diffusion process with multiplicative noise. The state space of the process is restricted from below by an inaccessible boundary. Further, the model is characterized by the presence of an absorbing threshold, the first hitting of which determines the length of each trajectory and which constrains the state space from above. We compare, both in the presence and in the absence of the absorbing threshold, the efficiency of different known estimators. In addition, we propose an estimator for the drift term, which is proved to be more efficient than the others, at least in the explored range of the parameters. The presence of the threshold makes the estimates of the drift term biased, and two methods to correct it are proposed.

Estimation of the input parameters of stochastic (leaky) integrate-and-fire neuronal models is studied. It is shown that the presence of a firing threshold brings a systematic error to the estimation procedure. Analytical formulas for the bias are given for two models, the randomized random walk and the perfect integrator. For the third model considered, the leaky integrate-and-fire model, the study is performed by using Monte Carlo simulated trajectories. The bias is compared with other errors appearing during the estimation, and it is documented that the effect of the bias has to be taken into account in experimental studies.

Starting from a characterization of admissible Cheataev and vakonomic variations in a field theory with constraints we show how the so called parametrized variational calculus can help to derive the vakonomic and the non-holonomic field equations. We present an example in field theory where the non-holonomic method proved to be unphysical.