Optimal Stabilization of Linear Stochastic System with Statistically Uncertain Piecewise Constant Drift

The paper presents an optimal control problem for the partially observable stochastic differential system driven by an external Markov jump process. The available controlled observations are indirect and corrupted by some Wiener noise. The goal is to optimize a linear function of the state (output) given a general quadratic criterion. The separation principle, verified for the system at hand, allows examination of the control problem apart from the filter optimization. The solution to the latter problem is provided by the Wonham filter. The solution to the former control problem is obtained by formulating an equivalent control problem with a linear drift/nonlinear diffusion stochastic process and with complete information. This problem, in turn, is immediately solved by the application of the dynamic programming method. The applicability of the obtained theoretical results is illustrated by a numerical example, where an optimal amplification/stabilization problem is solved for an unstable externally controlled step-wise mechanical actuator.

Mean square displacement for a discrete centroid model of cell motion

The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.

Categorical Functional Data Analysis. The cfda R Package

Categorical functional data represented by paths of a stochastic jump process with continuous time and a finite set of states are considered. As an extension of the multiple correspondence analysis to an infinite set of variables, optimal encodings of states over time are approximated using an arbitrary finite basis of functions. This allows dimension reduction, optimal representation, and visualisation of data in lower dimensional spaces. The methodology is implemented in the cfda R package and is illustrated using a real data set in the clustering framework.

Description of Colombian Electricity Pricing Derivatives

Electricity markets are becoming a popular field of research amongst academics because of the lack of appropriate models for describing electricity price behavior and pricing derivatives instruments. Models for price dynamics must consider seasonality and spiky behavior of jumps which seem hard to model by standard jump process. Without good models for electricity price dynamics, it is difficult to think about good models for futures, forward, swaps and option pricing. In this paper we attempt to introduce an algorithm for pricing derivatives to intuition from Colombian electricity market. The main ambition of this study is fourfold: 1) First we begin our approach through to simple stochastic models for electricity pricing. 2) Next, we derive analytical formulas for prices of electricity derivatives with different derivatives tools. 3) Then we extent short of the model for price risk in the electricity spot market 4) Finally we construct the model estimation under the physical measures for Colombian electricity market. And this paper end with conclusion.

Bayesian inference for continuous-time hidden Markov models with an unknown number of states

We consider the modeling of data generated by a latent continuous-time Markov jump process with a state space of finite but unknown dimensions. Typically in such models, the number of states has to be pre-specified, and Bayesian inference for a fixed number of states has not been studied until recently. In addition, although approaches to address the problem for discrete-time models have been developed, no method has been successfully implemented for the continuous-time case. We focus on reversible jump Markov chain Monte Carlo which allows the trans-dimensional move among different numbers of states in order to perform Bayesian inference for the unknown number of states. Specifically, we propose an efficient split-combine move which can facilitate the exploration of the parameter space, and demonstrate that it can be implemented effectively at scale. Subsequently, we extend this algorithm to the context of model-based clustering, allowing numbers of states and clusters both determined during the analysis. The model formulation, inference methodology, and associated algorithm are illustrated by simulation studies. Finally, we apply this method to real data from a Canadian healthcare system in Quebec.

Palmitic acid sophorolipid biosurfactant: from self-assembled fibrillar network (SAFiN) to hydrogels with fast recovery

Nanofibres are an interesting phase into which amphiphilic molecules can self-assemble. Described for a large number of synthetic lipids, they were seldom reported for natural lipids like microbial amphiphiles, known as biosurfactants. In this work, we show that the palmitic acid congener of sophorolipids (SLC16:0), one of the most studied families of biosurfactants, spontaneously forms a self-assembled fibre network (SAFiN) at pH below 6 through a pH jump process. pH-resolved in situ small-angle X-ray scattering (SAXS) shows a continuous micelle-to-fibre transition, characterized by an enhanced core–shell contrast between pH 9 and pH 7 and micellar fusion into a flat membrane between pH 7 and pH 6, approximately. Below pH 6, homogeneous, infinitely long nanofibres form by peeling off the membranes. Eventually, the nanofibre network spontaneously forms a thixotropic hydrogel with fast recovery rates after applying an oscillatory strain amplitude out of the linear viscoelastic regime: after being submitted to strain amplitudes during 5 min, the hydrogel recovers about 80% and 100% of its initial elastic modulus after, respectively, 20 s and 10 min. Finally, the strength of the hydrogel depends on the medium's final pH, with an elastic modulus fivefold higher at pH 3 than at pH 6. This article is part of the theme issue ‘Bio-derived and bioinspired sustainable advanced materials for emerging technologies (part 1)’.

Heavy-tailed distributions in a stochastic gene autoregulation model

Synthesis of gene products in bursts of multiple molecular copies is an important source of gene expression variability. This paper studies large deviations in a Markovian drift--jump process that combines exponentially distributed bursts with deterministic degradation. Large deviations occur as a cumulative effect of many bursts (as in diffusion) or, if the model includes negative feedback in burst size, in a single big jump. The latter possibility requires a modification in the WKB solution in the tail region. The main result of the paper is the construction, via a modified WKB scheme, of matched asymptotic approximations to the stationary distribution of the drift--jump process. The stationary distribution possesses a heavier tail than predicted by a routine application of the scheme.

Deciphering the Structural Characterization, Hirshfeld Surface Analysis, Raman Studies, and Temperature-Dependent Magnetodielectric Properties of BiMn2O5

We investigate the structural, Hirshfeld surface, magnetic, and magnetodielectric properties of BiMn2O5. The sample can be indexed with an orthorhombic phase associated with space group Pbam, with crystallographic parameters a = 7.54946 Å, b = 8.54962 Å and c = 5.753627 Å. The Hirshfeld surface analysis, associated with 2D fingerprint plots, was used to visualize and explore the significant intermolecular interactions in the crystal structure quantitatively. The Raman spectra, measured from 6 to 300 K in a frequency range between 250 and 750 cm−1, exhibit good agreement between the SHELL model calculations and the experimental measurement of the proximity of the phonon frequencies for our sample. Furthermore, magnetic measurements show that BiMn2O5 becomes antiferromagnetic below the Néel temperature (TN)—the temperature above which an antiferromagnetic material becomes paramagnetic (TN = 31 K). The relaxation at intermediate temperatures (200–300 K) can be attributed to the polar jump process at two charge transfer sites between the Mn3+ and Mn4+ ions, which, in combination with the special arrangement of the Mn3+/Mn4+ ions, is likely to produce the strong intrinsic magnetodielectric effect (MD) in the same temperature range.