Modeling and analysis of random and stochastic input flows in the chemostat model

In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (MINECO). EspañaJunta de Andalucí

Bistable forespore engulfment in Bacillus subtilis by a zipper mechanism in absence of the cell wall

To survive starvation, the bacterium Bacillus subtilis forms durable spores. The initial step of sporulation is asymmetric cell division, leading to a large mother-cell and a small forespore compartment. After division is completed and the dividing septum is thinned, the mother cell engulfs the forespore in a slow process based on cell-wall degradation and synthesis. However, recently a new cell-wall independent mechanism was shown to significantly contribute, which can even lead to fast engulfment in $\sim$ 60 $$ of the cases when the cell wall is completely removed. In this backup mechanism, strong ligand-receptor binding between mother-cell protein SpoIIIAH and forespore-protein SpoIIQ leads to zipper-like engulfment, but quantitative understanding is missing. In our work, we combined fluorescence image analysis and stochastic Langevin simulations of the fluctuating membrane to investigate the origin of fast bistable engulfment in absence of the cell wall. Our cell morphologies compare favorably with experimental time-lapse microscopy, with engulfment sensitive to the number of SpoIIQ-SpoIIIAH bonds in a threshold-like manner. By systematic exploration of model parameters, we predict regions of osmotic pressure and membrane-surface tension that produce successful engulfment. Indeed, decreasing the medium osmolarity in experiments prevents engulfment in line with our predictions. Forespore engulfment may thus not only be an ideal model system to study decision-making in single cells, but its biophysical principles are likely applicable to engulfment in other cell types, e.g. during phagocytosis in eukaryotes

Simulations of Melting of Encapsulated CaCl2·6H2O for Thermal Energy Storage Technologies

We present in this work simulations using the finite difference approximation in 2D for the melting of an encapsulated phase-change material suitable for heat storage applications; in particular, we study CaCl2·6H2O in a cylindrical encapsulation of internal radius 8 mm. We choose this particular salt hydrate due to its availability and economic feasibility in high thermal mass building walls or storage. Considering only heat conduction, a thermostat is placed far from the capsule, providing heat for the melting of the phase-change material (PCM), which is initially frozen in a water bath. The difference in density between the solid and liquid phases is taken into account by considering a void in the solid PCM. A simple theoretical model is also presented, based on solving the heat equation in the steady state. The kinetics of melting is monitored by the total solid fraction and temperatures in the inner and outer surfaces of the capsule. The effect of different parameters is presented (thermostat temperature, capsule thickness, capsule conductivity and natural convection in the bath), showing the potential application of the method to select materials or geometries of the capsule

Distributed Spanish Sign Language synthesizer architectures

This is an electronic version of the paper presented at the Congreso Internacional de Interacción Persona-Ordenador, held in Bercelona on 2009This work presents the design of a distributed Sign Language synthesis architecture. The main objective of this design is to adapt the synthesis process to the diversity of the user devices. The synthesis process has been divided into several independent modules that can be executed either in a synthesis server or in the client device. Depending on the modules assigned to the server or the client, four different scenarios have been defined. These scenarios may vary from a heavy client design which executes the whole synthesis, to a light client design similar to a video player. These four scenarios will provide the maximum signed message quality independently of the device hardware resource

Integration of a talking head into a Spanish Sign Language synthesizer

This is an electronic version of the paper presented at the Congreso Internacional de Interacción Persona-Ordenador, held in Bercelona on 2009In this paper, we present an integration of a talking head within a Spanish Sign Language synthesizer. The whole system consists of three different steps: First, the input acoustic signal is transformed into a sequence of phones by means of a speech recognition process. This sequence of phones is mapped in a second step to a sequence of visemes and finally, the resulting sequence of visemes is played by means of a talking head integrated into the avatar used in the Spanish Sign Language synthesizer

Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics

Dedicated to the memory of María José Garrido Atienza.This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random fluctuations on the input flow, which are modeled by means of the well-known Ornstein-Uhlenbeck process, are considered to obtain a much more realistic model fitting in a better way the phenomena observed by practitioners in real devices. Once the existence and uniqueness of global positive solution has been proved, as well as the existence of deterministic absorbing and attracting sets, the random dynamics inside the attracting set is studied in detail to provide conditions under which persistence of species is ensured, the main goal pursued from the practical point of view. Finally, we support the theoretical results with several numerical simulations.Junta de Andalucía P12-FQM-1492Ministerio de Ciencia, Innovación y Universidades (MCIU). España PGC2018-096540-B-I00Junta de Andalucía (Consejería de Economía y Conocimiento) FEDER US-1254251Junta de Andalucía (Consejería de Economía y Conocimiento) P18-FR-450

Dynamics of some stochastic chemostat models with multiplicative noise

In this paper we study two stochastic chemostat models, with and without wall growth, driven by a white noise. Specifically, we analyze the existence and uniqueness of solutions for these models, as well as the existence of the random attractor associated to the random dynamical system generated by the solution. The analysis will be carried out by means of the well-known Ornstein-Uhlenbeck process, that allows us to transform our stochastic chemostat models into random ones.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí