Emergence of planar cell polarity from the interplay of asymmetric interaction and tissue-level gradients

Planar cell polarity (PCP) - asymmetric localization of proteins at cell-cell interface - is essential for embryonic development and physiological functions. Abnormalities in PCP can lead to neural tube closure defects, misalignment in hair follicles etc. Thus, decoding the mechanism responsible for PCP establishment and maintenance remains an open fundamental question. While various molecules-broadly classified into 'global' and 'local' modules have been well investigated; their necessity and sufficiency in explaining PCP and connecting their perturbations and defects in experimentally observed patterns has not been examined. Here, we develop a minimal model that captures the proposed features of these two modules- a tissue level gradient (global) and asymmetric localization of protein complexes (local). Our model results suggest that while polarity can emerge in absence of a gradient; the gradient can provide the direction of polarity as well as offer robustness for maintenance of PCP in presence of stochastic perturbations. We also recapitulated swirling patterns (seen experimentally) and the features of non-domineering autonomy; using only three free parameters in the model - protein binding rate; concentration of proteins forming heterodimer across cell boundaries and steepness of gradient. Our results explain how self-stabilizing asymmetric localisations in presence of tissue-level gradient can lead to robust PCP patterns in diverse biological systems and reveals the minimal design principles for a polarized system.

Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

Lagrangian Integro-Difference Equation Model for Precipitation Nowcasting

Delivering reliable nowcasts (short-range forecasts) of severe rainfall and the resulting flash floods is important in densely populated urban areas. The conventional method is advection-based extrapolation of radar echoes. However, during rapidly evolving convective rainfall this so-called Lagrangian persistence (LP) approach is limited to deterministic and very short-range nowcasts. To address these limitations in the one-hour time range, a novel extension of LP, called Lagrangian INtegro-Difference equation model withAutoregression (LINDA), is proposed. The model consists of five components: 1) identification of rain cells, 2) advection, 3) autoregressive process describing growth and decay of the cells, 4) convolution describing loss of predictability at small scales and 5) stochastic perturbations to simulate forecast uncertainty. Advection is separated from the other components that are applied in the Lagrangian coordinates. The reliability of LINDA is evaluated using the NEXRAD WSR-88D radar that covers the Dallas-Fort Worth metropolitan area, as well as the NEXRAD mosaic covering the continental United States. This is done with two different configurations: LINDA-D for deterministic and LINDA-P for probabilistic nowcasts. The validation dataset consists of 11 rainfall events during 2018-2020. For predicting moderate to heavy rainfall (5-20 mm/h), LINDA outperforms the previously proposed LP-based approaches. The most significant improvement is seen for the ETS and POD statistics with the 5 mm/h threshold. For 30-minute nowcasts, they show 15% and 16% increase, respectively, to the second-best method and 48% and 34% increase compared to LP. For the 5 mm/h threshold, the increase in the ROC skill score of 30-minute nowcasts from the second-best method is 10%.

Stochastic analysis of a SIRI epidemic model with double saturated rates and relapse

Infectious diseases have for centuries been the leading causes of death and disability worldwide and the environmental fluctuation is a crucial part of an ecosystem in the natural world. In this paper, we proposed and discussed a stochastic SIRI epidemic model incorporating double saturated incidence rates and relapse. The dynamical properties of the model were analyzed. The existence and uniqueness of a global positive solution were proven. Sufficient conditions were derived to guarantee the extinction and persistence in mean of the epidemic model. Additionally, ergodic stationary distribution of the stochastic SIRI model was discussed. Our results indicated that the intensity of relapse and stochastic perturbations greatly affected the dynamics of epidemic systems and if the random fluctuations were large enough, the disease could be accelerated to extinction while the stronger relapse rate were detrimental to the control of the disease.

Observer-based robust controller design for fractional-order systems with stochastic perturbations: A diffusive representation approach

We investigate the fractional-order systems that are perturbed by stochastic input to achieve stabilization via sliding mode control (SMC) approach. It is assumed that the system states are unknown and there is uncertainty and time-delay in the system. We utilize the diffusive representation of the stochastic fractional-order dynamics to transform the system into an integer-order system perturbed by Brownian motion. Provided that some linear matrix inequalities (LMIs) are feasible, it is proven that the estimation error system is stochastically stabilized and the overall closed-loop system is stable in probability. A numerical simulation shows the effectiveness of the results.

Achieving realistic Arctic-midlatitude teleconnections in a climate model through stochastic process representation

The extent to which interannual variability in Arctic sea ice influences the midlatitude circulation has been extensively debated. While observational data supports the existence of a teleconnection between November sea ice in the Barents-Kara region and the subsequent winter circulation, climate models do not consistently reproduce such a link, with only very weak inter-model consensus. We show, using the EC-Earth3 climate model, that while a deterministic ensemble of coupled simulations shows no evidence of such a teleconnection, the inclusion of stochastic parameterizations to the ocean and sea ice component of EC-Earth3 results in the emergence of a robust teleconnection comparable in magnitude to that observed. We show that this can be accounted for entirely by an improved ice-ocean-atmosphere coupling due to the stochastic perturbations. In particular, the inconsistent signal in existing climate model studies may be due to model biases in surface coupling, with stochastic parameterizations being one possible remedy.