Modeling impairment of ionic regulation with extended Adaptive Exponential integrate-and-fire models

To model the dynamics of neuron membrane excitability many models can be considered, from the most biophysically detailed to the highest level of phenomenological description. Recent works at the single neuron level have shown the importance of taking into account the evolution of slow variables such as ionic concentration. A reduction of such a model to models of the integrate-and-fire family is interesting to then go to large network models. In this paper, we introduce a way to consider the impairment of ionic regulation by adding a third, slow, variable to the adaptive Exponential integrate-and-fire model (AdEx). We then implement and simulate a network including this model. We find that this network was able to generate normal and epileptic discharges. This model should be useful for the design of network simulations of normal and pathological states

Self-Composing Policies for Scalable Continual Reinforcement Learning

This work introduces a growable and modular neural network architecture that naturally avoids catastrophic forgetting and interference in con- tinual reinforcement learning. The structure of each module allows the selective combination of previous policies along with its internal policy, accelerating the learning process on the current task. Unlike previous growing neural network approaches, we show that the number of parame- ters of the proposed approach grows linearly with respect to the number of tasks, and does not sac- rifice plasticity to scale. Experiments conducted in benchmark continuous control and visual prob- lems reveal that the proposed approach achieves greater knowledge transfer and performance than alternative method

Multi-scale modeling of Snail-mediated response to hypoxia in tumor progression

Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and phenotypic changes. In this paper, we propose a novel multi-scale mathematical model to analyze the pivotal role of Snail protein expression in the cellular responses to hypoxia. Starting from the description of single-cell dynamics driven by the Snail protein, we construct the corresponding kinetic transport equation that describes the evolution of the cell distribution. Subsequently, we employ proper scaling arguments to formally derive the equations for the statistical moments of the cell distribution, which govern the macroscopic tumor dynamics. Numerical simulations of the model are performed in various scenarios with biological relevance to provide insights into the role of the multiple tactic terms, the impact of Snail expression on cell proliferation, and the emergence of hypoxia-induced migration patterns. Moreover, quantitative comparisons with experimental data show the model's reliability in measuring the impact of Snail transcription on cell migratory potential. Through our findings, we shed light on the potential of our mathematical framework in advancing the understanding of the biological mechanisms driving tumor progression.Italian Ministry of Education, Universities and Research, MIUR grant Dipartimento di Eccellenza 2018-2022, project E11G18000350001 (MC, GC, MD) National Group of Mathematical Physics (GNFM-INdAM), INdAM–GNFM Project (CUP E53C22001930001) "From kinetic to macroscopic models for tumor-immune system competition" Modeling Nature Research Unit, Grant QUAL21-011. Consejería de Universidad, Investigaciòn e Innovaciòn (Junta de Andalucía). City of Hope’s Global Scholar Progra

Mesoscale Transport of Enveloped Viruses

Enveloped viruses are characterized by spike proteins that protrude from and decorate the viral membrane. These proteins play a crucial role in host cell interactions and exhibit dynamic behaviors, such as tilting, sliding, and clustering, which vary across different types of enveloped viruses. For instance, SARS-CoV-2 spikes tilt to facilitate receptor binding, Influenza spikes migrate during infection, and HIV spikes migrate and cluster to enhance infectivity. In this study, we investigate how such dynamics influence the virus mobility. We characterize viral mobility through translational and rotational diffusion coefficients using a mesoscopic model that incorporates the dynamics of both the flexible spike proteins and the viral envelope. Using the smoothed dissipative particle dynamics (SDPD) method, we construct three virion models with varying spike flexibility. The first is a fully rigid virus with static spikes, the second is a model with spikes that tilt but remain fixed in position, and the third is a model allowing both tilting and sliding of spikes across the envelope. Our results show that spike flexibility primarily affects rotational diffusion, whereas the envelope dominates translational mobility of the virus. We also explore spike clustering driven purely by hydrodynamic interactions and compare with an experimental model reference using DNA-PAINT super-resolution imaging of HIV-like particles. We identify that hydrodynamic interactions alone can be responsible for dynamic clustering of spike proteins. Where, the characteristic size and lifespan of such clusters indicate predominantly doublets and triplets formations. Our findings highlight the role of spike dynamics in whole virion mobility, and motivate further investigations with time-resolved experimental evidence to fully characterize clustering behavior

The role of gap junctions and clustered connectivity in emergent synchronisation patterns of inhibitory neuronal networks

PID2023-146683OB-10

Morphological Transitions of Block Copolymer Micelles: Implications for Mesoporous Materials Ordering

The design of block-copolymer-based functional materials, including mesoporous membranes and nanoparticles, requires a comprehensive understanding of the hierarchical assembly of block copolymers in selective solvents into micelles and subsequent ordered phases. It is hypothesized that micellar ordering and characteristic assembly can be described using a set of phase parameters that account for entropic and enthalpic interactions. Dissipative particle dynamics (DPD) simulations are used to systematically investigate the self-assembly of semidiluted block copolymers, resembling isoporous membrane preparation conditions. The effect of Flory–Huggins interaction parameters, block lengths, and concentration on the morphology and polydispersity of the micelles is evaluated. The interaction parameters are mapped into Flory–Huggins theory by considering the block's conformation. These results reveal the effect of polymer concentration and solvent affinity on the morphological transition of the aggregates, in agreement with existing experimental evidence. It is identified that monodisperse-spherical micelles in solution are fundamental to stabilize ordered states. Weak solvent segregation of the largest block, curvature of the core-corona interface, and stretching of the corona-forming one are found to be key to stabilize monodisperse assemblies. These conditions can be predicted using spherical-micelles packing considerations and a global phase parameter from the Flory–Huggins theory. This study provides valuable insights into the self-assembly of diblock copolymers and offers a potential way to optimize the preparation of mesoporous ordered structures and micelle ordering in semidiluted systems

Degenerate Poincaré-Sobolev inequalities via fractional integration

We present a local weighted estimate for the Riesz potential in $\mathbb{R}^n$, which improves the main theorem of Alberico, Cianchi, and Sbordone [C. R. Math. Acad. Sci. Paris \textbf{347} (2009)] in several ways. As a consequence, we derive weighted Poincaré-Sobolev inequalities with sharp dependence on the constants. We answer positively to a conjecture proposed by Pérez and Rela [Trans. Amer. Math. Soc. \textbf{372} (2019)] related to the sharp exponent in the $A_1$ constant in the $(p^*,p)$ Poincaré-Sobolev inequality with $A_1$ weights. Our approach is versatile enough to prove Poincaré-Sobolev inequalities for high-order derivatives and fractional Poincaré-Sobolev inequalities with the BBM extra gain factor $(1-\delta)^\frac{1}{p}$. In particular, we improve one of the main results from Hurri-Syrjänen, Martínez-Perales, Pérez, and Vähäkangas [Int. Math. Res. Not. \textbf{20} (2023)].PRE2021-09909

Boundary layers for the upper-convected Beris–Edwards model of nematic liquid crystals

In this paper, we derive and analyze a set of Prandtl-type equations for the boundary layers in nematic liquid crystals. We focus on a two-dimensional model where the hydrodynamics are governed by the Beris–Edwards equations with a shape parameter ξ= 1, specifically emphasizing the upper convected derivative in the order-tensor equation. We introduce a novel decomposition of the order tensor, which, combined with an Ansatz inspired by Prandtl’s theory, leads to a set of limiting equations as the Reynolds, Ericksen, and Deborah numbers approach infinity. We explore two distinct regimes of the dimen- sionless parameters in the Beris–Edwards equations. The first regime results in a partial decoupling in the limiting equations, where the velocity field is unaffected by the order tensor, though the order tensor is influenced by the flow. In the second regime, we derive a fully coupled system. Our analytical investigation of the derived models reveals that, in the decoupled case, the limiting equations admit analytic-type solutions, while in the coupled setting, the equations allow for shear-flow type solutions

Minimax Risk Classifiers for Mislabeled Data: a Study on Patient Outcome Prediction Tasks

Healthcare datasets are often impacted by incorrect or mislabeled data, due to imperfect an- notations, data collection problems, ambiguity, and subjective interpretations. Incorrectly classified data, referred to as “noisy labels,” can significantly degrade the performance of supervised learning models. Namely, noisy labels hinder the algorithm’s ability to accurately capture the true underlying patterns from observed data. More importantly, evaluating the performance of a classifier when only noisy test labels are available is a significant complication. We hereby tackle the challenge of trusting the labeling process both in training and testing, as noisy patient outcome labels in healthcare raise methodological and ethical considerations. We propose a novel adaptation of Minimax Risk Classifiers (MRCs) for data subject to noisy labels, both in training and evaluation. We show that the upper bound of the MRC’s expected loss can serve as a useful estimator for the classifier’s performance, especially in situations where clean test data is not available. We demonstrate the benefits of the proposed methodology in healthcare tasks where patient outcomes are predicted from mislabeled data. The proposed technique is accurate and stable, avoiding overly optimistic assessments of prediction error, a significantly harmful burden in patient outcome prediction tasks in healthcare.PID2022-137063B-I00 CNS2022-13520