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A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…

Analysis of PDEs · Mathematics 2016-06-29 Charles M. Elliott , Carsten Gräser , Graham Hobbs , Ralf Kornhuber , Maren-Wanda Wolf

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical…

Soft Condensed Matter · Physics 2026-02-24 Sreekanth Ramesh , Prashant K. Purohit , Yashashree Kulkarni

Model checking is an established technique to formally verify automation systems which are required to be trusted. However, for sufficiently complex systems model checking becomes computationally infeasible. On the other hand, testing,…

Software Engineering · Computer Science 2019-07-30 Igor Buzhinsky , Valeriy Vyatkin

Bedwyr is a generalization of logic programming that allows model checking directly on syntactic expressions possibly containing bindings. This system, written in OCaml, is a direct implementation of two recent advances in the theory of…

Logic in Computer Science · Computer Science 2008-04-25 David Baelde , Andrew Gacek , Dale Miller , Gopalan Nadathur , Alwen Tiu

Pervasive user-centric applications are systems which are meant to sense the presence, mood, and intentions of users in order to optimize user comfort and performance. Building such applications requires not only state-of-the art techniques…

Software Engineering · Computer Science 2010-09-23 Martin Wirsing , Sebastian S. Bauer , Andreas Schroeder

Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them…

Neural and Evolutionary Computing · Computer Science 2021-02-15 Pietro Verzelli , Cesare Alippi , Lorenzo Livi , Peter Tino

We propose a mechanism for mechanical regulation at the membrane of living cells, based on the exchange of membrane area between the cell membrane and a membrane reservoir. The reservoir is composed of invaginated membrane microdomains…

Subcellular Processes · Quantitative Biology 2007-05-23 Pierre Sens , Matthew S. Turner

The present article introduces a reference framework for discussing resilience of computational systems. Rather than a property that may or may not be exhibited by a system, resilience is interpreted here as the emerging result of a dynamic…

Systems and Control · Computer Science 2015-04-13 Vincenzo De Florio

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…

Membrane systems represent a computational model that operates in a distributed and parallel manner, inspired by the behavior of biological cells. These systems feature objects that transform within a nested membrane structure. This…

Computational Complexity · Computer Science 2026-02-06 Vivien Ducros , Claudio Zandron

Design and control of autonomous systems that operate in uncertain or adversarial environments can be facilitated by formal modelling and analysis. Probabilistic model checking is a technique to automatically verify, for a given temporal…

Logic in Computer Science · Computer Science 2021-11-23 Marta Kwiatkowska , Gethin Norman , David Parker

Periodic control systems used in spacecrafts and automotives are usually period-driven and can be decomposed into different modes with each mode representing a system state observed from outside. Such systems may also involve intensive…

Logic in Computer Science · Computer Science 2013-01-03 Zheng Wang , Geguang Pu , Jianwen Li , Jifeng He , Shengchao Qin , Kim G. Larsen , Jan Madsen , Bin Gu

Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…

Molecular Networks · Quantitative Biology 2007-10-19 Aneil Mallavarapu , Matthew Thomson , Benjamin Ullian , Jeremy Gunawardena

The interaction between nano- or micro-sized particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the…

Probabilistic specifications are fast gaining ground as a tool for statistical modeling of probabilistic systems. One of the main goals of formal methods in this domain is to ensure that specific behavior is present or absent in the system,…

Logic in Computer Science · Computer Science 2022-06-14 Carlos Olarte , Camilo Rocha , Daniel Osorio

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…

Quantitative Methods · Quantitative Biology 2019-07-02 Eric Mjolsness

Modern software systems are often realized by coordinating multiple heterogeneous parts, each responsible for specific tasks. These parts must work together seamlessly to satisfy the overall system requirements. To verify such complex…

Software Engineering · Computer Science 2025-08-19 Tim Kräuter , Adrian Rutle , Yngve Lamo , Harald König , Francisco Durán

Numerical simulation is one of the mainstream methods in scientific research, typically performed by professional engineers. With the advancement of multi-agent technology, using collaborating agents to replicate human behavior shows…

Multiagent Systems · Computer Science 2026-01-13 Chunwei Yang , Yankai Wang , Jianxiang Tang , Haojie Qu , Ziqiang Zou , YuLiu , Chunrui Deng , Zhifang Qiu , Ming Ding

Safety of medical devices and of their interoperation is an unresolved issue causing severe and sometimes deadly accidents for patients with shocking frequency. Formal methods, particularly in support of highly reusable and provably safe…

Logic in Computer Science · Computer Science 2010-09-23 Mu Sun , José Meseguer

We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ…

Soft Condensed Matter · Physics 2009-11-11 Marcus Mueller , Kirill Katsov , Michael Schick
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