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Motivation: Biological Petri Nets (Bio-PNs) model biochemical pathways where multiple reactions simultaneously affect shared metabolites through convergent production or regulatory coupling. However, classical Petri net independence theory…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a…
A hybrid network--deterministic model for simulation of multiresistant pathogen spread in a healthcare system is presented. The model accounts for two paths of pathogen transmission between the healthcare facilities: inter-hospital patient…
We employ a multi-scale mechanistic approach to investigate radiation induced cell toxicities and deactivation mechanisms as a function of linear energy transfer in hadron therapy. Our theoretical model consists of a system of Markov chains…
We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over…
Human behavior plays a critical role in shaping epidemic trajectories. During health crises, people respond in diverse ways in terms of self-protection and adherence to recommended measures, largely reflecting differences in how individuals…
The focus of pancreatic cancer research has been shifted from pancreatic cancer cells towards their microenvironment, involving pancreatic stellate cells that interact with cancer cells and influence tumor progression. To quantitatively…
Pathway enrichment analysis has become a key tool for biomedical researchers to gain insight into the underlying biology of differentially expressed genes, proteins and metabolites. It reduces complexity and provides a system-level view of…
Oncolytic virotherapy, utilizing genetically modified viruses to combat cancer and trigger anti-cancer immune responses, has garnered significant attention in recent years. In our previous work arXiv:2305.12386, we developed a stochastic…
In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity…
Intratumor heterogeneity (ITH), referring to coexistence of different cell subpopulations in a single tumor, has been a major puzzle in cancer research for almost half a century. The lack of understanding of the underlying mechanism of ITH…
The study proposes a modeling framework for investigating the disease dynamics with adaptive human behavior during a disease outbreak, considering the impacts of both local observations and global information. One important application…
The NF-kB signalling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kB…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
The analysis of biological networks is characterized by the definition of precise linear constraints used to cumulatively reduce the solution space of the computed states of a multi-omic (for instance metabolic, transcriptomic and…
Neural processing systems typically represent data using leaky integrate and fire (LIF) neuron models that generate spikes or pulse trains at a rate proportional to their input amplitudes. This mechanism requires high firing rates when…
We introduce a multi-species diffuse interface model for tumor growth, characterized by its incorporation of essential features related to chemotaxis, angiogenesis and proliferation mechanisms. We establish the weak well-posedness of the…
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states.…
The tumour microenvironment (TME) strongly influences tumorigenesis and metastasis. Two of the most characterized properties of the TME are acidosis and hypoxia, both of which are considered hallmarks of tumours as well as critical factors…