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Abstract This paper presents a novel methodological framework to obtain superior reconstructions in limited data photoacoustic tomography. The proposed framework exploits the presence of Cauchy data on an accessible part of the observation domain and uses a Nash game-theoretic framework to complete the missing data on the inaccessible region. To solve the game-theoretic problem, a gradient-free sequential quadratic Hamiltonian scheme, which is based on Pontryagin’s maximum principle characterization, is combined with physics-informed neural networks to obtain the initial guess, leading to a robust and accurate reconstruction scheme. Numerical simulations with various phantoms, choice of accessible observation domains, and noise, demonstrate the effectiveness of our proposed framework to obtain high contrast and resolution reconstructions. 

Mathematical models of neuronal networks play a crucial role in understanding sleep dynamics and associated disorders. However, validating these models through parameter estimation remains a significant challenge. In this work, we introduce an automated parameter estimation framework for sleep models that satisfy two key assumptions: (i) they consist of competing neuronal populations, each driving a distinct sleep stage (stage-promoting), and (ii) their dynamics evolve independently of weakly observed variables or external inputs (self-contained). We apply our method to a system of coupled nonlinear ordinary differential equations (ODEs) representing three interacting neuronal populations. Direct firing rates of these populations are typically unobservable, and hypnograms provide only the dominant sleep stage at each time point. Despite the limited information available in hypnograms, we successfully estimate ODE parameters for the underlying neuronal population model directly from hypnogram data. We use a smoothed winner-takes-all strategy within a constrained minimization framework, reformulate the problem in an unconstrained setting through the Lagrangian, and derive the corresponding optimality conditions from state and adjoint equations. A projected nonlinear conjugate gradient scheme is then used to estimate the parameters numerically. We validate our approach by accurately reconstructing 111 out of 139 hypnograms from the Sleep-EDF database. The inferred population-level parameters provide insights into sleep regulation by capturing interaction strengths, timescale constants and non-rapid eye movement-related variability. 

Current treatments for hepatocellular carcinoma (HCC) include partial hepatectomy (PH), where two-thirds of the liver is removed. However, when some cancer remains after PH, competition for resources and survival occurs between healthy and cancerous cells. Recent studies suggest that hyperactivation of yes-associated protein (YAP) could be a non-invasive treatment option for HCC. In this study, we propose two simple ordinary differential equation models of resource competition in HCC livers after PH, one capturing the natural dynamics of resource competition between healthy and cancer cells and the other incorporating YAP hyperactivation therapy. We perform full qualitative and quantitative analyses of these models and validate them on experimental data. Our numerical simulations reveal that treatment schedules must be prescribed based on a patient’s tumor aggression. We also found that a high dose of treatment is necessary to completely clear a tumor in all patients, leading us to suggest prescribing YAP hyperactivation therapy in lower doses with other treatments for HCC for the best patient outcomes. 

This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game’s playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes. 

Nonstandard finite-difference (NSFD) methods, pioneered by R. E. Mickens, offer accurate and efficient solutions to various differential equation models in science and engineering. NSFD methods avoid numerical instabilities for large time steps, while numerically preserving important properties of exact solutions. However, most NSFD methods are only first-order accurate. This paper introduces two new classes of explicit second-order modified NSFD methods for solving n-dimensional autonomous dynamical systems. These explicit methods extend previous work by incorporating novel denominator functions to ensure both elementary stability and second-order accuracy. This paper also provides a detailed mathematical analysis and validates the methods through numerical simulations on various biological systems. 

Abstract On 3 February 2022, SpaceX launched 49 Starlink satellites, 38 of which unexpectedly de‐orbited. Although this event was attributed to space weather, definitive causality remained elusive because space weather conditions were not extreme. In this study, we identify solar sources of the interplanetary coronal mass ejections that were responsible for the geomagnetic storms around the time of launch of the Starlink satellites and for the first time, investigate their impact on Earth's magnetosphere using magnetohydrodynamic modeling. The model results demonstrate that the satellites were launched into an already disturbed space environment that persisted over several days. However, on performing comparative satellite orbital decay analyses, we find that space weather alone was not responsible but conspired together with a low‐altitude insertion and low satellite mass‐to‐area ratio to precipitate this unusual loss. Our work bridges space weather causality across the Sun–Earth system—with relevance for space‐based human technologies.