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It is well known that today nearly one in six of the world’s population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders, some fundamentals of the progression of associated diseases are in urgent need of further clarification. In this paper, we focus on Alzheimer’s disease, where it is believed that the concentration changes in amyloid-beta and tau proteins play a central role in its onset and development. A multiscale model is proposed to analyze the propagation of these concentrations in the brain connectome. In particular, we consider a modified heterodimer model for the protein–protein interactions. Higher toxic concentrations of amyloid-beta and tau proteins destroy the brain cell. We have studied these propagations for the primary and secondary and their mixed tauopathies. We model the damage of a brain cell by the nonlocal contributions of these toxic loads present in the brain cells. With the help of rigorous analysis, we check the stability behaviour of the stationary points corresponding to the homogeneous system. After integrating the brain connectome data into the developed model, we see that the spreading patterns of the toxic concentrations for the whole brain are the same, but their concentrations are different in different regions. Also, the time to propagate the damage in each region of the brain connectome is different.

A theoretical model for describing effective thermal conductivity (ETC) of nanocrystalline materials has been proposed, so that the ETC can be easily obtained from its grain size, single crystal thermal conductivity, single crystal phonon mean free path (PMFP) and the Kaptiza thermal resistance. In addition, the relative importance between grain boundaries (GBs) and size effects on the ETC of nanocrystalline diamond at 300  K has been studied. It has been demonstrated that with increasing grain size, both GBs and size effects become weaker, while size effects become stronger on thermal conductivity than GBs effects.

The events of the recent SARS-CoV-2 epidemics have shown the importance of social factors, especially given the large number of asymptomatic cases that effectively spread the virus, which can cause a medical emergency to very susceptible individuals. Besides, the SARS-CoV-2 virus survives for several hours on different surfaces, where a new host can contract it with a delay. These passive modes of infection transmission remain an unexplored area for traditional mean-field epidemic models. Here, we design an agent-based model for simulations of infection transmission in an open system driven by the dynamics of social activity; the model takes into account the personal characteristics of individuals, as well as the survival time of the virus and its potential mutations. A growing bipartite graph embodies this biosocial process, consisting of active carriers (host) nodes that produce viral nodes during their infectious period. With its directed edges passing through viral nodes between two successive hosts, this graph contains complete information about the routes leading to each infected individual. We determine temporal fluctuations of the number of exposed and the number of infected individuals, the number of active carriers and active viruses at hourly resolution. The simulated processes underpin the latent infection transmissions, contributing significantly to the spread of the virus within a large time window. More precisely, being brought by social dynamics and exposed to the currently existing infection, an individual passes through the infectious state until eventually spontaneously recovers or otherwise is moves to a controlled hospital environment. Our results reveal complex feedback mechanisms that shape the dependence of the infection curve on the intensity of social dynamics and other sociobiological factors. In particular, the results show how the lockdown effectively reduces the spread of infection and how it increases again after the lockdown is removed. Furthermore, a reduced level of social activity but prolonged exposure of susceptible individuals have adverse effects. On the other hand, virus mutations that can gradually reduce the transmission rate by hopping to each new host along the infection path can significantly reduce the extent of the infection, but can not stop the spreading without additional social strategies. Our stochastic processes, based on graphs at the interface of biology and social dynamics, provide a new mathematical framework for simulations of various epidemic control strategies with high temporal resolution and virus traceability.

Patterns in a semiarid ecosystem are important because they directly and indirectly affect ecological processes, biodiversity, and ecosystem resilience. Understanding the causes and effects of these patterns is critical for long-term land surface management and conservation efforts in semiarid regions, which are especially sensitive to climate change and human-caused disturbances. In addition, developing mathematical models is challenging because of the involvement of several interacting components within an ecosystem. It is known that there is a regular connection between the vegetation and the living species in a habitat since some animals evolved to live in a semiarid ecosystem and rely on plants for food. In this work, we have constructed a coupled mathematical model to connect the water resource, vegetation, and living organisms and have investigated how the soil surface affects the resulting patterns in the long term. This study contributes to a better understanding of ecological patterns and processes in semiarid environments by shedding light on the complex interaction mechanisms that depend on the structure of semiarid ecosystems. For example, the impact of intensive rainfall on ecosystem dynamics can be profound, triggering critical transitions and leading to significant yield loss. The energy lost as it moves from one trophic level to the next, the potential for diversity to exacerbate species extinction rates, and the role of water flow in driving the system towards more robust stripe pattern formations are all significant factors. Despite these complexities, the findings offer critical insights into the influence of efforts to enhance ecosystem resilience and adapt to the challenges of climate change and human activities.

Further enhancement of crude oil recovery in the enhanced recovery stage from calcite oil wells is a major global challenge for oil industry. Experimental results suggest that ions present in sea water, also called smart water, have a significant influence on the wettability alteration (less oil wet) of calcite surface. In this paper, by utilizing Density Functional Theory (DFT) and Quantum Molecular Dynamics (QMD) simulations, we investigate the effect of additive ions of sea water in oil recovery by using acetic acid as a model compound of crude oil molecules. We find that Na + ions precipitate to the calcite surface and form Na acetate. The binding energy of Na acetate is larger than original oil molecule (acetic acid), which reduces oil recovery. On the other hand, Mg 2+ and S O 4 2 − ions can also reach to the calcite surface in proximity and modify the calcite surface. The binding energy of oil molecule on modified calcite surface is smaller than on pure calcite surface, which enhances oil recovery. Our results might help in understanding interaction among oil, water and additives ions of smart water for further experimental investigations.

Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity.

Understanding how emotions and psychological states influence both individual and collective actions is critical for expressing the real complexity of biosocial and ecological systems. Recent breakthroughs in mathematical modeling have created new opportunities for systematically integrating these emotion-specific elements into dynamic frameworks ranging from human health to animal ecology and socio-technical systems. This review builds on mathematical modeling approaches by bringing together insights from neuroscience, psychology, epidemiology, ecology, and artificial intelligence to investigate how psychological effects such as fear, stress, and perception, as well as memory, motivation, and adaptation, can be integrated into modeling efforts. This article begins by examining the influence of psychological factors on brain networks, mental illness, and chronic physical diseases (CPDs), followed by a comparative discussion of model structures in human and animal psychology. It then turns to ecological systems, focusing on predator–prey interactions, and investigates how behavioral responses such as prey refuge, inducible defense, cooperative hunting, group behavior, etc., modulate population dynamics. Further sections investigate psychological impacts in epidemiological models, in which risk perception and fear-driven behavior greatly affect disease spread. This review article also covers newly developing uses in artificial intelligence, economics, and decision-making, where psychological realism improves model accuracy. Through combining these several strands, this paper argues for a more subtle, emotionally conscious way to replicate intricate adaptive systems. In fact, this study emphasizes the need to include emotion and cognition in quantitative models to improve their descriptive and predictive ability in many biosocial and environmental contexts.

Background/Objectives: Neuronal oscillations play a key role in the symptoms of Parkinson’s disease (PD). This study investigates the effects of random synaptic inputs, their correlations, and the interaction with synaptic dynamics and spike timing-dependent plasticity (STDP) on the membrane potential and firing patterns of subthalamic nucleus (STN) neurons, both in healthy and PD-affected states. Methods: We used a modified Hodgkin–Huxley model with a Langevin stochastic framework to study how synaptic conductance, random input fluctuations, and STDP affect STN neuron firing and membrane potential, including sensitivity to refractory period and synaptic depression variability. Results: Our results show that random inputs significantly affect the firing patterns of STN neurons, both in healthy cells and those with PD under DBS treatment. STDP, along with random refractory periods and fluctuating input currents, increases the irregularity of inter-spike intervals (ISIs) in output neuron spike trains. Sensitivity analyses highlight the key role of synaptic depression and refractory period variability in shaping firing patterns. Combining random inputs with STDP boosts the correlation between neuron activities. Furthermore, at fixed input noise levels, the model’s output closely matches experimental firing rate and ISI variability data from PD patients and animals, with statistical tests confirming significant effects of STDP on firing regularity. Conclusions: The findings suggest that the stochastic dynamics of STN neurons, combined with STDP, are crucial for shaping neuronal firing patterns in both healthy and PD-affected states. These insights improve our understanding of how noise and plasticity contribute to neural function and dysfunction, with implications for PD symptom management.

Alzheimer's disease (AD) is a common neurodegenerative disorder nowadays. Amyloid-beta (Aβ) and tau proteins are among the main contributors to the AD progression. In AD, Aβ proteins clump together to form plaques and disrupt cell functions. On the other hand, the abnormal chemical change in the brain helps to build sticky tau tangles that block the neuron's transport system. Astrocytes generally maintain a healthy balance in the brain by clearing the Aβ plaques (toxic Aβ). However, overactivated astrocytes release chemokines and cytokines in the presence of Aβ and react to pro-inflammatory cytokines, further increasing the production of Aβ. In this study, we construct a mathematical model that can capture astrocytes' dual behavior. Furthermore, we reveal that the disease progression depends on the current time instance and the disease's earlier status, called the “memory effect,” making non-Markovian processes an appropriate approach. We consider a fractional order network mathematical model to capture the influence of such memory effects on AD progression. We have integrated brain connectome data into the model and studied the memory effect, the dual role of astrocytes, and the brain's neuronal damage. Based on the pathology, primary, secondary, and mixed tauopathies parameters are considered in the model. Due to the mixed tauopathy, different brain nodes or regions in the brain connectome accumulate different toxic concentrations of Aβ and tau proteins. Finally, we explain how the memory effect can slow down the propagation of such toxic proteins in the brain, decreasing the rate of neuronal damage.