This project mathematically models the self-assembly of DNA nanostructures in the shape of select Archimedean graphs using the flexible tile model. Under three different sets of restrictions called scenarios, we employ principles of linear algebra and graph theory to determine the minimum number of different DNA branched molecules and bond types needed to construct the desired shapes, theoretically reducing laboratory costs and the waste of biomaterials. We determine exact values for $T_3(G)$, the minimum number of molecule (or ``tile") types needed for all six order 12 and 24 Archimedean graphs. We also determine exact values for $B_3(G)$, the minimum number of strand (or ``bond-edge") types, for three of the six graphs and establish bounds for the remaining three. Two algorithms, implemented as Python scripts, are used to analyze proposed design strategies for the graphs.

Foundation medical segmentation models, with MedSAM being the most popular, have achieved promising performance across organs and lesions. However, MedSAM still suffers from compromised performance on specific lesions with intricate structures and appearance, as well as bounding box prompt-induced perturbations. Although current test-time adaptation (TTA) methods for medical image segmentation may tackle this issue, partial (e.g., batch normalization) or whole parametric updates restrict their effectiveness due to limited update signals or catastrophic forgetting in large models. Meanwhile, these approaches ignore the computational complexity during adaptation, which is particularly significant for modern foundation models. To this end, our theoretical analyses reveal that directly refining image embeddings is feasible to approach the same goal as parametric updates under the MedSAM architecture, which enables us to realize high computational efficiency and segmentation performance without the risk of catastrophic forgetting. Under this framework, we propose to encourage maximizing factorized conditional probabilities of the posterior prediction probability using a proposed distribution-approximated latent conditional random field loss combined with an entropy minimization loss. Experiments show that we achieve about 3\% Dice score improvements across three datasets while reducing computational complexity by over 7 times.

Accurate prediction of the binding affinity between drugs and target proteins is a core task in computer-aided drug design. Existing deep learning methods tend to ignore the information of internal sub-structural features of drug molecules and drug-target interactions, resulting in limited prediction performance. In this paper, we propose a drug-target association prediction model HCAF-DTA based on cross-attention fusion hypergraph neural network. The model innovatively introduces hypergraph representation in the feature extraction stage: drug molecule hypergraphs are constructed based on the tree decomposition algorithm, and the sub-structural and global features extracted by fusing the hypergraph neural network with the graphical neural network through hopping connections, in which the hyper edges can efficiently characterise the functional functional groups and other key chemical features; for the protein feature extraction, a weighted graph is constructed based on the residues predicted by the ESM model contact maps to construct weighted graphs, and multilayer graph neural networks were used to capture spatial dependencies. In the prediction stage, a bidirectional multi-head cross-attention mechanism is designed to model intermolecular interactions from the dual viewpoints of atoms and amino acids, and cross-modal features with correlated information are fused by attention. Experiments on benchmark datasets such as Davis and KIBA show that HCAF-DTA outperforms state of the arts in all three performance evaluation metrics, with the MSE metrics reaching 0.198 and 0.122, respectively, with an improvement of up to 4% from the optimal baseline.

In primates, loci associated with adaptive trait variation often fall in non-coding regions. Understanding the mechanisms linking these regulatory variants to fitness-relevant phenotypes remains challenging, but can be addressed using functional genomic data. However, such data are rarely generated at scale in non-human primates. When they are, only select tissues, cell types, developmental stages, and cellular environments are typically considered, despite appreciation that adaptive variants often exhibit context-dependent effects. In this review, we 1) discuss why context-dependent regulatory loci might be especially evolutionarily relevant in primates, 2) explore challenges and emerging solutions for mapping such context-dependent variation, and 3) discuss the scientific questions these data could address. We argue that filling this gap will provide critical insights into evolutionary processes, human disease, and regulatory adaptation.

\textit{Aedes albopictus} mosquitoes are competent vectors for the spread of at least 24 different arboviruses, including dengue, Ross River, and Japanese encephalitis viruses. However, they remain less studied than their more urban cousins, \textit{Aedes aegypti}. We model an Incompatible Insect Technique (IIT) strategy for mosquito control, with bi-directional incompatibility between two strains of \textit{Wolbachia} (\walba/\walbb\, $\times$ \arwp) and age-based cytoplasmic incompatibility decay in a well-mixed population. An important consideration in bi-directional IIT control programs is reversibility when immigration is included. We explore the establishment probability after female contamination of an artificially-infected \textit{Wolbachia} mosquito strain, finding a conservative threshold of 40\% likely driven by mating inefficiencies -- this threshold needs validation in future field and lab experiments. We consider the suppression dynamics and probability of mosquito management success for different release strategies, showing differences in success between release cessation and six months later for different immigration rates. Importantly, our model suggests bi-directional IIT control programs are reversible with low amounts of immigration. We determine a corresponding cost proxy (numbers of mosquitoes released), showing similar short-term costs with differences in medium- and longer-term costs between release strategies. This work demonstrates opportunities to optimise the suppression of these medically important mosquitoes.

Understanding the stability of complex communities is a central focus in ecology, many important theoretical advancements have been made to identify drivers of ecological stability. However, previous results often rely on the continuous-time dynamics, assuming that species have overlapping generations. In contrast, numerous real-world communities consist of species with non-overlapping generations, whose quantitative behavior can only be precisely represented by discrete-time dynamics rather than continuous ones. Here, we develop a theoretical framework and propose a metric to quantify the stability of complex communities characterized by non-overlapping generations and diverse interaction types. In stark contrast to existing results for overlapping generations, we find that increasing self-regulation strength first stabilizes and then destabilizes complex communities. This pattern is further confirmed in both exploitative (E. aerogenes, P. aurantiaca, P. chlororaphis, P. citronellolis) and competitive (P. putida, P. veroni, S. marcescens) soil microbial communities. Moreover, we show that communities with diverse interaction types become the most stable, which is corroborated by empirical mouse microbial networks. Furthermore, we reveal that the prevalence of weak interactions can stabilize communities, which is consistent with findings from existing microbial experiments. Our analyses of complex communities with non-overlapping generations provide a more comprehensive understanding of ecological stability and informs practical strategies for ecological restoration and control.

The symbiotic relationship between the frameworks of classical game theory and evolutionary game theory is well-established. However, evolutionary game theorists have mostly tapped into the classical game of complete information where players are completely informed of all other players' payoffs. Of late, there is a surge of interest in eco-evolutionary interactions where the environment's state is changed by the players' actions which, in turn, are influenced by the changing environment. However, in real life, the information about the true environmental state must pass through some noisy channel (like usually imperfect sensory apparatus of the players) before it is perceived by the players: The players naturally are prone to sometimes perceive the true state erroneously. Given the uncertain perceived environment, the players may adopt bet-hedging kind of strategies in which they play different actions in different perceptions. In a population of such ill-informed players, a player would be confused about the information state of her opponent, and an incomplete information situation akin to a Bayesian game surfaces. In short, we contemplate possibility of natural emergence of symbiotic relationship between the frameworks of Bayesian games and eco-evolutionary games when the players are equipped with inefficient sensory apparatus. Herein, we illustrate this connection using a setup of infinitely large, well-mixed population of players equipped with two actions for exploiting a resource (the environment) at two different rates so that the resource state evolves accordingly. The state of the resource impacts every player's decision of playing particular action. We investigate continuous state environment in the presence of a Gaussian noisy channel. Employing the formalism of replicator dynamics, we find that noisy information can be effective in preventing resource from going extinct.

There has been interest in the interactions between infectious disease dynamics and behaviour for most of the history of mathematical epidemiology. This has included consideration of which mathematical models best capture each phenomenon, as well as their interaction, but typically in a manner that is agnostic to the exact behaviour in question. Here, we investigate interacting behaviour and disease dynamics specifically related to behaviours around testing and isolation. This epidemiological-behavioural interaction is of particular interest as, prospectively, it is well-placed to be informed by real-world data temporally monitoring test results and compliance with testing policy. To carry out our investigation we extend an existing "behaviour and disease" (BaD) model by incorporating the dynamics of symptomatic testing and isolation. We provide a dynamical systems analysis of the ordinary differential equations that define this model, providing theoretical results on its behaviour early in a new outbreak (particularly its basic reproduction number) and endemicity of the system (its steady states and associated stability criteria). We then supplement these findings with a numerical analysis to inform how temporal and cumulative outbreak metrics depend on the model parameter values for epidemic and endemic regimes. As the presented interdisciplinary modelling approach can accommodate further extensions (including, but not limited to, adding testing capacity, decay in behavioural effects and multiple pathogen variants), we hope that our work will encourage further modelling studies integrating specific measured behaviours and disease dynamics that may reduce the health and economic impacts of future epidemics.

Cerebral blood flow regulation is critical for brain function, and its disruption is implicated in various neurological disorders. Many existing models do not fully capture the complex, multiscale interactions among neuronal activity, astrocytic signaling, and vascular dynamics--especially in key brainstem regions. In this work, we present a 3D-1D-0D multiscale computational framework for modeling the neuro-glial-vascular unit (NGVU) in the dorsal vagal complex (DVC). Our approach integrates a quadripartite synapse model--which represents the interplay among excitatory and inhibitory neurons, astrocytes, and vascular smooth muscle cells--with a hierarchical description of vascular dynamics that couples a three-dimensional microcirculatory network with a one-dimensional macrocirculatory representation and a zero-dimensional synaptic component. By linking neuronal spiking, astrocytic calcium and gliotransmitter signaling, and vascular tone regulation, our model reproduces key features of functional hyperemia and elucidates the feedback loops that help maintain cerebral blood flow. Simulation results demonstrate that neurotransmitter release triggers astrocytic responses that modulate vessel radius to optimize oxygen and nutrient delivery. This integrated framework, to our knowledge the first model to combine these elements for the NGVU in the DVC, provides a robust and modular platform for future investigations into the pathophysiology of cerebral blood flow regulation and its role in autonomic control, including the regulation of stomach function.

We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or variances. Our comprehensive framework follows Bayesian principles and consists of specialized Markov chain Monte Carlo computational schemes that rely on modified Hamiltonian Monte Carlo to align with summary statistic constraints and a novel elliptical slice sampler adapted to the parameters of biological models. We benchmark our methods with synthetic data on microbial growth in batch culture and test them on real growth curve data from laboratory replication experiments on $\textit{Prochlorococcus}$ microbes. The results indicate that our learning framework can utilize experimental or historical data and lead to robust parameter estimation and data assimilation in ODE models of biological dynamics that outperform least-squares fitting.

Anemia is a decrease in hemoglobin and red blood cells and due to a decrease in hemoglobin, oxygen carrying capacity reduce. In this disease, the red blood cell the amount and volume decrease. In this research, healthy and live food powder were synthesized by a green route. This organic biomaterial was named NBS. The NBS healthy and live food powder has various vitamins, macro and micro molecules, and ingredients. Twenty Wistar rats were randomly divided into 4 equal groups, including control and treatment groups 1, 2 and 3. Nutritional supplements for healthy living were administered orally via gavage to rats in groups 1, 2, and 3 at 12.5, 25, and 50 mg/ kg, respectively, and within a period of 20 days, one day in between. There was no intervention in the control group in order to reach baseline blood factors. At the end of the study, blood samples were taken from the heart, including blood-red blood cells, hemoglobin, hematocrit and platelets using a fully automated blood cell counting machine. The results showed that the new dietary supplement reduced the level of hematocrit and platelets in the studied rats. The healthy and live food supplement at a concentration of 50 mg / kg increased blood levels compared to the control group. The results of this study showed that the use of healthy and live food supplement increased blood factors compared to the control group.

A fundamental characteristic of excitable systems is their ability to exhibit distinct subthreshold and suprathreshold behaviors. Precisely quantifying this distinction requires a proper definition of the threshold, which has remained elusive in neurodynamics. In this paper, we introduce a novel, energy-based threshold definition for excitable circuits grounded in dissipativity theory, specifically using the classical concept of required supply. According to our definition, the threshold corresponds to a local maximum of the required supply, clearly separating subthreshold passive responses from suprathreshold regenerative spikes. We illustrate and validate the proposed definition through analytical and numerical studies of three canonical systems: a simple RC circuit, the FitzHugh--Nagumo model, and the biophysically detailed Hodgkin--Huxley model.

While hydrodynamic coupling has long been considered essential for synchronisation of eukaryotic flagella, recent experiments on the unicellular biflagellate model organism {\it Chlamydomonas} demonstrate that -- at the single cell level -- intracellular mechanical coupling is necessary for coordination. It is therefore unclear what role, if any, hydrodynamic forces actually play in the synchronisation of multiple flagella within individual cells, arguably the building block of large scale coordination. Here we address this question experimentally by transiently blocking hydrodynamic coupling between the two flagella of single {\it Chlamydomonas}. Our results reveal that in wild type cells intracellularly-mediated forces are necessary and sufficient for flagellar synchronisation, with hydrodynamic coupling causing minimal changes in flagellar dynamics. However, fluid-mediated ciliary coupling is responsible for the extended periods of anti-phase synchronisation observed in a mutant with weaker intracellular coupling. At the single-cell level, therefore, flagellar coordination depends on a subtle balance between intracellular and extracellular forces.

Protein-Protein Interaction (PPI) prediction is a key task in uncovering cellular functional networks and disease mechanisms. However, traditional experimental methods are time-consuming and costly, and existing computational models face challenges in cross-modal feature fusion, robustness, and false-negative suppression. In this paper, we propose a novel supervised contrastive multimodal framework, SCMPPI, for PPI prediction. By integrating protein sequence features (AAC, DPC, CKSAAP-ESMC) with PPI network topology information (Node2Vec graph embedding), and combining an improved supervised contrastive learning strategy, SCMPPI significantly enhances PPI prediction performance. For the PPI task, SCMPPI introduces a negative sample filtering mechanism and modifies the contrastive loss function, effectively optimizing multimodal features. Experiments on eight benchmark datasets, including yeast, human, and H.pylori, show that SCMPPI outperforms existing state-of-the-art methods (such as DF-PPI and TAGPPI) in key metrics such as accuracy ( 98.01%) and AUC (99.62%), and demonstrates strong generalization in cross-species prediction (AUC > 99% on multi-species datasets). Furthermore, SCMPPI has been successfully applied to CD9 networks, the Wnt pathway, and cancer-specific networks, providing a reliable tool for disease target discovery. This framework also offers a new paradigm for multimodal biological information fusion and contrastive learning in collaborative optimization for various combined predictions.

This work presents a novel approach for characterizing the mechanical behavior of atrial tissue using constitutive neural networks. Based on experimental biaxial tensile test data of healthy human atria, we automatically discover the most appropriate constitutive material model, thereby overcoming the limitations of traditional, pre-defined models. This approach offers a new perspective on modeling atrial mechanics and is a significant step towards improved simulation and prediction of cardiac health.