q-bio.PE

arXiv:2501.01383v1 Announce Type: cross Abstract: A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on $X$ which is either observed directly or derived from a data set. For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response matrix either of which defines the network completely. We argue that these functions should be viewed as a similarity and a dissimilarity function on the set of the nodes moreover they are related via the covariance mapping also known as the Farris transform or the Gromov product. We will explore the properties of electrical networks from this point of view. It has been known for a while that the resistance matrix defines a metric on the nodes of the electrical networks. Moreover for a circular electrical network this metric obeys the Kalmanson property as it was shown recently. We will call such a metric an electrical Kalmanson metric. The main results of this paper is a complete description of the electrical Kalmanson metrics in the set of all Kalmanson metrics in terms of the geometry of the positive Isotropic Grassmannian whose connection to the theory of electrical networks was discovered earlier. One important area of applications where Kalmanson metrics are actively used is the theory of phylogenetic networks which are a generalization of phylogenetic trees. Our results allow us to use in phylogenetics the powerful methods of reconstruction of the minimal graphs of electrical networks and possibly open the door into data analysis for the methods of the theory of cluster algebras.

arXiv:2305.03340v2 Announce Type: replace-cross Abstract: As Evolutionary Dynamics moves from the realm of theory into application, algorithms are needed to move beyond simple models. Yet few such methods exist in the literature. Ecological and physiological factors are known to be central to evolution in realistic contexts, but accounting for them generally renders problems intractable to existing methods. We introduce a formulation of evolutionary games which accounts for ecology and physiology by modeling both as computations and use this to analyze the problem of directed evolution via methods from Reinforcement Learning. This combination enables us to develop first-of-their-kind results on the algorithmic problem of learning to control an evolving population of cells. We prove a complexity bound on eco-evolutionary control in situations with limited prior knowledge of cellular physiology or ecology, give the first results on the most general version of the mathematical problem of directed evolution, and establish a new link between AI and biology.

arXiv:2409.00795v2 Announce Type: replace-cross Abstract: Malaria is one of the deadliest diseases in the world, every year millions of people become victims of this disease and many even lose their lives. Medical professionals and the government could take accurate measures to protect the people only when the disease dynamics are understood clearly. In this work, we propose a compartmental model to study the dynamics of malaria. We consider the transmission rate dependent on temperature and altitude. We performed the steady state analysis on the proposed model and checked the stability of the disease-free and endemic steady state. An artificial neural network (ANN) is applied to the formulated model to predict the trajectory of all five compartments following the mathematical analysis. Three different neural network architectures namely Artificial neural network (ANN), convolution neural network (CNN), and Recurrent neural network (RNN) are used to estimate these parameters from the trajectory of the data. To understand the severity of a disease, it is essential to calculate the risk associated with the disease. In this work, the risk is calculated using dynamic mode decomposition(DMD) from the trajectory of the infected people.

arXiv:2412.16249v1 Announce Type: new Abstract: Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the imitation learning framework. Here, we adopt the reinforcement learning paradigm, where individuals make their moves aiming to maximize their accumulated rewards. Specifically, we apply Q-learning to UG, where each player is assigned two Q-tables to guide decisions for the roles of proposer and responder. In a two-player scenario, fairness emerges prominently when both experiences and future rewards are appreciated. In particular, the probability of successful deals increases with higher offers, which aligns with observations in behavioral experiments. Our mechanism analysis reveals that the system undergoes two phases, eventually stabilizing into fair or rational strategies. These results are robust when the rotating role assignment is replaced by a random or fixed manner, or the scenario is extended to a latticed population. Our findings thus conclude that the endogenous factor is sufficient to explain the emergence of fairness, exogenous factors are not needed.

arXiv:2404.00866v1 Announce Type: cross Abstract: We have developed a nonlinear method of time series analysis that allows us to obtain multiple nonlinear trends without harmonics from a given set of numerical data. We propose to apply the method to recognize the ongoing status of COVID-19 infection with an analytical equation for nonlinear trends. We found that there is only a single nonlinear trend, and this result justifies the use of a week-based infection growth rate. In addition, the fit with the obtained analytical equation for the nonlinear trend holds for a duration of more than three months for the Delta variant infection time series. The fitting also visualizes the transition to the Omicron variant.