相关论文: Dynamical Complexity in the C.elegans Neural Netwo…
Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify…
Complex systems, from the human brain to the global economy, are made of multiple elements that interact in such ways that the behaviour of the `whole' often seems to be more than what is readily explainable in terms of the `sum of the…
We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…
Biological neurons exhibit remarkable intelligence: they maintain internal states, communicate selectively with other neurons, and self-organize into complex graphs rather than rigid hierarchical layers. What if artificial intelligence…
In large neuronal networks, it is believed that functions emerge through the collective behavior of many interconnected neurons. Recently, the development of experimental techniques that allow simultaneous recording of calcium concentration…
Probing the developing neural circuitry in Caenorhabditis elegans has enhanced our understanding of nervous systems. The C. elegans connectome, like those of other species, is characterized by a rich club of densely connected neurons…
Recent whole brain imaging experiments on $\textit{C. elegans}$ has revealed that the neural population dynamics encode motor commands and stereotyped transitions between behaviors on low dimensional manifolds. Efforts to characterize the…
This paper extends our previous work~(Szumi\'nski and Maciejewski, 2024), where we explored the dynamics and integrability of the double-spring pendulum. Here, we investigate the variable-length double pendulum, a three-degree-of-freedom…
We explore the interplay between the topological relevance of a neuron and its dynamical traces in experimental cultured neuronal networks. We monitor the growth and development of these networks to characterise the evolution of their…
Brain research has been driven by enquiry for principles of brain structure organization and its control mechanisms. The neuronal wiring map of C. elegans, the only complete connectome available till date, presents an incredible opportunity…
We present a study on the emergence of a variety of spatio temporal patterns among neurons that are connected in a multiplex framework, with neurons on two layers with different functional couplings. With the Hindmarsh-Rose model for the…
This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with…
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN…
We exploit the reduced space of C. elegans postures to develop a novel tracking algorithm which captures both simple shapes and also self-occluding coils, an important, yet unexplored, component of worm behavior. We apply our algorithm to…
The availability of empirical data that capture the structure and behavior of complex networked systems has been greatly increased in recent years, however a versatile computational toolbox for unveiling a complex system's nodal and…
Studies regarding knowledge organization and acquisition are of great importance to understand areas related to science and technology. A common way to model the relationship between different concepts is through complex networks. In such…
A new mathematical model for complex neural networks of the partly diffusive Hindmasrh-Rose equations with boundary coupling is proposed. Through analysis of absorbing dynamics for the solution semiflow, the asymptotic synchronization of…
We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…