Related papers: Dynamics and Synchronization of Complex Neural Net…

The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…

This paper proposes a novel active boundary loss for semantic segmentation. It can progressively encourage the alignment between predicted boundaries and ground-truth boundaries during end-to-end training, which is not explicitly enforced…

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

This letter investigates the problem of output synchronisation in heterogeneous dynamical networks with nonlinear diffusive couplings in the presence of disturbances on the coupling links. By exploiting relative dissipativity properties…

Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…

We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all to all, whereas the inter-network interactions involve only a…

Leveraging recent advances in neuroscience and control theory, this paper presents a neuromimetic network model with dynamic symmetric connections governed by Hebbian learning rules. Formal analysis grounded in graph theory and classical…

We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave…

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…

A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the…

In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…

We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale's Law --- each neuron makes either excitatory or inhibitory connections onto its post-synaptic targets. We find that this…

The emergence of collective behaviors in networks of dynamical units in pairwise interaction has been explained as the effect of diffusive coupling. How does the presence of higher-order interaction impact the onset of spontaneous or…

This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly…

Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy, are based on integrals over the segmentation regions. Unfortunately, for highly unbalanced segmentations, such regional summations have values that differ by…

The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…

Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…

A feedforward neural network, including hidden layers, motivated by nonlinear functions (such as Tanh, ReLU, and Sigmoid functions), exhibits uniform approximation properties in Sobolev space, and discontinuous neural networks can reduce…

We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through…