Related papers: Morse Index Classification and Landscape of Kuramo…
In the context of realistic calculations for strongly-correlated materials with $d$- or $f$-electrons the efficient computation of multi-orbital models is of paramount importance. Here we introduce a set of invariants for the…
We consider the mean-field noisy Kuramoto-Daido model, which is a McKean-Vlasov equation on the circle with bimodal interaction $W(\theta)=\cos\theta+m\cos2\theta$ for $m\ge 0$ and interaction strength $K$, generalizing the celebrated noisy…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
Class imbalance is a common challenge in real-world binary classification tasks, often leading to predictions biased toward the majority class and reduced recognition of the minority class. This issue is particularly critical in domains…
This paper is concerned with the existence of multiple stable fixed point solutions of the homogeneous Kuramoto model. We develop a necessary condition for the existence of stable fixed points for the general network Kuramoto model. This…
Reservoir computing is a powerful tool to explain how the brain learns temporal sequences, such as movements, but existing learning schemes are either biologically implausible or too inefficient to explain animal performance. We show that a…
In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a…
In this paper, we construct local Morse homology in a new way and compute the local Morse homology of the critical points of the Lagrange problem. As a corollary, we prove for the first time that each of the linear critical points is either…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
We consider a Kuramoto model for the dynamics of an excitable system consisting of two coupled active rotators. Depending on both the coupling strength and the noise, the two rotators can be in a synchronized or desynchronized state. The…
This paper introduces an algorithmic approach to the analysis of Jacobi stability of systems of second order ordinary differential equations (ODEs) via the Kosambi--Cartan--Chern (KCC) theory. We develop an efficient symbolic program using…
We study the stability of the Quantum Critical Point (QCP) for itinerant ferromagnets commonly described by the Hertz-Millis-Moriya (HMM) theory. We argue that in $D \leq 3$, long-range spatial correlations associated with the Landau…
In dynamical systems, the full stability of fixed point solutions is determined by their basin of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works…
We discuss the recently proposed description of Kuramoto model in terms of hyperbolic space and relate it to the information geometry. In particular the dynamical equation in Kuramoto all-to-all model is identified with the gradient flow of…
This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…
We show that the stability problem and the problem of constructing Barabanov norms can be resolved for planar linear switching systems in an explicit form. This can be done for every compact control set of $2 \times 2$ matrices. If the…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model (E(5/12)) to describe odd nuclei at the critical point in the transition from the spherical to $\gamma$-unstable behaviour. In the model, a…
We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this…
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…