Related papers: Weak and Semi-Contraction for Network Systems and …
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This…
We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
In this note we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix measure as a framework to study stability of monotone and…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…
A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…
This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Multistationarity - the existence of multiple equilibrium points - is a common phenomenon in dynamical systems from a variety of fields, including neuroscience, opinion dynamics, systems biology, and power systems. A recently proposed…
In the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristic (attribute) of nodes (or edges) of networks. Each isospectral compression (when a…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…
Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple…
In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process…