Related papers: Embedding Information onto a Dynamical System

We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…

We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are…

A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross-section of the position-time sine-Gordon amplitude profile. Here we…

Representing token embeddings as probability distributions over learned manifolds allows for more flexible contextual inference, reducing representational rigidity while enhancing semantic granularity. Comparative evaluations demonstrate…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

We present a unified framework for embedding and analyzing dynamical systems using generalized projection operators rooted in local conservation laws. By representing physical, biological, and engineered systems as graphs with incidence and…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…

This article introduces a novel and fast method for refining pre-trained static word or, more generally, token embeddings. By incorporating the embeddings of neighboring tokens in text corpora, it continuously updates the representation of…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

We study the Euler Alignment system of collective behavior, equipped with `topological' interaction protocols, which were introduced to the mathematical literature by Shvydkoy and Tadmor. Interactions subject to these protocols may depend…

This paper deals with the design of Excitation and Measurement Patterns (EMPs) for the identification of dynamical networks, when the objective is to identify only a subnetwork embedded in a larger network. Recent results have shown how to…

Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple decomposition method is presented that decouples the…

We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…

Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream…

Model Predictive Controllers (MPC) require a good model for the controlled process. In this paper I infer inductive biases about a physical system. I use these biases to derive a new neural network architecture that can model this real…

We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…

Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation for each node in the network. The learned embeddings could advance various learning tasks such as node classification, network…