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In matching markets such as kidney exchanges and freight exchanges, delayed matching has been shown to improve overall market efficiency. The benefits of delay are highly sensitive to participants' sojourn times and departure behavior, and…
We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary…
This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust…
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
A number of recent self-supervised learning methods have shown impressive performance on image classification and other tasks. A somewhat bewildering variety of techniques have been used, not always with a clear understanding of the reasons…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
Representation learning on graphs has emerged as a powerful mechanism to automate feature vector generation for downstream machine learning tasks. The advances in representation on graphs have centered on both homogeneous and heterogeneous…
The wide spread use of positioning and photographing devices gives rise to a deluge of traffic trajectory data (e.g., vehicle passage records and taxi trajectory data), with each record having at least three attributes: object ID, location…
We address tracking and prediction of multiple moving objects in visual data streams as inference and sampling in a disentangled latent state-space model. By encoding objects separately and including explicit position information in the…
During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure…
We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha)\cdot x_{n-1}),$…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
This work introduces a learning-enhanced observer (LEO) for linear time-invariant systems with uncertain dynamics. Rather than relying solely on nominal models, the proposed framework treats the system matrices as optimizable variables and…