Related papers: How Stands Collapse I
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
We explore self-similar collapse solutions to the Einstein-axion-dilaton system in arbitrary spacetime dimensions, which are invariant under spacetime dilation combined with internal $SL(2,R)$ transformations. We set up a numerical…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of…
The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if…
In this paper we establish the existence of solutions for a model describing the evolution of a linearly viscoelastic body which is constrained to remain confined in a prescribed half-space. The confinement condition under consideration is…
While state-of-the-art contrastive Self-Supervised Learning (SSL) models produce results competitive with their supervised counterparts, they lack the ability to infer latent variables. In contrast, prescribed latent variable (LV) models…
In an earlier paper \cite{yu2021Finiteness}, we showed that there are finitely many stationary configurations (consisting of equilibria, rigidly translating configurations, relative equilibria and collapse configurations) in the planar…
In this article, we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow the recently developed system level synthesis (SLS) approach and impose locality structure on the resulting…
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…
We derive stationary solutions to the two-dimensional hyperbolic discrete nonlinear Schr\"odinger (HDNLS) equation by starting from the anti-continuum limit and extending solutions to include nearest-neighbor interactions in the coupling…
Generalized method of moments estimators based on higher-order moment conditions derived from independent shocks can be used to identify and estimate the simultaneous interaction in structural vector autoregressions. This study highlights…
This work is to provide a comprehensive treatment of the relationship between the theory of the generalized (palindromic) eigenvalue problem and the theory of the Sylvester-type equations. Under a regularity assumption for a specific matrix…
One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe $n$ independent indicator variables $I_1,I_2,\dotsc,I_n$ sequentially and we try to stop on the last…
Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback…
We study several cosmological models with Bianchi \textrm{VI}$_{0}$ symmetries under the self-similar approach. In order to study how the \textquotedblleft constants\textquotedblright\ $G$ and $\Lambda$ may vary, we propose three scenarios…
In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…
We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In particular, we…
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration…
Catastrophic forgetting is a major problem in continual learning, and lots of approaches arise to reduce it. However, most of them are evaluated through task accuracy, which ignores the internal model structure. Recent research suggests…