26 papers · ranked by Valyu relevance
Yen‐Chi Chen
A solution manifold is the collection of points in a d-dimensional space satisfying a system of s equations with s < d. Solution manifolds occur in several statistical problems including missing data, algorithmic fairness, hypothesis testing, partial identifications, and nonparametric set estimation. We theoretically…
Anirvan M. Sengupta, Mariano Tepper, Cengiz Pehlevan, Alexander Genkin + 1 more
Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e., they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise? Here, we propose that localized receptive fields emerge in…
Serena Hughes, Timothy Hamilton, Tom Kolokotrones, Eric J. Deeds
Manifold learning builds on the “manifold hypothesis,” which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to define manifolds mathematically. These tools also cannot assess whether the manifold…
Asger M. Haugaard, Yilun Shang
Predicting extrema of chaotic systems in high-dimensional phase space remains a challenge. Methods, which give extrema that are valid in the long term, have thus far been restricted to models of only a few variables. Here, a method is presented which treats extrema of chaotic systems as belonging to discretised…
Fan Zhang, Lee Lindblom
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been constructed on a selection of manifolds having positive, negative, and vanishing spatial…
Han Zhou, Kai Cao, Yang Young Lu
Rapid advancements in single-cell sequencing technologies have empowered biologists to collect high-resolution omics profiles at the cellular level. Integrating such heterogeneous single-cell data, essential for gaining deeper insights into biological processes, is a formidable challenge. The difficulty arises from the…
Daphne Nesenberend, Arjen Doelman, Frits Veerman
The exact mechanisms behind many morphogenic processes are still a mystery. Mechanical cues, such as curvature, play an important role when tissue or cell shape is formed. In this work, we derive and analyze a mechanochemical model. This particular spatially one-dimensional model describes the deformation of a tissue-…
K. L. Duggal
We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present…
Bartosz Bieganowski, Pietro d’Avenia, Jacopo Schino, Daniel Strzelecki
In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-constant mean curvature. In particular, the non-constant mean curvature gives rise to supercritical terms in the equation, on top of singular…
Alberto Enciso, Willi Kepplinger, Daniel Peralta-Salas
Title: Significance In the study of the stationary incompressible fluid flows, one finds a subtle interplay between flexibility and rigidity properties, that is, between the existence of a wealth of solutions and the significant constraints that they must satisfy. A recent survey by Drivas and Elgindi draws attention…
Rodrigo Ávalos, Jorge H. de Lira
The reduced thin-sandwich equations (RTSE) appear within Wheeler's thin-sandwich approach towards the Einstein constraint equations (ECE) of general relativity. It is known that these equations cannot be well-posed in general, but, on closed manifolds, sufficient conditions for well-posedness have been established. In…
Robert L. Bryant, Jeanne N. Clelland
> Abstract. The following problem is addressed: A 3-manifold M is endowed with a triple Ω = Ω 1 , Ω 2 , Ω 3 of closed 2-forms. One wants to construct a coframing ω = ω 1 , ω2 , ω3 of M such that, first, dω i = Ωi for i = 1, 2, 3, and, second, the Riemannian metric g = ω 1 2 + ω 2 2 + ω 3 2 be flat. We show that, in the…
Weijie Lu, Manuel Pinto, Yonghui Xia
In this paper, we present a theory of smooth stable manifold for the non-instantaneous impulsive differential equations on the Banach space or Hilbert space. Assume that the non-instantaneous linear impulsive evolution differential equation admits a uniform exponential dichotomy, we give the conditions of the existence…
Letizia Branca, Giulio Colombo, Paolo Mastrolia, Filippo Mastropietro + 1 more
In this paper we study the geometry of φ-static perfect fluid spacetimes (φ-SPFST, for short). In the context of Einstein's General Relativity, they arise from a space-time whose matter content is described by a perfect fluid in addition to a nonlinear field expressed by a smooth map φ with values in a Riemannian…
Volker Branding
We study harmonic maps from surfaces coupled to a scalar and a two-form potential, which arise as critical points of the action of the full bosonic string. We investigate several analytic and geometric properties of these maps and prove an existence result by the heat-flow method.
Takashi Sakajo
A steady solution of the incompressible Euler equation on a toroidal surface $T_{R,r}$ of major radius R and minor radius r is provided. Its streamfunction is represented by an exact solution to the modified Liouville equation, $∇_{T_{R,r}}^{2}ψ=c \text{e}dψ+(8(/)d)κ$, where $∇_{T_{R,r}}^{2}$ and κ denote the…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…
Cris R. Hasan, Bernd Krauskopf, Hinke M. Osinga
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{4}$\end{document} R 4 and Application to the Full Hodgkin–Huxley Model Authors: ['Cris R. Hasan' 'Bernd…
Absos Ali Shaikh, Chandan Kumar Mondal
In this paper we consider the Ricci curvature of a Ricci soliton. In particular, we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
David Thompson, Johan Gielis
Our understanding of quantum phenomena often begins with simple particle-in-a-box style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. Simple model geometries of confinement afford analytic solutions, which are readily derivable, easily…
Diego Artacho, Marie-Amélie Lawn, Miguel Ortega‐Sánchez
Examples of such solutions which are invariant under a group of translations are the socalled translators, which have been extensively studied in the literature –see e.g. [CSS07, GLW11, MSHS15]. In [ALR19] the authors extend the concept of self-similar mean curvature flow to a more general setting, introducing the idea…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Siddhartha Sen, Tomas Ryan, David Muldowney, Maurizio Pezzoli
A special charged surface network with surface spin half particles on it, that can be arranged in topologically inequivalent ways, is introduced. It is shown that action potential-like signals can be generated in the network in response to local surface deformations of a particular kind. Signals generated in this way…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Yair Zarmi, Dennis Salahub
The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts) are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for…