Related papers: Gradient formula for linearly self-interacting bra…
Extending the analysis of hep-th/0504128, we obtain a formal expression for the coupling between brane matter and the radion in a Randall-Sundrum braneworld. This effective theory is correct to all orders in derivatives of the radion in the…
This review is devoted to strings and branes. Firstly, perturbative string theory is introduced. The appearance of various types of branes is discussed. These include orbifold fixed planes, D-branes and orientifold planes. The connection to…
We investigate the existence of brane solutions in braneworld scenarios described by real scalar field in the presence of modified $f(R)$ gravity with a single extra dimension. In the case of constant curvature, we obtain first-order…
The N=1 superspace generalization of the 3-brane action in 6 dimensions with partially broken N=2 supersymmetry can be constructed using N=1 chiral, complex linear, or real linear superfields. The physical scalars of these multiplets give…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
We critically assess a recent assertion (arXiv:1508.01124) concerning using delta-functions to analyze how higher-codimension branes back-react on their environment. We also briefly summarize the state of the art: describing how…
We study a codimension 2 braneworld in the Einstein-Gauss-Bonnet gravity. In the linear regime, we show the conventional Einstein gravity can be recovered on the brane. While, in the nonlinear regime, we find corrections due to the…
In this paper, the solutions of the pure geometric thick $f(R)$ brane are investigated. The formulation of $f(R)$ is chosen as $f(R)=\sum_{i=1}^{n}a_{i}R^{i}+\Lambda$. For the certain value of $n$, the brane solution can be calculated, and…
A candidate explanation of the good empirical performance of deep neural networks is the implicit regularization effect of first order optimization methods. Inspired by this, we prove a convergence theorem for nonconvex composite…
We present the explicit forms of supergravity solutions for the various intersecting two BPS branes in eleven and ten dimensions, where one brane is localized at the delocalized other brane. Our partially localized supergravity solutions…
We give a classification of all multiple intersections of D-branes in ten dimensions and M-branes in eleven dimensions that corresponds to threshold BPS bound states. The residual supersymmetry of these composite branes is determined. By…
The curvature on codimension-two and higher branes is not regular for arbitrary matter sources. Nevertheless, the low-energy theory for an observer on such a brane should be well-defined and independent to any regularization procedure. This…
We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the gradient…
This work deal with braneworld scenarios with generalized gravity. We investigate models where the potential of the scalar field is polynomial or nonpolynomial. We obtain exact and approximated solutions for the scalar field, warp factor…
We discuss a new class of brane models (extending both p-brane and Dp-brane cases) where the brane tension appears as an additional dynamical degree of freedom instead of being put in by hand as an ad hoc dimensionfull scale. Consistency of…
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these…
Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…
We study the regularization of theories of ``brane induced'' gravity in codimension $N>1$. The brane can be interpreted as a thin dielectric with a large dielectric constant, embedded in a higher dimensional space. The kinetic term for the…