相关论文: Membrane topology and matrix regularization

We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…

It is suggested that topological membranes play a fundamental role in the recently proposed topological M-theory. We formulate a topological theory of membranes wrapping associative three-cycles in a seven-dimensional target space with G_2…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…

Membranes holomorphically embedded in flat noncompact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static…

This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…

We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = infinity limit of the supersymmetric matrix quantum mechanics describing D0-branes. The evidence for the conjecture consists of…

In this work we present a framework for studying the eigenvalues of a family of matrices with a particular displacement structure. The family admits a specific decomposition as the product of an upper and a lower triangular matrices having…

We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left…

Some exact solutions to the classical matrix model equations that arise in the context of M(embrane) theory are given, and their topological nature is identified.

The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…

Motivated by the recent achievements in the framework of the semiclassical limit of the M-theory/field theory correspondence, we propose an approach for obtaining exact membrane solutions in general enough M-theory backgrounds, having field…

We consider smooth bounded surfaces with a smooth boundary and a prescribed background metric g_0. We now consider all metrics g conformal to g_0 which have a prescribed volume M. We now minimize the first eigenvalue of the Laplace operator…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices leads to the…

The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…

Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may…