相关论文: Generalising holographic fishchain

This paper challenges the prevailing view that convolutional neural network (CNN) filters become increasingly specialized in deeper layers. Motivated by recent observations of clusterable repeating patterns in depthwise separable CNNs…

This thesis is mainly devoted to studying integrable deformations of the ${\rm AdS}_5 \times {\rm S}^5$ superstring and generalized supergravity. We start to give a brief review of the ${\rm AdS}_5 \times {\rm S}^5$ superstring formulated…

This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). Integrability corresponds to the…

The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…

In this paper we continue our studies of Hitchin systems on singular curves (started in hep-th/0303069). We consider a rather general class of curves which can be obtained from the projective line by gluing two subschemes together (i.e.…

Set-based learning is an essential component of modern deep learning and network science. Graph Neural Networks (GNNs) and their edge-free counterparts Deepsets have proven remarkably useful on ragged and topologically challenging datasets.…

The class of fighting fish is a recently introduced model of branching surfaces generalizing parallelogram polyominoes. We can alternatively see them as gluings of cells, walks on the square lattice confined to the quadrant or shuffle of…

The present article studies holomorphic isometric embeddings of arbitrary complex Grassmannians into quadrics, generalising results in [13]. The moduli spaces of these embeddings up to gauge and image equivalence are discussed using a…

We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with microlocal analytic continuation, this leads to uniqueness and…

In this paper we find new integrable one-dimensional lattice models of electrons. We classify all such nearest-neighbour integrable models with su(2)xsu(2) symmetry following the procedure first introduced in arXiv:1904.12005. We find 12…

In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels…

Convolutional Networks (ConvNets) have recently improved image recognition performance thanks to end-to-end learning of deep feed-forward models from raw pixels. Deep learning is a marked departure from the previous state of the art, the…

We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases…

In this paper we develop a general approach to dimer models analogous to Krichever's scheme in the theory of integrable systems. We start with a Riemann surface and the simplest generic meromorphic functions on it and demonstrate how to…

We generalise the techniques of arXiv:0908.1963 to describe derived deformations in simplicial categories. This allows us to consider deformation problems with higher automorphisms, such as chain complexes (which have homotopies) and stacks…

We extend the generalised hodograph method to regular non- diagonalisable integrable systems of hydrodynamic type, in light of the relation between such systems and F-manifolds with compatible connection. The method allows the construction…

We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed…

The predictions of the Mirror Symmetry are extended in dimensions n>3 and are proven for projective complete intersections Calabi-Yau varieties. Precisely, we prove that the total collection of rational Gromov-Witten invariants of such…

A flexible model is developed for multivariate generalized spherical distributions, i.e. ones with level sets that are star shaped. To work in dimension above 2 requires tools from computational geometry and multivariate numerical…

In this work, we introduce ShipHullGAN, a generic parametric modeller built using deep convolutional generative adversarial networks (GANs) for the versatile representation and generation of ship hulls. At a high level, the new model…