A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Transformers predict scattering amplitudes in theoretical physics.
New sigma models compute graviton scattering amplitudes from quaternionic geometry.
Ambitwistor string matches superstring chiral integrands at zero tension.
We give a self-contained derivation of the MHV amplitudes for gravity and use the associated twistor generating function to define a twistor action for the MHV diagram approach to gravity. Starting from a background field calculation on a spacetime with anti self-dual curvature, we obtain a simple spacetime formula for…
Twistor space constructions and actions are given for full Yang-Mills and conformal gravity using almost complex structures that are not, in general, integrable. These are used as the basis of a derivation of the twistor-string generating functionals for tree level perturbative scattering amplitudes of Yang-Mills and c…
The amplituhedra arise as images of the totally nonnegative Grassmannians by projections that are induced by linear maps. They were introduced in Physics by Arkani-Hamed \& Trnka (Journal of High Energy Physics, 2014) as model spaces that should provide a better understanding of the scattering amplitudes of quantum fie…
In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in t…
The reduction problem of the chiral field equation on symmetric spaces is studied. It is shown that the symmetric chiral field has infinitely many local conservation laws. A recursive formula for these conservation laws is derived and the first associated integral of motion are given explicitly. Furthermore, the Zakhar…
CAP-BM learns complex-valued data's amplitude and phase distributions.
A new RBM model handles both linear and log-amplitude spectrograms.
Gravitational interactions of higher spin fields are generically plagued by inconsistencies. We present a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang--Mills d…
Quantum computer method for pricing rainbow options efficiently.
This paper shows how learning the phase-amplitude coupling improves bio-signal classification.
New insights connect strong coupling SYM amplitudes to hyperkähler geometry.
A fast method for estimating radar amplitude density parameters.
Improved formulation of spinfoam quantum gravity with cosmological constant, ensuring all amplitudes are finite and providing semiclassical asymptotics.
Atiyah classes of DG manifolds of positive amplitude are invariant under weak equivalences.
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert ac…
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
We define a topological quantum membrane theory on a seven dimensional manifold of holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is quantum amplitudes of non-local observables …
Paper computes Atiyah class for DG manifolds of amplitude +1.
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…
We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In parti…
Paper explains scattering diagrams' role in mirror symmetry.
New method uses broken scattering to uniquely identify Finsler manifolds.
GSAN learns adaptive node representations using geometric scattering and attention.
New method learns soliton dynamics from scattering data without assuming known equations.
Scattering representations simplify SBI for images without extra compression.
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
We review aspects of twistor theory, its aims and achievements spanning thelast five decades. In the twistor approach, space--time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three--fold -- the twistor space. After giving an elementary construction of this s…
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtai…
Paper develops formulas for shape derivatives in wave scattering.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and gra…
Study scattering rigidity on stationary manifolds using geodesics.
We study topological open string amplitudes on orientifolds without fixed planes. We determine the contributions of the untwisted and twisted sectors as well as the BPS structure of the amplitudes. We illustrate our general results in various examples involving D-branes in toric orientifolds. We perform the computation…
MODWST improves classification tasks with wavelet scattering.
Study on scattering geodesics on modular surface and their sojourn times.
Scattering theory on Riemann surfaces with explicit matrix and generalized period mappings.
Study on recovering Lorentzian metrics from scattering data.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric…
The paper proves a category of dg manifolds with finite positive amplitude.
Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.
Bayesian Scattering offers a simple baseline for image data uncertainty.
Scattering theory for linearised gravity on Schwarzschild black hole exterior.
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducin…
We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean for . The metric perturbation may have arbitrarily small support.