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.
Study on black holes and photon surfaces in 4D spacetimes, proving uniqueness theorems.
Characterizes photon surfaces in static spacetimes, proving uniqueness.
Paper proves uniqueness of black holes and photon surfaces in higher dimensions.
Photon surfaces are timelike, totally umbilic hypersurfaces of Lorentzian spacetimes. In the first part of this paper, we locally characterize all possible photon surfaces in a class of static, spherically symmetric spacetimes that includes Schwarzschild, Reissner--Nordström, Schwarzschild-anti de Sitter, etc., in $n+1…
New proofs of unique photon surfaces in 4D spacetimes, extending previous work.
Paper proves rigidity of static manifolds and applies to metric extensions.
We establish two geometric inequalities, respectively, for harmonic functions in exterior Dirichlet problems, and for Green's functions in interior Dirichlet problems, where the boundary surfaces are smooth and convex. Both inequalities involve integrals over the mean curvature and the Gaussian curvature on an equipote…
In this paper we form relations for the determination of the elements of the Eötvös matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the normal equipotential surface and the Gauss curvature of the actual equipotential surface both passing through the point P is presented…
This thesis discusses the Newtonian limit of General Relativity for static isolated systems with compactly supported matter. We call these systems "geometrostatic" to underline their geometric nature. We introduce new quasi-local notions of mass and center of mass that can be read off locally in the vicinity of the mat…
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
Study maximal representations of surface groups via pleated surfaces in pseudo-Riemannian space.
The paper explores how topological methods can reveal insights into electric charge distributions on knots.
Unified framework for photon and massive particle hypersurfaces in stationary spacetimes.
Designs chiral photonic structures using machine learning for efficient optical properties.
Study null energy condition impacts on special hypersurfaces in static spacetimes.
Let be a harmonic function that solves an exterior Dirichlet problem. If all the level sets of are smooth Jordan curves, then there are several geometric inequalities that correlate the curvature with the ma…
Derives exact gradients for linear optics with single photons.
In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole uniqueness. In this note we establish uniqueness of photon spheres by adapting the argument of Bunting and Masood-ul-Alam, wh…
The paper simplifies FLRW photon propagators using geometric embeddings.
Photonic quantum reinforcement learning for control problems.
Researchers extend parametrization of Margulis spacetimes using strip deformations.
Machine learning classifies topological phases in leaky photonic lattices.
Enhances quantum machine learning models using Fock states.
Study improves chiral photonic metasurface design using neural networks and genetic algorithms.
We study the set of trapped photons of a subcritical (a<M) Kerr spacetime as a subset of the phase space. First, we present an explicit proof that the photons of constant Boyer--Lindquist coordinate radius are the only photons in the Kerr exterior region that are trapped in the sense that they stay away both from the h…
Adapting Israel's proof of static black hole uniqueness, we show that the Schwarzschild spacetime is the only static vacuum asymptotically flat spacetime that possesses a suitably defined photon sphere.
Photonic chip speeds up option pricing with GAN for financial efficiency.
In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asympt…
Photonic co-processor speeds up training of large neural networks.
We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that th…
We show a uniqueness result for the n-dimensional spatial Reissner-Nordström manifold: a static, electrovacuum, asymptotically flat system which is asymptotically Reissner-Nordström is a subextremal Reissner-Nordström manifold with positive mass, provided that its inner boundary is a (possibly disconnected) photon sphe…
Quantum computing at room temperature achieves high accuracy in image classification.
Proves a Minkowski inequality for static Einstein-Maxwell space-time.
Any surface can be foliated into equipotential hypersurfaces of the level sets. A current result is that the contours are the progressing wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The lev…
Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the poin…
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing curves subject to an area constraint are circles, and discuss implications for the ph…
Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.
We show that degenerate horizons exhibit a new trapping effect. Specifically, we obtain a non-degenerate Morawetz estimate for the wave equation in the domain of outer communications of extremal Reissner-Nordstrom up to and including the future event horizon. We show that such an estimate requires 1) a higher degree of…
Active learning method for neural population dynamics using optogenetics.
The paper extends IPC framework to stationary physical systems and validates it with a photonic system.
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
Most cryptocurrencies rely on Proof-of-Work (PoW) "mining" for resistance to Sybil and double-spending attacks, as well as a mechanism for currency issuance. Hashcash PoW has successfully secured the Bitcoin network since its inception, however, as the network has expanded to take on additional value storage and transa…
Paper constructs and proves existence of chiral triply-periodic minimal surfaces.
The paper develops methods for monitoring TPL machine health.
We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare …
Optical co-processor speeds up neural network training.
This paper is devoted to the study of the Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacet…
Paper tackles Bayesian image restoration in low-photon Poisson imaging problems.