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 cosmic structures using Topological Data Analysis and Persistence Energy.
Dark matter in the universe evolves through gravity to form a complex network of halos, filaments, sheets and voids, that is known as the cosmic web. Computational models of the underlying physical processes, such as classical N-body simulations, are extremely resource intensive, as they track the action of gravity in …
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, wa…
Bayesian neural networks improve cosmic parameter estimation from modified gravity simulations.
The study proves strong cosmic censorship violation for spherically symmetric dust clouds.
Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.
Penrose's conjecture links black holes and gravitational singularities.
Proves weak cosmic censorship for a specific Einstein-scalar field system in 2+1 dimensions.
Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.
New model reduces bias in cosmic shear measurements.
This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature of the symmetric surfaces and the cosmological constant $…
We consider how microlocal methods developed for tomographic problems can be used to detect singularities of the Lorentzian metric of the Universe using measurements of the Cosmic Microwave Background radiation. The physical model we study is mathematically rigorous but highly idealized.
We explore the use of random forest and gradient boosting, two powerful tree-based machine learning algorithms, for the detection of cosmic strings in maps of the cosmic microwave background (CMB), through their unique Gott-Kaiser-Stebbins effect on the temperature anisotropies.The information in the maps is compressed…
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
Study geometric properties of generalized vacuum static spaces.
We address the issue of strong cosmic censorship for T^2-symmetric spacetimes with positive cosmological constant. In the case of collisionless matter, we complete the proof of the C^2 formulation of the conjecture for this class of spacetimes. In the vacuum case, we prove that the conjecture holds for the special case…
CoSMIC extends flow-based SVI to transdimensional problems.
The paper connects Diophantine approximation to black hole behavior, proving blow-up conditions.
Proves conditions for Cauchy horizons in low-regularity spacetimes.
Study of cosmic microwave background polarization using spin random fields.
Bayesian Gaussian Processes improve exoplanet transit and Hubble constant inference.
New singularity concept in GR: volume singularities.
Formula calculates MOY webs and link polynomials.
Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.
We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is lineari…
Classifies hexagonal circular 3-webs with cubic polar curves.
Proof confirms cosmic censorship for charged gravitational collapse.
We construct flat 3-webs via semi-simple geometric Frobenius manifolds of dimension three and give geometric interpretation of the Chern connection of the web. These webs turned out to be biholomorphic to the characteristic webs on the solutions of the corresponding associativity equation. We show that such webs are he…
We give various results and applications using the connection associated with a -web. Precisely, we exhibit fundamental invariants of the web related to the differential equation of first order which presents the web. They cast some new lights on the connection and its construction, both conceptually an…
Proves inextendibility of weak null singularities from curvature blow-up.
We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply a recently found in [AGL] the linearizability conditions for 4-webs in the plane to confirm that a 4-web MW (Mayrhofer's web) with equal curvature forms of its 3-subwebs and a nonconstant basic invariant is …
In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n+2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provided that one of web foliations is pointed, there is also associated a unique affine struc…
In this paper we construct new solutions of the Kahler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, that we call gravitating vortex equations, describe Abelian vortices on the Riemann surface with b…
Study local invariants of divergence-free webs in geometry.
This paper has been withdrawn by the authors due to the fact that the webs considered in the paper are ``Veronese-like webs'' which are different from Veronese webs.
Investigates webs related to cluster algebras and polylogarithms.
We present a projectively invariant description of planar linear 3-webs. For a non-hexagonal 3-web, we introduce family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion. Finally, we propose an algorithm for resolving the …
TomOpt optimizes muon detector designs using differentiable programming.
The article characterizes a hemisphere using a Laplace operator and a differential equation.
Much information available on the web is copied, reused or rephrased. The phenomenon that multiple web sources pick up certain information is often called trend. A central problem in the context of web data mining is to detect those web sources that are first to publish information which will give rise to a trend. We p…
For a four-dimensional (nonisoclinicly geodesic) three-web W (3, 2, 2), a transversal distribution is defined by the torsion tensor of the web. In general, this distribution is not integrable. The authors find necessary and sufficient conditions of its integrability and prove the existence theorem for webs W (3, 2,…
In this paper we study the linearizability problem for 3-webs on a 2-dimensional manifold. With an explicit computation based on the theory developed in the paper "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp. 2643-2654), we examine a 3-web whose linearizability was claimed in the same paper. We …
Veronese webs appear as the natural way of passing to the quotient of curves in the projective space. In thi paper, we give the link between classical multidimensionnal webs and veronse webs by mean of interpolation.
We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology…
New hexagonal circular 3-webs with reducible curves classified.
In this paper, we reconstruct Kuperberg's web space. We introduce a new web (a trivalent diagram) and new relations between Kuperberg's web diagrams and the new diagram. Using the webs, we define crossing formulas corresponding to R-matrices associated to some irreducible representations and calculate…
Study on static perfect fluid space-time geometry and boundary estimates.
Gronwall conjecture states that a planar 3-web which admits more than one distinct linearization is locally equivalent to an algebraic web. We give a partial answer to the conjecture in the affirmative for the class of planar 3-webs with the web curvature that vanishes to order three at a point. The differential relati…