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 classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
In this paper we study some global properties of static potentials on asymptotically flat -manifolds in the nonvacuum setting. Heuristically, a static potential represents the (signed) length along of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…
Study proves a sharp upper bound for the zero set area of a static manifold's potential.
Study on Sturm-Liouville problems with zero potential and Neumann boundary conditions.
Study uses zero-shot models to forecast mortality rates globally.
We examine the fixed points to first-order RG flow of a non-linear sigma model with background metric, dilaton and tachyon fields. We show that on compact target spaces, the existence of fixed points with non-zero tachyon is linked to the sign of the second derivative of the tachyon potential (this is the anal…
We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must c…
The paper studies static manifolds with boundary and their properties.
We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in $\r^2$. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a charactisation of the nodal set, and use this to obtain bounds on the mul…
New method uses diffusion models to generate proteins with specific motifs.
We study the modularity of the genus zero open Gromov-Witten potentials and its generating matrix factorizations for elliptic orbifolds. These objects constructed by Lagrangian Floer theory are a priori well-defined only around the large volume limit. It follows from modularity that they can be analytically continued o…
Problems of segmentation, denoising, registration and 3D reconstruction are often addressed with the graph cut algorithm. However, solving an unconstrained graph cut problem is NP-hard. For tractable optimization, pairwise potentials have to fulfill the submodularity inequality. In our learning paradigm, pairwise poten…
We consider the question whether a static potential on an asymptotically flat 3-manifold can have nonempty zero set which extends to the infinity. We prove that this does not occur if the metric is asymptotically Schwarzschild with nonzero mass. If the asymptotic assumption is relaxed to the usual assumption under whic…
Paper proposes a new framework for predictive optimization without training data.
We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schrödinger operator with convex potential and Dirichlet boundary data on a convex domain is bounded below by the spectral gap on an interval of the same diameter with zero poten…
Statistical Lie algebras with constant curvature are linked to locally conformally Kähler structures.
Paper improves zero-shot protein stability prediction by clarifying free-energy foundations.
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
In this paper we provide a new method for establishing the rotational symmetry of the solutions to a couple of very classical overdetermined problems arising in potential theory, in both the exterior and the interior punctured domain. Thanks to a conformal reformulation of the problems, we obtain Riemannian manifolds w…
In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of for which the pressure map exhibits a phase transition. By a careful choice of the metric at the cusp w…
Randomly initialized wide neural networks with zero-mean activations are nearly independent, potentially solving AI interpretability limits.
The paper explores transformations between power law problems and geodesics on cones.
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the Heisenberg group, thought of as a three-dimensional sub-Riemannian manifold. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the fundamental solution to the sub-Laplaci…
Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.
Study of metrics on positive-definite matrices from power potential, linking to power means.
Generative classifiers show surprising human-like performance.
Upper bounds for magnetic Laplacian eigenvalues on planar domains.
Proposes efficient FOBO algorithms for global maxima of expensive functions.
Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
A new model synthesizes population with fewer structural and sampling zeros.
Large deep learning models offer significant accuracy gains, but training billions to trillions of parameters is challenging. Existing solutions such as data and model parallelisms exhibit fundamental limitations to fit these models into limited device memory, while obtaining computation, communication and development …
OTSeg uses multi-prompt Sinkhorn attention to improve zero-shot semantic segmentation.
A conformal geometry determines a distinguished, potentially singular, variant of the usual Yamabe problem, where the conformal factor can change sign. When a smooth solution does change sign, its zero locus is a smoothly embedded separating hypersurface that, in dimension three, is necessarily a Willmore energy minimi…
The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian converges in a norm-resolvent sense to a Schroedinger operator on the limit…
We show how to parameterise solutions of the general relativistic vector constraint equation on Einstein manifolds by unconstrained potentials. We provide a similar construction for the trace-free part of tensors satisfying the linearised scalar constraint. Previous work of ours has provided similar different construct…
A new geometric framework resolves singularities in anomalous transport.
Study finds solutions to inequality decay to zero on warped cylinders.
We show that for a Schrödinger operator with bounded potential on a manifold with cylindrical ends the space of solutions which grows at most exponentially at infinity is finite dimensional and, for a dense set of potentials (or, equivalently for a surface, for a fixed potential and a dense set of metrics), the constan…
Paper explores using 0-surgery to find exotic 4-manifolds.
Paper proves no nontrivial solutions to certain elliptic equations on graphs.
Paper explores using LLMs for zero-shot reinforcement learning in continuous spaces.
Study electric field and potential of torus knots, focusing on z-axis.
Study on heat flow across two half-lines with special boundary conditions.
We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as well as expanding soltions with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with low…
The Ma-Trudinger-Wang curvature --- or cross-curvature --- is an object arising in the regularity theory of optimal transportation. If the transportation cost is derived from a Hamiltonian action, we show its cross-curvature can be expressed in terms of the associated Jacobi fields. Using this expression, we show the l…
While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely Kahler metrics. We establish its convergence on Kahler manifolds for suitable initia…
Study on symmetric hyperbolic systems with nonlocal potentials, proving well-posedness and existence of solutions.
A new algorithm optimizes softmax units in large language models.