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.
Gauge theory for families helps compare 4-manifold groups.
We describe a mathematical link between aspects of information theory, called pairwise comparisons, and discretized gauge theories. The link is made by the notion of holonomy along the edges of a simplex. This correspondance leads to open questions in both field.
Uniform Laplace comparison for Kähler Ricci flow on Fano manifolds.
Proves curvature comparison theorem for manifolds with conical singularities.
We give a version of the comparison principle from pluripotential theory where the Monge-Ampère measure is replaced by the Bergman kernel and use it to derive a maximum principle
Spider category comparison proves equivalence to Sikora's quotient category.
We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the s…
New model for pairwise comparisons without stochastic transitivity.
The paper compares Steklov and Laplacian eigenvalues on graphs.
This note explores comparison geometry concepts and theorems.
Paper proves a sharp weighted Isoperimetric inequality for substatic manifolds.
New proofs and refined theorems on bounded cohomology.
Abstract cone operators prove scalar curvature comparisons on singular manifolds.
New signs and gradings enable detailed comparison in Heegaard Floer theory.
The paper proves a comparison principle for complex Monge-Ampère flows and solves a uniqueness problem.
We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry-Émery curvature. The model…
In this paper, we study the theory of geodesics with respect to the Tanaka-Webster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some Hopf-Rinow type, Cartan-Hadamard type and Bonnet-Myers type results are establi…
Developing a non-symmetric strainer theory for spaces with non-negative curvature beyond Alexandrov geometry.
This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured la…
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this homology theory with one term and two term (rack) homology theori…
We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spin-c Dirac quantization is also included.
Bounding characteristic numbers of Riemannian manifolds via volume.
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves th…
Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expe…
Paper proposes a new method to compare classifiers across multiple datasets.
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to possess various desirable properties along with a characteristic exploratory fl…
We treat the vakonomic dynamics with general constraints within a new geometric framework which will be appropriate to study optimal control problems. We compare our formulation with Vershik-Gershkovich one in the case of linear constraints. We show how nonholonomic mechanics also admits a new geometrical description w…
Study controlled contagion with state-dependent killing, proving a comparison principle.
Study on deep neural networks for reward modeling with pairwise comparison data.
This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants o…
Study compares two knot pairings and their equivalence.
Introduces Alexandrov spaces with curvature below, covering various theorems.
The paper develops new methods to study sharp isoperimetric properties on complex spaces.
We analyze training dynamics in Gaussian mixture models using a comparison theorem.
We calibrate and test various variants of field theory models of the interest rate with data from eurodollars futures. A model based on a simple psychological factor are seen to provide the best fit to the market. We make a model independent determination of the volatility function of the forward rates from market data…
In this paper, we obtain a localization formula in differential K-theory for -action. Then by combining an extension of Goette's result on the comparison of two types of equivariant -invariants, we establish a version of localization formula for equivariant -invariants. An important step of our approach is t…
This work introduces a method to compare sparse neural network topologies using graph theory.
By explicitly comparing constructions, we prove that the higher torsion invariants of smooth bundles defined by Igusa and Klein via Morse theory agree with the higher torsion invariants defined by Badzioch, Dorabiala, Dwyer, Weiss, and Williams using homotopy theoretical methods.
Interdisciplinary study linking potential theory and elliptic PDEs.
Refines Khovanov homology using signed Burnside categories.
We study the volume of extrinsic balls and the capacity of extrinsic annuli in minimal submanifolds which are properly immersed with controlled radial sectional curvatures into an ambient manifold with a pole. The key results are concerned with the comparison of those volumes and capacities with the corresponding entit…
With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active learning, in which algorithms with access to large pools of data may adaptively choose …
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…
This study compares Markowitz and Single-Index models for Malaysian stocks.
New index theory proves Gromov's dihedral conjectures.
Establishing criteria for top cell inertness in complexes.
We provide several results on the existence of metrics of non-negative sectional curvature on vector bundles over certain cohomogeneity one manifolds and homogeneous spaces up to suitable stabilization. Beside explicit constructions of the metrics, this is achieved by identifying equivariant structures upon these vecto…
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-d…