arXiv research

New inequality for refined knot invariants in a specific space.

Refines Khovanov homology using stable homotopy theory.

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…

Refines neural network predictions using background knowledge for improved accuracy.

New research shows label refinement and weak training have limitations for aligning LLMs.

Refines Khovanov homology for knots with involution.

In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …

New homotopy refinements for tangle invariants defined.

New homotopy refinements for tangle invariants.

Refined 3D index uses surgery and gradings to distinguish 3-manifolds.

The paper refines large N duality for knots using M-theory and string theory.

Refines deep generative models to improve data density precision.

Established a stable cohomotopy refinement for Pin(2) monopole invariants.

Refined 1-cocycle for knots helps quantify isotopies.

Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …

EGR refines and assesses protein complex structures.

A novel framework refines diffusion models iteratively for better downstream reward optimization.

A new framework forecasts implied volatility surfaces by separating learning and refinement stages.

Formula conjectured for refined SU(3) Vafa-Witten invariants of surfaces.

Study uses AI to refine loan assessments, improving credit default predictions.

Let $E$ be a flat complex vector bundle over a closed oriented odd dimensional manifold $M$ endowed with a flat connection $\nabla$. The refined analytic torsion for $(M,E)$ was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…

The refined analytic torsion, defined by M. Braverman and T. Kappeler on closed manifolds, can be viewed as a refinement of the Ray-Singer torsion, since it is a canonical choice of an element with Ray-Singer norm one, in case of unitary representations. The complex phase of the refinement is given by the rho-invariant…

Refined BN-S model improves crude oil hedging with machine learning.

The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the underlying data distribution setting where connections to maximal marginal diver…

Refined invariants for 4D 2-handlebodies, linking quantum groups and cohomology.

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Herm…

Quantifies scalar curvature under $C^0$ convergence, proving a refined version in all dimensions.

Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula…

Improved graph embedding through refined linear transformation and community recovery.

We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action. We give an explicit solution of the theory, in terms of a one-parameter refi…

A bicategory approach to differential cohomology is presented. Based on the axioms of Bunke-Schick, a symmetric monoidal groupoid is associated to differential refinements of cohomology theories. It is proven that such differential refinements are unique up to equivalence of the corresponding symmetric monoidal groupoi…

This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an…

Refined theorem on linear perturbations with applications in singularity theory and optimization.

We prove a refined Kato inequality for closed and coclosed differential $(p,q)$ forms on a Kahler manifold.

Graph neural networks refine speaker embeddings for better session-level diarization.

IterefinE combines KG refinement with embeddings to improve KG quality.

For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an analytic counterpart of the refined combina…

Proposes a new Hodge conjecture in Bott-Chern cohomology.

We establish refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator. Our main result is a general expression which gives the value of the constants appearing in the refined inequalities. These consta…

Improved anti-cancer drug sensitivity prediction using REFINED CNN ensemble learning.

AURA: Adaptive Uncertainty-aware Refinement for LLM-as-a-Judge Auditing

In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without boundary. We now derive a gluing formula for our construction, which can be viewed as…

We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. Roberts' definition of the Turaev-Viro state sum is exploited. Fu…

Refines Kronheimer-Mrowka's invariant for 4-manifolds with specific boundary conditions.

Method retrieves similar fashion items from images and text, enabling style refinement.

Automated refinement of sensor labels improves process mining models in smart homes.

Refines Hurwitz numbers with a two-parameter theory.

Let a $A$ be the 1-skeleton of a triangulated topological annulus. We establish bounds on the combinatorial modulus of a refinement $A'$, formed by attaching new vertices and edges to $A$, that depend only on the refinement and not on the structure of $A$ itself. This immediately applies to showing that a disk triangul…