Study categorifies link invariants using Soergel bimodules.
problem Categorification of link invariants.
method Explicit computation of derived traces of Soergel bimodules.
result Derived annular Khovanov-Rozansky link invariant.
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48 results for “derived traces”
New methods derive a generalized Frenkel trace formula for Lie groups.
problem Deriving a generalized Frenkel trace formula for Lie groups.
method Applying supersymmetric localization to quantum mechanical and gauged sigma models.
result Presented two complementary approaches for the derivation of the trace formula.
Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.
problem Deriving and generalizing the Selberg trace formula.
method Supersymmetric localization principle and path integral derivation.
result Derives Selberg trace formula on arbitrary compact Riemann surfaces and generic compact locally symmetric spaces.
A novel method for parallel transport and geodesics on submanifolds.
problem Understanding parallel transport and geodesics on submanifolds.
method Rolling tangent space to visualize and analyze parallel transport and geodesics.
result Conditions for parallel transport and geodesics are simplified and visualized in the tangent space.
Derives a sharp inequality for trace-free matrices with applications to hypersurfaces.
problem Classifying conformally flat hypersurfaces and characterizing rotational hypersurfaces.
method Derives a sharp inequality relating eigenvalues of trace-free matrices and applies it to hypersurfaces.
result New proof of the classification of conformally flat hypersurfaces and construction of a functional for rotational hypersurfaces.
The paper analyzes heat trace asymptotics for de Rham and Dolbeault complexes in both real and complex settings.
problem Examining heat trace asymptotics for de Rham and Dolbeault complexes in different geometric settings.
method Analyzing the derived heat trace asymptotics for generalized Witten perturbations in both real and complex settings.
result The integral of the local density for the derived heat trace asymptotics is related to the Euler characteristic and characteristic numbers of the tangent and twisting vector bundles.
Lagrangian traces help understand Johnson filtration in handlebody groups.
problem Understanding the Johnson filtration in handlebody groups.
method Defining Lagrangian traces on derivations of free Lie algebra.
result Lagrangian traces vanish on Johnson filtration elements.
Motivated by a recent work of Ache and Chang concerning the sharp Sobolev trace inequality and Lebedev-Milin inequalities of order four on the Euclidean unit ball, we derive such inequalities on the Euclidean unit ball for higher order derivatives. By using, among other things, the scattering theory on hyperbolic space…
The abstract theorem is extended to higher genus surfaces.
problem Generalizing the web trace theorem to higher genus surfaces.
method Geometric derivation and spin geometry of embedded loops.
result Expansion of twisted Kasteleyn matrices for higher genus surfaces.
New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
Paper derives trace formula for magnetic Laplacian at zero energy.
problem Trace formula for magnetic Laplacian at zero energy.
method Generalizes Gutzwiller trace formula, focuses on zero energy level.
result Derives trace formula at zero energy level.
We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions…
We derive a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with conic singularities, using the Singular Asymptotics Lemma of Jochen Bruening and Robert T. Seeley [BS]. In the subsequent paper we investigate how the terms in the expansion reflect the geometry …
In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace we derive isotopy invariants for framed and classical knots and links in the so…
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method …
Off-policy reinforcement learning with eligibility traces is challenging because of the discrepancy between target policy and behavior policy. One common approach is to measure the difference between two policies in a probabilistic way, such as importance sampling and tree-backup. However, existing off-policy learning …
Ray tracing sampler improves neural network sampling efficiency and resilience.
problem Sampling neural network posterior distributions efficiently and robustly.
method Markov Chain Monte Carlo using ray tracing through likelihood space.
result Significantly higher resilience to gradient heating compared to HMC.
Paper derives constraints for Bayesian Knowledge Tracing parameters.
problem Issues with EM algorithm in BKT parameter estimation.
method From first principles, derives constraints on BKT parameter space.
result Novel algorithm respects derived constraints for parameter estimation.
We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schroedinger operators and Schroedinger operators on immersed manifolds. In particular, we prove bounds on the eigenvalue lambda_{N+1} in terms of the lower spectrum, bou…
We prove involutivity of Einstein, Einstein-Maxwell and other field equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kahler theory are derived.
New method estimates log-determinant using trace powers, avoiding classical limitations.
problem Estimating log-determinant of large matrices efficiently and accurately.
method Interpolating moment-generating function and its derivative at zero using trace powers.
result No continuous estimator using finite moments can be uniformly accurate over unbounded conditioning.
Study of Hamiltonian flows on character varieties for self-intersecting curves.
problem Analyzing periodic orbits of Hamiltonian flows on character varieties.
method Explicit computations in Fock-Goncharov coordinates.
result Hamiltonian flows of trace functions associated to self-intersecting curves on a pair of pants have periodic orbits.
We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of normalized orbital integrals associated to the hyperbolic conjugacy classes of this …
Formula derived for zeta functions of 3D foliated systems.
problem Analyzing zeta functions of 3D Riemannian foliated dynamical systems.
method Relating dynamical spectral -functions to zeta functions using the distributional dynamical Lefschetz trace formula.
result Proved a regularized determinant formula for zeta functions.
New heat trace coefficients reveal curvature effects in polygonal domains.
problem Understanding heat trace behavior in polygonal domains with curved corners.
method Local heat trace expansion through order , analyzing both Dirichlet and Neumann boundary conditions.
result Sharp sign law for the Dirichlet angular factor of the first corner-curvature heat invariant.
The paper finds torsion in Johnson homomorphisms' cokernels for large genus surfaces.
problem Existence of torsion in the cokernels of Johnson homomorphisms.
method Defined a map on Ker(Tr)∩D(H) whose image is 2-torsion and vanishes on the image of τ.
result Found 2-torsion in the cokernels of Johnson homomorphisms for large genus surfaces.
Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theorystat.ML
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.
TRACE analyzes risk changes in models trained on shifted data.
problem Understanding performance changes when a model trained on shifted data is used.
method TRACE framework decomposes risk change into four factors: generalization gaps, model change penalty, and covariate shift penalty.
result TRACE provides a diagnostic tool to understand and quantify risk changes due to covariate shift.
The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral -invariants using lifted …
Defines observer-invariant time derivatives on moving surfaces.
problem Deriving appropriate definitions for time derivatives on surfaces that move.
method Systematically derived from spacetime settings, considering observer-invariance and covariance principles.
result Formulations applicable for computations of tangential n-tensor fields on moving surfaces.
Method calculates systolic length of modular curves.
problem Computing upper bounds on systolic length of Riemann surfaces.
method Using congruence subgroups of hyperbolic triangle groups and traces of generators.
result Systolic length grows logarithmically with genus.
Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.
problem Heat kernel expansions on non-compact spaces, especially for Witten Laplacians.
method Introduced parabolic distance and used it to derive asymptotic expansions.
result Derived an asymptotic expansion of trace of heat kernel for small-time .
Study on Dirac operator spectrum on hyperbolic surfaces with shrinking geodesics.
problem Spectrum of spin Dirac operator on hyperbolic surfaces with pinched geodesics.
method Trace formula for Dirac operator, Huber's theorem, small-time heat trace asymptotic expansion.
result Convergence of Selberg zeta function for degenerating hyperbolic surfaces.
New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.
problem Stability and deformation theory of Einstein metrics.
method Introduces Chen-Nagano gauge condition, linking Lichnerowicz Laplacian to shifted scalar operator.
result Chen-Nagano gauge collapses to classical transverse-traceless gauge under spectral pinching assumptions.
Study of torus surgeries on knot traces, finding exotic surfaces and traces.
problem Understanding exotic surfaces and traces through torus surgeries.
method Realizing annulus twisting as torus surgery, using key technical insight.
result Exotic elliptic surfaces and traces discovered, improving known geography.
Classifies knot traces with specific trisection genus limits.
problem Classifying knot traces with specific trisection genus limits.
method Classifying knot traces with specific trisection genus limits.
result Infinitely many knots have traces with trisection genus 3 and 4, and arbitrarily large trisection genus.
We concern -compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are , or . By conducting a quantitative analysis of a linear equation associated with the problem, we prove that the trace-free second fundamental…
Guillemin trace formula adapted for group actions.
problem Distributional trace for proper, cocompact group actions.
method Developing an equivariant version of the distributional trace.
result Equivariant Guillemin trace formula for group actions.
Gynaecologists and obstetricians visually interpret cardiotocography (CTG) traces using the International Federation of Gynaecology and Obstetrics (FIGO) guidelines to assess the wellbeing of the foetus during antenatal care. This approach has raised concerns among professionals with regards to inter- and intra-variabi…
Researchers derive asymptotic expansions for thermoelastic operators on manifolds.
problem Determining precise geometric information from thermoelastic spectra.
method Asymptotic expansions with Dirichlet and Neumann boundary conditions.
result Explicit calculation of first two coefficients for volumes.
In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.
Examines a new type of analytic torsion on Riemannian manifolds.
problem Analyzing a new trace formula for Riemannian manifolds.
method Uses residue-trace instead of spectral zeta function quasi-trace.
result Defines and examines the residue analytic torsion.
Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of differential operators which we call correlation functions. These correlation functions a…
Extensions and Applications of Stein-Weiss Operators to the Study of Traceless Symmetric Tensorsmath.DG
The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.
problem Understanding Stein-Weiss operators on symmetric tensors of arbitrary rank.
method Analyzing the decomposition of tensor spaces into irreducible components and computing Weitzenbock formulas.
result Unified framework for second-order Stein-Weiss operators and tools for geometric analysis.
We generalize Hamilton's matrix Li-Yau-type Harnack estimate for the Ricci flow by considering the space of all LYH (Li-Yau-Hamilton) quadratics that arise as curvature tensors of space-time connections satisfying the Ricci flow with respect to the natural space-time degenerate metric. As a special case, we employ scal…
CausalSim corrects bias in trace-driven simulations for more accurate results.
problem Bias in trace-driven simulations due to system conditions during trace collection.
method CausalSim learns a causal model of system dynamics and latent factors from an RCT to remove bias from trace data.
result CausalSim reduces simulation errors by 53% and 61% compared to baselines, providing more accurate insights.