In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
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48 results for “trace maximization”
Extends flat submanifold properties from hyperbolic plane to symmetric spaces.
problem Spectral asymptotics for orbital integrals in symmetric spaces.
method Generalizes geodesic properties to maximal flat submanifolds.
result Establishes geometric properties of maximal flat submanifolds in symmetric spaces.
New proof shows maximal arithmetic groups are finite.
problem Finiteness of maximal arithmetic reflection groups.
method Arithmetic Margulis lemma without automorphic forms.
result Finiteness of maximal arithmetic reflection groups proven.
Study of elliptic boundary value problems on non-compact manifolds.
problem Analyzing elliptic differential operators on manifolds with non-compact boundaries.
method Regularity theory and trace theorems for sections in the maximal domain under various assumptions.
result Systematic study of local and nonlocal boundary conditions, including the Atiyah-Patodi-Singer condition.
We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for pattern recognition and feature extraction, existing methods …
This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the corr…
We trace the initiative by Professor Meghnad Saha to develop a (statistical) physics model of market economy and his search for the mechanism to constrain the entropy maximized width of the income distribution in a society such that the spread of inequality can be minimized.
Improves modeling of sets with permutation invariant densities.
problem Challenges in calculating trace limit practicality of current methods.
method Proposes an alternative approach to define permutation equivariant transformations with closed form trace.
result Improves both training and final performance.
Explainable, Stable, and Scalable Graph Convolutional Networks for Learning Graph Representationcs.LG
New GCNs solve graph embedding problems efficiently and interpretably.
problem Graph embedding for scalable and interpretable machine learning.
method Proposed two GCNs: CAFE-GCN and sphere-GCN, based on constrained optimization.
result Both GCNs yield good approximations of dominant eigenvectors and perform dimensionality reduction.
Paper proposes ASCCA for sparse CCA with trace Lasso regularization.
problem Sparse CCA in high-dimensional settings with correlated variables.
method Trace Lasso regularization, reformulated to Riemannian manifolds, inexact augmented Lagrangian method.
result Improved stability and interpretation of sparse CCA.
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…
Consider a Riemannian symmetric space of non-compact type, where denotes a connected, real, semi-simple Lie group with finite center, and a maximal compact subgroup of . Let be its Oshima compactification, and the regular representation of on $\widet…
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.
Suppose that N is a geometrically finite orientable hyperbolic 3-manifold. Let P(N,C) be the space of all geometrically finite hyperbolic structures on N whose convex core is bent along a set C of simple closed curves. We prove that the map which associates to each structure in P(N,C) the lengths of the curves in the b…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the tra…
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points, which was the case for previous such constructions. No…
In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichmüller curv…
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.
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.
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.
It is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model. The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maxim…
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.
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.
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…
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.
Higher index theorem for Dirac operators on finite-volume spaces.
problem Index of Dirac operators on finite-volume spaces.
method Using algebraic K-theory and traces defined by orbital integrals.
result Nonzero and computable results for higher orbital integrals.
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.
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.
Consider a proper, isometric action by a unimodular, locally compact group on a complete Riemannian manifold . For equivariant elliptic operators that are invertible outside a cocompact subset of , we show that a localised index in the -theory of the maximal group -algebra of is well-defined. The …
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.
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.
L-spaces and knot tracesmath.GT
New findings on knots and their traces, distinguishing L-space knots by their 0-trace.
problem Characterizing knots by their traces and Dehn surgeries.
method Combining Heegaard Floer homology with surface homeomorphisms and dynamics.
result The 0-trace detects every L-space knot, contrasting with characterizing surgeries.
This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the same trace field, and infinitely many 1-cusped finite volume hyperbolic 3-manifo…
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
Clarifies a trace for Heisenberg operators on contact manifolds.
problem Calculating the index of Heisenberg elliptic operators on contact manifolds.
method Introduced a new trace on Heisenberg pseudodifferential operators and constructed a cocycle in periodic cyclic cohomology.
result Simplified the construction of the trace on Heisenberg pseudodifferential operators.
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.
Sharp inequality found on three-balls for fourth order Sobolev traces.
problem Fourth order Sobolev trace inequality on three-balls.
method Established through equivalence to a third order Sobolev inequality on two-spheres.
result Sharp fourth order Sobolev trace inequality on three-balls.
Infinite knots have non-integer trace values.
problem Finding knots with non-integer trace values.
method Proved existence of infinitely many non-homeomorphic hyperbolic knot complements with specific trace properties.
result Infinitely many non-homeomorphic hyperbolic knot complements with non-integer trace values.
Introduces expected eligibility traces for more efficient credit assignment in reinforcement learning.
problem Efficiently assigning credit to states and actions in reinforcement learning.
method Introduces expected eligibility traces, allowing updates to counterfactual sequences.
result Substantial improvements in temporal-difference learning can be achieved with expected traces.
Quantum trace map defined for 3-manifolds with torus boundaries.
problem Quantifying topological structures of 3-manifolds with torus boundaries.
method Defining a quantum trace map from skein module to a quantum torus module.
result Established a 3D quantum trace map for 3-manifolds with torus boundaries.
New knots found that resist trace detection.
problem Knots not detected by any trace.
method Extended existing results to new knots.
result Knots exist that share traces with infinitely many distinct knots and are not detected by any trace.
Quantum heat tracesmath-ph
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the u…
New hyperbolic manifolds found with same trace ring.
problem Finding non-commensurable hyperbolic manifolds with identical trace rings.
method Proved existence of infinitely many non-commensurable manifolds with same ambient group and trace ring.
result Infinitely many non-commensurable hyperbolic manifolds with the same ambient group and trace ring.
Sub-Riemannian Selberg trace formulae for compact quotients of SL(2, R)
problem Computing zeta-regularized determinants of sub-Laplacians
method Using Fourier decomposition and Selberg trace formulae
result Compact determinant formula expressed in terms of base hyperbolic surface and relative Selberg product
The abstract discusses detecting knotted spheres through their traces in high dimensions.
problem Detecting knotted spheres in high-dimensional spaces.
method Generalizing the RBG link construction to all dimensions and using surgery.
result Existence of non-isotopic smooth -knots with diffeomorphic traces.
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.
The study computes trace fields and minimal polynomials for specific knots and links.
problem Computing trace fields and minimal polynomials for specific knots and links.
method Using factorization theorems for sparse polynomials.
result Results depend on the degrees of the trace fields over Q being sufficiently large.