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.
Sharp pseudospectral bounds prevent transient amplification in coupled gradient descent.
We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in terms of the spectral flow on S, the spectral flow on X (with certain Atiyah-Pato…
The paper introduces a trilinear functional to recover torsion in spectral triples.
A coupling method and an analytic one allow us to prove new lower bounds for the spectral gap of reversible diffusions on compact manifolds. Those bounds are based on the a notion of curvature of the diffusion, like the coarse Ricci curvature or the Bakry--Emery curvature-dimension inequalities. We show that when this …
Lobb observed in [arXiv:1103.1412] that each equivariant sl(N) Khovanov-Rozansky homology over C[a] admits a standard decomposition of a simple form. In the present paper, we derive a formula for the corresponding Lee-Gornik spectral sequence in terms of this decomposition. Based on this formula, we give a simple alter…
New theorem shows gaps in magnetic Schrödinger operator spectra for large coupling.
Witten deformation connects manifold spectra to Morse functions.
Study on spectral stability of an embedded annulus under curve shortening and Ricci flows.
A fast method learns plasma collision kernels from simulations, improving kinetic models.
A new method detects hidden driving forces in systems with multiple observables.
New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.
In this paper, we study a refined L2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral projections (and not just their traces) and obtain an information about classes of t…
Spectral feature learning improves IV regression for causal effect estimation.
Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.
TopoNTK kernel captures higher-order interactions in simplicial complexes.
DiffObs predicts global precipitation with realistic wave modes and low frequency variations.
Free lunch from noise reveals linear spectral features for RL.
The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group…
A criterion for training-free time-lagged spectral embeddings of multivariate time series
Study Dirac operators on finite warped cylinders with gauge fields.
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the…
We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Foc…
Community detection has been one of the central problems in network studies and directed network is particularly challenging due to asymmetry among its links. In this paper, we found that incorporating the direction of links reveals new perspectives on communities regarding to two different roles, source and terminal, …
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative structure and a spectral model of gravity coupled with matter which fits with expe…
Partial convexification improves tractability of low-rank spectral optimization problems.
Study of correlated Wigner matrices with BBP transitions.
Financial frequency combs emerge from macroeconomic long-range memory.
HyFAD improves time series imputation by combining time and frequency diffusion.
Study complex structures and curvature equations on compact manifolds.
We propose a new algorithm for hyperparameter selection in machine learning algorithms. The algorithm is a novel modification of Harmonica, a spectral hyperparameter selection approach using sparse recovery methods. In particular, we show that a special encoding of hyperparameter space enables a natural group-sparse re…
A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the res…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local structure/consistency of GM have been investigated as popular choices in practice. Howev…
This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding…
Study optimal spectral estimator for semi-supervised node classification.
Model tracks structural changes in Brownian particle configurations on a sphere.
FHRN uses continuous-time dynamics to stabilize reentrant neural computation.
Study wave functions in complex Chern-Simons theory, finding integrality and rational points.
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes conjecture, on coarse geometry and on higher index theory, 3) The geometrization of the …
Paper analyzes Langevin dynamics for multimodal Gaussian mixtures, controlling errors across dimensions.
Study of surface defects in gauge theories leads to duality and separation of variables.
Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intu…
Study on neural networks with non-normal interactions reveals unique spectral properties.
Drago optimizes DRO problems with faster convergence.
Study shows how anisotropic data affects learning dynamics in phase retrieval.
Motivated by the study of coupled Kähler-Einstein metrics by Hultgren and Witt Nyström and coupled Kähler-Ricci solitons by Hultgren, we study in this paper coupled Sasaki-Einstein metrics and coupled Sasaki-Ricci solitons. We first show an isomorphism between the Lie algebra of all transverse holomorphic vector fields…
We compute eta invariants of various Dirac type operators on circle bundles over Riemann surfaces via two approaches: an adiabatic approach based on the results of Bismut-Cheeger-Dai and a direct elementary one. These results, coupled with some delicate spectral flow computations are then used to determine the virtual …
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
Study of singular solutions to a fourth order system in a ball with a singularity.