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.
Computes minimal dilatation for Thurston maps on surfaces.
We study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions, adjoints and self-adjointness of such realizations are discussed. We construct regu…
New spectral sequences derived from shellable tilings.
Cappell and Shaneson pointed out in 1978 interesting properties of Browder - Livesay invariants which are similar to differentials in some spectral sequence. Such spectral sequence was constructed in 1991 by Hambleton and Kharshiladze. This spectral sequence is closely related to a problem of realization of elements of…
Study improves Hayashi-Yoshida estimator for high-dimensional stock covolatility.
We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to geometrically realize these results to produce a hypersurface with prescribed sectional curv…
The paper develops spectral networks in symplectic topology and their relation to Lagrangian fillings.
Spectral flow connects manifold geometry to rigidity criteria.
A simple equation explains standard model coupled to gravity.
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and …
We give a method of decomposing bundle-valued polynomials compatible with the action of the Lie group , where important tools are -equivariant operators and their spectral decompositions. In particular, the top irreducible component is realized as an intersection of kernels of these operators.
The paper studies obstructions to homotopy invariance of loop coproducts.
In this paper we investigate the spectral sequence associated to a Riemannian foliation which arises naturally on a Vaisman manifold. Using the Betti numbers of the underlying manifold we establish a lower bound for the dimension of some terms of this cohomological object. This way we obtain cohomological obstructions …
Algorithm learns graph ARMA processes for missing signal estimation.
The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the underlying materials in a given hyperspectral image by selecting a small subset of…
There are a number of homological knot invariants, each satisfying an unoriented skein exact sequence, which can be realized as the limit page of a spectral sequence starting at a version of the Khovanov chain complex. Compositions of elementary 1-handle movie moves induce a morphism of spectral sequences. These morphi…
Proposes CRG_IMSC for better clustering of multi-view data.
New method filters large networks from financial data to reveal key subnetworks.
Let (M,g,J) be a compact Hermitian manifold with a smooth boundary. Let and be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M,g,J) is Kaehler if and only if $Spec(Δ_p)=S…
Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci operator of an oriented closed Riemannian manifold can be realized as a spectral functional, namely the functional defined by the zeta function …
To a link L in the 3-sphere, we associate a spectral sequence whose E^2 page is the reduced Khovanov homology of L and which converges to a version of the monopole Floer homology of the branched double cover. The pages E^k for k > 1 depend only on the mutation equivalence class of L. We define a mod 2 grading on the sp…
Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.
The paper extends Strichartz's conjecture to spinor bundles over real hyperbolic spaces.
We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension and the observati…
Proposes a spectral method for jointly smooth functions on multiple manifolds.
We present a solution to scale spectral algorithms for learning sequence functions. We are interested in the case where these functions are sparse (that is, for most sequences they return 0). Spectral algorithms reduce the learning problem to the task of computing an SVD decomposition over a special type of matrix call…
Graph Signal Processing improves stock market volatility forecasting.
We discuss a variant of `blind' community detection, in which we aim to partition an unobserved network from the observation of a (dynamical) graph signal defined on the network. We consider a scenario where our observed graph signals are obtained by filtering white noise input, and the underlying network is different …
A proof of the Willmore conjecture is presented. With the help of the global Weierstrass representation the variational problem of the Willmore functional is transformed into a constrained variational problem on the moduli space of all spectral curves corresponding to periodic solutions of the Davey-Stewartson equation…
SNJ recovers latent tree models from similarity matrices.
Develops quantum cluster algebra approach to solve tetrahedron equation.
Suppose that one particular block in a stochastic block model is of interest, but block labels are only observed for a few of the vertices in the network. Utilizing a graph realized from the model and the observed block labels, the vertex nomination task is to order the vertices with unobserved block labels into a rank…
This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be…
New method detects and analyzes correlation in multiple network data.
A new method for spectral barycentre of graph datasets.
Model tracks structural changes in Brownian particle configurations on a sphere.
The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of the fractional part of the eta-invariant in this case. The method used to obtai…
We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give nece…
Optimization geometrodynamics simplifies adaptive optimizer dynamics.
Unified method to compute Laplace spectra on homogeneous principal bundles.
Jones-Wenzl projectors lifted to Khovanov spectra, proving knot conjectures.
Quantum reservoir computing needs coherence influx for effective information processing.
Constructs Lagrangian correspondences for Higgs bundles and holomorphic connections.
Paper predicts interference for better LA in URLLC.
Paper addresses uncertainty in model generalization under regime shifts.
We establish spectral theorems for random walks on mapping class groups of connected, closed, oriented, hyperbolic surfaces, and on . In both cases, we relate the asymptotics of the stretching factor of the diffeomorphism/automorphism obtained at time of the random walk to the Lyapunov exponent of …
A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a …
Develops an L^p theory for Dolbeault-Dirac operators on compact Kähler manifolds.