arXiv research

Study on estimating unstable open-loop matrices from state trajectories.

With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance mat…

Study cohomology of GL₂n(Z) and graph complexes using Pfaffian forms.

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in sma…

Bayesian algorithm stabilizes unknown continuous-time systems from unstable data.

Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We…

Ricci flow simulations show unstable Fubini-Study metrics develop singularities.

Study finds limits for conical Kähler-Einstein metrics on unstable surfaces.

Noncompact Ricci-flat solutions have infinite unstable dimensions.

Improved stability for matrix recovery from rank-one measurements.

New loss function helps learn unstable dynamical systems.

Hybrid ResNet and RMT improve covariance matrix estimation for cryptocurrency portfolios.

Unstable minimal surfaces in n-space link to hyperbolic products.

Segre varieties' hyperplane sections are unstable under certain conditions.

Proves transitivity of real Anosov diffeomorphisms with specific properties.

Study shows instability of specific cone solutions in high-dimensional spaces.

In this note we show that the bi-invariant Einstein metric on the compact Lie group $G_{2}$ is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi-invariant metrics on the compact, connected, simple Lie groups. Interestingly, $G_{2}$ is the only unstable exceptional…

Algorithm identifies and transfers unstable features to create robust classifiers.

Survey of computations for Riemann surface moduli spaces, focusing on unstable homology.

GeoHNN models physics laws for stable, accurate predictions.

The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.

Constructs a family to handle unstable fibers on complex surfaces.

SFB uses stable features to adapt unstable ones for better performance.

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.

In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like $g_{ij}=(1+\frac{1}{l})^{2}δ_{ij}+O(l^{-2})$. The existence of uns…

Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic acc…

In banking practice, rating transition matrices have become the standard approach of deriving multi-year probabilities of default (PDs) from one-year PDs, the latter normally being available from Basel ratings. Rating transition matrices have gained in importance with the newly adopted IFRS 9 accounting standard. Here,…

New proof associates partitions to isotopic pseudo-Anosov homeomorphisms.

We show that the pair $(X, -K_X)$ is K-unstable for a del Pezzo manifold $X$ of degree five with dimension four or five. This disprove a conjecture of Odaka and Okada.

A crypto coin designed to provide a stabilization instrument backed up by minded like financial investments instruments to maintain the purchase value of savings across time, in order to construct new tools for unstable economies.

We show that a strict, nearly Kähler $6$-manifold with either second or third Betti number nonzero is linearly unstable with respect to the $ν$-entropy of Perelman and hence is dynamically unstable for the Ricci flow.

In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).

This article deals with stability issues related to geodesic X-ray transforms, where an interplay between the (attenuation type) weight in the transform and the underlying geometry strongly impact whether the problem is stable or unstable. In the unstable case, we also explain what types of artifacts are expected in te…

The paper proves regularity of states on manifolds with unstable dynamics.

We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the work of Song-Weinkove on the J-flow.

Node2vec embeddings are unstable and unstable with parameter choices.

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly unstable for most inverse problems beyond denoising. In th…

We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown-Peterson cohomology, we show that the corresponding Hodge filtered spaces satisfy an analog of Wilson's unstable splitting. As a consequence, we obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology fo…

The paper shows measures equidistribute on affine submanifolds with a rate.

The paper explores maximal destabilizers for both K-stability and Chow-stability in unstable situations.

Study finds Kähler-Einstein metrics on two Pasquier varieties.

CV inference can be invalid for relatively unstable model comparisons.

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semi-stable and unstable cases are new, and it is shown that the flow …

Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that very often, only nearly unstable Hawkes processes are able to fit the data properl…

In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed submanifold in Heisenberg group, we give some conditions on Weingarten maps to obtain …

We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficientl…

Constructs flow lines connecting unstable to stable self-expanders.