arXiv research

Benchmark data sets are of vital importance in machine learning research, as indicated by the number of repositories that exist to make them publicly available. Although many of these are usable in the stream mining context as well, it is less obvious which data sets can be used to evaluate data stream clustering algor…

The family of Wilder continua in cubes of dimension > 2 and its two subfamilies-of continuum-wise Wilder continua and of hereditarily arcwise connected continua-are recognized as coanalytic absorbers in the hyperspace of subcontinua of the cubes. In particular, each of them is homeomorphic to the set of all nonempty co…

Develops a new trend power indicator using DSP techniques.

Study homology manifolds using spectral sheaves and spectral six functor formalism.

WILD-SCAV benchmarks AI in complex 3D FPS environments.

Let $C$ and $D$ be a pair of crumpled $n$-cubes and $h$ a homeomorphism of $\text{Bd }C$ to $\text{Bd }D$ for which there exists a map $f_h: C\to D$ such that $f_h|\text{Bd }C =h$ and $f_{h}^{-1}(\text{Bd }D)=\text{Bd }C$. In our view the presence of such a triple $(C,D,h)$ suggests that $C$ is "at least as wild as" $D…

Robots hold promise in many scenarios involving outdoor use, such as search-and-rescue, wildlife management, and collecting data to improve environment, climate, and weather forecasting. However, autonomous navigation of outdoor trails remains a challenging problem. Recent work has sought to address this issue using de…

We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and $\rm W_{Hα}$ vs. [NII]/H$α$ (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLI…

Double-well transitions are stiffer than minimal surfaces.

The main task in oil and gas exploration is to gain an understanding of the distribution and nature of rocks and fluids in the subsurface. Well logs are records of petro-physical data acquired along a borehole, providing direct information about what is in the subsurface. The data collected by logging wells can have si…

Well-quasi-orders proved on embedded planar graphs.

Study shows quasipositive fiber surfaces can't be well-ordered.

Paper solves local well-posedness for Schrödinger flow into sphere with natural boundary conditions.

Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.

The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.

(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backwa…

In this paper, we study the well adapted connection attached to a $(J^{2}=\pm 1)$-metric manifold, proving it exists for any of the four geometries and obtaining a explicit formula as a derivation law. Besides we characterize the coincidence of the well adapted connection with the Levi Civita and the Chern connections.

We prove that the well-rounded retract of SO_n\SL_n(R) is a minimal SL_n(Z)-invariant spine.

Optimizes task allocation for financial analysts to balance work efficiency and well-being.

Recent studies have shown that online portfolio selection strategies that exploit the mean reversion property can achieve excess return from equity markets. This paper empirically investigates the performance of state-of-the-art mean reversion strategies on real market data. The aims of the study are twofold. The first…

Study proves well-posedness and scattering for wave equations on hyperbolic spaces with singular data.

Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…

This paper studies a deformation retraction of Teichmüller space and its analogy with well-rounded retractions.

New findings show some designs can't be robustly recovered in linear regression.

Proves a quasi-order on fibre surfaces of positive braid links.

Proves well-posedness for Einstein equations with specific boundary conditions.

We study the question of well-posedness of the Cauchy problem for Schrödinger maps from $\rone \times \rtwo$ to the sphere $\stwo$ or to ${\mathbb H^2}$, the hyperbolic space. The idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear Schrödinger system of equa…

Efficient approach improves prediction calibration for domain shifts.

Proves well-posedness for Einstein equations with specific boundary data.

The moduli space metric and its Kahler potential for well-separated non-Abelian vortices are obtained in U(N) gauge theories with N Higgs fields in the fundamental representation.

In many applications, one works with neural network models trained by someone else. For such pretrained models, one may not have access to training data or test data. Moreover, one may not know details about the model, e.g., the specifics of the training data, the loss function, the hyperparameter values, etc. Given on…

What predicts the evolution over time of subjective well-being? We correlate the trends of subjective well-being with the trends of social capital and/or GDP. We find that in the long and medium run social capital largely predicts the trends of subjective wellbeing in our sample of countries. In the short-term this rel…

Outer space and Teichmüller space fail well-rounded retract analogy.

Gradient flow on diffeomorphisms for image registration, with well-posedness proven.

The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice and may be inappropriate in some contexts. Our concept sim…

For data sets populated by a very well modeled process and by another process of unknown probability density function (PDF), a desired feature when manipulating the fraction of the unknown process (either for enhancing it or suppressing it) consists in avoiding to modify the kinematic distributions of the well modeled …

Total torsion of 3D lines of curvature is an integer multiple of 2π.

We prove that the geodesic equations of all Sobolev metrics of fractional order one and higher on spaces of diffeomorphisms and, more generally, immersions are locally well posed. This result builds on the recently established real analytic dependence of fractional Laplacians on the underlying Riemannian metric. It ext…

We establish both local and global well-posedness for the heat flow of polyharmonic maps from $R^n$ to a compact Riemannian manifold without boundary for initial data with small BMO norms.

We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market …

In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric deformation, The characteristic form of this class of equations is changing its signs i…

Proves well-posedness of gradient solitons on bundle gerbe.

The commuting vector fields approach, devised for strichartz estimates in [13], was developed for proving the local well-posedness in the Sobolev spaces $H^s$ with $s>2+\frac{2-\sqrt{3}}{2}$ for general quasi-linear wave equation in ${\mathbb R}^{1+3}$ by Klainerman and Rodnianski. Via this approach they obtained the l…

This paper establish the local (or global, resp.) well-posedness of the heat flow of biharmonic maps from $R^n$ to a compact Riemannian manifold without boundary with small local BMO (or BMO, resp.) norms.

This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of int…

The reduced thin-sandwich equations (RTSE) appear within Wheeler's thin-sandwich approach towards the Einstein constraint equations (ECE) of general relativity. It is known that these equations cannot be well-posed in general, but, on closed manifolds, sufficient conditions for well-posedness have been established. In …

Study of Ricci iterations on Kähler metrics, proving new theorems.

The question why deep learning algorithms generalize so well has attracted increasing research interest. However, most of the well-established approaches, such as hypothesis capacity, stability or sparseness, have not provided complete explanations (Zhang et al., 2016; Kawaguchi et al., 2017). In this work, we focus on…