Related papers: Thorn forking, weak normality, and theories with s…
We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of…
Weak-to-strong generalization, where weakly supervised strong models outperform their weaker teachers, offers a promising approach to aligning superhuman models with human values. To deepen the understanding of this approach, we provide…
In the article 'Criteria for Strong and Weak Random Attractors' necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.
We introduce and study semi-equational and weakly semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong…
We use the martingale convergence method to get the weak convergence theorem on general functionals of partial sums of independent heavy-tailed random variables. The limiting process is the stochastic integral driven by $\alpha-$stable…
We prove the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray-Lions operator with nonstandard growth conditions. The proof of our main result uses variational methods and the…
Counterfactual explanations are widely used to interpret machine learning predictions by identifying minimal changes to input features that would alter a model's decision. However, most existing counterfactual methods have not been tested…
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…
A random vector ${\bf X}$ is weakly stable iff for all $a,b\in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X}+b{\bf X}'\stackrel{d}{=}{\bf X}\Theta$. This is equivalent (see \cite{MOU}) with the condition that for…
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
The problem whether weighted estimates for multilinear Fourier multipliers with Sobolev regularity hold under weak condition on weights is considered.
The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This…
We present a systematic analysis of the $B^{(*)}\to\pi\,\ell\,\nu$ weak decay form factors to order $1/m_b$ in the heavy quark effective theory, including a discussion of renormalization group effects. These processes are described by a set…
We further develop the notion of perinormality from our last paper, showing that it is preserved by many pullback constructions. In doing so, we introduce the concepts of relative perinormality and fragility for ring extensions.
We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…
The convergence of DP Fourier series which are neither strongly convergent nor strongly divergent is discussed in terms of the Taylor series of the corresponding inner analytic functions. These are the cases in which the maximum disk of…
We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and H\"older regularity…