Related papers: An introduction to extended Gevrey regularity

The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and Hemisphere, and in 3D for the Rectangle. The cases of the 2D…

We study how maximal regularity estimates with respect to the continuous functions improve automatically in cases where the spatial norm is fundamentally different from the supremum norm. More precisely, we invoke properties such as weak…

We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded…

Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…

The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…

We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; (ii) In case of Lie groups, representations of the…

Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…

We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains $C$, with non-smooth boundary, in possibly non-compact manifolds. Assuming $C$ is a submanifold with corners, or…

A new robust class of multivariate skew distributions is introduced. Practical aspects such as parameter estimation method of the proposed class are discussed, we show that the proposed class can be fitted under a reasonable time frame. Our…

In anomaly detection, the degree of irregularity is often summarized as a real-valued anomaly score. We address the problem of attributing such anomaly scores to input features for interpreting the results of anomaly detection. We…

We introduce a class of rings using which we define the concept of skew regularity for quaternion-valued functions over quaternions. It is shown that the notion of skew regularity coincides with the concept of slice regularity over…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…

We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in \cite{STtopo}. While these systems exhibit flocking behavior emerging from purely local…

Penalties that induce smoothness are common in nonparametric regression. In many settings, the amount of smoothness in the data generating function will not be known. Simon and Shojaie (2021) derived convergence rates for nonparametric…

We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…

We review and extend a technique for recovering a smooth function from its averages over a wide class of curves in a general region of Euclidean space. The method is based on complexification of the underlying vector fields defining the…

We use Levy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter as p grows large. This generalizes the class of local-global shrinkage rules based on scale mixtures of normals,…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…