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Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…

Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…

We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known…

In this paper, we are revisiting pattern mining and especially itemset mining, which allows one to analyze binary datasets in searching for interesting and meaningful association rules and respective itemsets in an unsupervised way. While a…

Not every positive functional defined on bi-variate polynomials of a prescribed degree bound is represented by the integration against a positive measure. We isolate a couple of conditions filling this gap, either by restricting the class…

Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…

The definition of the centroid in finite dimensions does not apply in a function space because of the lack of a translation invariant measure. Another approach, suggested by Nik Weaver, is to use a suitable collection of finite-dimensional…

The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…

The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…

Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…

The level of a function f on an n-dimensional space encloses a region. The volume of a region between two such levels depends on both levels. Fixing one of them the volume becomes a function of the remaining level. We show that if the…

Let $f$ be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we prove the monotonicity of spectral radii of vertical scaling matrices without additional assumptions. We also obtain the…

We construct functions $f \colon [0,1] \to [0,1]$ whose graph as a subset of $\mathbb{R}^2$ has Hausdorff dimension greater than any given value $\alpha \in (1,2)$ but conformal dimension $1$. These functions have the property that a…

Though calculations based on density functional theory (DFT) are used remarkably widely in chemistry, physics, materials science, and biomolecular research and though the modern form of DFT has been studied for almost 60 years, some…

Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On…

We use the Brascamp--Lieb inequality from functional analysis to prove novel inequalities for the upper box, packing, and Assouad dimensions of fractal sets in terms of the dimensions of certain projections. Analogous inequalities do not…

Depth from a monocular video can enable billions of devices and robots with a single camera to see the world in 3D. In this paper, we present an approach with a differentiable flow-to-depth layer for video depth estimation. The model…