Related papers: Designing plateaued Boolean functions in spectral …
In this work, we study functions that can be obtained by restricting a vectorial Boolean function $F \colon \mathbb{F}_2^n \rightarrow \mathbb{F}_2^n$ to an affine hyperplane of dimension $n-1$ and then projecting the output to an…
The inverse design of metamaterial architectures presents a significant challenge, particularly for nonlinear mechanical properties involving large deformations, buckling, contact, and plasticity. Traditional methods, such as gradient-based…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
Planar functions over finite fields give rise to finite projective planes. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and codebooks. They were originally defined only in finite fields with…
In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…
We introduce a method based on Bezout's theorem on intersection points of two projective plane curves, for determining the nonlinearity of some classes of quadratic functions on $\mathbb{F}_{2^{2m}}$. Among those are the functions of…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch bundles, we obtain decay rates of Wannier functions in…
Unsupervised feature selection (UFS) is an important task in data engineering. However, most UFS methods construct models from a single perspective and often fail to simultaneously evaluate feature importance and preserve their inherent…
Audio or visual data analysis tasks usually have to deal with high-dimensional and nonnegative signals. However, most data analysis methods suffer from overfitting and numerical problems when data have more than a few dimensions needing a…
Linear codes over finite fields parameterized by functions have proven to be a powerful tool in coding theory, yielding optimal and few-weight codes with significant applications in secret sharing, authentication codes, and association…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…
We introduce the Banach-Butterfly Invariant (BBT), an influence-adaptive Banach geometry on the Walsh-Hadamard butterfly factorization. For a Boolean function $f:\{-1,+1\}^n\to\{-1,+1\}$ with coordinate influences $\mathrm{Inf}_\ell(f)$,…
The Walsh transform $\widehat{Q}$ of a quadratic function $Q:F_{p^n}\rightarrow F_p$ satisfies $|\widehat{Q}(b)| \in \{0,p^{\frac{n+s}{2}}\}$ for all $b\in F_{p^n}$, where $0\le s\le n-1$ is an integer depending on $Q$. In this article, we…
This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime. Assuming that charge carriers are described by the Dirac equation in curved-space and…
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
This work concerns resonant scattering by a perfectly conducting slab with periodically arranged subwavelength slits, with two slits per period. There are two classes of resonances, corresponding to poles of a scattering problem. A sequence…
Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…