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In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of…

Complex Variables · Mathematics 2009-07-30 S. Ponnusamy , A. Vasudevarao , M. Vuorinen

The infimum of the Weyl functional is shown to be surprisingly small on many compact 4-manifolds that admit positive-scalar-curvature metrics. Results are also proved that systematically compare the scalar and self-dual Weyl curvatures of…

Differential Geometry · Mathematics 2022-03-14 Claude LeBrun

We characterize the power of constant-depth Boolean circuits in generating uniform symmetric distributions. Let $f\colon\{0,1\}^m\to\{0,1\}^n$ be a Boolean function where each output bit of $f$ depends only on $O(1)$ input bits. Assume the…

Computational Complexity · Computer Science 2025-02-27 Daniel M. Kane , Anthony Ostuni , Kewen Wu

In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of…

Discrete Mathematics · Computer Science 2024-07-23 Valérie Gillot , Philippe Langevin , Alexandr Polujan

We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)] to study a four-point dynamic density correlation function. We re-sum a class of diagrams…

Statistical Mechanics · Physics 2009-11-13 Grzegorz Szamel

In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…

Combinatorics · Mathematics 2023-10-19 Lukas Kölsch , Alexandr Polujan

We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…

Combinatorics · Mathematics 2007-05-23 Alex Samorodnitsky

We show how to characterize the indistinguishability of up to four identical, bosonic or fermionic particles, which are rendered partially distinguishable through their internal degrees of freedom prepared in mixed states. This is…

Quantum Physics · Physics 2021-08-25 Alexander M. Minke , Andreas Buchleitner , Christoph Dittel

In this paper an algorithm is designed which generates in-equivalent Boolean functions of any number of variables from the four Boolean functions of single variable. The grammar for such set of Boolean function is provided. The Turing…

Logic in Computer Science · Computer Science 2008-02-29 Birendra Kumar Nayak , Sudhakar Sahoo

Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the c-differential uniformity of power functions over finite fields. Based on some known almost…

Information Theory · Computer Science 2020-08-28 Zhengbang Zha , Lei Hu

In this paper we generalize Dillon's switching method to characterize the exact $c$-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known $c$-differential…

Information Theory · Computer Science 2022-04-20 Chunlei Li , Constanza Riera , Pantelimon Stanica

An explicit construction of closed, orientable, smooth, aspherical 4-manifolds with any odd Euler characteristic greater than 12 is presented. The manifolds constructed here are all Haken manifolds in the sense of B. Foozwell and H.…

Geometric Topology · Mathematics 2017-10-18 Allan L. Edmonds

Boolean functions are mathematical objects used in diverse applications. Different applications also have different requirements, making the research on Boolean functions very active. In the last 30 years, evolutionary algorithms have been…

Neural and Evolutionary Computing · Computer Science 2024-02-16 Claude Carlet , Marko Ðurasevic , Domagoj Jakobovic , Stjepan Picek , Luca Mariot

n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…

Complex Variables · Mathematics 2019-05-07 See Keong Lee , Saminathan Ponnusamy , Karl-Joachim Wirths

We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…

Computational Complexity · Computer Science 2022-12-02 Edinah K. Gnang , Rongyu Xu

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

Optimization and Control · Mathematics 2014-11-04 Nguyen Mau Nam , Dang Van Cuong

We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its…

Differential Geometry · Mathematics 2020-10-20 Luigi Verdiani , Wolfgang Ziller

Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of…

Combinatorics · Mathematics 2021-02-05 Daniele Bartoli , Marco Calderini

In this paper, we present several new constructions of differentially 4-uniform permutations over $\F_{2^{2m}}$ by modifying the values of the inverse function on some subsets of $\F_{2^{2m}}$. The resulted differentially 4-uniform…

Information Theory · Computer Science 2023-07-19 Zhengbang Zha , Lei Hu , Siwei Sun , Jinyong Shan

We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…

Functional Analysis · Mathematics 2009-06-13 Uwe Franz