Related papers: On the intriguing search for good permutations
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in…
Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…
We consider nonregular fractions of factorial experiments for a class of linear models. These models have a common general mean and main effects, however they may have different 2-factor interactions. Here we assume for simplicity that…
Let R(n,k) denote the number of permutations of {1,2,...,n} with k alternating runs. We find a grammatical description of the numbers R(n,k) and then present several convolution formulas involving the generating function for the numbers…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…
In a previous work, B\'ona and Pantone studied permutations that avoided all but one pattern of length $k$ that began with a length $k-1$ increasing subsequence. We draw the connection between that idea and distant patterns, first discussed…
The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. That is, for every permutation $\pi = \pi_{1} \pi_{2} ... \pi_{n+1}$ there is a directed edge from the standardization of…
A permutation P on {1,..,N} is a_fast_forward_permutation_ if for each m the computational complexity of evaluating P^m(x)$ is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions.…
We study the distribution of the statistics 'number of fixed points' and 'number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving…
The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested…
In this paper we give an overview of recent results on (upper and lower) discrepancy estimates for (concrete) sequences in the unit-cube. In particular we also give an overview of discrepancy estimates for certain classes of hybrid…
Finding relevant prior art is crucial when deciding whether to file a new patent application or invalidate an existing patent. However, searching for prior art is challenging due to the large number of patent documents and the need for…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern $q$ in permutations that avoid another given pattern $r$. In some cases, we find the pattern that occurs least often, (resp. most…