Related papers: Three experimental pearls in Costas arrays
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
We consider Coulomb gas models for which the empirical measure typically concentrates, when the number of particles becomes large, on an equilibrium measure minimizing an electrostatic energy. We study the behavior when the gas is…
Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much…
The two-particle momentum correlation functions between charm mesons ($\mathrm{D^{*\pm}}$ and $\mathrm{D}^\pm$) and charged light-flavor mesons ($\pi^{\pm}$ and K$^{\pm}$) in all charge-combinations are measured for the first time by the…
In the classic multi-stage Stern$-$Gerlach experiment conducted by Frisch and Segr\`e, the Majorana (Landau$-$Zener) and Rabi formulae diverge afar from the experimental observation while the physical mechanism for electron-spin collapse…
An analysis is made of the results of a recent polarization correlation experiment by Bovino (unpublished) where about 60,000 data have been obtained. I assume that the state of the photon pairs produced in the source (a non-linear crystal)…
We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the uniformly frustrated two dimensional XY model, for a sequence of frustrations f converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp first…
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are…
One of humanity's earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus exhibit repeated spirals, which appear with an…
We consider four examples of combinatorial triangles $\left(T(n,k)\right)_{0\le k\le n}$ (Pascal, Stirling of both types, Euler) : through saddle-point asymptotics, their \emph{Pascal's formulas} define four vector fields, together with…
We adopt a physically motivated empirical approach to the characterisation of the distributions of twin and triplet primes within the set of primes, rather than in the set of all natural numbers. Remarkably, the occurrences of twins or…
In this case-study in computer-human collaboration, we develop, implement, and execute symbolic-computational algorithms for the automatic discovery and proof of explicit expressions for the expectation, variance, and higher moments of a…
We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T=0. A…
The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex)…
A deterministic sequence of real numbers in the unit interval is called \emph{equidistributed} if its empirical distribution converges to the uniform distribution. Furthermore, the limit distribution of the pair correlation statistics of a…
We prescribe the minimal set of experimental data and parameters that should be reported for random-laser experiments and models. This prescript allows for a quantitative comparison between different experiments, and for a criterion whether…
The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…
We generalize a parity result of Fleishner and Stiebitz that being combined with Alon--Tarsi polynomial method allowed them to prove that a 4-regular graph formed by a Hamiltonian cycle and several disjoint triangles is always 3-choosable.…
Motivated by the work of Lubotzky, we use Galois cohomology to study the difference between the number of generators and the minimal number of relations in a presentation of the Galois group $G_S(k)$ of the maximal extension of a global…