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We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a…
In a delightful article, Richard Stanley derived, algebraically, the surprisingly simple formula, 3 times 7 to the power n-1, for the sum of the cubes of the n-th row of Stern's diatomic array. In this note, we find an elegant bijective…
Due to that the polarization states in optical fibers change randomly during transmission, polarization-independent (PID) devices are demanded to receive lights with arbitrary polarization states. Compared with their orthogonal polarization…
We study an urn process with two urns, initialized with a ball each. Balls are added sequentially, the urn being chosen independently with probability proportional to the $\alpha^{th}$ power $(\alpha >1)$ of the existing number of balls. We…
The East process is a 1D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that its…
CCD light curves of the Algol type eclipsing binaries DP Cep, AL Gem, FG Gem, UU Leo, CF Tau and AW Vul were analysed using the Wilson-Deninney code and new geometric and absolute parameters were derived. Due to cyclic apparent orbital…
Linear scaling methods provide total energy, but no energy levels and canonical wavefuctions. From the density matrix computed through the density matrix purification methods, we propose an order-N (O(N)) method for calculating both the…
We investigate the dispersion relations for light coupled to one-dimensional ensembles of atoms with different level schemes. The unifying feature of all the considered setups is that the forward and backward propagating quantum fields are…
We study the electrostatic energy of binary ionic mixtures (BIMs) in the form of Coulomb crystals with the main focus on ordered crystals. We consider 15 different binary bcc-like lattices, accurately calculate their electrostatic energies…
Consider a balls-in-bins process in which each new ball goes into a given bin with probability proportional to f(n), where n is the number of balls currently in the bin and f is a fixed positive function. It is known that these so-called…
We study a Markov chain with very different mixing rates depending on how mixing is measured. The chain is the "Burnside process on the hypercube $C_2^n$." Started at the all-zeros state, it mixes in a bounded number of steps, no matter how…
This paper considers the $(n,k)$-Bernoulli--Laplace model in the case when there are two urns, the total number of red and white balls is the same, and the number of selections $k$ at each step is on the same asymptotic order as the number…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
We consider the billiard dynamics in a strip-like set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems…
Given $n$ colored balls, we want to detect if more than $\lfloor n/2\rfloor$ of them have the same color, and if so find one ball with such majority color. We are only allowed to choose two balls and compare their colors, and the goal is to…
The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the…
When a circumbinary disk surrounds a binary whose secondary's mass is at least $\sim 10^{-2}\times$ the primary's mass, a nearly empty cavity with radius a few times the binary separation is carved out of the disk. Narrow streams of…
The probability density function of the arrival time of \v{C}erenkov light on a photo-multiplier tube has been studied. This study covers light production, transmission and detection. The light production includes the light from a muon, the…
Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with step boundaries. The Green function for a 2-dimensional homogeneous dielectric…
Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…