Related papers: Clubbed Binomial Approximation for the Lightbulb P…
Given n buttons and n bulbs so that the ith button toggles the ith bulb and at most two other bulbs, we compute the sharp lower bound on the number of bulbs that can be lit regardless of the action of the buttons.
In this work, a theoretical generalization of Lloyd's quantum illumination to signal beams described by two entangled photon states is developed. It is shown that the new protocol offers a method to find the range of the target, reduces the…
Chung, Diaconis, and Graham considered random processes of the form X_{n+1}=a_n X_n+b_n (mod p) where p is odd, X_0=0, a_n=2 always, and b_n are i.i.d. for n=0,1,2,... . In this paper, we show that if P(b_n=-1)=P{b_n=0)=P(b_n=1)=1/3, then…
Binomial Theorem for (N+n)^r is described with non-commuting variables N and n.
Light localization and intensity enhancement in a woodpile layer-by-layer photonic crystal, whose interlayer distance along the propagation direction is gradually varied, has been theoretically predicted and experimentally demonstrated. The…
Let $(X_{i}, i\in J)$ be a family of locally dependent nonnegative integer-valued random variables, and consider the sum $W=\sum\nolimits_{i\in J}X_i$. We first establish a general error upper bound for $d_{TV}(W, M)$ using Stein's method,…
Let $X_1,...,X_n$ be $n$ independent unbounded real random variables which have common, roughly speaking, light-tailed type distribution. Denote by $S_1^n$ their sum and by $\pi^{a_n}$ the tilted density of $X_1$, where $a_n…
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal…
In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number of particles with expectation greater…
We evaluate the light baryonium spectrum, viz. the baryon-antibaryon states, in the framework of QCD sum rules. The nonperturbative contributions up to dimension 12 are taken into account. Numerical results indicate that there might exist…
The statistical model with exact conservation of baryon number, electric charge, and strangeness - the Canonical Statistical Model (CSM) - is used to analyze the dependence of yields of light nuclei at midrapidity on charged pion…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
The photon statistics of the light emitted from an atomic ensemble into a single field mode of an optical cavity is investigated as a function of the number of atoms. The light is produced in a Raman transition driven by a pump laser and…
The cumulants and factorial moments of photon distribution for squeezed and correlated light are calculated in terms of Chebyshev, Legendre and Laguerre polynomials. The phenomenon of strong oscillations of the ratio of the cumulant to…
We consider binomial Thue equations of type $x^n-my^n=\pm 1$ in $x,y\in Z$. Optimizing the method of Peth\H o we perform an extensive calculation by a high performance computer to determine all solutions with $\max(|x|,|y|)<10^{500}$ of…
The binary signed-digit representation of integers is used for efficient computation in various settings. The Stern polynomial is a polynomial extension of the well-studied Stern diatomic sequence, and has itself has been investigated in…
These supplementary materials detail some calculations and some experimental results related to the propagation of light in the photonic billiard. We first justify why we focus only on the rays that are transmitted through the cylinders and…
A scheme is proposed here to achieve swapping and entangling of photonic and atomic qubits with high fidelity. The mechanism is based on the scattering of a single photon from a $\Lambda$-type three-level atom. The evolution of the coupled…
Solid-state single-photon emitters provide a versatile platform for exploring quantum technologies such as optically connected quantum networks. A key challenge is to ensure optical coherence and spectral stability of the emitters. Here, we…
An experiment for checking the Dynamical Spacetime approach to wavefunction collapse is proposed. The Dynamical Spacetime approach predicts deviations from Born's rule, when a solid evolves into a three-state superposition, and when the…