Related papers: Cantor-solus and Cantor-multus Distributions
We consider the propagation of classical and quantum strings on cosmological space-times which interpolate from a collapsing phase to an expanding phase. We begin by considering the classical propagation of strings on space-times with…
In this short note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with same Diophantine constatnts), showing that, Diophantine sets are not always Cantor sets.…
An experimentally realizable scheme is formulated which can test any postulated quantum mechanical approach for calculating the arrival time distribution. This is specifically illustrated by using the modulus of the probability current…
A continuous key distribution scheme is proposed that relies on a pair of canonically conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a…
In the worst-case distributed source coding (DSC) problem of [1], the smaller cardinality of the support-set describing the correlation in informant data, may neither imply that fewer informant bits are required nor that fewer informants…
We consider the problem of distributed multi-choice voting in a setting that each node can communicate with its neighbors merely by sending beep signals. Given its simplicity, the beep communication model is of practical importance in…
A quantum key distribution and identification protocol is proposed, which is based on entanglement swapping. Through choosing particles by twos from the sequence and performing Bell measurements, two communicators can detect eavesdropping,…
We prove that a self-similar Cantor set in $\mathbb{Z}_N \times \mathbb{Z}_N$ has a fractal uncertainty principle if and only if it does not contain a pair of orthogonal lines. The key ingredient in our proof is a quantitative form of…
In music source separation, the number of sources may vary for each piece and some of the sources may belong to the same family of instruments, thus sharing timbral characteristics and making the sources more correlated. This leads to…
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
This paper examines the possibilities of extending Cantor's two arguments on the uncountable nature of the set of real numbers to one of its proper denumerable subsets: the set of rational numbers. The paper proves that, unless certain…
We discuss controversial results for the statistics of charge transport through coherent conductors. Two distribution functions for the charge transmitted was obtained previously, first by L.Levitov and G.Lesovik, [JETP Letters Vol.55 p.555…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
Quantum key distribution is a key application of quantum mechanics, shaping the future of privacy and secure communications. Many protocols require single photons, often approximated by strongly attenuated laser pulses. Here, we harness the…
We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both…
Directional or Circular statistics are pertaining to the analysis and interpretation of directions or rotations. In this work, a novel probability distribution is proposed to model multidimensional sparse directional data. The Generalised…
This paper extends work done to date on quantum computation by associating potentials with different types of computation steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding…
If the information is encoded into the state of the subsystem $S$ of a quantum system initially (at $t=0$), then it becomes distributed over the whole quantum system at $t>0$ due to the quantum interactions. Consequently, this information,…