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A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources.…
A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…
A common issue for classification in scientific research and industry is the existence of imbalanced classes. When sample sizes of different classes are imbalanced in training data, naively implementing a classification method often leads…
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms.Here, we introduce…
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example…
In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…
We consider the problem of sampling from the distribution of measurement outcomes when applying a POVM to a superposition $|\Psi\rangle = \sum_{j=0}^{\chi-1} c_j |\psi_j\rangle$ of $\chi$ pure states. We relate this problem to that of…
With the recent claim of a quantum advantage demonstration in photonics by Zhong et al, the question of the computation of lower-order approximations of boson sampling with arbitrary quantum states at arbitrary distinguishability has come…
Estimating the number $n$ of unseen species from a $k-$sample displaying only $p\leq k$ distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a…
We study the hardness of classically simulating Gaussian boson sampling at nonzero photon distinguishability. We find that similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference…
When dealing with clinical text classification on a small dataset recent studies have confirmed that a well-tuned multilayer perceptron outperforms other generative classifiers, including deep learning ones. To increase the performance of…
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly…
We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…
The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression…
A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of $\mathbb{R}^n$ or a stationary Poisson…
Poisson thinning is an elementary result in probability, which is of great importance in the theory of Poisson point processes. In this article, we record a couple of characterization results on Poisson thinning. We also consider several…
We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are…