Related papers: Sequences with Low Correlation
The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of…
We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Global Navigation Satellite Systems (GNSS) are a widely used technology for positioning and navigation. GNSS positioning relies on pseudorange measurements from satellites to receivers. A pseudorange is the apparent distance between two…
The Pursley-Sarwate criterion of a pair of finite complex-valued sequences measures the collective smallness of the aperiodic autocorrelations and the aperiodic crosscorrelations of the two sequences. It is known that this quantity is…
Recent research has revealed that machine learning models have a tendency to leverage spurious correlations that exist in the training set but may not hold true in general circumstances. For instance, a sentiment classifier may erroneously…
The aim of this Thesis is to present five new tests for random numbers, which are widely used {\em e.g.} in computer simulations in physics applications. The first two tests, the cluster test and the autocorrelation test, are based on…
We study the relationship between two measures of pseudorandomness for families of binary sequences: family complexity and cross-correlation measure introduced by Ahlswede et al.\ in 2003 and recently by Gyarmati et al., respectively. More…
Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable…
The autocorrelation function and the run structure are two basic notions for binary sequences, and have been used as two independent postulates to test randomness of binary sequences ever since Golomb 1955. In this paper, we prove for…
Optical single-short measurement of the cross-correlation function between periodic sequences is demonstrated. The sequences are encoded into the broadband ultrashort phase-shaped pulses which are mixed in the nonlinear medium with…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The linear complexity of a periodic sequence over $GF(p^m)$ plays an important role in cryptography and communication [12]. In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal…
Unimodular sequences with low autocorrelations are desired in many applications, especially in the area of radar and code-division multiple access (CDMA). In this paper, we propose a new algorithm to design unimodular sequences with low…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
Simple and efficient algorithm based on heuristic search by shotgun hill climbing to construct binary sequences with small peak sidelobe levels (PSL) is suggested. The algorithm is applied for generation of binary sequences of lengths…
In any dimension $d \geq 2$, there is no known example of a low-discrepancy sequence which possess Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have $\beta$-Poissonian pair…
Low-count time series describe sparse or intermittent events, which are prevalent in large-scale online platforms that capture and monitor diverse data types. Several distinct challenges surface when modelling low-count time series,…