Related papers: Correlation, Linear Complexity, Maximum order Comp…
Two parties observe independent copies of a $d$-dimensional vector and a scalar. They seek to test if their data is correlated or not, namely they seek to test if the norm $\|\rho\|_2$ of the correlation vector $\rho$ between their…
We investigate the $k$-error linear complexity over $\mathbb{F}_p$ of binary sequences of length $2p$ with optimal three-level autocorrelation. These balanced sequences are constructed by cyclotomic classes of order four using a method…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize…
While investigating quantum correlations in atomic systems, we note that single measurements contain information about these correlations. Using a simple model of measurement -- analogous to the one used in quantum optics -- we show how to…
This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…
Multiplicity correlation measurements provide insight into the dynamics of high energy collisions. Models describing these collisions need these correlation measurements to tune the strengths of the underlying QCD processes which influence…
A new method for the experimental study of bin-bin correlations is proposed. It is shown that this method is able to reveal important additional information on bin-bin correlations, beyond that of factorial-correlator measurements.
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
Higher order parametric level correlations in disordered systems with broken time-reversal symmetry are studied by mapping the problem onto a model of coupled Hermitian random matrices. Closed analytical expression is derived for parametric…
Correlation testing provides a quick method of discriminating amongst potential terms to include in a nuclear mass formula or functional and is a necessary tool for further nuclear mass models; however a firm mathematical foundation of the…
In this paper, we present a computational search for best-known merit factors of longer binary sequences with an odd length. Finding low autocorrelation binary sequences with optimal or suboptimal merit factors is a very difficult…
We show that any sequence $(x_n)_{n \in \mathbb{N}} \subseteq [0,1]$ that has Poissonian correlations of $k$-th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend…
Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
A few years ago new quantitative measures of pseudorandomness of binary sequences have been introduced. Since that these measures have been studied in many papers and many constructions have been given along these lines. In this paper the…
In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a…
The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…