Related papers: Analytically solvable autocorrelation function for…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the…
Sleep is crucial for daytime functioning, cognitive performance and general well-being. These aspects of daily life are known to be impaired after extended wake, yet, the underlying neuronal correlates have been difficult to identify.…
Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the…
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…
Recovering a unique causal graph from observational data is an ill-posed problem because multiple generating mechanisms can lead to the same observational distribution. This problem becomes solvable only by exploiting specific structural or…
We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures which should give similar results…
The decay of current autocorrelation functions is investigated for quantum systems featuring strong 'interactions'. Here, the term interaction refers to that part of the Hamiltonian causing the (major) decay of the current. On the time…
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…
Causal mediation analysis seeks to investigate how the treatment effect of an exposure on outcomes is mediated through intermediate variables. Although many applications involve longitudinal data, the existing methods are not directly…
The wave functions, the autocorrelation functions of which decay faster than $t^{-2}$, for both the one-dimensional free particle system and the repulsive-potential system are examined. It is then shown that such wave functions constitute a…
Mediation analysis aims to decipher the underlying causal mechanisms between an exposure, an outcome, and intermediate variables called mediators. Initially developed for fixed-time mediator and outcome, it has been extended to the…
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the…
In settings where Machine Learning (ML) algorithms automate or inform consequential decisions about people, individual decision subjects are often incentivized to strategically modify their observable attributes to receive more favorable…
Autocatalytic sets are sets of entities that mutually catalyse each other's production through chemical reactions from a basic food source. Recently, the reflexively autocatalytic and food generated theory has introduced a formal definition…
We review data analysis techniques that can be used to study temporal correlations among conductance traces in break junction measurements. We show that temporal histograms are a simple but efficient tool to check the temporal homogeneity…
Auto-correlation functions in an equilibrium stochastic process are well-characterized by Bochner's theorem as Fourier transforms of a finite symmetric Borel measure. The existence of a long-time limit of these correlation functions depends…
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents $\alpha$. By permuting the independently drawn samples from a power-law distribution, we present non-trivial…
This proposal is motivated by an analysis of the English Longitudinal Study of Ageing (ELSA), which aims to investigate the role of loneliness in explaining the negative impact of hearing loss on dementia. The methodological challenges that…
The energy-energy correlator (EEC) is an event shape observable which probes the angular correlations of energy depositions in detectors at high energy collider facilities. It has been investigated extensively in the context of precision…