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In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for…
We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the…
This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved,…
Different statistical samples (e.g., from different locations) offer populations and learning systems observations with distinct statistical properties. Samples under (1) 'Unconfounded' growth preserve systems' ability to determine the…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
Counts in cells are used to analyse the higher order properties of the statistics of the EDSGC survey. The probability distribution is obtained from an equal area projection source catalog with infinite oversampling over the range…
We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in…
Representation learning plays a central role in structuring internal embeddings to capture the statistical properties of language, influencing the coherence and contextual consistency of generated text. Statistical Coherence Alignment is…
We introduce a statistical regression model to investigate the impact of dyadic relations on complex networks generated from observed repeated interactions. It is based on generalised hypergeometric ensembles (gHypEG), a class of…
Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of…
This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…
We study two aspects of information semantics: (i) the collection of all relationships, (ii) tracking and spotting anomaly and change. The first is implemented by endowing all relevant information spaces with a Euclidean metric in a common…