Related papers: Complexity of hierarchical ensembles
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external…
With advances in sequencing technologies, there are now massive amounts of genomic data from across all life, leading to the possibility that a robust Tree of Life can be constructed. However, "gene tree heterogeneity", which is when…
Whereas for strings, higher-order empirical entropy is the standard entropy measure, several different notions of empirical entropy for trees have been proposed in the past, notably label entropy, degree entropy, conditional versions of the…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the…
We study Nielsen's circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. In a multiple quench scenario, it is shown that the complexity shows remarkably different behaviour compared to the other…
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that…
We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
The time series theory is set in this work under the domain of general elliptically contoured distributions. The advent of a time series approach that is in accordance with the expected reality of dependence between errors, transfers the…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits…
We answer the natural question: when are a regular Poisson structure along with a complex structure transverse to its symplectic leaves induced by generalized complex structure? The leafwise symplectic form and transverse complex structure…
We investigate vertex levels of containment in a random hypergraph grown in the spirit of a recursive tree. We consider a local profile tracking the evolution of the containment of a particular vertex over time, and a global profile…
We introduce a framework to dynamically combine heterogeneous models called \texttt{DYCHEM}, which forecasts a set of time series that are related through an aggregation hierarchy. Different types of forecasting models can be employed as…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…