Related papers: Entropy evaluation sheds light on ecosystem comple…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
Understanding the assembly of ecosystems to estimate the number of species at different spatial scales is a challenging problem. Until now, maximum entropy approaches have lacked the important feature of considering space in an explicit…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Ecosystems are commonly organized into trophic levels -- organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…