Related papers: Trajectory analysis through entropy characterizati…
A formalism is proposed to describe entangled quantum histories, and their entanglement entropy. We define a history vector, living in a tensor space with basis elements corresponding to the allowed histories, i.e. histories with…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
Methods to quantify the complexity of trajectory datasets are still a missing piece in benchmarking human trajectory prediction models. In order to gain a better understanding of the complexity of trajectory prediction tasks and following…
Trajectory representation learning on a network enhances our understanding of vehicular traffic patterns and benefits numerous downstream applications. Existing approaches using classic machine learning or deep learning embed trajectories…
Transfer entropy in information theory was recently demonstrated [Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. There, only pairs of…
A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.
Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…
This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Transfer entropy is used to establish a measure of causal relationships between two variables. Symbolic transfer entropy, as an estimation method for transfer entropy, is widely applied due to its robustness against non-stationarity. This…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
In problem-solving, a path towards solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
Recurrence rate, determinism, average line length, and entropy of line lengths are measures of complexity in recurrence quantification analysis, that help to understand the structure, predictability and complexity of dynamical systems. In…
An important task in trajectory analysis is clustering. The results of a clustering are often summarized by a single representative trajectory and an associated size of each cluster. We study the problem of computing a suitable…
This paper introduces an objective metric for evaluating a parsing scheme. It is based on Shannon's original work with letter sequences, which can be extended to part-of-speech tag sequences. It is shown that this regular language is an…
Developmental trajectories are known to be canalized, or robust to both environmental and genetic perturbations. However, even when these trajectories are decanalized by an environmental perturbation outside of the range of conditions to…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…