Related papers: Measuring Complexity through Average Symmetry
Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
Given the increasing popularity of algorithms for overlapping clustering, in particular in social network analysis, quantitative measures are needed to measure the accuracy of a method. Given a set of true clusters, and the set of clusters…
Summarizing data samples by quantitative measures has a long history, with descriptive statistics being a case in point. However, as natural language processing methods flourish, there are still insufficient characteristic metrics to…
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
Disorder in point patterns can be quantified by means of the complexity, rather than in terms of geometric attributes of pattern structure. A complexity-based disorder-quantifying statistic indicates the practical difficulties associated…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to…
Despite the common misconception of nearly static organisms, plants do interact continuously with the environment and with each other. It is fair to assume that during their evolution they developed particular features to overcome problems…
For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features.…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
Thermodynamic irreversibility is a fundamental concept in statistical physics, yet its experimental measurement remains challenging, especially for complex systems. We introduce a novel random coarse-graining framework to identify…
We investigate in detail a recently introduced "coherent averaging scheme" in terms of its usefulness for achieving Heisenberg limited sensitivity in the measurement of different parameters. In the scheme, $N$ quantum probes in a product…
Several important complex network measures that helped discovering common patterns across real-world networks ignore edge weights, an important information in real-world networks. We propose a new methodology for generalizing measures of…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
In the context of cluster analysis and graph partitioning, many external evaluation measures have been proposed in the literature to compare two partitions of the same set. This makes the task of selecting the most appropriate measure for a…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…