Related papers: Cluster Scaling and Critical Points: A Cautionary …
A critical point of the energy dispersion is the momentum where electron velocity vanishes. At the corresponding energy, the density of states (DOS) exhibits non-analyticity such as divergence. Critical points can be first classified as…
Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs…
Earthquake network captures the complexity of seismicity in a peculiar manner. Given a seismic data, the procedure of constructing an earthquake network proposed in [S. Abe, N, Suzuki, Europhys. Lett. 65 (2004) 581] contains as a single…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…
The exponential sensitivity of cluster number counts to the properties of the dark energy implies a comparable sensitivity to not only the mean but also the actual_distribution_ of an observable mass proxy given the true cluster mass. For…
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…
We propose a picture of stock market crashes as critical points in a hierachical system with discrete scaling. The critical exponent is then complex, leading to log-periodic fluctuations in stock market indexes. We present ``experimental''…
We study a rational expectation model of bubbles and crashes. The model has two components : (1) our key assumption is that a crash may be caused by local self-reinforcing imitation between noise traders. If the tendency for noise traders…
We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
We investigate the distribution of clusters of galaxies and determine the cluster correlation function and power spectrum. Clusters of galaxies located in rich superclusters with at least 8 members form a quasiregular network of…
This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for…
Complex systems universally exhibit emergence, where macroscopic dynamics arise from local interactions, but a predictive law governing this process has been absent. We establish and verify such a law. We define a system's causal power at a…
Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m…
Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…
We develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in (Saichev and Sornette, 2007), which describes the distribution of inter-event times in the framework of a general…
A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…
Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…