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We present new results for LambdaCC and MotifCC, two recently introduced variants of the well-studied correlation clustering problem. Both variants are motivated by applications to network analysis and community detection, and have…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular…
We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…
Several more and more efficient component--by--component (CBC) constructions for suitable rank-1 lattices were developed during the last decades. On the one hand, there exist constructions that are based on minimizing some error functional.…
In this paper we consider statistical estimates of threshold and strength of percolation clusters on square lattices. The percolation threshold $p_c$ and the strength of percolation clusters $P_\infty$ for a square lattice with $(1,…
We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato-Jiao algorithm. For the site threshold, which gives the fraction of…
The reduced density matrix is variationally optimized for the two-dimensional Hubbard model. Exploiting all symmetries present in the system, we have been able to study $6\times6$ lattices at various fillings and different values for the…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
This paper introduces a new percolation model motivated from polymer materials. The mathematical model is defined over a random cubical set in the $d$-dimensional space $\mathbb{R}^d$ and focuses on generations and percolations of…
Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in…
Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…
For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is…
In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+\sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we…
Effective light cones, characterized by Lieb-Robinson bounds, emerge in nonrelativistic local quantum systems. Here, we present several analytical results derived from logarithmic light cones (LLCs). Possible origins of LLCs include the…
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance to the origin. Assuming the existence of…
Problem statement: Clustering has a number of techniques that have been developed in statistics, pattern recognition, data mining, and other fields. Subspace clustering enumerates clusters of objects in all subspaces of a dataset. It tends…
We study a version of compact directed percolation (CDP) in one dimension in which occupation of a site for the first time requires that a "mine" or antiparticle be eliminated. This process is analogous to the variant of directed…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as…