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A concurrent binary tree (CBT) is a GPU-friendly data-structure suitable for the generation of bisection based terrain tessellations, i.e., adaptive triangulations over square domains. In this paper, we expand the benefits of this…
We study the distribution of finite clusters in slightly supercritical ($p \downarrow p_c$) Bernoulli bond percolation on transitive nonamenable graphs, proving in particular that if $G$ is a transitive nonamenable graph satisfying the…
Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…
Monte Carlo simulations of layered BSCCO samples are used to investigate the behavior of vortex matter at low fields, particularly in connection with the possible occurrence of a Bragg glass (BrG) phase at low density of columnar defects, a…
Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group method could handle the system in…
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
Suggested by Scullard's recent star-triangle relation for bond correlated systems, we propose a general "cell/dual-cell" transformation, which allows in principle an infinite variety of lattices with exact percolation thresholds to be…
Behavior trees (BTs) are an optimally modular framework to assemble hierarchical hybrid control policies from a set of low-level control policies using a tree structure. Many robotic tasks are naturally decomposed into a hierarchy of…
The relaxation dynamics of correlated electron transport (ET) along molecular chains is studied based on a substantially improved numerically exact path integral Monte Carlo (PIMC) approach. As archetypical model we consider a Hubbard chain…
The logarithmic conformal field theory describing critical percolation is further explored using Watts' determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition…
We show how to generalize the Lattice Switch Monte Carlo method to calculate the phase diagram of a binary system. A global coordinate transformation is combined with a modification of particle diameters, enabling the multi-component system…
In 2000, Evans et al. [Eva+00] proved the subadditivity of the mutual information in the broadcasting on tree model with binary vertex labels and symmetric channels. They raised the question of whether such subadditivity extends to loopy…
One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is decidable in…
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing…
We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…
Two-dimensional bootstrap percolation is usually characterized by bulk observables, but whether increasing the activation threshold qualitatively reorganizes the geometry of the absorbing state has remained unclear. Here we show that the…
We investigate transport and magnetotransport properties of binary networks composed of superconducting (MgB2) and ferromagnetic (CrO2 or LSMO) nanoparticles. While for the LSMO/MgB2 system a single percolation threshold is observed, for…
We study the phase diagram of the spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the effective field theory (EFT) with…