Related papers: Notes on oriented percolation
We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an oriented graph $G_0$ of initially occupied edges on $n$…
The purpose of this note is to correct statements of some assertions in \cite{l}.
A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to…
The investigation of the orientation of galaxies is a standard test concerning to scenarios of galaxy formation, because different theories of galaxy formation make various predictions regarding to the angular momentum of galaxies. The new…
Transformer is a ubiquitous model for natural language processing and has attracted wide attentions in computer vision. The attention maps are indispensable for a transformer model to encode the dependencies among input tokens. However,…
The purpose of this note is to point out ambiguities that appear in the calculation of angular momentum and its radiated counterpart when some simple formulae are used to compute them. We illustrate, in two simple different examples, how…
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
Diffusion models have emerged as the leading paradigm in generative modeling, excelling in various applications. Despite their success, these models often misalign with human intentions and generate results with undesired properties or even…
Misprints in eq. (7), which propagate up to eq. (13), are corrected. References are updated.
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…
In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we…
The author has recognized an error in the section of the text regarding induced Compton scattering. The paper has been withdrawn pending a revision to this section.
The way in which an opinion rejecting reform can finally become the consensus of everyone was studied by Galam (2002) in a probabilistic model. We now replace his clusters by those formed via random percolation by letting particles diffuse…
We introduce the simplest model which relates the emergence of collective social/economic phenomena to the existence of a (possibly self-organized) percolation transition. We suggest a series of extensions to financial, economic, political…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.