Related papers: Predicting First Passage Percolation Shapes Using …
We study the shape fluctuation in the first passage percolation on $\mathbb{Z}^d$. It is known that it diverges when the distribution obeys Bernoulli in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation.…
We study non-random fluctuation in the first passage percolation on $\mathbb{Z}^d$ and show that it diverges for any dimension. We also prove the divergence of the non-random shape fluctuation, which was conjectured in [Yu Zhang. The…
First passage percolation with recovery is a process aimed at modeling the spread of epidemics. On a graph $G$ place a red particle at a reference vertex $o$ and colorless particles (seeds) at all other vertices. The red particle starts…
Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We present a general approach to study a class of random growth models in $n$-dimensional Euclidean space. These models are designed to capture basic growth features which are expected to manifest at the mesoscopic level for several…
In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability…
One aim shared by multiple settings, such as continual learning or transfer learning, is to leverage previously acquired knowledge to converge faster on the current task. Usually this is done through fine-tuning, where an implicit…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
Increase in data, size, or compute can lead to sudden learning of specific capabilities by a neural network -- a phenomenon often called "emergence''. Beyond scientific understanding, establishing the causal factors underlying such emergent…
Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This…
Neural network (connectionist) models are designed to encode image features and provide the building blocks for object and shape recognition. These models generally call for: a) initial diffuse connections from one neuron population to…
This paper is a survey of various results and techniques in first passage percolation, a random process modeling a spreading fluid on an infinite graph. The latter half of the paper focuses on the connection between first passage…
We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping…
We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as…
We celebrate the 50th anniversary of one the most classical models in probability theory. In this survey, we describe the main results of first passage percolation, paying special attention to the recent burst of advances of the past 5…
Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification.…
A fundamental question in learning to classify 3D shapes is how to treat the data in a way that would allow us to construct efficient and accurate geometric processing and analysis procedures. Here, we restrict ourselves to networks that…
Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…
We consider two competing first passage percolation processes started from uniformly chosen subsets of a random regular graph on $N$ vertices. The processes are allowed to spread with different rates, start from vertex subsets of different…