Related papers: Predicting First Passage Percolation Shapes Using …
Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to…
Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
Void nucleation in ductile materials subjected to high strain-rate loading remains a critical yet elusive phenomenon to understand. Traditional methods to understand void nucleation typically rely on experiments and molecular dynamics and…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
It is a central challenge in deep learning to understand how neural networks learn representations. A leading approach is the Neural Feature Ansatz (NFA) (Radhakrishnan et al. 2024), a conjectured mechanism for how feature learning occurs.…
This study delves into first-passage percolation on random geometric graphs in the supercritical regime, where the graphs exhibit a unique infinite connected component. We investigate properties such as geodesic paths, moderate deviations,…
This paper proposes a novel Convolutional Neural Network model for contour data analysis (ContourCNN) and shape classification. A contour is a circular sequence of points representing a closed shape. For handling the cyclical property of…
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Detection of cell nuclei in microscopic images is a challenging research topic, because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
This paper studies the first passage percolation (FPP) model: each edge in the cubic lattice is assigned a random passage time, and consideration is given to the behavior of the percolation region $B(t)$, which consists of those vertices…
Consider the first passage percolation model on ${\bf Z}^d$ for $d\geq 2$. In this model we assign independently to each edge the value zero with probability $p$ and the value one with probability $1-p$. We denote by $T({\bf 0}, v)$ the…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
Recent advances in machine learning have become increasingly popular in the applications of phase transitions and critical phenomena. By machine learning approaches, we try to identify the physical characteristics in the two-dimensional…
We consider the first passage percolation model on the square lattice. In this model, $\{t(e): e{an edge of}{\bf Z}^2 \}$ is an independent identically distributed family with a common distribution $F$. We denote by $T({\bf 0}, v)$ the…
Model stitching (Lenc & Vedaldi 2015) is a compelling methodology to compare different neural network representations, because it allows us to measure to what degree they may be interchanged. We expand on a previous work from Bansal,…
We consider first passage percolation on the configuration model. Once the network has been generated each edge is assigned an i.i.d. weight modeling the passage time of a message along this edge. Then independently two vertices are chosen…