Related papers: Predicting First Passage Percolation Shapes Using …
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of…
In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs), known as frog model. The dynamics of this process is described as follows: There are some active particles, which perform independent SRWs, and sleeping…
Current deep-learning models for object recognition are known to be heavily biased toward texture. In contrast, human visual systems are known to be biased toward shape and structure. What could be the design principles in human visual…
We consider standard first-passage percolation on $\Z^d$. Let $e_1$ be the first coordinate vector. Let $a(n)$ be the expected passage time from the origin to $ne_1$. In this short paper, we note that $a(n)$ is increasing under some strong…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
We introduce SCORES, a recursive neural network for shape composition. Our network takes as input sets of parts from two or more source 3D shapes and a rough initial placement of the parts. It outputs an optimized part structure for the…
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
Generative models that produce point clouds have emerged as a powerful tool to represent 3D surfaces, and the best current ones rely on learning an ensemble of parametric representations. Unfortunately, they offer no control over the…
Modern artificial neural networks, including convolutional neural networks and vision transformers, have mastered several computer vision tasks, including object recognition. However, there are many significant differences between the…
In this letter, motivated by the question that whether the empirical fitting of data by neural network can yield the same structure of physical laws, we apply the neural network to a simple quantum mechanical two-body scattering problem…
Recent advancements in deep learning have been primarily driven by the use of large models trained on increasingly vast datasets. While neural scaling laws have emerged to predict network performance given a specific level of computational…
This study proposes a deep learning methodology to predict the propagation of traffic shockwaves. The input to the deep neural network is time-space diagram of the study segment, and the output of the network is the predicted (future)…
We propose a deep neural network for supervised learning on neuroanatomical shapes. The network directly operates on raw point clouds without the need for mesh processing or the identification of point correspondences, as spatial…
We investigate how a residual network can learn to predict the dynamics of interacting shapes purely as an image-to-image regression task. With a simple 2d physics simulator, we generate short sequences composed of rectangles put in motion…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
We introduce and study a non-oriented first passage percolation model having a property of statistical invariance by time reversal. This model is defined in a graph having directed edges and the passage times associated with each set of…
In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force,…
We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\mathbb{Z}^d$, $d\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla \phi$…
Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…