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Convolutional neural networks (CNNs) are powerful tools in Deep Learning mainly due to their ability to exploit the translational symmetry present in images, as they are equivariant to translations. Other datasets present different types of symmetries (e.g ...
This paper formulates a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. The smoothness requirement softens the tra ...
Exploring design space is an important process in finding solutions to a design task. In this paper, we present BloomGraph, an online application developed for florist apprentices to explore the space of bouquet designs. BloomGraph provides a graph-based i ...
The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...
Graph Signal Processing generalizes classical signal processing to signal or data indexed by the vertices of a weighted graph. So far, the research efforts have been focused on static graph signals. However numerous applications involve graph signals evolv ...
Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...
We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs. ...
We analyze the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...
The symmetry theory of halving objects into two identical fragments is developed and illustrated by examples. La coupe du roi is a fascinating way to slice an apple into chiral fragments with the same handedness. It may be applied to any object with point ...
In this note we present a method to compute approximate descriptions of a class of stochastic systems. For the method to apply, the system must be presented as a Markov chain on a state space consisting in graphs or graph-like objects, and jumps must be de ...