Related papers: Shearing in some simple rank one theories
Solid aggregates in turbulent suspensions may break under the action of shear stresses. We explore the use of Graph Neural Networks (GNN) to infer aggregate fragmentation once the aggregate structure and flow velocity gradients are known.…
We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…
In this article, we propose the approach to structural optimization of neural networks, based on the braid theory. The paper describes the basics of braid theory as applied to the description of graph structures of neural networks. It is…
Concentrated suspensions may shear-thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a na\"ive model the suspension is described by a mean…
In a recent paper, Chernikov and Starchenko prove that graphs defined in distal theories have strong regularity properties, generalizing previous results about graphs defined by semi-algebraic relations. We give a shorter, purely…
In this note we develop and clarify some of the basic combinatorial properties of the new notion of $n$-dependence (for $1\leq n < \omega$) recently introduced by Shelah. In the same way as dependence of a theory means its inability to…
Consider a connected graph $G=(E,V)$ with $N=|V|$ vertices. The main purpose of this paper is to explore the question of uniform sampling of a subtree of $G$ with $n$ nodes, for some $n\leq N$ (the spanning tree case correspond to $n=N$,…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Set Shaping Theory (SST) moves beyond the classical fixed-space model by constructing bijective mappings the original sequence set into structured regions of a larger sequence space. These shaped subsets are characterized by a reduced…
In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…
Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern, which…
An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output,…
We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality to this…
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…