Related papers: Tableau evacuation and webs
Traditional methods for crawling and parsing web applications predominantly rely on extracting hyperlinks from initial pages and recursively following linked resources. This approach constructs a graph where nodes represent unstructured…
We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of…
A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Beyond the information stored in pages of the World Wide Web, novel types of ``meta-information'' are created when they connect to each other. This information is a collective effect of independent users writing and linking pages, hidden…
The nonelliptic $\mathsf{A_2}$-webs with $k$ "$+$"s on the top boundary and $3n-2k$ "$-$"s on the bottom boundary combinatorially model the space $\mathsf{Hom}_{\mathfrak{sl}_3}(\mathsf{V}^{\otimes (3n-2k)}, \mathsf{V}^{\otimes k})$ of…
Recommendation plays a key role in e-commerce and in the entertainment industry. We propose to consider successive recommendations to users under the form of graphs of recommendations. We give models for this representation. Motivated by…
We introduce a topological intersection number for an ordered pair of $\operatorname{SL}_3$-webs on a decorated surface. Using this intersection pairing between reduced $(\operatorname{SL}_3,\mathcal{A})$-webs and a collection of…
The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…
There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the…
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to…
We introduce a novel tool for analyzing complex network dynamics, allowing for cascades of causally-related events, which we call causal webs (c-webs), to be separated from other non-causally-related events. This tool shows that…
Understanding the connections between unstructured text and semi-structured table is an important yet neglected problem in natural language processing. In this work, we focus on content-based table retrieval. Given a query, the task is to…
Networks provide a skeleton for the spread of contagions, like, information, ideas, behaviors and diseases. Many times networks over which contagions diffuse are unobserved and need to be inferred. Here we apply survival theory to develop…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adapt the definition of a spider's web to the punctured plane.…
Traffic modeling of communication networks such as Internet has become a very important field of research. A number of interesting phenomena are found in measurements and traffic simulations. One of them is the propagation of congestion…
A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual…
Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…