Related papers: Topology and Higher Concurrencies
Game-theoretical approach to the analysis of parallel algorithms is proposed. The approach is based on presentation of the parallel computing as a congestion game. In the game processes compete for resources such as core of a central…
We are dealing with the problem of space layout planning here. We present an architectural conceptual CAD approach. Starting with design specifications in terms of constraints over spaces, a specific enumeration heuristics leads to a…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Comparing document semantics is one of the toughest tasks in both Natural Language Processing and Information Retrieval. To date, on one hand, the tools for this task are still rare. On the other hand, most relevant methods are devised from…
For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…
We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
AI tasks differ in complexity and are best addressed with different computation strategies (e.g., combinations of models and decoding methods). Hence, an effective routing system that maps tasks to the appropriate strategies is crucial.…
quest for processing speed potential. In fact, we always get a fraction of the technically available computing power (so-called {\em theoretical peak}), and the gap is likely to go hand-to-hand with the hardware complexity of the target…
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…
The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…