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Shapelets are discriminative time series subsequences that allow generation of interpretable classification models, which provide faster and generally better classification than the nearest neighbor approach. However, the shapelet discovery…
We revisit the notion of initial sets by Xu and Cayrol, i.e., non-empty minimal admissible sets in abstract argumentation frameworks. Initial sets are a simple concept for analysing conflicts in an abstract argumentation framework and to…
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show…
Few-shot abstractive summarization has become a challenging task in natural language generation. To support it, we designed a novel soft prompts architecture coupled with a prompt pre-training plus fine-tuning paradigm that is effective and…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Automatic security protocol analysis is currently feasible only for small protocols. Since larger protocols quite often are composed of many small protocols, compositional analysis is an attractive, but non-trivial approach. We have…
Recent advances in visual generative models have enabled high-fidelity image editing guided by human instructions. However, these models often struggle with complex instructions involving combinatorial editing operations or inter-step…
Fix a finite set of points in Euclidean $n$-space $\euc^n$, thought of as a point-cloud sampling of a certain domain $D\subset\euc^n$. The Rips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an…
We consider a multi-parameter model for randomly constructing simplicial complexes. This model interpolates between random clique complexes and Linial-Meshulam random $k$-dimensional complexes, two models that have been extensively studied.…
Due to the high inter-class similarity caused by the complex composition and the co-existing objects across scenes, numerous studies have explored object semantic knowledge within scenes to improve scene recognition. However, a resulting…
Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections…
The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in…
Large language models have exhibited intriguing in-context learning capability, achieving promising zero- and few-shot performance without updating the parameters. However, conventional in-context learning is usually restricted by length…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
A theory of sections of simplicial height functions is developed. At the core of this theory lies the section complex, which is assembled from higher section spaces. The latter encode flow lines along the height, as well as their…
Graphs are ubiquitous to model the irregular (non-Euclidean) structure of complex data, but they are limited to pairwise relationships and fail to model the complexities of the datasets exhibiting higher-order interactions. In that context,…
We generalize some homotopy calculation techniques such as splittings and matching trees that are introduced for the computations in the case of the independence complexes of graphs to arbitrary simplicial complexes, and exemplify their…
Complex network topology might get pretty complicated challenging many network analysis objectives, such as community detection for example. This however makes common emergent network phenomena such as scale-free topology or small-world…