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pro vyhledávání: '"Lavore A"'
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose a simple
Externí odkaz:
http://arxiv.org/abs/2410.10643
We introduce effectful Mealy machines - a general notion of Mealy machine with global effects - and give them semantics in terms of both effectful bisimilarity and traces. Bisimilarity of effectful Mealy machines is characterised syntactically in ter
Externí odkaz:
http://arxiv.org/abs/2410.10627
Tape diagrams provide a convenient notation for arrows of rig categories, i.e., categories equipped with two monoidal products, $\oplus$ and $\otimes$, where $\otimes$ distributes over $\oplus $. In this work, we extend tape diagrams with traces over
Externí odkaz:
http://arxiv.org/abs/2410.03561
Autor:
Barbiero, Pietro, Fioravanti, Stefano, Giannini, Francesco, Tonda, Alberto, Lio, Pietro, Di Lavore, Elena
Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation" which still
Externí odkaz:
http://arxiv.org/abs/2304.14094
Autor:
Di Lavore, Elena, Román, Mario
We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a synthetic Bayes th
Externí odkaz:
http://arxiv.org/abs/2301.12989
We introduce monoidal streams. Monoidal streams are a generalization of causal stream functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric monoidal categories. In the same way that streams provide semantics to data
Externí odkaz:
http://arxiv.org/abs/2212.14494
Autor:
Di Lavore, Elena, Sobociński, Paweł
Publikováno v:
Logical Methods in Computer Science, Volume 19, Issue 3 (September 4, 2023) lmcs:10552
We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition:
Externí odkaz:
http://arxiv.org/abs/2212.13229
Autor:
Di Lavore, Elena, Sobociński, Paweł
Publikováno v:
EPTCS 380, 2023, pp. 268-283
Monoidal width was recently introduced by the authors as a measure of the complexity of decomposing morphisms in monoidal categories. We have shown that in a monoidal category of cospans of graphs, monoidal width and its variants can be used to captu
Externí odkaz:
http://arxiv.org/abs/2205.08916
Autor:
Fabrizio A. Pennacchio, Alessandro Poli, Francesca Michela Pramotton, Stefania Lavore, Ilaria Rancati, Mario Cinquanta, Daan Vorselen, Elisabetta Prina, Orso Maria Romano, Aldo Ferrari, Matthieu Piel, Marco Cosentino Lagomarsino, Paolo Maiuri
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-10 (2024)
Abstract In eukaryotes, cytoplasmic and nuclear volumes are tightly regulated to ensure proper cell homeostasis. However, current methods to measure cytoplasmic and nuclear volumes, including confocal 3D reconstruction, have limitations, such as rely
Externí odkaz:
https://doaj.org/article/28d7b0b6342e4134aecf5e7c110002be
Autor:
Di Lavore, Elena, Sobociński, Paweł
We introduce monoidal width as a measure of the difficulty of decomposing morphisms in monoidal categories. For graphs, we show that monoidal width and two variations capture existing notions, namely branch width, tree width and path width. We propos
Externí odkaz:
http://arxiv.org/abs/2202.07582