Zobrazeno 1 - 10
of 805
pro vyhledávání: '"P, Oudot"'
Given an unknown $\mathbb{R}^n$-valued function $f$ on a metric space $X$, can we approximate the persistent homology of $f$ from a finite sampling of $X$ with known pairwise distances and function values? This question has been answered in the case
Externí odkaz:
http://arxiv.org/abs/2412.04162
Autor:
Oudot, Steve
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other areas of math
Externí odkaz:
http://arxiv.org/abs/2411.00493
Autor:
Steffinlongo, Anna, Navarro, Mariana, Cenni, Marina, Valcarce, Xavier, Acín, Antonio, Oudot, Enky
Device-independent quantum key distribution (DIQKD) provides the strongest form of quantum security, as it allows two honest users to establish secure communication channels even when using fully uncharacterized quantum devices. The security proof of
Externí odkaz:
http://arxiv.org/abs/2409.17075
The $\gamma$-linear projected barcode was recently introduced as an alternative to the well-known fibered barcode for multiparameter persistence, in which restrictions of the modules to lines are replaced by pushforwards of the modules along linear f
Externí odkaz:
http://arxiv.org/abs/2408.01065
Multimodality has recently gained attention in the medical domain, where imaging or video modalities may be integrated with biomedical signals or health records. Yet, two challenges remain: balancing the contributions of modalities, especially in cas
Externí odkaz:
http://arxiv.org/abs/2407.03836
Publikováno v:
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:43986-44011, 2024
Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-value
Externí odkaz:
http://arxiv.org/abs/2406.07224
End-to-end topological learning using 1-parameter persistence is well-known. We show that the framework can be enhanced using 2-parameter persistence by adopting a recently introduced 2-parameter persistence based vectorization technique called GRIL.
Externí odkaz:
http://arxiv.org/abs/2406.07100
Topological integral transforms have found many applications in shape analysis, from prediction of clinical outcomes in brain cancer to analysis of barley seeds. Using Euler characteristic as a measure, these objects record rich geometric information
Externí odkaz:
http://arxiv.org/abs/2405.02256
Local conditions for the direct summands of a persistence module to belong to a certain class of indecomposables have been proposed in the 2-parameter setting, notably for the class of indecomposables called block modules, which plays a prominent rol
Externí odkaz:
http://arxiv.org/abs/2402.16624
We analyze Bell inequalities violations in photonic experiments for which the measurement apparatuses are restricted to homodyne measurements. Through numerical optimization of the Clauser-Horne-Shimony-Holt inequality over homodyne measurements and
Externí odkaz:
http://arxiv.org/abs/2402.01530