@inproceedings{15093, abstract = {We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right.}, author = {Cultrera di Montesano, Sebastiano and Edelsbrunner, Herbert and Henzinger, Monika H and Ost, Lara}, booktitle = {Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)}, editor = {Woodruff, David P.}, location = {Alexandria, VA, USA}, pages = {243 -- 295}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Dynamically maintaining the persistent homology of time series}}, doi = {10.1137/1.9781611977912.11}, year = {2024}, } @unpublished{15091, abstract = {Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.}, author = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, booktitle = {arXiv}, title = {{Chromatic alpha complexes}}, year = {2024}, } @article{15171, abstract = {The brain’s functionality is developed and maintained through synaptic plasticity. As synapses undergo plasticity, they also affect each other. The nature of such ‘co-dependency’ is difficult to disentangle experimentally, because multiple synapses must be monitored simultaneously. To help understand the experimentally observed phenomena, we introduce a framework that formalizes synaptic co-dependency between different connection types. The resulting model explains how inhibition can gate excitatory plasticity while neighboring excitatory–excitatory interactions determine the strength of long-term potentiation. Furthermore, we show how the interplay between excitatory and inhibitory synapses can account for the quick rise and long-term stability of a variety of synaptic weight profiles, such as orientation tuning and dendritic clustering of co-active synapses. In recurrent neuronal networks, co-dependent plasticity produces rich and stable motor cortex-like dynamics with high input sensitivity. Our results suggest an essential role for the neighborly synaptic interaction during learning, connecting micro-level physiology with network-wide phenomena.}, author = {Agnes, Everton J. and Vogels, Tim P}, issn = {1546-1726}, journal = {Nature Neuroscience}, publisher = {Springer Nature}, title = {{Co-dependent excitatory and inhibitory plasticity accounts for quick, stable and long-lasting memories in biological networks}}, doi = {10.1038/s41593-024-01597-4}, year = {2024}, } @article{15170, abstract = {The James Webb Space Telescope is revealing a new population of dust-reddened broad-line active galactic nuclei (AGN) at redshifts z ≳ 5. Here we present deep NIRSpec/Prism spectroscopy from the Cycle 1 Treasury program Ultradeep NIRSpec and NIRCam ObserVations before the Epoch of Reionization (UNCOVER) of 15 AGN candidates selected to be compact, with red continua in the rest-frame optical but with blue slopes in the UV. From NIRCam photometry alone, they could have been dominated by dusty star formation or an AGN. Here we show that the majority of the compact red sources in UNCOVER are dust-reddened AGN: 60% show definitive evidence for broad-line Hα with a FWHM > 2000 km s −1, 20% of the current data are inconclusive, and 20% are brown dwarf stars. We propose an updated photometric criterion to select red z > 5 AGN that excludes brown dwarfs and is expected to yield >80% AGN. Remarkably, among all zphot > 5 galaxies with F277W – F444W > 1 in UNCOVER at least 33% are AGN regardless of compactness, climbing to at least 80% AGN for sources with F277W – F444W > 1.6. The confirmed AGN have black hole masses of 107–109M⊙. While their UV luminosities (−16 > MUV > −20 AB mag) are low compared to UV-selected AGN at these epochs, consistent with percent-level scattered AGN light or low levels of unobscured star formation, the inferred bolometric luminosities are typical of 107–109M⊙ black holes radiating at ∼10%–40% the Eddington limit. The number densities are surprisingly high at ∼10−5 Mpc−3 mag−1, 100 times more common than the faintest UV-selected quasars, while accounting for ∼1% of the UV-selected galaxies. While their UV faintness suggests they may not contribute strongly to reionization, their ubiquity poses challenges to models of black hole growth.}, author = {Greene, Jenny E. and Labbe, Ivo and Goulding, Andy D. and Furtak, Lukas J. and Chemerynska, Iryna and Kokorev, Vasily and Dayal, Pratika and Volonteri, Marta and Williams, Christina C. and Wang, Bingjie and Setton, David J. and Burgasser, Adam J. and Bezanson, Rachel and Atek, Hakim and Brammer, Gabriel and Cutler, Sam E. and Feldmann, Robert and Fujimoto, Seiji and Glazebrook, Karl and De Graaff, Anna and Khullar, Gourav and Leja, Joel and Marchesini, Danilo and Maseda, Michael V. and Matthee, Jorryt J and Miller, Tim B. and Naidu, Rohan P. and Nanayakkara, Themiya and Oesch, Pascal A. and Pan, Richard and Papovich, Casey and Price, Sedona H. and Van Dokkum, Pieter and Weaver, John R. and Whitaker, Katherine E. and Zitrin, Adi}, issn = {1538-4357}, journal = {Astrophysical Journal}, publisher = {IOP Publishing}, title = {{UNCOVER spectroscopy confirms the surprising ubiquity of active galactic nuclei in red sources at z > 5}}, doi = {10.3847/1538-4357/ad1e5f}, volume = {964}, year = {2024}, } @inproceedings{15168, abstract = {A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, … , k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the "linearly ordered chromatic number" of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).}, author = {Filakovský, Marek and Nakajima, Tamio Vesa and Opršal, Jakub and Tasinato, Gianluca and Wagner, Uli}, booktitle = {41st International Symposium on Theoretical Aspects of Computer Science}, isbn = {9783959773119}, issn = {1868-8969}, location = {Clermont-Ferrand, France}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs}}, doi = {10.4230/LIPIcs.STACS.2024.34}, volume = {289}, year = {2024}, }