@unpublished{15091, abstract = {Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective.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}}, doi = {10.48550/arXiv.2212.03128}, year = {2024}, } @inproceedings{17898, abstract = {There is an ever-growing zoo of modern neural network models that can efficiently learn end-to-end control from visual observations. These advanced deep models, ranging from convolutional to Vision Transformers, from small to gigantic networks, have been extensively tested on offline image classification tasks. In this paper, we study these vision models with respect to the open-loop training to closed-loop generalization abilities, i.e., deployment realizes a causal feedback loop that is not present during training. This causality gap typically emerges in robotics applications such as autonomous driving, where a network is trained to imitate the control commands of a human. In this setting, two situations arise: 1) Closed-loop testing in-distribution, where the test environment shares properties with those of offline training data. 2) Closed-loop testing under distribution shifts and out-of-distribution. Contrary to recently reported results, we show that under proper training guidelines, all vision architectures perform indistinguishably well on in-distribution deployment, resolving the causality gap. In situation 2, We observe that scale is the strongest factor in improving closed-loop generalization regardless of the choice of the model architecture. Our results predict the trend that in the future we will see larger and larger models being used in offline-training-online-deployment imitation learning tasks in robotic applications.}, author = {Lechner, Mathias and Hasani, Ramin and Amini, Alexander and Wang, Tsun Hsuan and Henzinger, Thomas A and Rus, Daniela}, booktitle = {Proceedings of the 2024 IEEE International Conference on Robotics and Automation}, isbn = {9798350384574}, issn = {1050-4729}, location = {Yokohama, Japan}, pages = {2774--2782}, publisher = {IEEE}, title = {{Overparametrization helps offline-to-online generalization of closed-loop control from pixels}}, doi = {10.1109/ICRA57147.2024.10610284}, year = {2024}, } @inproceedings{17893, abstract = {Strong data processing inequalities (SDPI) are an important object of study in Information Theory and have been well studied for f -divergences. Universal upper and lower bounds have been provided along with several applications, connecting them to impossibility (converse) results, concentration of measure, hypercontractivity, and so on. In this paper, we study Renyi divergence and the corresponding SDPI constant whose behavior seems to deviate from that of ordinary <1>-divergences. In particular, one can find examples showing that the universal upper bound relating its SDPI constant to the one of Total Variation does not hold in general. In this work, we prove, however, that the universal lower bound involving the SDPI constant of the Chi-square divergence does indeed hold. Furthermore, we also provide a characterization of the distribution that achieves the supremum when is equal to 2 and consequently compute the SDPI constant for Renyi divergence of the general binary channel.}, author = {Jin, Lifu and Esposito, Amedeo Roberto and Gastpar, Michael}, booktitle = {Proceedings of the 2024 IEEE International Symposium on Information Theory}, isbn = {9798350382846}, issn = {2157-8095}, location = {Athens, Greece}, pages = {3178--3183}, publisher = {IEEE}, title = {{Properties of the strong data processing constant for Rényi divergence}}, doi = {10.1109/ISIT57864.2024.10619367}, year = {2024}, } @inproceedings{17895, abstract = {We propose a concatenated code construction for a class of discrete-alphabet oblivious arbitrarily varying channels (AVCs) with cost constraints. The code has time and space complexity polynomial in the blocklength n . It uses a Reed-Solomon outer code, logarithmic blocklength random inner codes, and stochastic encoding by permuting the codeword before transmission. When the channel satisfies a condition called strong DS-nonsymmetrizability (a modified version of nonsymmetrizability originally due to Dobrushin and Stambler), we show that the code achieves a rate that for a variety of oblivious AVCs (such as classically studied error/erasure channels) match the known capacities.}, author = {Dey, B. K. and Jaggi, S. and Langberg, M. and Sarwate, A. D. and Zhang, Yihan}, booktitle = {Proceedings of the 2024 IEEE International Symposium on Information Theory }, isbn = {9798350382846}, issn = {2157-8095}, location = {Athens, Greece}, pages = {1586--1591}, publisher = {IEEE}, title = {{Computationally efficient codes for strongly Dobrushin-Stambler nonsymmetrizable oblivious AVCs}}, doi = {10.1109/ISIT57864.2024.10619362}, year = {2024}, } @inproceedings{17894, abstract = {Sibson's α -mutual information has received renewed attention recently in several contexts: concentration of measure under dependence, statistical learning, hypothesis testing, and estimation theory. In this work, we introduce several variational representations of Sibson's α -mutual information: 1) as a supremum over joint distributions of (a combination of) KL divergences; and 2) as a supremum over functions of opportune expected values. Leveraging them, we produce a variety of novel and known results, including a generalization of transportation-cost inequalities and Fano's inequality.}, author = {Esposito, Amedeo Roberto and Gastpar, Michael and Issa, Ibrahim}, booktitle = {Proceedings of the 2024 IEEE International Symposium on Information Theory }, isbn = {9798350382846}, issn = {2157-8095}, location = {Athens, Greece}, pages = {2110--2115}, publisher = {IEEE}, title = {{Variational characterizations of Sibson's α-mutual information}}, doi = {10.1109/ISIT57864.2024.10619378}, year = {2024}, } @article{18630, abstract = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, issn = {1860-5974}, journal = {Logical Methods in Computer Science}, number = {4}, pages = {11:1--11:34}, publisher = {EPI Sciences}, title = {{Stochastic processes with expected stopping time}}, doi = {10.46298/lmcs-20(4:11)2024}, volume = {20}, year = {2024}, } @inproceedings{18450, abstract = {In this work we present the engineering of a portable platform for sensing SERS signals in droplets microfluidics. This system comprised not only the read-out platform but also a design for the microfluidic devices optimized to enhanced the obtained SERS signals.}, author = {Quintero, Sergio and Relvas, Maria and Aranda, Marta and Nodal, Fernando and Dieguez, Lorena and Abalde-Cela, Sara}, booktitle = {2024 International Conference on Optical MEMS and Nanophotonics}, isbn = {9798350384925}, issn = {2160-5041}, location = {San Sebastian, Spain}, publisher = {IEEE}, title = {{Portable Raman platform for SERS droplets microfludics}}, doi = {10.1109/OMN61224.2024.10685279}, year = {2024}, } @article{18923, abstract = {Combinatorial optimization is a challenging problem applicable in a wide range of fields from logistics to finance. Recently, quantum computing has been used to attempt to solve these problems using a range of algorithms, including parameterized quantum circuits, adiabatic protocols, and quantum annealing. These solutions typically have several challenges: 1) there is little to no performance gain over classical methods; 2) not all constraints and objectives may be efficiently encoded in the quantum ansatz; and 3) the solution domain of the objective function may not be the same as the bit strings of measurement outcomes. This work presents “nonnative hybrid algorithms”: a framework to overcome these challenges by integrating quantum and classical resources with a hybrid approach. By designing nonnative quantum variational anosatzes that inherit some but not all problem structure, measurement outcomes from the quantum computer can act as a resource to be used by classical routines to indirectly compute optimal solutions, partially overcoming the challenges of contemporary quantum optimization approaches. These methods are demonstrated using a publicly available neutral-atom quantum computer on two simple problems of Max k-Cut and maximum independent set. We find improvements in solution quality when comparing the hybrid algorithm to its “no quantum” version, a demonstration of a “comparative advantage.”}, author = {Wurtz, Jonathan and Sack, Stefan and Wang, Sheng-Tao}, issn = {2689-1808}, journal = {IEEE Transactions on Quantum Engineering}, pages = {1--14}, publisher = {IEEE}, title = {{Solving nonnative combinatorial optimization problems using hybrid quantum–classical algorithms}}, doi = {10.1109/tqe.2024.3443660}, volume = {5}, year = {2024}, } @article{22563, abstract = {The ascent of water from the soil to the leaves of vascular plants, described by the study of plant hydraulics, regulates ecosystem responses to environmental forcing and recovery from stress periods. Several approaches to model plant hydraulics have been proposed. In this study, we introduce four different versions of plant hydraulics representations in the terrestrial biosphere model T&C to understand the significance of plant hydraulics to ecosystem functioning. We tested representations of plant hydraulics, investigating plant water capacitance, and long-term xylem damages following drought. The four models we tested were a combination of representations including or neglecting capacitance and including or neglecting xylem damage legacies. Using the models at six case studies spanning semiarid to tropical ecosystems, we quantify how plant xylem flow, plant water storage and long-term xylem damage can modulate overall water and carbon dynamics across multiple time scales. We show that as drought develops, models with plant hydraulics predict a slower onset of plant water stress, and a diurnal variability of water and carbon fluxes closer to observations. Plant water storage was found to be particularly important for the diurnal dynamics of water and carbon fluxes, with models that include plant water capacitance yielding better results. Models including permanent damage to conducting plant tissues show an additional significant drought legacy effect, limiting plant productivity during the recovery phase following major droughts. However, when considering ecosystem responses to the observed climate variability, plant hydraulic modules alone cannot significantly improve the overall model performance, even though they reproduce more realistic water and carbon dynamics. This opens new avenues for model development, explicitly linking plant hydraulics with additional ecosystem processes, such as plant phenology and improved carbon allocation algorithms.}, author = {Paschalis, Athanasios and De Kauwe, Martin G. and Sabot, Manon and Fatichi, Simone}, issn = {1365-2486}, journal = {Global Change Biology}, keywords = {Ecosystem recovery, Ecosystem responses, Plant hydraulics, Terrestrial biosphere model, Water stress}, number = {1}, publisher = {Wiley}, title = {{When do plant hydraulics matter in terrestrial biosphere modelling?}}, doi = {10.1111/gcb.17022}, volume = {30}, year = {2024}, } @article{22583, abstract = {Accurately predicting weather and climate in cities is critical for safeguarding human health and strengthening urban resilience. Multimodel evaluations can lead to model improvements; however, there have been no major intercomparisons of urban-focussed land surface models in over a decade. Here, in Phase 1 of the Urban-PLUMBER project, we evaluate the ability of 30 land surface models to simulate surface energy fluxes critical to atmospheric meteorological and air quality simulations. We establish minimum and upper performance expectations for participating models using simple information-limited models as benchmarks. Compared with the last major model intercomparison at the same site, we find broad improvement in the current cohort's predictions of short-wave radiation, sensible and latent heat fluxes, but little or no improvement in long-wave radiation and momentum fluxes. Models with a simple urban representation (e.g., ‘slab’ schemes) generally perform well, particularly when combined with sophisticated hydrological/vegetation models. Some mid-complexity models (e.g., ‘canyon’ schemes) also perform well, indicating efforts to integrate vegetation and hydrology processes have paid dividends. The most complex models that resolve three-dimensional interactions between buildings in general did not perform as well as other categories. However, these models also tended to have the simplest representations of hydrology and vegetation. Models without any urban representation (i.e., vegetation-only land surface models) performed poorly for latent heat fluxes, and reasonably for other energy fluxes at this suburban site. Our analysis identified widespread human errors in initial submissions that substantially affected model performances. Although significant efforts are applied to correct these errors, we conclude that human factors are likely to influence results in this (or any) model intercomparison, particularly where participating scientists have varying experience and first languages. These initial results are for one suburban site, and future phases of Urban-PLUMBER will evaluate models across 20 sites in different urban and regional climate zones.}, author = {Lipson, Mathew J. and Grimmond, Sue and Best, Martin and Abramowitz, Gab and Coutts, Andrew and Tapper, Nigel and Baik, Jong‐Jin and Beyers, Meiring and Blunn, Lewis and Boussetta, Souhail and Bou‐Zeid, Elie and De Kauwe, Martin G. and de Munck, Cécile and Demuzere, Matthias and Fatichi, Simone and Fortuniak, Krzysztof and Han, Beom‐Soon and Hendry, Margaret A. and Kikegawa, Yukihiro and Kondo, Hiroaki and Lee, Doo‐Il and Lee, Sang‐Hyun and Lemonsu, Aude and Machado, Tiago and Manoli, Gabriele and Martilli, Alberto and Masson, Valéry and McNorton, Joe and Meili, Naika and Meyer, David and Nice, Kerry A. and Oleson, Keith W. and Park, Seung‐Bu and Roth, Michael and Schoetter, Robert and Simón‐Moral, Andrés and Steeneveld, Gert‐Jan and Sun, Ting and Takane, Yuya and Thatcher, Marcus and Tsiringakis, Aristofanis and Varentsov, Mikhail and Wang, Chenghao and Wang, Zhi‐Hua and Pitman, Andy J.}, issn = {1477-870X}, journal = {Quarterly Journal of the Royal Meteorological Society}, keywords = {Benchmark, Energy balance, Intercomparison, Model evaluation, Urban climate, Urban meteorology}, number = {758}, pages = {126--169}, publisher = {Wiley}, title = {{Evaluation of 30 urban land surface models in the Urban-PLUMBER project: Phase 1 results}}, doi = {10.1002/qj.4589}, volume = {150}, year = {2024}, } @article{17481, abstract = {Phase-field models such as the Allen–Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen–Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow. In the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: as long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen–Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε 1/2 ). Our approach is based on the gradient-flow structure of the Allen–Cahn equation and its limiting motion: building on the recent concept of “gradient-flow calibrations” for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen–Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen–Cahn operator or additional convergence hypotheses for the energy at positive times.}, author = {Fischer, Julian L and Marveggio, Alice}, issn = {1873-1430}, journal = {Annales de l'Institut Henri Poincaré C}, number = {5}, pages = {1117--1178}, publisher = {EMS Press}, title = {{Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow}}, doi = {10.4171/AIHPC/109}, volume = {41}, year = {2024}, } @article{15048, abstract = {Embryogenesis results from the coordinated activities of different signaling pathways controlling cell fate specification and morphogenesis. In vertebrate gastrulation, both Nodal and BMP signaling play key roles in germ layer specification and morphogenesis, yet their interplay to coordinate embryo patterning with morphogenesis is still insufficiently understood. Here, we took a reductionist approach using zebrafish embryonic explants to study the coordination of Nodal and BMP signaling for embryo patterning and morphogenesis. We show that Nodal signaling triggers explant elongation by inducing mesendodermal progenitors but also suppressing BMP signaling activity at the site of mesendoderm induction. Consistent with this, ectopic BMP signaling in the mesendoderm blocks cell alignment and oriented mesendoderm intercalations, key processes during explant elongation. Translating these ex vivo observations to the intact embryo showed that, similar to explants, Nodal signaling suppresses the effect of BMP signaling on cell intercalations in the dorsal domain, thus allowing robust embryonic axis elongation. These findings suggest a dual function of Nodal signaling in embryonic axis elongation by both inducing mesendoderm and suppressing BMP effects in the dorsal portion of the mesendoderm.}, author = {Schauer, Alexandra and Pranjic-Ferscha, Kornelija and Hauschild, Robert and Heisenberg, Carl-Philipp J}, issn = {1477-9129}, journal = {Development}, number = {4}, pages = {1--18}, publisher = {Company of Biologists}, title = {{Robust axis elongation by Nodal-dependent restriction of BMP signaling}}, doi = {10.1242/dev.202316}, volume = {151}, year = {2024}, } @article{17458, abstract = {Changes in gene dosage can have tremendous evolutionary potential (e.g. whole-genome duplications), but without compensatory mechanisms, they can also lead to gene dysregulation and pathologies. Sex chromosomes are a paradigmatic example of naturally occurring gene dosage differences and their compensation. In species with chromosome-based sex determination, individuals within the same population necessarily show ‘natural’ differences in gene dosage for the sex chromosomes. In this Review, we focus on the mammalian X chromosome and discuss recent new insights into the dosage-compensation mechanisms that evolved along with the emergence of sex chromosomes, namely X-inactivation and X-upregulation. We also discuss the evolution of the genetic loci and molecular players involved, as well as the regulatory diversity and potentially different requirements for dosage compensation across mammalian species.}, author = {Cecalev, Daniela and Vicoso, Beatriz and Galupa, Rafael}, issn = {1477-9129}, journal = {Development}, number = {15}, publisher = {Company of Biologists}, title = {{Compensation of gene dosage on the mammalian X}}, doi = {10.1242/dev.202891}, volume = {151}, year = {2024}, } @misc{14926, author = {Hauschild, Robert}, publisher = {Institute of Science and Technology Austria}, title = {{Matlab script for analysis of clone dispersal}}, doi = {10.15479/AT:ISTA:14926}, year = {2024}, } @misc{22234, abstract = {Lists of nontrivial integral points on some (families of) cubic surfaces. (2024-07-18)}, author = {Browning, Timothy D and Sutherland, Andrew}, publisher = {Göttingen Research Online Data}, title = {{Data and code for: Integral points on cubic surfaces: heuristics and numerics}}, doi = {10.25625/4FLFH8}, year = {2024}, } @article{17457, abstract = {Autoantibodies against the protein leucine-rich glioma inactivated 1 (LGI1) cause the most common subtype of autoimmune encephalitis with predominant involvement of the limbic system, associated with seizures and memory deficits. LGI1 and its receptor ADAM22 are part of a transsynaptic protein complex that includes several proteins involved in presynaptic neurotransmitter release and postsynaptic glutamate sensing. Autoantibodies against LGI1 increase excitatory synaptic strength, but studies that genetically disrupt the LGI1-ADAM22 complex report a reduction in postsynaptic glutamate receptor-mediated responses. Thus, the mechanisms underlying the increased synaptic strength induced by LGI1 autoantibodies remain elusive, and the contributions of presynaptic molecules to the LGI1-transsynaptic complex remain unclear. We therefore investigated the presynaptic mechanisms that mediate autoantibody-induced synaptic strengthening.}, author = {Ritzau-Jost, Andreas and Gsell, Felix and Sell, Josefine and Sachs, Stefan and Montanaro-Punzengruber, Jacqueline-Claire and Kirmann, Toni and Maaß, Sebastian and Irani, Sarosh R. and Werner, Christian and Geis, Christian and Sauer, Markus and Shigemoto, Ryuichi and Hallermann, Stefan}, issn = {2332-7812}, journal = {Neurology, Neuroimmunology & Neuroinflammation}, number = {5}, pages = {e200284}, publisher = {Wolters Kluwer}, title = {{LGI1 autoantibodies enhance synaptic transmission by presynaptic Kv1 loss and increased action potential broadening}}, doi = {10.1212/NXI.0000000000200284}, volume = {11}, year = {2024}, } @unpublished{19063, abstract = {Instruction-tuned Large Language Models (LLMs) show impressive results in numerous practical applications, but they lack essential safety features that are common in other areas of computer science, particularly an explicit separation of instructions and data. This makes them vulnerable to manipulations such as indirect prompt injections and generally unsuitable for safety-critical tasks. Surprisingly, there is currently no established definition or benchmark to quantify this phenomenon. In this work, we close this gap by introducing a formal measure for instruction-data separation and an empirical variant that is calculable from a model's outputs. We also present a new dataset, SEP, that allows estimating the measure for real-world models. Our results on various LLMs show that the problem of instruction-data separation is real: all models fail to achieve high separation, and canonical mitigation techniques, such as prompt engineering and fine-tuning, either fail to substantially improve separation or reduce model utility. The source code and SEP dataset are openly accessible at https://github.com/egozverev/Shold-It-Be-Executed-Or-Processed. }, author = {Zverev, Egor and Abdelnabi, Sahar and Tabesh, Soroush and Fritz, Mario and Lampert, Christoph}, booktitle = {arXiv}, title = {{Can LLMs separate instructions from data? And what do we even mean by that?}}, doi = {10.48550/arXiv.2403.06833}, year = {2024}, } @article{15401, abstract = {Amide-proton-detected magic-angle-spinning NMR of deuterated proteins has become a main technique in NMR-based structural biology. In standard deuteration protocols that rely on D2O-based culture media, non-exchangeable amide sites remain deuterated, making these sites unobservable. Here we demonstrate that proteins produced with a H2O-based culture medium doped with deuterated cell lysate allow scientists to overcome this “reprotonation bottleneck” while retaining a high level of deuteration (ca. 80 %) and narrow linewidths. We quantified coherence lifetimes of several proteins prepared with this labeling pattern over a range of magic-angle-spinning (MAS) frequencies (40–100 kHz). We demonstrate that under commonly used conditions (50–60 kHz MAS), the amide 1H linewidths with our labeling approach are comparable to those of perdeuterated proteins and better than those of protonated samples at 100 kHz. For three proteins in the 33–50 kDa size range, many previously unobserved amides become visible. We report how to prepare the deuterated cell lysate for our approach from fractions of perdeuterated cultures which are usually discarded, and we show that such media can be used identically to commercial media. The residual protonation of Hα sites allows for well-resolved Hα-detected spectra and Hα resonance assignment, exemplified by the de novo assignment of 168 Hα sites in a 39 kDa protein. The approach based on this H2O/cell-lysate deuteration and MAS frequencies compatible with 1.3 or 1.9 mm rotors presents a strong sensitivity benefit over 0.7 mm 100 kHz MAS experiments.}, author = {Napoli, Federico and Guan, Jia-Ying and Arnaud, Charles-Adrien and Macek, Pavel and Fraga, Hugo and Breyton, Cécile and Schanda, Paul}, issn = {2699-0016}, journal = {Magnetic Resonance}, number = {1}, pages = {33--49}, publisher = {Copernicus Publications}, title = {{Deuteration of proteins boosted by cell lysates: High-resolution amide and Ha magic-angle-spinning (MAS) NMR without the reprotonation bottleneck}}, doi = {10.5194/mr-5-33-2024}, volume = {5}, year = {2024}, } @phdthesis{15094, abstract = {Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in discrete geometry that have captivated mathematicians for centuries, if not millennia. This thesis seeks to cast new light on these structures by illustrating specific instances where a topological perspective, specifically through discrete Morse theory and persistent homology, provides valuable insights. At first glance, the topology of these geometric objects might seem uneventful: point sets essentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which is a contractible space, and the topology of a network primarily involves the enumeration of connected components and cycles within the network. However, beneath this apparent simplicity, there lies an array of intriguing structures, a small subset of which will be uncovered in this thesis. Focused on three case studies, each addressing one of the mentioned objects, this work will showcase connections that intertwine topology with diverse fields such as combinatorial geometry, algorithms and data structures, and emerging applications like spatial biology. }, author = {Cultrera di Montesano, Sebastiano}, issn = {2663-337X}, pages = {108}, publisher = {Institute of Science and Technology Austria}, title = {{Persistence and Morse theory for discrete geometric structures}}, doi = {10.15479/at:ista:15094}, year = {2024}, } @article{13182, abstract = {We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining a collection of sorted lists together with its persistence diagram.}, author = {Biswas, Ranita and Cultrera Di Montesano, Sebastiano and Edelsbrunner, Herbert and Saghafian, Morteza}, issn = {2367-1734}, journal = {Journal of Applied and Computational Topology}, pages = {1101--1119}, publisher = {Springer Nature}, title = {{Geometric characterization of the persistence of 1D maps}}, doi = {10.1007/s41468-023-00126-9}, volume = {8}, year = {2024}, }