@article{7463,
abstract = {Resting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. A distinctive attribute of systems at criticality is the presence of long-range correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow-band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, brain activity is a broadband phenomenon, and a significant piece of information useful to precisely discriminate between normal (critical) and pathological behavior (non-critical), may be encoded in the broadband spatio-temporal cortical dynamics. Here we propose to characterize the temporal correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that the avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms.},
author = {Lombardi, Fabrizio and Shriki, Oren and Herrmann, Hans J and de Arcangelis, Lucilla},
issn = {1872-8286},
journal = {Neurocomputing},
pages = {657--666},
publisher = {Elsevier},
title = {{Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches}},
doi = {10.1016/j.neucom.2020.05.126},
volume = {461},
year = {2021},
}
@article{7551,
abstract = {Novelty facilitates formation of memories. The detection of novelty and storage of contextual memories are both mediated by the hippocampus, yet the mechanisms that link these two functions remain to be defined. Dentate granule cells (GCs) of the dorsal hippocampus fire upon novelty exposure forming engrams of contextual memory. However, their key excitatory inputs from the entorhinal cortex are not responsive to novelty and are insufficient to make dorsal GCs fire reliably. Here we uncover a powerful glutamatergic pathway to dorsal GCs from ventral hippocampal mossy cells (MCs) that relays novelty, and is necessary and sufficient for driving dorsal GCs activation. Furthermore, manipulation of ventral MCs activity bidirectionally regulates novelty-induced contextual memory acquisition. Our results show that ventral MCs activity controls memory formation through an intra-hippocampal interaction mechanism gated by novelty.},
author = {Fredes Tolorza, Felipe A and Silva Sifuentes, Maria A and Koppensteiner, Peter and Kobayashi, Kenta and Jösch, Maximilian A and Shigemoto, Ryuichi},
journal = {Current Biology},
number = {1},
pages = {P25--38.E5},
publisher = {Elsevier},
title = {{Ventro-dorsal hippocampal pathway gates novelty-induced contextual memory formation}},
doi = {10.1016/j.cub.2020.09.074},
volume = {31},
year = {2021},
}
@article{7553,
abstract = {Normative theories and statistical inference provide complementary approaches for the study of biological systems. A normative theory postulates that organisms have adapted to efficiently solve essential tasks, and proceeds to mathematically work out testable consequences of such optimality; parameters that maximize the hypothesized organismal function can be derived ab initio, without reference to experimental data. In contrast, statistical inference focuses on efficient utilization of data to learn model parameters, without reference to any a priori notion of biological function, utility, or fitness. Traditionally, these two approaches were developed independently and applied separately. Here we unify them in a coherent Bayesian framework that embeds a normative theory into a family of maximum-entropy “optimization priors.” This family defines a smooth interpolation between a data-rich inference regime (characteristic of “bottom-up” statistical models), and a data-limited ab inito prediction regime (characteristic of “top-down” normative theory). We demonstrate the applicability of our framework using data from the visual cortex, and argue that the flexibility it affords is essential to address a number of fundamental challenges relating to inference and prediction in complex, high-dimensional biological problems.},
author = {Mlynarski, Wiktor F and Hledik, Michal and Sokolowski, Thomas R and Tkačik, Gašper},
journal = {Neuron},
number = {7},
pages = {1227--1241.e5},
publisher = {Cell Press},
title = {{Statistical analysis and optimality of neural systems}},
doi = {10.1016/j.neuron.2021.01.020},
volume = {109},
year = {2021},
}
@article{7685,
abstract = {We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.},
author = {Boccato, Chiara},
issn = {0129-055X},
journal = {Reviews in Mathematical Physics},
number = {1},
publisher = {World Scientific},
title = {{The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime}},
doi = {10.1142/S0129055X20600065},
volume = {33},
year = {2021},
}
@inproceedings{10552,
abstract = {We study a class of convex-concave saddle-point problems of the form minxmaxy⟨Kx,y⟩+fP(x)−h∗(y) where K is a linear operator, fP is the sum of a convex function f with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope P, and h∗ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle (lmo) for fP and an efficient proximal map for h∗ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case h∗ is the indicator function of a linear constraint and function f is quadratic, we show a O(1/n2) convergence rate on the dual objective, requiring O(nlogn) calls of lmo. If the problem comes from the constrained optimization problem minx∈Rd{fP(x)|Ax−b=0} then we additionally get bound O(1/n2) both on the primal gap and on the infeasibility gap. In the most general case, we show a O(1/n) convergence rate of the primal-dual gap again requiring O(nlogn) calls of lmo. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision.},
author = {Kolmogorov, Vladimir and Pock, Thomas},
booktitle = {38th International Conference on Machine Learning},
location = {Virtual},
title = {{One-sided Frank-Wolfe algorithms for saddle problems}},
year = {2021},
}
@inproceedings{10553,
abstract = {The popularity of permissioned blockchain systems demands BFT SMR protocols that are efficient under good network conditions (synchrony) and robust under bad network conditions (asynchrony). The state-of-the-art partially synchronous BFT SMR protocols provide optimal linear communication cost per decision under synchrony and good leaders, but lose liveness under asynchrony. On the other hand, the state-of-the-art asynchronous BFT SMR protocols are live even under asynchrony, but always pay quadratic cost even under synchrony. In this paper, we propose a BFT SMR protocol that achieves the best of both worlds -- optimal linear cost per decision under good networks and leaders, optimal quadratic cost per decision under bad networks, and remains always live.},
author = {Gelashvili, Rati and Kokoris Kogias, Eleftherios and Spiegelman, Alexander and Xiang, Zhuolun},
booktitle = {Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing},
isbn = {9-781-4503-8548-0},
keywords = {optimal, state machine replication, fallback, asynchrony, byzantine faults},
location = {Virtual, Italy},
pages = {187--190},
publisher = {Association for Computing Machinery},
title = {{Brief announcement: Be prepared when network goes bad: An asynchronous view-change protocol}},
doi = {10.1145/3465084.3467941},
year = {2021},
}
@inproceedings{10554,
abstract = {We present DAG-Rider, the first asynchronous Byzantine Atomic Broadcast protocol that achieves optimal resilience, optimal amortized communication complexity, and optimal time complexity. DAG-Rider is post-quantum safe and ensures that all values proposed by correct processes eventually get delivered. We construct DAG-Rider in two layers: In the first layer, processes reliably broadcast their proposals and build a structured Directed Acyclic Graph (DAG) of the communication among them. In the second layer, processes locally observe their DAGs and totally order all proposals with no extra communication.},
author = {Keidar, Idit and Kokoris Kogias, Eleftherios and Naor, Oded and Spiegelman, Alexander},
booktitle = {Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing},
isbn = {978-1-4503-8548-0},
location = {Virtual, Italy},
pages = {165--175},
publisher = {Association for Computing Machinery},
title = {{All You Need is DAG}},
doi = {10.1145/3465084.3467905},
year = {2021},
}
@inproceedings{10556,
abstract = {In this paper, we present the first Asynchronous Distributed Key Generation (ADKG) algorithm which is also the first distributed key generation algorithm that can generate cryptographic keys with a dual (f,2f+1)-threshold (where f is the number of faulty parties). As a result, using our ADKG we remove the trusted setup assumption that the most scalable consensus algorithms make. In order to create a DKG with a dual (f,2f+1)- threshold we first answer in the affirmative the open question posed by Cachin et al. [7] on how to create an Asynchronous Verifiable Secret Sharing (AVSS) protocol with a reconstruction threshold of f+11 . To prove these results, we use the original ideas of Adiprasito, Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon theorem and slightly modified version of the celebrated Maurey lemma.},
author = {Ivanov, Grigory},
issn = {14692120},
journal = {Bulletin of the London Mathematical Society},
number = {2},
pages = {631--641},
publisher = {London Mathematical Society},
title = {{No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p}},
doi = {10.1112/blms.12449},
volume = {53},
year = {2021},
}
@article{9038,
abstract = {Layered materials in which individual atomic layers are bonded by weak van der Waals forces (vdW materials) constitute one of the most prominent platforms for materials research. Particularly, polar vdW crystals, such as hexagonal boron nitride (h-BN), alpha-molybdenum trioxide (α-MoO3) or alpha-vanadium pentoxide (α-V2O5), have received significant attention in nano-optics, since they support phonon polaritons (PhPs)―light coupled to lattice vibrations― with strong electromagnetic confinement and low optical losses. Recently, correlative far- and near-field studies of α-MoO3 have been demonstrated as an effective strategy to accurately extract the permittivity of this material. Here, we use this accurately characterized and low-loss polaritonic material to sense its local dielectric environment, namely silica (SiO2), one of the most widespread substrates in nanotechnology. By studying the propagation of PhPs on α-MoO3 flakes with different thicknesses laying on SiO2 substrates via near-field microscopy (s-SNOM), we extract locally the infrared permittivity of SiO2. Our work reveals PhPs nanoimaging as a versatile method for the quantitative characterization of the local optical properties of dielectric substrates, crucial for understanding and predicting the response of nanomaterials and for the future scalability of integrated nanophotonic devices. },
author = {Aguilar-Merino, Patricia and Álvarez-Pérez, Gonzalo and Taboada-Gutiérrez, Javier and Duan, Jiahua and Prieto Gonzalez, Ivan and Álvarez-Prado, Luis Manuel and Nikitin, Alexey Y. and Martín-Sánchez, Javier and Alonso-González, Pablo},
issn = {20794991},
journal = {Nanomaterials},
number = {1},
publisher = {MDPI},
title = {{Extracting the infrared permittivity of SiO2 substrates locally by near-field imaging of phonon polaritons in a van der Waals crystal}},
doi = {10.3390/nano11010120},
volume = {11},
year = {2021},
}
@article{9046,
author = {Römhild, Roderich and Andersson, Dan I.},
issn = {15537374},
journal = {PLoS Pathogens},
number = {1},
publisher = {Public Library of Science},
title = {{Mechanisms and therapeutic potential of collateral sensitivity to antibiotics}},
doi = {10.1371/journal.ppat.1009172},
volume = {17},
year = {2021},
}
@article{9047,
abstract = {This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is O(N1−1/μ) , where N is the block length and μ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate 0 or 1.},
author = {Mondelli, Marco and Hashemi, Seyyed Ali and Cioffi, John M. and Goldsmith, Andrea},
issn = {15582248},
journal = {IEEE Transactions on Wireless Communications},
number = {1},
pages = {18--27},
publisher = {IEEE},
title = {{Sublinear latency for simplified successive cancellation decoding of polar codes}},
doi = {10.1109/TWC.2020.3022922},
volume = {20},
year = {2021},
}
@article{9048,
abstract = {The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of “precession” and “entanglement” DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.},
author = {De Nicola, Stefano and Michailidis, Alexios and Serbyn, Maksym},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {General Physics and Astronomy},
number = {4},
publisher = {American Physical Society},
title = {{Entanglement view of dynamical quantum phase transitions}},
doi = {10.1103/physrevlett.126.040602},
volume = {126},
year = {2021},
}
@phdthesis{9056,
abstract = {In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,
and thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration
function on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets.},
author = {Osang, Georg F},
issn = {2663-337X},
pages = {134},
publisher = {IST Austria},
title = {{Multi-cover persistence and Delaunay mosaics}},
doi = {10.15479/AT:ISTA:9056},
year = {2021},
}
@unpublished{9082,
abstract = {Acquired mutations are sufficiently frequent such that the genome of a single cell offers a record of its history of cell divisions. Among more common somatic genomic alterations are loss of heterozygosity (LOH). Large LOH events are potentially detectable in single cell RNA sequencing (scRNA-seq) datasets as tracts of monoallelic expression for constitutionally heterozygous single nucleotide variants (SNVs) located among contiguous genes. We identified runs of monoallelic expression, consistent with LOH, uniquely distributed throughout the genome in single cell brain cortex transcriptomes of F1 hybrids involving different inbred mouse strains. We then phylogenetically reconstructed single cell lineages and simultaneously identified cell types by corresponding gene expression patterns. Our results are consistent with progenitor cells giving rise to multiple cortical cell types through stereotyped expansion and distinct waves of neurogenesis. Compared to engineered recording systems, LOH events accumulate throughout the genome and across the lifetime of an organism, affording tremendous capacity for encoding lineage information and increasing resolution for later cell divisions. This approach can conceivably be computationally incorporated into scRNA-seq analysis and may be useful for organisms where genetic engineering is prohibitive, such as humans.},
author = {Anderson, Donovan J. and Pauler, Florian and McKenna, Aaron and Shendure, Jay and Hippenmeyer, Simon and Horwitz, Marshall S.},
booktitle = {bioRxiv},
publisher = {Cold Spring Harbor Laboratory},
title = {{Simultaneous identification of brain cell type and lineage via single cell RNA sequencing}},
doi = {10.1101/2020.12.31.425016},
year = {2021},
}
@article{9093,
abstract = {We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schrödinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.},
author = {Marchukov, Oleksandr and Volosniev, Artem},
issn = {2542-4653},
journal = {SciPost Physics},
number = {2},
publisher = {SciPost Foundation},
title = {{Shape of a sound wave in a weakly-perturbed Bose gas}},
doi = {10.21468/scipostphys.10.2.025},
volume = {10},
year = {2021},
}
@article{9098,
abstract = {We study properties of the volume of projections of the n-dimensional
cross-polytope $\crosp^n = \{ x \in \R^n \mid |x_1| + \dots + |x_n| \leqslant 1\}.$ We prove that the projection of $\crosp^n$ onto a k-dimensional coordinate subspace has the maximum possible volume for k=2 and for k=3.
We obtain the exact lower bound on the volume of such a projection onto a two-dimensional plane. Also, we show that there exist local maxima which are not global ones for the volume of a projection of $\crosp^n$ onto a k-dimensional subspace for any n>k⩾2.},
author = {Ivanov, Grigory},
issn = {0012365X},
journal = {Discrete Mathematics},
number = {5},
publisher = {Elsevier},
title = {{On the volume of projections of the cross-polytope}},
doi = {10.1016/j.disc.2021.112312},
volume = {344},
year = {2021},
}
@article{9099,
abstract = {We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to a field of characteristic zero as a morphism vanishes if and only if it vanishes for lifting it as a derived autoequivalence. We also compare the deformation space of these two types of deformations.},
author = {Srivastava, Tanya K},
issn = {14208938},
journal = {Archiv der Mathematik},
number = {5},
pages = {515--527},
publisher = {Springer Nature},
title = {{Lifting automorphisms on Abelian varieties as derived autoequivalences}},
doi = {10.1007/s00013-020-01564-y},
volume = {116},
year = {2021},
}
@article{9100,
abstract = {Marine environments are inhabited by a broad representation of the tree of life, yet our understanding of speciation in marine ecosystems is extremely limited compared with terrestrial and freshwater environments. Developing a more comprehensive picture of speciation in marine environments requires that we 'dive under the surface' by studying a wider range of taxa and ecosystems is necessary for a more comprehensive picture of speciation. Although studying marine evolutionary processes is often challenging, recent technological advances in different fields, from maritime engineering to genomics, are making it increasingly possible to study speciation of marine life forms across diverse ecosystems and taxa. Motivated by recent research in the field, including the 14 contributions in this issue, we highlight and discuss six axes of research that we think will deepen our understanding of speciation in the marine realm: (a) study a broader range of marine environments and organisms; (b) identify the reproductive barriers driving speciation between marine taxa; (c) understand the role of different genomic architectures underlying reproductive isolation; (d) infer the evolutionary history of divergence using model‐based approaches; (e) study patterns of hybridization and introgression between marine taxa; and (f) implement highly interdisciplinary, collaborative research programmes. In outlining these goals, we hope to inspire researchers to continue filling this critical knowledge gap surrounding the origins of marine biodiversity.},
author = {Faria, Rui and Johannesson, Kerstin and Stankowski, Sean},
issn = {14209101},
journal = {Journal of Evolutionary Biology},
number = {1},
pages = {4--15},
publisher = {Wiley},
title = {{Speciation in marine environments: Diving under the surface}},
doi = {10.1111/jeb.13756},
volume = {34},
year = {2021},
}
@article{9101,
abstract = {Behavioral predispositions are innate tendencies of animals to behave in a given way without the input of learning. They increase survival chances and, due to environmental and ecological challenges, may vary substantially even between closely related taxa. These differences are likely to be especially pronounced in long-lived species like crocodilians. This order is particularly relevant for comparative cognition due to its phylogenetic proximity to birds. Here we compared early life behavioral predispositions in two Alligatoridae species. We exposed American alligator and spectacled caiman hatchlings to three different novel situations: a novel object, a novel environment that was open and a novel environment with a shelter. This was then repeated a week later. During exposure to the novel environments, alligators moved around more and explored a larger range of the arena than the caimans. When exposed to the novel object, the alligators reduced the mean distance to the novel object in the second phase, while the caimans further increased it, indicating diametrically opposite ontogenetic development in behavioral predispositions. Although all crocodilian hatchlings face comparable challenges, e.g., high predation pressure, the effectiveness of parental protection might explain the observed pattern. American alligators are apex predators capable of protecting their offspring against most dangers, whereas adult spectacled caimans are frequently predated themselves. Their distancing behavior might be related to increased predator avoidance and also explain the success of invasive spectacled caimans in the natural habitats of other crocodilians.},
author = {Reber, Stephan A. and Oh, Jinook and Janisch, Judith and Stevenson, Colin and Foggett, Shaun and Wilkinson, Anna},
issn = {14359456},
journal = {Animal Cognition},
number = {4},
pages = {753--764},
publisher = {Springer Nature},
title = {{Early life differences in behavioral predispositions in two Alligatoridae species}},
doi = {10.1007/s10071-020-01461-5},
volume = {24},
year = {2021},
}
@article{9111,
abstract = {We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data.},
author = {Brown, Adam and Bobrowski, Omer and Munch, Elizabeth and Wang, Bei},
issn = {2367-1726},
journal = {Journal of Applied and Computational Topology},
number = {1},
pages = {99--140},
publisher = {Springer Nature},
title = {{Probabilistic convergence and stability of random mapper graphs}},
doi = {10.1007/s41468-020-00063-x},
volume = {5},
year = {2021},
}