@article{9770,
abstract = {We study an effective one-dimensional quantum model that includes friction and spin-orbit coupling (SOC), and show that the model exhibits spin polarization when both terms are finite. Most important, strong spin polarization can be observed even for moderate SOC, provided that the friction is strong. Our findings might help to explain the pronounced effect of chirality on spin distribution and transport in chiral molecules. In particular, our model implies static magnetic properties of a chiral molecule, which lead to Shiba-like states when a molecule is placed on a superconductor, in accordance with recent experimental data.},
author = {Volosniev, Artem and Alpern, Hen and Paltiel, Yossi and Millo, Oded and Lemeshko, Mikhail and Ghazaryan, Areg},
issn = {2469-9969},
journal = {Physical Review B},
number = {2},
publisher = {American Physical Society},
title = {{Interplay between friction and spin-orbit coupling as a source of spin polarization}},
doi = {10.1103/physrevb.104.024430},
volume = {104},
year = {2021},
}
@article{9548,
abstract = {We extend the notion of the minimal volume ellipsoid containing a convex body in Rd to the setting of logarithmically concave functions. We consider a vast class of logarithmically concave functions whose superlevel sets are concentric ellipsoids. For a fixed function from this class, we consider the set of all its “affine” positions. For any log-concave function f on Rd, we consider functions belonging to this set of “affine” positions, and find the one with the minimal integral under the condition that it is pointwise greater than or equal to f. We study the properties of existence and uniqueness of the solution to this problem. For any s∈[0,+∞), we consider the construction dual to the recently defined John s-function (Ivanov and Naszódi in Functional John ellipsoids. arXiv preprint: arXiv:2006.09934, 2020). We prove that such a construction determines a unique function and call it the Löwner s-function of f. We study the Löwner s-functions as s tends to zero and to infinity. Finally, extending the notion of the outer volume ratio, we define the outer integral ratio of a log-concave function and give an asymptotically tight bound on it.},
author = {Ivanov, Grigory and Tsiutsiurupa, Igor},
issn = {1559-002X},
journal = {Journal of Geometric Analysis},
publisher = {Springer},
title = {{Functional Löwner ellipsoids}},
doi = {10.1007/s12220-021-00691-4},
year = {2021},
}
@article{9558,
abstract = {We show that turbulent dynamics that arise in simulations of the three-dimensional Navier--Stokes equations in a triply-periodic domain under sinusoidal forcing can be described as transient visits to the neighborhoods of unstable time-periodic solutions. Based on this description, we reduce the original system with more than 10^5 degrees of freedom to a 17-node Markov chain where each node corresponds to the neighborhood of a periodic orbit. The model accurately reproduces long-term averages of the system's observables as weighted sums over the periodic orbits.
},
author = {Yalniz, Gökhan and Hof, Björn and Budanur, Nazmi B},
issn = {1079-7114},
journal = {Physical Review Letters},
number = {24},
publisher = {American Physical Society},
title = {{Coarse graining the state space of a turbulent flow using periodic orbits}},
doi = {10.1103/PhysRevLett.126.244502},
volume = {126},
year = {2021},
}
@article{9606,
abstract = {Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover, and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys. Rev. Lett. 124, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.},
author = {Tononi, A. and Cappellaro, Alberto and Bighin, Giacomo and Salasnich, L.},
issn = {24699934},
journal = {Physical Review A},
number = {6},
publisher = {American Physical Society},
title = {{Propagation of first and second sound in a two-dimensional Fermi superfluid}},
doi = {10.1103/PhysRevA.103.L061303},
volume = {103},
year = {2021},
}
@article{9570,
abstract = {We present conductance-matrix measurements in long, three-terminal hybrid superconductor-semiconductor nanowires, and compare with theoretical predictions of a magnetic-field-driven, topological quantum phase transition. By examining the nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zero-bias peaks, ruling out spurious gap-closure signatures from localized states. We observe that after the gap closes, nonlocal signals and zero-bias peaks fluctuate strongly at both ends, inconsistent with a simple picture of clean topological superconductivity.},
author = {Puglia, Denise and Martinez, E. A. and Ménard, G. C. and Pöschl, A. and Gronin, S. and Gardner, G. C. and Kallaher, R. and Manfra, M. J. and Marcus, C. M. and Higginbotham, Andrew P and Casparis, L.},
issn = {24699969},
journal = {Physical Review B},
number = {23},
publisher = {American Physical Society},
title = {{Closing of the induced gap in a hybrid superconductor-semiconductor nanowire}},
doi = {10.1103/PhysRevB.103.235201},
volume = {103},
year = {2021},
}
@article{9815,
abstract = {The quantum bits (qubits) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical frequencies is therefore a potential enabling technology for quantum devices. However, in such a device the optical pump can be a source of thermal noise and thus degrade the fidelity; the similarity of input microwave state to the output optical state. In order to investigate the magnitude of this effect we model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion.},
author = {Mobassem, Sonia and Lambert, Nicholas J. and Rueda Sanchez, Alfredo R and Fink, Johannes M and Leuchs, Gerd and Schwefel, Harald G.L.},
issn = {20589565},
journal = {Quantum Science and Technology},
number = {4},
publisher = {Quantum},
title = {{Thermal noise in electro-optic devices at cryogenic temperatures}},
doi = {10.1088/2058-9565/ac0f36},
volume = {6},
year = {2021},
}
@unpublished{9651,
abstract = {We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞). Two separated nets are called ϕ-displacement equivalent if, roughly speaking, there is a bijection between them which, for large radii R, displaces points of norm at most R by something of order at most ϕ(R). We show that the spectrum of ϕ-displacement equivalence spans from the established notion of bounded displacement equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation, coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞. We further undertake a comparison of our notion of ϕ-displacement equivalence with previously studied relations on separated nets. Particular attention is given to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz equivalence.},
author = {Dymond, Michael and Kaluza, Vojtech},
booktitle = {arXiv},
title = {{Divergence of separated nets with respect to displacement equivalence}},
year = {2021},
}
@article{9769,
abstract = {A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.},
author = {Brauneis, Fabian and Hammer, Hans-Werner and Lemeshko, Mikhail and Volosniev, Artem},
issn = {2542-4653},
journal = {SciPost Physics},
number = {1},
publisher = {SciPost},
title = {{Impurities in a one-dimensional Bose gas: The flow equation approach}},
doi = {10.21468/scipostphys.11.1.008},
volume = {11},
year = {2021},
}
@inproceedings{9825,
abstract = {The dual attack has long been considered a relevant attack on lattice-based cryptographic schemes relying on the hardness of learning with errors (LWE) and its structured variants. As solving LWE corresponds to finding a nearest point on a lattice, one may naturally wonder how efficient this dual approach is for solving more general closest vector problems, such as the classical closest vector problem (CVP), the variants bounded distance decoding (BDD) and approximate CVP, and preprocessing versions of these problems. While primal, sieving-based solutions to these problems (with preprocessing) were recently studied in a series of works on approximate Voronoi cells [Laa16b, DLdW19, Laa20, DLvW20], for the dual attack no such overview exists, especially for problems with preprocessing. With one of the take-away messages of the approximate Voronoi cell line of work being that primal attacks work well for approximate CVP(P) but scale poorly for BDD(P), one may further wonder if the dual attack suffers the same drawbacks, or if it is perhaps a better solution when trying to solve BDD(P).
In this work we provide an overview of cost estimates for dual algorithms for solving these “classical” closest lattice vector problems. Heuristically we expect to solve the search version of average-case CVPP in time and space 20.293𝑑+𝑜(𝑑) in the single-target model. The distinguishing version of average-case CVPP, where we wish to distinguish between random targets and targets planted at distance (say) 0.99⋅𝑔𝑑 from the lattice, has the same complexity in the single-target model, but can be solved in time and space 20.195𝑑+𝑜(𝑑) in the multi-target setting, when given a large number of targets from either target distribution. This suggests an inequivalence between distinguishing and searching, as we do not expect a similar improvement in the multi-target setting to hold for search-CVPP. We analyze three slightly different decoders, both for distinguishing and searching, and experimentally obtain concrete cost estimates for the dual attack in dimensions 50 to 80, which confirm our heuristic assumptions, and show that the hidden order terms in the asymptotic estimates are quite small.
Our main take-away message is that the dual attack appears to mirror the approximate Voronoi cell line of work – whereas using approximate Voronoi cells works well for approximate CVP(P) but scales poorly for BDD(P), the dual approach scales well for BDD(P) instances but performs poorly on approximate CVP(P).},
author = {Laarhoven, Thijs and Walter, Michael},
booktitle = {Topics in Cryptology – CT-RSA 2021},
isbn = {9783030755386},
issn = {16113349},
location = {Virtual Event},
pages = {478--502},
publisher = {Springer Nature},
title = {{Dual lattice attacks for closest vector problems (with preprocessing)}},
doi = {10.1007/978-3-030-75539-3_20},
volume = {12704},
year = {2021},
}
@inproceedings{9823,
abstract = {Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that
all the outputs are within distance 1 of one another, and
each output value lies on a shortest path between two input values.
From prior work, it is known that there is no wait-free algorithm among 𝑛≥3 processes for this problem on any cycle of length 𝑐≥4 , by reduction from 2-set agreement (Castañeda et al. 2018).
In this work, we investigate the solvability and complexity of this task on general graphs. We give a new, direct proof of the impossibility of approximate agreement on cycles of length 𝑐≥4 , via a generalisation of Sperner’s Lemma to convex polygons. We also extend the reduction from 2-set agreement to a larger class of graphs, showing that approximate agreement on these graphs is unsolvable. On the positive side, we present a wait-free algorithm for a class of graphs that properly contains the class of chordal graphs.},
author = {Alistarh, Dan-Adrian and Ellen, Faith and Rybicki, Joel},
booktitle = {Structural Information and Communication Complexity},
isbn = {9783030795269},
issn = {16113349},
location = {Wrocław, Poland},
pages = {87--105},
publisher = {Springer Nature},
title = {{Wait-free approximate agreement on graphs}},
doi = {10.1007/978-3-030-79527-6_6},
volume = {12810},
year = {2021},
}
@article{9746,
abstract = {Evolutionary adaptation is a major source of antibiotic resistance in bacterial pathogens. Evolution-informed therapy aims to constrain resistance by accounting for bacterial evolvability. Sequential treatments with antibiotics that target different bacterial processes were previously shown to limit adaptation through genetic resistance trade-offs and negative hysteresis. Treatment with homogeneous sets of antibiotics is generally viewed to be disadvantageous, as it should rapidly lead to cross-resistance. We here challenged this assumption by determining the evolutionary response of Pseudomonas aeruginosa to experimental sequential treatments involving both heterogenous and homogeneous antibiotic sets. To our surprise, we found that fast switching between only β-lactam antibiotics resulted in increased extinction of bacterial populations. We demonstrate that extinction is favored by low rates of spontaneous resistance emergence and low levels of spontaneous cross-resistance among the antibiotics in sequence. The uncovered principles may help to guide the optimized use of available antibiotics in highly potent, evolution-informed treatment designs.},
author = {Batra, Aditi and Römhild, Roderich and Rousseau, Emilie and Franzenburg, Sören and Niemann, Stefan and Schulenburg, Hinrich},
issn = {2050-084X},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{High potency of sequential therapy with only beta-lactam antibiotics}},
doi = {10.7554/elife.68876},
volume = {10},
year = {2021},
}
@article{8723,
abstract = {Deep learning at scale is dominated by communication time. Distributing samples across nodes usually yields the best performance, but poses scaling challenges due to global information dissemination and load imbalance across uneven sample lengths. State-of-the-art decentralized optimizers mitigate the problem, but require more iterations to achieve the same accuracy as their globally-communicating counterparts. We present Wait-Avoiding Group Model Averaging (WAGMA) SGD, a wait-avoiding stochastic optimizer that reduces global communication via subgroup weight exchange. The key insight is a combination of algorithmic changes to the averaging scheme and the use of a group allreduce operation. We prove the convergence of WAGMA-SGD, and empirically show that it retains convergence rates similar to Allreduce-SGD. For evaluation, we train ResNet-50 on ImageNet; Transformer for machine translation; and deep reinforcement learning for navigation at scale. Compared with state-of-the-art decentralized SGD variants, WAGMA-SGD significantly improves training throughput (e.g., 2.1× on 1,024 GPUs for reinforcement learning), and achieves the fastest time-to-solution (e.g., the highest score using the shortest training time for Transformer).},
author = {Li, Shigang and Tal Ben-Nun, Tal Ben-Nun and Nadiradze, Giorgi and Girolamo, Salvatore Di and Dryden, Nikoli and Alistarh, Dan-Adrian and Hoefler, Torsten},
issn = {10459219},
journal = {IEEE Transactions on Parallel and Distributed Systems},
number = {7},
publisher = {IEEE},
title = {{Breaking (global) barriers in parallel stochastic optimization with wait-avoiding group averaging}},
doi = {10.1109/TPDS.2020.3040606},
volume = {32},
year = {2021},
}
@article{9437,
abstract = {The synaptic connection from medial habenula (MHb) to interpeduncular nucleus (IPN) is critical for emotion-related behaviors and uniquely expresses R-type Ca2+ channels (Cav2.3) and auxiliary GABAB receptor (GBR) subunits, the K+-channel tetramerization domain-containing proteins (KCTDs). Activation of GBRs facilitates or inhibits transmitter release from MHb terminals depending on the IPN subnucleus, but the role of KCTDs is unknown. We therefore examined the localization and function of Cav2.3, GBRs, and KCTDs in this pathway in mice. We show in heterologous cells that KCTD8 and KCTD12b directly bind to Cav2.3 and that KCTD8 potentiates Cav2.3 currents in the absence of GBRs. In the rostral IPN, KCTD8, KCTD12b, and Cav2.3 co-localize at the presynaptic active zone. Genetic deletion indicated a bidirectional modulation of Cav2.3-mediated release by these KCTDs with a compensatory increase of KCTD8 in the active zone in KCTD12b-deficient mice. The interaction of Cav2.3 with KCTDs therefore scales synaptic strength independent of GBR activation.},
author = {Bhandari, Pradeep and Vandael, David H and Fernández-Fernández, Diego and Fritzius, Thorsten and Kleindienst, David and Önal, Hüseyin C and Montanaro-Punzengruber, Jacqueline-Claire and Gassmann, Martin and Jonas, Peter M and Kulik, Akos and Bettler, Bernhard and Shigemoto, Ryuichi and Koppensteiner, Peter},
issn = {2050-084X},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{GABAB receptor auxiliary subunits modulate Cav2.3-mediated release from medial habenula terminals}},
doi = {10.7554/ELIFE.68274},
volume = {10},
year = {2021},
}
@article{9877,
abstract = {Parent-of-origin–dependent gene expression in mammals and flowering plants results from differing chromatin imprints (genomic imprinting) between maternally and paternally inherited alleles. Imprinted gene expression in the endosperm of seeds is associated with localized hypomethylation of maternally but not paternally inherited DNA, with certain small RNAs also displaying parent-of-origin–specific expression. To understand the evolution of imprinting mechanisms in Oryza sativa (rice), we analyzed imprinting divergence among four cultivars that span both japonica and indica subspecies: Nipponbare, Kitaake, 93-11, and IR64. Most imprinted genes are imprinted across cultivars and enriched for functions in chromatin and transcriptional regulation, development, and signaling. However, 4 to 11% of imprinted genes display divergent imprinting. Analyses of DNA methylation and small RNAs revealed that endosperm-specific 24-nt small RNA–producing loci show weak RNA-directed DNA methylation, frequently overlap genes, and are imprinted four times more often than genes. However, imprinting divergence most often correlated with local DNA methylation epimutations (9 of 17 assessable loci), which were largely stable within subspecies. Small insertion/deletion events and transposable element insertions accompanied 4 of the 9 locally epimutated loci and associated with imprinting divergence at another 4 of the remaining 8 loci. Correlating epigenetic and genetic variation occurred at key regulatory regions—the promoter and transcription start site of maternally biased genes, and the promoter and gene body of paternally biased genes. Our results reinforce models for the role of maternal-specific DNA hypomethylation in imprinting of both maternally and paternally biased genes, and highlight the role of transposition and epimutation in rice imprinting evolution.},
author = {Rodrigues, Jessica A. and Hsieh, Ping-Hung and Ruan, Deling and Nishimura, Toshiro and Sharma, Manoj K. and Sharma, Rita and Ye, XinYi and Nguyen, Nicholas D. and Nijjar, Sukhranjan and Ronald, Pamela C. and Fischer, Robert L. and ZILBERMAN, Daniel},
issn = {1091-6490},
journal = {Proceedings of the National Academy of Sciences},
number = {29},
publisher = {National Academy of Sciences},
title = {{Divergence among rice cultivars reveals roles for transposition and epimutation in ongoing evolution of genomic imprinting}},
doi = {10.1073/pnas.2104445118},
volume = {118},
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{8966,
abstract = {During development, a single cell is transformed into a highly complex organism through progressive cell division, specification and rearrangement. An important prerequisite for the emergence of patterns within the developing organism is to establish asymmetries at various scales, ranging from individual cells to the entire embryo, eventually giving rise to the different body structures. This becomes especially apparent during gastrulation, when the earliest major lineage restriction events lead to the formation of the different germ layers. Traditionally, the unfolding of the developmental program from symmetry breaking to germ layer formation has been studied by dissecting the contributions of different signaling pathways and cellular rearrangements in the in vivo context of intact embryos. Recent efforts, using the intrinsic capacity of embryonic stem cells to self-assemble and generate embryo-like structures de novo, have opened new avenues for understanding the many ways by which an embryo can be built and the influence of extrinsic factors therein. Here, we discuss and compare divergent and conserved strategies leading to germ layer formation in embryos as compared to in vitro systems, their upstream molecular cascades and the role of extrinsic factors in this process.},
author = {Schauer, Alexandra and Heisenberg, Carl-Philipp J},
issn = {0012-1606},
journal = {Developmental Biology},
keywords = {Developmental Biology, Cell Biology, Molecular Biology},
pages = {71--81},
publisher = {Elsevier},
title = {{Reassembling gastrulation}},
doi = {10.1016/j.ydbio.2020.12.014},
volume = {474},
year = {2021},
}
@article{9188,
abstract = {Genomic imprinting is an epigenetic mechanism that results in parental allele-specific expression of ~1% of all genes in mouse and human. Imprinted genes are key developmental regulators and play pivotal roles in many biological processes such as nutrient transfer from the mother to offspring and neuronal development. Imprinted genes are also involved in human disease, including neurodevelopmental disorders, and often occur in clusters that are regulated by a common imprint control region (ICR). In extra-embryonic tissues ICRs can act over large distances, with the largest surrounding Igf2r spanning over 10 million base-pairs. Besides classical imprinted expression that shows near exclusive maternal or paternal expression, widespread biased imprinted expression has been identified mainly in brain. In this review we discuss recent developments mapping cell type specific imprinted expression in extra-embryonic tissues and neocortex in the mouse. We highlight the advantages of using an inducible uniparental chromosome disomy (UPD) system to generate cells carrying either two maternal or two paternal copies of a specific chromosome to analyze the functional consequences of genomic imprinting. Mosaic Analysis with Double Markers (MADM) allows fluorescent labeling and concomitant induction of UPD sparsely in specific cell types, and thus to over-express or suppress all imprinted genes on that chromosome. To illustrate the utility of this technique, we explain how MADM-induced UPD revealed new insights about the function of the well-studied Cdkn1c imprinted gene, and how MADM-induced UPDs led to identification of highly cell type specific phenotypes related to perturbed imprinted expression in the mouse neocortex. Finally, we give an outlook on how MADM could be used to probe cell type specific imprinted expression in other tissues in mouse, particularly in extra-embryonic tissues.},
author = {Pauler, Florian and Hudson, Quanah and Laukoter, Susanne and Hippenmeyer, Simon},
issn = {0197-0186},
journal = {Neurochemistry International},
keywords = {Cell Biology, Cellular and Molecular Neuroscience},
number = {5},
publisher = {Elsevier},
title = {{Inducible uniparental chromosome disomy to probe genomic imprinting at single-cell level in brain and beyond}},
doi = {10.1016/j.neuint.2021.104986},
volume = {145},
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},
}
@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{9234,
abstract = {In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.},
author = {Izuchukwu, Chinedu and Shehu, Yekini},
issn = {1566-113X},
journal = {Networks and Spatial Economics},
keywords = {Computer Networks and Communications, Software, Artificial Intelligence},
number = {2},
pages = {291--323},
publisher = {Springer Nature},
title = {{New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity}},
doi = {10.1007/s11067-021-09517-w},
volume = {21},
year = {2021},
}