@article{11417, abstract = {Over the past few years, the field of quantum information science has seen tremendous progress toward realizing large-scale quantum computers. With demonstrations of quantum computers outperforming classical computers for a select range of problems,1–3 we have finally entered the noisy, intermediate-scale quantum (NISQ) computing era. While the quantum computers of today are technological marvels, they are not yet error corrected, and it is unclear whether any system will scale beyond a few hundred logical qubits without significant changes to architecture and control schemes. Today's quantum systems are analogous to the ENIAC (Electronic Numerical Integrator And Computer) and EDVAC (Electronic Discrete Variable Automatic Computer) systems of the 1940s, which ran on vacuum tubes. These machines were built on a solid, nominally scalable architecture and when they were developed, nobody could have predicted the development of the transistor and the impact of the resulting semiconductor industry. Simply put, the computers of today are nothing like the early computers of the 1940s. We believe that the qubits of future fault-tolerant quantum systems will look quite different from the qubits of the NISQ machines in operation today. This Special Topic issue is devoted to new and emerging quantum systems with a focus on enabling technologies that can eventually lead to the quantum analog to the transistor. We have solicited both research4–18 and perspective articles19–21 to discuss new and emerging qubit systems with a focus on novel materials, encodings, and architectures. We are proud to present a collection that touches on a wide range of technologies including superconductors,7–13,21 semiconductors,15–17,19 and individual atomic qubits.18 }, author = {Sigillito, Anthony J. and Covey, Jacob P. and Fink, Johannes M and Petersson, Karl and Preble, Stefan}, issn = {0003-6951}, journal = {Applied Physics Letters}, number = {19}, publisher = {American Institute of Physics}, title = {{Emerging qubit systems: Guest editorial}}, doi = {10.1063/5.0097339}, volume = {120}, year = {2022}, } @inproceedings{11428, abstract = {The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible.}, author = {Chambers, Erin and Fillmore, Christopher D and Stephenson, Elizabeth R and Wintraecken, Mathijs}, booktitle = {38th International Symposium on Computational Geometry}, editor = {Goaoc, Xavier and Kerber, Michael}, isbn = {978-3-95977-227-3}, issn = {1868-8969}, location = {Berlin, Germany}, pages = {66:1--66:9}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{A cautionary tale: Burning the medial axis is unstable}}, doi = {10.4230/LIPIcs.SoCG.2022.66}, volume = {224}, year = {2022}, } @book{11429, abstract = {This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022. The 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks.}, editor = {Karimipour, Farid and Storandt, Sabine}, isbn = {9783031062445}, issn = {1611-3349}, pages = {153}, publisher = {Springer Nature}, title = {{Web and Wireless Geographical Information Systems}}, doi = {10.1007/978-3-031-06245-2}, volume = {13238}, year = {2022}, } @article{11435, abstract = {We introduce a new variant of quantitative Helly-type theorems: the minimal homothetic distance of the intersection of a family of convex sets to the intersection of a subfamily of a fixed size. As an application, we establish the following quantitative Helly-type result for the diameter. If $K$ is the intersection of finitely many convex bodies in $\mathbb{R}^d$, then one can select $2d$ of these bodies whose intersection is of diameter at most $(2d)^3{diam}(K)$. The best previously known estimate, due to Brazitikos [Bull. Hellenic Math. Soc., 62 (2018), pp. 19--25], is $c d^{11/2}$. Moreover, we confirm that the multiplicative factor $c d^{1/2}$ conjectured by Bárány, Katchalski, and Pach [Proc. Amer. Math. Soc., 86 (1982), pp. 109--114] cannot be improved. The bounds above follow from our key result that concerns sparse approximation of a convex polytope by the convex hull of a well-chosen subset of its vertices: Assume that $Q \subset {\mathbb R}^d$ is a polytope whose centroid is the origin. Then there exist at most 2d vertices of $Q$ whose convex hull $Q^{\prime \prime}$ satisfies $Q \subset - 8d^3 Q^{\prime \prime}.$}, author = {Ivanov, Grigory and Naszodi, Marton}, issn = {0895-4801}, journal = {SIAM Journal on Discrete Mathematics}, number = {2}, pages = {951--957}, publisher = {Society for Industrial and Applied Mathematics}, title = {{A quantitative Helly-type theorem: Containment in a homothet}}, doi = {10.1137/21M1403308}, volume = {36}, year = {2022}, } @article{21079, abstract = {AbstractA series of aromatic oligoamide foldamer sequences containing different proportions of three δ‐amino acids derived from quinoline, pyridine, and benzene and possessing varying flexibility, for example due to methylene bridges, were synthesized. Crystallographic structures of two key sequences and 1H NMR data in water concur to show that a canonical aromatic helix fold prevails in almost all cases and that helix stability critically depends on the ratio between rigid and flexible units. Notwithstanding subtle variations of curvature, i. e. the numbers of units per turn, the aromatic δ‐peptide helix is therefore shown to be general and tolerant of a great number of sp3 centers. We also demonstrate canonical helical folding upon alternating two monomers that do not promote folding when taken separately: folding occurs with two methylenes between every other unit, not with one methylene between every unit. These findings highlight that a fine‐tuning of helix handedness inversion kinetics, curvature, and side chain positioning in aromatic δ‐peptidic foldamers can be realized by systematically combining different yet compatible δ‐amino acids.}, author = {Bindl, Daniel and Mandal, Pradeep K and Huc, Ivan}, issn = {1521-3765}, journal = {Chemistry – A European Journal}, number = {31}, publisher = {Wiley}, title = {{Generalizing the aromatic δ‐amino acid foldamer helix}}, doi = {10.1002/chem.202200538}, volume = {28}, year = {2022}, } @article{17066, abstract = {A cell’s size affects the likelihood that it will die. But how is cell size controlled in this context and how does cell size impact commitment to the cell death fate? We present evidence that the caspase CED-3 interacts with the RhoGEF ECT-2 in Caenorhabditis elegans neuroblasts that generate “unwanted” cells. We propose that this interaction promotes polar actomyosin contractility, which leads to unequal neuroblast division and the generation of a daughter cell that is below the critical “lethal” size threshold. Furthermore, we find that hyperactivation of ECT-2 RhoGEF reduces the sizes of unwanted cells. Importantly, this suppresses the “cell death abnormal” phenotype caused by the partial loss of ced-3 caspase and therefore increases the likelihood that unwanted cells die. A putative null mutation of ced-3 caspase, however, is not suppressed, which indicates that cell size affects CED-3 caspase activation and/or activity. Therefore, we have uncovered novel sequential and reciprocal interactions between the apoptosis pathway and cell size that impact a cell’s commitment to the cell death fate.}, author = {Sethi, Aditya and Wei, Hai and Mishra, Nikhil and Segos, Ioannis and Lambie, Eric J. and Zanin, Esther and Conradt, Barbara}, issn = {1545-7885}, journal = {PLOS Biology}, number = {10}, publisher = {Public Library of Science}, title = {{A caspase–RhoGEF axis contributes to the cell size threshold for apoptotic death in developing Caenorhabditis elegans}}, doi = {10.1371/journal.pbio.3001786}, volume = {20}, year = {2022}, } @inbook{17075, abstract = {Disorders associated with the malfunction of amino acid transporters mainly affect the function of the intestine, kidney, brain, and liver. Mutations of brain amino acid transporters, for example, alter neuronal excitability (e.g., episodic ataxia due to SLC1A3 (EAAT1) defect and hyperekplexia due to SLC6A5 (GLYT2) deficiency) or brain development (SLC1A1 (EAAT3), SLC3A2/SLC7A5 (CD98hc/LAT1), and SLC1A4 (ASCT1) deficiencies). Mutations of renal and intestinal amino acid transporters SLC3A1/SLC7A9 (rBAT/b0,+AT) and SLC1A1 (EAAT3) cause renal problems (cystinuria and dicarboxylic aminoaciduria, respectively) and malabsorption that can affect whole-body homoeostasis (Hartnup disorder SLC6A19 (B0AT1), lysinuric protein intolerance SLC3A2/SLC7A7 (CD98hc/y+LAT1), and hyperdibasic aminoaciduria type 1). Mutations in the neuronal system A amino acid transporter SLC38A8 (SNAT8) cause eye developmental and visual defects. Inborn errors associated with mitochondrial SLC25 family members such as SLC25A12 (neuronal- and muscle-specific mitochondrial aspartate/glutamate transporter 1; AGC1) (global cerebral hypomyelination), SLC25A13 (aspartate/glutamate transporter 2) (citrin deficiency), SLC25A15 (ornithine-citrulline carrier 2) (homocitrullinuria, hyperornithinemia, and hyperammonemia syndrome), and SLC25A22 (mitochondrial glutamate/H+ symporter 1, GC1) (neonatal myoclonic epilepsy) will be dealt within Chap. 43 (defects of mitochondrial carriers).}, author = {Palacín, Manuel and Bröer, Stefan and Novarino, Gaia}, booktitle = {Physician's Guide to the Diagnosis, Treatment, and Follow-Up of Inherited Metabolic Diseases}, editor = {Blau, Nenad and Vici, Carlo Dionisi and Ferreira, Carlos R. and Vianey-Saban, Christine and van Karnebeek, Clara D.M.}, isbn = {9783030677268}, pages = {291--312}, publisher = {Springer Nature}, title = {{Amino Acid Transport Defects}}, doi = {10.1007/978-3-030-67727-5_18}, year = {2022}, } @unpublished{17115, abstract = {Cascades are RNA-guided multi-subunit CRISPR-Cas surveillances complexes that target foreign nucleic acids for destruction. Here, we present a 2.9-Å resolution cryo-electron (cryo-EM) structure of the D. vulgaris type I-C Cascade bound to a double-stranded (ds)DNA target. Our data shows how the 5’-TTC-3’ protospacer adjacent motif (PAM) sequence is recognized, and provides a unique mechanism through which the displaced, single-stranded non-target strand (NTS) is stabilized via stacking interactions with protein subunits in order to favor R-loop formation and prevent dsDNA re-annealing. Additionally, we provide structural insights into how diverse anti-CRISPR (Acr) proteins utilize distinct strategies to achieve a shared mechanism of type I-C Cascade inhibition by blocking initial DNA binding. These observations provide a structural basis for directional R-loop formation and reveal how divergent Acr proteins have converged upon common molecular mechanisms to efficiently shut down CRISPR immunity.}, author = {O’Brien, Roisin E. and Bravo, Jack Peter Kelly and Ramos, Delisa and Hibshman, Grace N. and Wright, Jacquelyn T. and Taylor, David W.}, booktitle = {bioRxiv}, publisher = {Cold Spring Harbor Laboratory}, title = {{Modes of inhibition used by phage anti-CRISPRs to evade type I-C Cascade}}, doi = {10.1101/2022.06.15.496202}, year = {2022}, } @article{17553, abstract = {Linear analysis of gas flows around orbiting binaries suggests that a centrifugal barrier ought to clear a low-density cavity around the binary and inhibit mass transfer onto it. Modern hydrodynamics simulations have confirmed the low-density cavity, but show that any mass flowing from large scales into the circumbinary disk is eventually transferred onto the binary components. Even though many numerical studies confirm this picture, it is still not understood precisely how gas parcels overcome the centrifugal barrier and ultimately accrete. We present a detailed analysis of the binary accretion process, using an accurate prescription for evolving grid-based hydrodynamics with Lagrangian tracer particles that track the trajectories of individual gas parcels. We find that binary accretion can be described in four phases: (1) gas is viscously transported through the circumbinary disk up to the centrifugal barrier at the cavity wall, (2) the cavity wall is tidally distorted into accretion streams consisting of near-ballistic gas parcels on eccentric orbits, (3) the portion of each stream moving inwards of an ``accretion horizon'' radius r¯≃a -- the radius beyond which no material is returned to the cavity wall -- becomes bound to a minidisk orbiting an individual binary component, and (4) the minidisk gas accretes onto the binary component through the combined effect of viscous and tidal stresses.}, author = {Tiede, Christopher and Zrake, Jonathan and MacFadyen, Andrew and Haiman, Zoltán}, issn = {0004-637X}, journal = {The Astrophysical Journal}, number = {1}, publisher = {American Astronomical Society}, title = {{How binaries accrete: Hydrodynamic simulations with passive tracer particles}}, doi = {10.3847/1538-4357/ac6c2b}, volume = {932}, year = {2022}, } @article{17561, abstract = {Active galactic nuclei (AGNs) can funnel stars and stellar remnants from the vicinity of the galactic center into the inner plane of the AGN disk. Stars reaching this inner region can be tidally disrupted by the stellar-mass black holes in the disk. Such micro tidal disruption events (micro-TDEs) could be a useful probe of stellar interaction with the AGN disk. We find that micro-TDEs in AGNs occur at a rate of ∼170 Gpc−3 yr−1. Their cleanest observational probe may be the electromagnetic detection of tidal disruption in AGNs by heavy supermassive black holes (M• ≳ 108 M⊙) that cannot tidally disrupt solar-type stars. The reconstructed rate of such events from observations, nonetheless, appears to be much lower than our estimated micro-TDE rate. We discuss two such micro-TDE candidates observed to date (ASASSN-15lh and ZTF19aailpwl).}, author = {Yang, Y. and Bartos, I. and Fragione, G. and Haiman, Zoltán and Kowalski, M. and Márka, S. and Perna, R. and Tagawa, H.}, issn = {2041-8205}, journal = {The Astrophysical Journal Letters}, number = {2}, publisher = {American Astronomical Society}, title = {{Tidal disruption on stellar-mass black holes in active galactic nuclei}}, doi = {10.3847/2041-8213/ac7c0b}, volume = {933}, year = {2022}, } @article{17571, abstract = {The existence of 109 M⊙ supermassive black holes (SMBHs) within the first billion years of the Universe remains a puzzle in our conventional understanding of black hole formation and growth. Several suggested formation pathways for these SMBHs lead to a heavy seed, with an initial black hole mass of 104–106 M⊙. This can lead to an overly massive BH galaxy (OMBG), whose nuclear black hole’s mass is comparable to or even greater than the surrounding stellar mass: the black hole to stellar mass ratio is Mbh/M* ≫ 10−3, well in excess of the typical values at lower redshift. We investigate how long these newborn BHs remain outliers in the Mbh − M* relation, by exploring the subsequent evolution of two OMBGs previously identified in the Renaissance simulations. We find that both OMBGs have Mbh/M* > 1 during their entire life, from their birth at z ≈ 15 until they merge with much more massive haloes at z ≈ 8. We find that the OMBGs are spatially resolvable from their more massive, 1011 M⊙, neighbouring haloes until their mergers are complete at z ≈ 8. This affords a window for future observations with JWST and sensitive X-ray telescopes to diagnose the heavy-seed scenario, by detecting similar OMBGs and establishing their uniquely high black hole-to-stellar mass ratio.}, author = {Scoggins, Matthew T and Haiman, Zoltán and Wise, John H}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {2}, pages = {2155--2168}, publisher = {Oxford University Press}, title = {{How long do high redshift massive black hole seeds remain outliers in black hole versus host galaxy relations?}}, doi = {10.1093/mnras/stac3715}, volume = {519}, year = {2022}, } @article{17580, abstract = {We present a study of optically selected dual Active Galactic Nuclei (AGN) with projected separations of 3–97 kpc. Using multiwavelength (MWL) information (optical, X-ray, mid-IR), we characterized the intrinsic nuclear properties of this sample and compared them with those of isolated systems. Among the 124 X-ray-detected AGN candidates, 52 appear in pairs and 72 as single X-ray sources. Through MWL analysis, we confirmed the presence of the AGN in >80 per cent of the detected targets in pairs (42 out of 52). X-ray spectral analysis confirms the trend of increasing AGN luminosity with decreasing separation, suggesting that mergers may have contributed to triggering more luminous AGN. Through X-ray/mid-IR ratio versus X-ray colours, we estimated a fraction of Compton-thin AGN (with 1022 cm−2 < NH < 1024 cm−2) of about 80 per cent, while about 16 per cent are Compton-thick sources (with NH > 1024 cm−2). These fractions of obscured sources are larger than those found in samples of isolated AGN, confirming that pairs of AGN show higher obscuration. This trend is further confirmed by comparing the de-reddened [O iii] emission with the observed X-ray luminosity. However, the derived fraction of Compton-thick sources in this sample at the early stages of merging is lower than that reported for late-merging dual-AGN samples. Comparing NH from X-rays with that derived from E(B − V) from narrow-line regions, we found that the absorbing material is likely to be associated with the torus or broad-line regions. We also explored the X-ray detection efficiency of dual-AGN candidates, finding that, when observed properly (at on-axis positions and with long exposures), X-ray data represent a powerful way to confirm and investigate dual-AGN systems.}, author = {De Rosa, Alessandra and Vignali, Cristian and Severgnini, Paola and Bianchi, Stefano and Bogdanović, Tamara and Charisi, Maria and Guainazzi, Matteo and Haiman, Zoltán and Komossa, S and Paragi, Zsolt and Perez-Torres, Miguel and Piconcelli, Enrico and Ducci, Lorenzo and Parvatikar, Manali and Serafinelli, Roberto}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {4}, pages = {5149--5160}, publisher = {Oxford University Press}, title = {{The X-ray view of optically selected dual AGN}}, doi = {10.1093/mnras/stac3664}, volume = {519}, year = {2022}, } @inproceedings{11839, abstract = {It is a highly desirable property for deep networks to be robust against small input changes. One popular way to achieve this property is by designing networks with a small Lipschitz constant. In this work, we propose a new technique for constructing such Lipschitz networks that has a number of desirable properties: it can be applied to any linear network layer (fully-connected or convolutional), it provides formal guarantees on the Lipschitz constant, it is easy to implement and efficient to run, and it can be combined with any training objective and optimization method. In fact, our technique is the first one in the literature that achieves all of these properties simultaneously. Our main contribution is a rescaling-based weight matrix parametrization that guarantees each network layer to have a Lipschitz constant of at most 1 and results in the learned weight matrices to be close to orthogonal. Hence we call such layers almost-orthogonal Lipschitz (AOL). Experiments and ablation studies in the context of image classification with certified robust accuracy confirm that AOL layers achieve results that are on par with most existing methods. Yet, they are simpler to implement and more broadly applicable, because they do not require computationally expensive matrix orthogonalization or inversion steps as part of the network architecture. We provide code at https://github.com/berndprach/AOL.}, author = {Prach, Bernd and Lampert, Christoph}, booktitle = {Computer Vision – ECCV 2022}, isbn = {9783031198021}, location = {Tel Aviv, Israel}, pages = {350--365}, publisher = {Springer Nature}, title = {{Almost-orthogonal layers for efficient general-purpose Lipschitz networks}}, doi = {10.1007/978-3-031-19803-8_21}, volume = {13681}, year = {2022}, } @article{11478, abstract = {Cerebral organoids differentiated from human-induced pluripotent stem cells (hiPSC) provide a unique opportunity to investigate brain development. However, organoids usually lack microglia, brain-resident immune cells, which are present in the early embryonic brain and participate in neuronal circuit development. Here, we find IBA1+ microglia-like cells alongside retinal cups between week 3 and 4 in 2.5D culture with an unguided retinal organoid differentiation protocol. Microglia do not infiltrate the neuroectoderm and instead enrich within non-pigmented, 3D-cystic compartments that develop in parallel to the 3D-retinal organoids. When we guide the retinal organoid differentiation with low-dosed BMP4, we prevent cup development and enhance microglia and 3D-cysts formation. Mass spectrometry identifies these 3D-cysts to express mesenchymal and epithelial markers. We confirmed this microglia-preferred environment also within the unguided protocol, providing insight into microglial behavior and migration and offer a model to study how they enter and distribute within the human brain.}, author = {Bartalska, Katarina and Hübschmann, Verena and Korkut, Medina and Cubero, Ryan J and Venturino, Alessandro and Rössler, Karl and Czech, Thomas and Siegert, Sandra}, issn = {2589-0042}, journal = {iScience}, number = {7}, publisher = {Elsevier}, title = {{A systematic characterization of microglia-like cell occurrence during retinal organoid differentiation}}, doi = {10.1016/j.isci.2022.104580}, volume = {25}, year = {2022}, } @inproceedings{11775, abstract = {Quantitative monitoring can be universal and approximate: For every finite sequence of observations, the specification provides a value and the monitor outputs a best-effort approximation of it. The quality of the approximation may depend on the resources that are available to the monitor. By taking to the limit the sequences of specification values and monitor outputs, we obtain precision-resource trade-offs also for limit monitoring. This paper provides a formal framework for studying such trade-offs using an abstract interpretation for monitors: For each natural number n, the aggregate semantics of a monitor at time n is an equivalence relation over all sequences of at most n observations so that two equivalent sequences are indistinguishable to the monitor and thus mapped to the same output. This abstract interpretation of quantitative monitors allows us to measure the number of equivalence classes (or “resource use”) that is necessary for a certain precision up to a certain time, or at any time. Our framework offers several insights. For example, we identify a family of specifications for which any resource-optimal exact limit monitor is independent of any error permitted over finite traces. Moreover, we present a specification for which any resource-optimal approximate limit monitor does not minimize its resource use at any time. }, author = {Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {22nd International Conference on Runtime Verification}, issn = {0302-9743}, location = {Tbilisi, Georgia}, pages = {200--220}, publisher = {Springer Nature}, title = {{Abstract monitors for quantitative specifications}}, doi = {10.1007/978-3-031-17196-3_11}, volume = {13498}, year = {2022}, } @inproceedings{12176, abstract = {A proof of exponentiation (PoE) in a group G of unknown order allows a prover to convince a verifier that a tuple (x,q,T,y)∈G×N×N×G satisfies xqT=y. This primitive has recently found exciting applications in the constructions of verifiable delay functions and succinct arguments of knowledge. The most practical PoEs only achieve soundness either under computational assumptions, i.e., they are arguments (Wesolowski, Journal of Cryptology 2020), or in groups that come with the promise of not having any small subgroups (Pietrzak, ITCS 2019). The only statistically-sound PoE in general groups of unknown order is due to Block et al. (CRYPTO 2021), and can be seen as an elaborate parallel repetition of Pietrzak’s PoE: to achieve λ bits of security, say λ=80, the number of repetitions required (and thus the blow-up in communication) is as large as λ. In this work, we propose a statistically-sound PoE for the case where the exponent q is the product of all primes up to some bound B. We show that, in this case, it suffices to run only λ/log(B) parallel instances of Pietrzak’s PoE, which reduces the concrete proof-size compared to Block et al. by an order of magnitude. Furthermore, we show that in the known applications where PoEs are used as a building block such structured exponents are viable. Finally, we also discuss batching of our PoE, showing that many proofs (for the same G and q but different x and T) can be batched by adding only a single element to the proof per additional statement.}, author = {Hoffmann, Charlotte and Hubáček, Pavel and Kamath, Chethan and Klein, Karen and Pietrzak, Krzysztof Z}, booktitle = {Advances in Cryptology – CRYPTO 2022}, isbn = {9783031159787}, issn = {1611-3349}, location = {Santa Barbara, CA, United States}, pages = {370--399}, publisher = {Springer Nature}, title = {{Practical statistically-sound proofs of exponentiation in any group}}, doi = {10.1007/978-3-031-15979-4_13}, volume = {13508}, year = {2022}, } @unpublished{18293, abstract = {Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3, we show that the number of rational points of height at most |P| is O(|P|3+ε) for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the number of rational points away from any rational line contained in X is bounded by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer a question of Davenport regarding the number of solutions of bounded height to x31+x32+x33=x34+x35+x36 with xi∈Fq[t].}, author = {Glas, Jakob and Hochfilzer, Leonhard}, booktitle = {arXiv}, title = {{On a question of Davenport and diagonal cubic forms over Fq(t)}}, doi = {10.48550/arXiv.2208.05422}, year = {2022}, } @inbook{11440, abstract = {To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation.}, author = {Bleile, Bea and Garin, Adélie and Heiss, Teresa and Maggs, Kelly and Robins, Vanessa}, booktitle = {Research in Computational Topology 2}, editor = {Gasparovic, Ellen and Robins, Vanessa and Turner, Katharine}, isbn = {9783030955182}, pages = {1--26}, publisher = {Springer Nature}, title = {{The persistent homology of dual digital image constructions}}, doi = {10.1007/978-3-030-95519-9_1}, volume = {30}, year = {2022}, } @inproceedings{11476, abstract = {Messaging platforms like Signal are widely deployed and provide strong security in an asynchronous setting. It is a challenging problem to construct a protocol with similar security guarantees that can efficiently scale to large groups. A major bottleneck are the frequent key rotations users need to perform to achieve post compromise forward security. In current proposals – most notably in TreeKEM (which is part of the IETF’s Messaging Layer Security (MLS) protocol draft) – for users in a group of size n to rotate their keys, they must each craft a message of size log(n) to be broadcast to the group using an (untrusted) delivery server. In larger groups, having users sequentially rotate their keys requires too much bandwidth (or takes too long), so variants allowing any T≤n users to simultaneously rotate their keys in just 2 communication rounds have been suggested (e.g. “Propose and Commit” by MLS). Unfortunately, 2-round concurrent updates are either damaging or expensive (or both); i.e. they either result in future operations being more costly (e.g. via “blanking” or “tainting”) or are costly themselves requiring Ω(T) communication for each user [Bienstock et al., TCC’20]. In this paper we propose CoCoA; a new scheme that allows for T concurrent updates that are neither damaging nor costly. That is, they add no cost to future operations yet they only require Ω(log2(n)) communication per user. To circumvent the [Bienstock et al.] lower bound, CoCoA increases the number of rounds needed to complete all updates from 2 up to (at most) log(n); though typically fewer rounds are needed. The key insight of our protocol is the following: in the (non-concurrent version of) TreeKEM, a delivery server which gets T concurrent update requests will approve one and reject the remaining T−1. In contrast, our server attempts to apply all of them. If more than one user requests to rotate the same key during a round, the server arbitrarily picks a winner. Surprisingly, we prove that regardless of how the server chooses the winners, all previously compromised users will recover after at most log(n) such update rounds. To keep the communication complexity low, CoCoA is a server-aided CGKA. That is, the delivery server no longer blindly forwards packets, but instead actively computes individualized packets tailored to each user. As the server is untrusted, this change requires us to develop new mechanisms ensuring robustness of the protocol.}, author = {Alwen, Joël and Auerbach, Benedikt and Cueto Noval, Miguel and Klein, Karen and Pascual Perez, Guillermo and Pietrzak, Krzysztof Z and Walter, Michael}, booktitle = {Advances in Cryptology – EUROCRYPT 2022}, isbn = {9783031070846}, issn = {1611-3349}, location = {Trondheim, Norway}, pages = {815–844}, publisher = {Springer Nature}, title = {{CoCoA: Concurrent continuous group key agreement}}, doi = {10.1007/978-3-031-07085-3_28}, volume = {13276}, year = {2022}, } @article{11732, abstract = {We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.}, author = {Henheik, Sven Joscha and Lauritsen, Asbjørn Bækgaard}, issn = {1572-9613}, journal = {Journal of Statistical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, publisher = {Springer Nature}, title = {{The BCS energy gap at high density}}, doi = {10.1007/s10955-022-02965-9}, volume = {189}, year = {2022}, }