On a Cohen-Lenstra Heuristic for Jacobians of Random Graphs

In this paper, we make specific conjectures about the distribution of Jacobians of random graphs with their canonical duality pairings. Our conjectures are based on a Cohen-Lenstra type heuristic saying that a finite abelian group with duality pairing appears with frequency inversely proportional to the size of the group times the size of the group of automorphisms that preserve the pairing. We conjecture that the Jacobian of a random graph is cyclic with probability a little over .7935. We determine the values of several other statistics on Jacobians of random graphs that would follow from our conjectures. In support of the conjectures, we prove that random symmetric matrices over the p-adic integers, distributed according to Haar measure, have cokernels distributed according to the above heuristic. We also give experimental evidence in support of our conjectures.Comment: 20 pages. v2: Improved exposition and appended code used to generate experimental evidence after the \end{document} line in the source file. To appear in J. Algebraic Combi

Ergodicity and Conservativity of products of infinite transformations and their inverses

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ of the transformation with itself is ergodic, but the product $T\times T^{-1}$ of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.Comment: Added references and revised some arguments; removed old section 6; main results unchange

The SARS-CoV-2 viral load in COVID-19 patients is lower on face mask filters than on nasopharyngeal swabs.

Face masks and personal respirators are used to curb the transmission of SARS-CoV-2 in respiratory droplets; filters embedded in some personal protective equipment could be used as a non-invasive sample source for applications, including at-home testing, but information is needed about whether filters are suited to capture viral particles for SARS-CoV-2 detection. In this study, we generated inactivated virus-laden aerosols of 0.3-2 microns in diameter (0.9 µm mean diameter by mass) and dispersed the aerosolized viral particles onto electrostatic face mask filters. The limit of detection for inactivated coronaviruses SARS-CoV-2 and HCoV-NL63 extracted from filters was between 10 to 100 copies/filter for both viruses. Testing for SARS-CoV-2, using face mask filters and nasopharyngeal swabs collected from hospitalized COVID-19-patients, showed that filter samples offered reduced sensitivity (8.5% compared to nasopharyngeal swabs). The low concordance of SARS-CoV-2 detection between filters and nasopharyngeal swabs indicated that number of viral particles collected on the face mask filter was below the limit of detection for all patients but those with the highest viral loads. This indicated face masks are unsuitable to replace diagnostic nasopharyngeal swabs in COVID-19 diagnosis. The ability to detect nucleic acids on face mask filters may, however, find other uses worth future investigation

Control of Metabolic Homeostasis by Stress Signaling Is Mediated by the Lipocalin NLaz

Metabolic homeostasis in metazoans is regulated by endocrine control of insulin/IGF signaling (IIS) activity. Stress and inflammatory signaling pathways—such as Jun-N-terminal Kinase (JNK) signaling—repress IIS, curtailing anabolic processes to promote stress tolerance and extend lifespan. While this interaction constitutes an adaptive response that allows managing energy resources under stress conditions, excessive JNK activity in adipose tissue of vertebrates has been found to cause insulin resistance, promoting type II diabetes. Thus, the interaction between JNK and IIS has to be tightly regulated to ensure proper metabolic adaptation to environmental challenges. Here, we identify a new regulatory mechanism by which JNK influences metabolism systemically. We show that JNK signaling is required for metabolic homeostasis in flies and that this function is mediated by the Drosophila Lipocalin family member Neural Lazarillo (NLaz), a homologue of vertebrate Apolipoprotein D (ApoD) and Retinol Binding Protein 4 (RBP4). Lipocalins are emerging as central regulators of peripheral insulin sensitivity and have been implicated in metabolic diseases. NLaz is transcriptionally regulated by JNK signaling and is required for JNK-mediated stress and starvation tolerance. Loss of NLaz function reduces stress resistance and lifespan, while its over-expression represses growth, promotes stress tolerance and extends lifespan—phenotypes that are consistent with reduced IIS activity. Accordingly, we find that NLaz represses IIS activity in larvae and adult flies. Our results show that JNK-NLaz signaling antagonizes IIS and is critical for metabolic adaptation of the organism to environmental challenges. The JNK pathway and Lipocalins are structurally and functionally conserved, suggesting that similar interactions represent an evolutionarily conserved system for the control of metabolic homeostasis

Event reconstruction for KM3NeT/ORCA using convolutional neural networks

The KM3NeT research infrastructure is currently under construction at two locations in the Mediterranean Sea. The KM3NeT/ORCA water-Cherenkov neutrino detector off the French coast will instrument several megatons of seawater with photosensors. Its main objective is the determination of the neutrino mass ordering. This work aims at demonstrating the general applicability of deep convolutional neural networks to neutrino telescopes, using simulated datasets for the KM3NeT/ORCA detector as an example. To this end, the networks are employed to achieve reconstruction and classification tasks that constitute an alternative to the analysis pipeline presented for KM3NeT/ORCA in the KM3NeT Letter of Intent. They are used to infer event reconstruction estimates for the energy, the direction, and the interaction point of incident neutrinos. The spatial distribution of Cherenkov light generated by charged particles induced in neutrino interactions is classified as shower- or track-like, and the main background processes associated with the detection of atmospheric neutrinos are recognized. Performance comparisons to machine-learning classification and maximum-likelihood reconstruction algorithms previously developed for KM3NeT/ORCA are provided. It is shown that this application of deep convolutional neural networks to simulated datasets for a large-volume neutrino telescope yields competitive reconstruction results and performance improvements with respect to classical approaches

Event reconstruction for KM3NeT/ORCA using convolutional neural networks

The KM3NeT research infrastructure is currently under construction at two locations in the Mediterranean Sea. The KM3NeT/ORCA water-Cherenkov neutrino de tector off the French coast will instrument several megatons of seawater with photosensors. Its main objective is the determination of the neutrino mass ordering. This work aims at demonstrating the general applicability of deep convolutional neural networks to neutrino telescopes, using simulated datasets for the KM3NeT/ORCA detector as an example. To this end, the networks are employed to achieve reconstruction and classification tasks that constitute an alternative to the analysis pipeline presented for KM3NeT/ORCA in the KM3NeT Letter of Intent. They are used to infer event reconstruction estimates for the energy, the direction, and the interaction point of incident neutrinos. The spatial distribution of Cherenkov light generated by charged particles induced in neutrino interactions is classified as shower-or track-like, and the main background processes associated with the detection of atmospheric neutrinos are recognized. Performance comparisons to machine-learning classification and maximum-likelihood reconstruction algorithms previously developed for KM3NeT/ORCA are provided. It is shown that this application of deep convolutional neural networks to simulated datasets for a large-volume neutrino telescope yields competitive reconstruction results and performance improvements with respect to classical approaches

Interpolating Spline Curves of Measures

When dealing with classical, Euclidean data, the statistician's toolkit is enviably deep: from linear and nonlinear regression, to dealing with sparse or structured data, to interpolation techniques, most any problem dealing with vector or matrix data is amenable to several different statistical methods. Yet modern data is often not Euclidean in nature. The semantic content of natural images does not have a vector structure; shifting an image one pixel to the right does not perceptibly change it, but its vector representation is very different. For model cross-validation or bootstrapping, each data point is a dataset in its own right, and one might want to consider an "average dataset''. In an ensemble method, experts may express their beliefs as prior distributions; how would we perform a statistical analysis of these? Recently much attention has been paid to a framework which subsumes all of these problems: the Wasserstein space of measures with finite second moment. Works on point estimation, generalized means, and linear regression have appeared, as have some on smooth interpolation, greatly expanding the statistical toolkit for modern data. In this vein, the present work is broadly a theoretical and computational exploration of curves of measures which in some sense minimize curvature while interpolating data, as splines do in Euclidean space. We answer several questions about the relationship between the intrinsic Wasserstein-Riemannian curvature of such curves and a particle flow-based, "fluid-dynamical" formulation, and provide fast and accurate smooth interpolation techniques. We also study a related probabilistic interpolation problem unique to the measure setting, which asks for particle trajectories that satisfy certain interpolation constrains and minimize a KL divergence, in analogy with the Schrödinger bridge problem. We conclude with an extension of our methods to the case of unbalanced measures in the Wasserstein-Fisher-Rao space.Ph.D

KCNE1 and KCNE3 beta-subunits regulate membrane surface expression of Kv12.2 K(+) channels in vitro and form a tripartite complex in vivo.

Voltage-gated potassium channels that activate near the neuronal resting membrane potential are important regulators of excitation in the nervous system, but their functional diversity is still not well understood. For instance, Kv12.2 (ELK2, KCNH3) channels are highly expressed in the cerebral cortex and hippocampus, and although they are most likely to contribute to resting potassium conductance, surprisingly little is known about their function or regulation. Here we demonstrate that the auxiliary MinK (KCNE1) and MiRP2 (KCNE3) proteins are important regulators of Kv12.2 channel function. Reduction of endogenous KCNE1 or KCNE3 expression by siRNA silencing, significantly increased macroscopic Kv12.2 currents in Xenopus oocytes by around 4-fold. Interestingly, an almost 9-fold increase in Kv12.2 currents was observed with the dual injection of KCNE1 and KCNE3 siRNA, suggesting an additive effect. Consistent with these findings, over-expression of KCNE1 and/or KCNE3 suppressed Kv12.2 currents. Membrane surface biotinylation assays showed that surface expression of Kv12.2 was significantly increased by KCNE1 and KCNE3 siRNA, whereas total protein expression of Kv12.2 was not affected. KCNE1 and KCNE3 siRNA shifted the voltages for half-maximal activation to more hyperpolarized voltages, indicating that KCNE1 and KCNE3 may also inhibit activation gating of Kv12.2. Native co-immunoprecipitation assays from mouse brain membranes imply that KCNE1 and KCNE3 interact with Kv12.2 simultaneously in vivo, suggesting the existence of novel KCNE1-KCNE3-Kv12.2 channel tripartite complexes. Together these data indicate that KCNE1 and KCNE3 interact directly with Kv12.2 channels to regulate channel membrane trafficking