cssi/SciSciGPT-SciSciNet huggingface dataset:
A Negative Mass Theorem for the 2-Torus

Let M be a closed surface. For a metric g on M, denote the area element by dA and the Laplace-Beltrami operator by Δ = Δg. We define the Robin mass m(p) at the point\({{p \in\, M}}\) to be the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off, and we define trace \({{\Delta^{-1}=\int_M m(p)\, dA}}\) . This regularized trace can also be obtained by regularization of the spectral zeta function and is hence a spectral invariant which heuristically measures the total wavelength of the surface.We define the Δ-mass of (M, g) to equal\({{({\rm trace} \, \Delta_{g}^{-1}-{\rm trace} \, \Delta_{S^2,A}^{-1})/A}}\) , where\({{\Delta_{S^2,A}}}\) is the Laplacian on the round sphere of area A. This scale invariant quantity is a non-trivial analog for closed surfaces of the ADM mass for higher dimensional asymptotically flat manifolds.In this paper we show that in each conformal class \({{\mathcal C}}\) for the 2-torus, there exists a metric with negative Δ-mass. From this it follows that the minimum of the Δ-mass on \({{\mathcal C}}\) is negative and attained by some metric \({{g\in\mathcal C}}\) . For this minimizing metric g, one gets a sharp logarithmic Hardy-Littlewood-Sobolev inequality and an Onofri-type inequality.We remark that if the flat metric in \({{\mathcal C}}\) is sufficiently long and thin then the minimizing metric g is non-flat. The proof of our result depends on analyzing the ordinary differential equation\({{\phi''=1-e^\phi}}\) which is equivalent to h′′ = 1 − 1/h. The solutions are periodic and we need to establish quite delicate, asymptotically sharp inequalities relating the period to the maximum value.
Performance and quality control of a radiation-hard 12-bit 40 MSPS ADC for the ATLAS Liquid Argon calorimeter trigger readout electronics Phase-I upgrade at the LHC

A radiation-hard quad-channel 12-bit 40 MSPS pipeline analog-to-digital converter (ADC) has been designed for the trigger readout electronics Phase-I upgrade of the ATLAS Liquid Argon calorimeter, at the CERN Large Hadron Collider. The final version of the custom design, fabricated in a commercial 130 nm CMOS process, is presented and found to meet the system requirements for analog performance and radiation tolerance. The procedure for quality control of 17200 ADCs is described and the results are presented.
Variational bounds on the energy dissipation rate in body-forced shear flow

A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier–Stokes equations. The resulting min–max problem is investigated computationally, producing new estimates that quantitatively improve previously obtained rigorous bounds. The results are compared with data from direct numerical simulations.
Nicotinic α7 acetylcholine receptor-mediated currents are not modulated by the tryptophan metabolite kynurenic acid in adult hippocampal interneurons

The tryptophan metabolite, kynurenic acid (KYNA), is classically known to be an antagonist of ionotropic glutamate receptors. Within the last decade several reports have been published suggesting that KYNA also blocks nicotinic acetylcholine receptors (nAChRs) containing the α7 subunit (α7*). Most of these reports involve either indirect measurements of KYNA effects on α7 nAChR function, or are reports of KYNA effects in complicated in vivo systems. However, a recent report investigating KYNA interactions with α7 nAChRs failed to detect an interaction using direct measurements of α7 nAChRs function. Further, it showed that a KYNA blockade of α7 nAChR stimulated GABA release (an indirect measure of α7 nAChR function) was not due to KYNA blockade of the α7 nAChRs. The current study measured the direct effects of KYNA on α7-containing nAChRs expressed on interneurons in the hilar and CA1 stratum radiatum regions of the mouse hippocampus and on interneurons in the CA1 region of the rat hippocampus. Here we show that KYNA does not block α7* nACHRs using direct patch--clamp recording of α7 currents in adult brain slices.
On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends

Symplectic field theory is the study of J-holomorphic curves in almost complex manifolds with cylindrical ends. One natural generalization is to replace “cylindrical” by “asymptotically cylindrical”. We generalize a number of asymptotic results about the behavior of J-holomorphic curves near infinity to the asymptotically cylindrical setting. We also sketch how these asymptotic results allow compactness theorems in symplectic field theory to be extended to the asymptotically cylindrical case.
Computational illumination for high-speed in vitro Fourier ptychographic microscopy

We demonstrate a new computational illumination technique that achieves a large space–bandwidth–time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either a large field of view (FOV) or high resolution, and not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixel-scale image having both a wide FOV and high resolution, i.e., a large space–bandwidth product. FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (of the order of minutes), limiting throughput. Faster capture times would not only improve the imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g., pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4× FOV with subsecond capture times. We propose an improved algorithm and a new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time.
Bigger Bursts from Merging Neutron Stars

GRB 990123 may have produced 4×1054 ergs in gamma rays unless, as seems to be the case, it was significantly beamed. Even with beaming, it may be beyond the limiting binding energy available for neutron star mergers in the Schwarzschild metric. Neutron stars of ~10 M☉ are permitted in the Yilmaz metric. A merger of two neutron stars of about 10 M☉ could release approximately 3×1055 ergs. The spectral state switches of the galactic black hole candidates may be the signatures of the magnetic fields of such massive neutron stars.
Absence of point spectrum for the self-dual extended Harper's model

We give a simple proof of absence of point spectrum for the self-dual extended Harper's model. We get a sharp result which improves that of Avila-Jitomirskaya-Marx in the isotropic self-dual regime.
Numerical Modeling of Multi-wavelength Spectra of M87 Core Emission

Spectral fits to M87 core data from radio to hard X-ray are generated via a specially selected software suite, comprised of the High-Accuracy Relativistic Magnetohydrodynamics GRMHD accretion disk model and a two-dimensional Monte Carlo radiation transport code. By determining appropriate parameter changes necessary to fit X-ray-quiescent and flaring behavior of M87's core, we assess the reasonableness of various flaring mechanisms. This shows that an accretion disk model of M87's core out to 28 GM/c{sup 2} can describe the inner emissions. High spin rates show GRMHD-driven polar outflow generation, without citing an external jet model. Our results favor accretion rate changes as the dominant mechanism of X-ray flux and index changes, with variations in density of approximately 20% necessary to scale between the average X-ray spectrum and flaring or quiescent spectra. The best-fit parameters are black hole spin a/M > 0.8 and maximum accretion flow density n {<=} 3 Multiplication-Sign 10{sup 7} cm{sup -3}, equivalent to horizon accretion rates between m-dot = M-dot / M-dot{sub Edd}{approx}2 Multiplication-Sign 10{sup -6} and 1 Multiplication-Sign 10{sup -5} (with M-dot{sub Edd} defined assuming a radiative efficiency {eta} = 0.1). These results demonstrate that the immediate surroundings of M87's core are appropriate to explain observed X-raymore » variability.« less
Clebsch-Gordan coefficients of discrete groups in subgroup bases

We express each Clebsch–Gordan (CG) coefficient of a discrete group as a product of a CG coefficient of its subgroup and a factor, which we call an embedding factor. With an appropriate definition,...
Quantum effects on dislocation motion from ring-polymer molecular dynamics

Quantum motion of atoms known as zero-point vibration was recently proposed to explain a long-standing discrepancy between theoretically computed and experimentally measured low-temperature plastic strength of iron and possibly other metals with high atomic masses. This finding challenges the traditional notion that quantum motion of atoms is relatively unimportant in solids comprised of heavy atoms. Here we report quantum dynamic simulations of quantum effects on dislocation motion within the exact formalism of Ring-Polymer Molecular Dynamics (RPMD). To extend the reach of quantum atomistic simulations to length and time scales relevant for extended defects in materials, we implemented RPMD in the open-source code LAMMPS thus making the RPMD method widely available to the community. We use our RPMD/LAMMPS approach for direct calculations of dislocation mobility and its effects on the yield strength of α-iron. Our simulation results establish that quantum effects are noticeable at temperatures below 50 K but account for only a modest (≈13% at T = 0 K) overall reduction in the Peierls barrier, at variance with the factor of two reduction predicted earlier based on the more approximate framework of harmonic transition state theory. Our results confirm that zero-point vibrations provide ample additional agitation for atomic motion that increases with decreasing temperature, however its enhancing effect on dislocation mobility is largely offset by an increase in the effective atom size, an effect known as quantum dispersion that has not been accounted for in the previous calculations. Large ring-polymer molecular dynamics can accurately simulate quantum effects on dislocation motion. A team led by Rodrigo Freitas at the University of California, Berkeley and Lawrence Livermore National Laboratory, U.S.A., investigated the effect of atomic quantum motion on the Peirels stress, i.e., the low-temperature resistance to dislocation motion. While classical molecular dynamics yielded the expected overestimation of the Peirels stress compared to experiments, ring-polymer molecular dynamics on 150,000 atoms using parallel computing showed a smaller discrepancy between simulations and experiments. This indicated that earlier quantum corrections overestimated the agitation effect of zero-point-vibrations and downplayed the effect of atomic neighbor confinement. Implementing efficient ring-polymer molecular dynamics can help us study extended defects in materials, while accurately accounting for quantum corrections to atom dynamics.
From Navier-Stokes to Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p + 1 dimensions, there is a uniquely associated “dual” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “near-horizon” limit in which Σc becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For p = 2, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70’s and resurfaced recently in studies of the AdS/CFT correspondence.
Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of a Laplacian on self-similar fractals using the results of Kigami and Lapidus (based on renewal theory) and the newer results by Hambly and Kajino based on heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true for the examples that have been analyzed in the existing literature.
Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead

We explore the use of the stochastic resolution-of-the-identity (sRI) with the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method. sRI is combined with four existing local energy evaluation strategies in ph-AFQMC, namely, (1) the half-rotated electron repulsion integral tensor (HR), (2) Cholesky decomposition (CD), (3) tensor hypercontraction (THC), or (4) low-rank factorization (LR). We demonstrate that HR–sRI achieves no scaling reduction, CD–sRI scales as O(N3), and THC–sRI and LR–sRI scale as O(N2), albeit with a potentially large prefactor. Furthermore, the walker-specific extra memory requirement in CD is reduced from O(N3) to O(N2) with sRI, while sRI-based THC and LR algorithms lead to a reduction from O(N2) extra memory to O(N). Based on numerical results for one-dimensional hydrogen chains and water clusters, we demonstrated that, along with the use of a variance reduction technique, CD–sRI achieves cubic-scaling without overhead. In particular, we find that for the systems studied, the observed scaling of standard CD is O(N3–4), while for CD–sRI, it is reduced to O(N2–3). Once a memory bottleneck is reached, we expect THC–sRI and LR–sRI to be preferred methods due to their quadratic-scaling memory requirements and their quadratic-scaling of the local energy evaluation (with a potentially large prefactor). The theoretical framework developed here should facilitate large-scale ph-AFQMC applications that were previously difficult or impossible to carry out with standard computational resources.
A tutorial on generalizing the default Bayesian t -test via posterior sampling and encompassing priors

With the advent of so-called “default” Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise, requiring the analyst to accept a one-size-fits-all approach to hypothesis testing. Further, such tests may not have the flexibility to test problems the scientist really cares about. In this tutorial, I demonstrate a flexible approach to generalizing one specific default test (the JZS t-test) (Rouder et al., Psychonomic Bulletin & Review, 16, 225-237, 2009) that is becoming increasingly popular in the social and behavioral sciences. The approach uses two results, the Savage-Dickey density ratio (Dickey and Lientz, 1980) and the technique of encompassing priors (Klugkist et al., Statistica Neerlandica, 59, 57-69, 2005) in combination with MCMC sampling via an easy-to-use probabilistic modeling package for R called Greta. Through a comprehensive mathematical description of the techniques as well as illustrative examples, the reader is presented with a general, flexible workflow that can be extended to solve problems relevant to his or her own work.
On the number and location of short geodesics in moduli space

A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.
Joint Radial Velocity and Direct Imaging Planet Yield Calculations. I. Self-consistent Planet Populations

Planet yield calculations may be used to inform the target selection strategy and science operations of space observatories. Forthcoming and proposed NASA missions, such as the Wide-Field Infrared Survey Telescope (WFIRST), the Habitable Exoplanet Imaging Mission (HabEx), and the Large UV/Optical/IR Surveyor (LUVOIR), are expected to be equipped with sensitive coronagraphs and/or starshades. We are developing a suite of numerical simulations to quantify the extent to which ground-based radial velocity (RV) surveys could boost the detection efficiency of direct imaging missions. In this paper, we discuss the first step in the process of estimating planet yields: generating synthetic planetary systems consistent with observed occurrence rates from multiple detection methods. In an attempt to self-consistently populate stars with orbiting planets, it is found that naive extrapolation of occurrence rates (mass, semi-major axis) results in an unrealistically large number-density of Neptune-mass planets beyond the ice-line ($a \gtrsim 5$au), causing dynamic interactions that would destabilize orbits. We impose a stability criterion for multi-planet systems based on mutual Hill radii separation. Considering the influence of compact configurations containing Jovian-mass and Neptune-mass planets results in a marked suppression in the number of terrestrial planets that can exist at large radii. This result has a pronounced impact on planet yield calculations particularly in regions accessible to high-contrast imaging and microlensing. The dynamically compact configurations and occurrence rates that we develop may be incorporated as input into joint RV and direct imaging yield calculations to place meaningful limits on the number of detectable planets with future missions.
Effects of dopants on the glass forming ability in Al-based metallic alloy

The effect of dopants on the metallic glass forming ability is usually considered based on the analysis of changes in the liquid structure or thermodynamics. What is missing in such considerations is an analysis of how a dopant changes the properties of the crystal phases which can form instead of the glass. In order to illuminate this aspect we performed molecular dynamics simulations to study the effects of Mg and Sm dopants on the crystal nucleation in Al. The simulation data were found to be consistent with the experimental observations that addition of Mg to Al does not lead to vitrification but addition of only 8% Sm does. The significant effect of Sm doping was related to the intolerance of Al to this dopant. This leads to increase in the solid-liquid interfacial free energy, and therefore, to increase in the nucleation barrier and to a dramatic decrease in the nucleation rate. The intolerance mechanism also significantly affects the growth kinetics.
Space-Time in the SYK Model

We consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions. This results in a dual theory with Euclidean AdS signature with additional legfactors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2d string theory.
Legendrian knots and constructible sheaves

We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible sheaves on the surface itself. Consequently, our category can be described as constructible sheaves with singular support controlled by the front projection of the knot. We use a theorem of Guillermou–Kashiwara–Schapira to show that the resulting category is invariant under Legendrian isotopies. A subsequent article establishes its equivalence to a category of representations of the Chekanov–Eliashberg differential graded algebra. We also find two connections to topological knot theory. First, drawing a positive braid closure on the annulus, the moduli space of rank-n objects maps to the space of local systems on a circle. The second page of the spectral sequence associated to the weight filtration on the pushforward of the constant sheaf is the (colored-by-n) triply-graded Khovanov–Rozansky homology. Second, drawing a positive braid closure in the plane, the number of points of our moduli spaces over a finite field with q elements recovers the lowest coefficient in ‘a’ of the HOMFLY polynomial of the braid closure.
Efficient Transformer-based Large Scale Language Representations using Hardware-friendly Block Structured Pruning.

Pretrained large-scale language models have increasingly demonstrated high accuracy on many natural language processing (NLP) tasks. However, the limited weight storage and computational speed on hardware platforms have impeded the popularity of pretrained models, especially in the era of edge computing. In this work, we propose an efficient transformer-based large-scale language representation using hardware-friendly block structure pruning. We incorporate the reweighted group Lasso into block-structured pruning for optimization. Besides the significantly reduced weight storage and computation, the proposed approach achieves high compression rates. Experimental results on different models (BERT, RoBERTa, and DistilBERT) on the General Language Understanding Evaluation (GLUE) benchmark tasks show that we achieve up to 5.0x with zero or minor accuracy degradation on certain task(s). Our proposed method is also orthogonal to existing compact pretrained language models such as DistilBERT using knowledge distillation, since a further 1.79x average compression rate can be achieved on top of DistilBERT with zero or minor accuracy degradation. It is suitable to deploy the final compressed model on resource-constrained edge devices.
Optimal Achievable Rates for Interference Networks With Random Codes

The optimal rate region for interference networks is characterized when encoding is restricted to random code ensembles with superposition coding and time sharing. A simple simultaneous nonunique decoding rule, under which each receiver decodes for the intended message as well as the interfering messages, is shown to achieve this optimal rate region regardless of the relative strengths of signal, interference, and noise. This result implies that the Han-Kobayashi bound, the best known inner bound on the capacity region of the two-user pair interference channel, cannot be improved merely by using the optimal maximum likelihood decoder.
Aspects of hot Galilean field theory

We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.
From Interstellar Clouds to Stars

I review (1) Physics of Star Formation & Open Questions; (2) Structure & Dynamics of Star-Forming Clouds & Young Clusters; (3) Star Formation Rates: Observations & Theoretical Implications.
First-principles simulation of electron mean-free-path spectra and thermoelectric properties in silicon

The mean free paths (MFPs) of energy carriers are of critical importance to the nano-engineering of better thermoelectric materials. Despite significant progress in the first-principles–based understanding of the spectral distribution of phonon MFPs in recent years, the spectral distribution of electron MFPs remains unclear. In this work, we compute the energy-dependent electron scatterings and MFPs in silicon from first principles. The electrical conductivity accumulation with respect to electron MFPs is compared to that of the phonon thermal conductivity accumulation to illustrate the quantitative impact of nanostructuring on electron and phonon transport. By combining all electron and phonon transport properties from first principles, we predict the thermoelectric properties of the bulk and nanostructured silicon, and find that silicon with 20 nm nanograins can result in a higher than five times enhancement in their thermoelectric figure of merit as the grain boundaries scatter phonons more significantly than that of electrons due to their disparate MFP distributions.
A note on noncommutative D-brane actions

Abstract We use the nonabelian action of N coincident D(−1) branes in constant background fields, in the N→∞ limit, to construct noncommutative D-brane actions in an arbitrary noncommutative description and comment on tachyon condensation from this perspective.
FAILED THEORIES OF SUPERCONDUCTIVITY

Almost half a century passed between the discovery of superconductivity by Kamerlingh Onnes and the theoretical explanation of the phenomenon by Bardeen, Cooper and Schrieffer. During the intervening years the brightest minds in theoretical physics tried and failed to develop a microscopic understanding of the effect. A summary of some of those unsuccessful attempts to understand superconductivity not only demonstrates the extraordinary achievement made by formulating the BCS theory, but also illustrates that mistakes are a natural and healthy part of scientific discourse, and that inapplicable, even incorrect theories can turn out to be interesting and inspiring.
Possible astrophysical clues of dark matter

Abstract The supernova physics may provide a clue of the cosmological dark matter. In the absence of new physics, the supernova calculations do not explain the observed velocities of pulsars. However, if there exists a singlet fermion with mass in the 1–20 keV range and a small mixing with neutrinos, this particle could be emitted asymmetrically from a cooling neutron star in the event of a supernova explosion. The asymmetry could explain the long-standing puzzle of pulsar velocities. The same particle could be the dark matter. Observations of X-ray telescopes, as well as a future detection of gravitational waves from a nearby supernova can confirm or rule out this possibility.
Privacy in Index Coding: Improved Bounds and Coding Schemes

It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach to mitigate such concerns is the use of k-limited-access schemes [1], that restrict each client to learn only part of the index coding matrix, and in particular, at most $k$ rows. These schemes transform a linear index coding matrix of rank $T$ to an alternate one, such that each client needs to learn at most $k$ of the coding matrix rows to decode its requested message. This paper analyzes k-limited-access schemes. First, a worst-case scenario, where the total number of clients $n$ is $2^{T}-1$ is studied. For this case, a novel construction of the coding matrix is provided and shown to be order-optimal in the number of transmissions. Then, the case of a general $n$ is considered and two different schemes are designed and analytically and numerically assessed in their performance. It is shown that these schemes perform better than the one designed for the case $n=2^{T}-1$ .
Secret-Sharing LDPC Codes for the BPSK-Constrained Gaussian Wiretap Channel

The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination channel; namely, the source can transmit only binary phase-shift-keyed (BPSK) symbols, and symbol-by-symbol hard-decision quantization is applied to the received symbols of the destination. An error-free public channel is also available for the source and destination to exchange messages in order to help the secret-sharing process. The wiretapper can perfectly observe all messages in the public channel. It is shown that a secret-sharing scheme that employs a random ensemble of regular low-density parity-check (LDPC) codes can achieve the key capacity of the BPSK-constrained Gaussian wiretap channel asymptotically with increasing block length. To accommodate practical constraints of finite block length and limited decoding complexity, fixed irregular LDPC codes are also designed to replace the regular LDPC code ensemble in the proposed secret-sharing scheme.
Pulling out all the tops with computer vision and deep learning

We apply computer vision with deep learning — in the form of a convolutional neural network (CNN) — to build a highly effective boosted top tagger. Previous work (the “DeepTop” tagger of Kasieczka et al) has shown that a CNN-based top tagger can achieve comparable performance to state-of-the-art conventional top taggers based on high-level inputs. Here, we introduce a number of improvements to the DeepTop tagger, including architecture, training, image preprocessing, sample size and color pixels. Our final CNN top tagger outperforms BDTs based on high-level inputs by a factor of ∼ 2-3 or more in background rejection, over a wide range of tagging efficiencies and fiducial jet selections. As reference points, we achieve a QCD background rejection factor of 500 (60) at 50% top tagging efficiency for fully-merged (non-merged) top jets with pT in the 800-900 GeV (350-450 GeV) range. Our CNN can also be straightforwardly extended to the classification of other types of jets, and the lessons learned here may be useful to others designing their own deep NNs for LHC applications.
Constraints from Gravitational Recoil on the Growth of Supermassive Black Holes at High Redshift

Recent studies have suggested that during their coalescence, binary supermassive black holes (SMBHs) experience typical gravitational recoil velocities that may be as large as 100 km s-1. These velocities exceed the escape velocity vesc from typical dark matter (DM) halos at high redshift (z 6), and therefore put constraints on scenarios in which early SMBHs grow at the centers of DM halos. Here we quantify these constraints for the most distant known SMBH, with an inferred mass in excess of 109 M☉, powering the bright quasar SDSS J1148+5251 discovered in the Sloan Digital Sky Survey at z = 6.43. We assume that this SMBH grew via a combination of accretion and mergers between preexisting seed BHs in individual progenitor halos, and that mergers between progenitors with vesc < vkick disrupt the BH growth process. Our results suggest that under these assumptions, the z ≈ 6 SMBHs had a phase during which they gained mass vary rapidly. In particular, typical z ≈ 3 quasars with luminosities similar to that of SDSS J1148+5251 have recently been inferred to have an average radiative efficiency of ≈ 20%. The growth rate of the SMBH in SDSS J1148+5251 must have significantly exceeded the Eddington accretion rate with this efficiency.
Reduced Diversity of Life around Proxima Centauri and TRAPPIST-1

The recent discovery of potentially habitable exoplanets around Proxima Centauri and TRAPPIST-1 has attracted much attention due to their potential for hosting life. We delineate a simple model that accurately describes the evolution of biological diversity on Earth. Combining this model with constraints on atmospheric erosion and the maximal evolutionary timescale arising from the star's lifetime, we arrive at two striking conclusions: (i) Earth-analogs orbiting low-mass M-dwarfs are unlikely to be inhabited, and (ii) K-dwarfs and some G-type stars are potentially capable of hosting more complex biospheres than the Earth. Hence, future searches for biosignatures may have higher chances of success when targeting planets around K-dwarf stars.
A representation theory approach to integral moments of $L$-functions over function fields

We propose a new heuristic approach to integral moments of L-functions over function fields, which we demonstrate in the case of Dirichlet characters ramified at one place (the function field analogue of the moments of the Riemann zeta function, where we think of the character nit as ramified at the infinite place). We represent the moment as a sum of traces of Frobenius on cohomology groups associated to irreducible representations. Conditional on a hypothesis on the vanishing of some of these cohomology groups, we calculate the moments of the L-function and they match the predictions of the Conry, Farmer, Keating, Rubinstein, and Snaith recipe (Proc. Lond. Math. Soc. (3) 91 (2005), 33–104). In this case, the decomposition into irreducible representations seems to separate the main term and error term, which are mixed together in the long sums obtained from the approximate functional equation, even when it is dyadically decomposed. This makes our heuristic statement relatively simple, once the geometric background is set up. We hope that this will clarify the situation in more difficult cases like the L-functions of quadratic Dirichlet characters to squarefree modulus. There is also some hope for a geometric proof of this cohomological hypothesis, which would resolve the moment problem for these L-functions in the large degree limit over function fields.
On the Floer homology of plumbed three-manifolds

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specied by certain graphs. Our class of graphs is sufciently large to describe, for example, all Seifert bered rational homology spheres. These calculations can be used to determine also these groups for other three-manifolds, including the product of a circle with a genus two surface.
The Amazing Old Nova Q Cygni: A Far-Ultraviolet Synthetic Spectral Analysis

Q Cygni (Nova Cygni 1876) is the third-oldest old novae (after WY Sge and V841 Oph), with a long orbital period of 10.08 hr and spectroscopic peculiarities in the optical, including the presence of variable wind outflow revealed by optical P Cygni profiles in the He i lines and Hαβ. We have carried out a synthetic spectral analysis of a far-ultraviolet IUE archival spectrum of Q Cygni using our optically thick, steady state, accretion disk models and model white dwarf photospheres. We find that the accretion light of a luminous accretion disk dominates the FUV flux of the hot component with a rate of accretion of 2–3 × 10-9 M⊙ yr-1. We find that Q Cygni lies at a distance of 741 ± 110 pc. The implications of our results for theoretical predictions for old novae are presented.
The geometry of the knot concordance space

Most of the 5 0 years of study of the set of knot concordance classes, ℂ , has focused on its structure as an abelian group. Here we take a different approach, namely we study ℂ as a metric space admitting many natural geometric operators. We focus especially on the coarse geometry of satellite operators. We consider several knot concordance spaces, corresponding to different categories of concordance, and two different metrics. We establish the existence of quasi- n –flats for every n , implying that ℂ admits no quasi-isometric embedding into a finite product of (Gromov) hyperbolic spaces. We show that every satellite operator is a quasihomomorphism P : ℂ → ℂ . We show that winding number one satellite operators induce quasi-isometries with respect to the metric induced by slice genus. We prove that strong winding number one patterns induce isometric embeddings for certain metrics. By contrast, winding number zero satellite operators are bounded functions and hence quasicontractions. These results contribute to the suggestion that ℂ is a fractal space. We establish various other results about the large-scale geometry of arbitrary satellite operators.
Identification of all dark matter as black holes

For the universe I use dimensionless entropy S/k = ln Ω for which the most convenient unit is the googol (10100) and take all dark matter as black holes whereupon the present entropy is about a thousand googols independently of whether dark energy possesses entropy. While the energy of the universe has been established to be about 0.04 baryons, 0.24 dark matter and 0.72 dark energy, the cosmological entropy is almost entirely, about (1−10−15), from black holes and only 10−15 from everything else. This identification of all dark matter as black holes is natural in statistical mechanics.
Perpendicular Magnetic Anisotropy and Spin Glass-like Behavior in Molecular Beam Epitaxy Grown Chromium Telluride Thin Films

Reflection high-energy electron diffraction (RHEED), scanning tunneling microscopy (STM), vibrating sample magnetometry, and other physical property measurements are used to investigate the structure, morphology, magnetic, and magnetotransport properties of (001)-oriented Cr2Te3 thin films grown on Al2O3(0001) and Si(111)-(7×7) surfaces by molecular beam epitaxy. Streaky RHEED patterns indicate flat smooth film growth on both substrates. STM studies show the hexagonal arrangements of surface atoms. Determination of the lattice parameter from the atomically resolved STM image is consistent with the bulk crystal structures. Magnetic measurements show the film is ferromagnetic, having a Curie temperature of about 180 K, and a spin glass-like behavior was observed below 35 K. Magnetotransport measurements show the metallic nature of the film with a perpendicular magnetic anisotropy along the c-axis.
New Class of Quantum Error-Correcting Codes for a Bosonic Mode

Optimal quantum error-correction codes are necessary to extend the lifetime of quantum memories. A new error-correction code to rectify photon loss, gain, and dephasing errors in electromagnetic cavities is presented.
Constructing equivariant spectra via categorical Mackey functors

We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key element of our construction is a spectrally enriched functor from a spectrally enriched version of permutative categories to the category of spectra that is built using an appropriate version of K–theory. As applications of our general construction, we produce a new functorial construction of equivariant Eilenberg–Mac Lane spectra for Mackey functors and for suspension spectra for finite G –sets.
Universal correlations of one-dimensional interacting electrons in the gas phase

Abstract We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.
Entanglement and correlation functions of the quantum Motzkin spin-chain

We present exact results on the exactly solvable spin chain of Bravyi et al. [Phys. Rev. Lett. 109, 207202 (2012)]. This model is a spin one chain and has a Hamiltonian that is local and translationally invariant in the bulk. It has a unique (frustration free) ground state with an energy gap that is polynomially small in the system’s size (2n). The half-chain entanglement entropy of the ground state is 12logn+const.[Bravyi et al., Phys. Rev. Lett. 109, 207202 (2012)]. Here we first write the Hamiltonian in the standard spin-basis representation. We prove that at zero temperature, the magnetization is along the z-direction, i.e., ⟨sx⟩=⟨sy⟩=0 (everywhere on the chain). We then analytically calculate ⟨sz⟩ and the two-point correlation functions of sz. By analytically diagonalizing the reduced density matrices, we calculate the Schmidt rank, von Neumann, and Renyi entanglement entropies for the following: 1. Any partition of the chain into two pieces (not necessarily in the middle) and 2. L consecutive spins ...
Conley conjecture and local Floer homology

In this paper we connect algebraic properties of the pair-of-pants product in local Floer homology and Hamiltonian dynamics. We show that for an isolated periodic orbit, the product is non-uniformly nilpotent and use this fact to give a simple proof of the Conley conjecture for closed manifolds with aspherical symplectic form. More precisely, we prove that on a closed symplectic manifold, the mean action spectrum of a Hamiltonian diffeomorphism with isolated periodic orbits is infinite.
TRACING EMBEDDED STELLAR POPULATIONS IN CLUSTERS AND GALAXIES USING MOLECULAR EMISSION: METHANOL AS A SIGNATURE OF THE LOW-MASS END OF THE IMF

Most low-mass protostars form in clusters, in particular high-mass clusters; however, how low-mass stars form in high-mass clusters and what the mass distribution is are still open questions both in our own Galaxy and elsewhere. To access the population of forming embedded low-mass protostars observationally, we propose using molecular outflows as tracers. Because the outflow emission scales with mass, the effective contrast between low-mass protostars and their high-mass cousins is greatly lowered. In particular, maps of methanol emission at 338.4 GHz (J = 70–60 A+) in low-mass clusters illustrate that this transition is an excellent probe of the low-mass population. We present here a model of a forming cluster where methanol emission is assigned to every embedded low-mass protostar. The resulting model image of methanol emission is compared to recent ALMA observations toward a high-mass cluster and the similarity is striking: the toy model reproduces observations to better than a factor of two and suggests that approximately 50% of the total flux originates in low-mass outflows. Future fine-tuning of the model will eventually make it a tool for interpreting the embedded low-mass population of distant regions within our own Galaxy and ultimately higher-redshift starburst galaxies, not just for methanol emission but also water and high-J CO.
Microwave dynamics of high aspect ratio superconducting nanowires studied using self-resonance

We study the microwave impedance of extremely high aspect ratio (length/width ≈ 5000) superconducting niobium nitride nanowires. The nanowires are fabricated in a compact meander geometry that is in series with the center conductor of a 50 Ω coplanar waveguide transmission line. The transmission coefficient of the sample is measured up to 20 GHz. At high frequency, a peak in the transmission coefficient is seen. Numerical simulations show that this is a half-wave resonance along the length of the nanowire, where the nanowire acts as a high impedance, slow wave transmission line. This resonance sets the upper frequency limit for these nanowires as inductive elements. Fitting simulations to the measured resonance enables a precise determination of the nanowire's complex sheet impedance at the resonance frequency. The real part is a measure of dissipation, while the imaginary part is dominated by kinetic inductance. We characterize the dependence of the sheet resistance and sheet inductance on both temperatu...
Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method.
An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions

We assess the utility of Hartree-Fock (HF) trial wavefunctions in performing phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) on the uniform electron gas (UEG) model. The combination of ph-AFQMC with spin-restricted HF (RHF+ph-AFQMC) was found to be highly accurate and efficient for systems containing up to 114 electrons in 2109 orbitals, particularly for rs ≤ 2.0. Compared to spin-restricted coupled-cluster (RCC) methods, we found that RHF+ph-AFQMC performs better than CC with singles, doubles, and triples (RCCSDT) and similarly to or slightly worse than CC with singles, doubles, triples, and quadruples (RCCSDTQ) for rs ≤ 3.0 in the 14-electron UEG model. With the 54-electron, we found RHF+ph-AFQMC to be nearly exact for rs ≤ 2.0 and pointed out potential biases in existing benchmarks. Encouraged by these, we performed RHF+ph-AFQMC on the 114-electron UEG model for rs ≤ 2.0 and provided new benchmark data for future method development. We found that the UEG models with rs = 5.0 remain to be challenging for RHF+ph-AFQMC. Employing nonorthogonal configuration expansions or unrestricted HF states as trial wavefunctions was also found to be ineffective in the case of the 14-electron UEG model with rs = 5.0. We emphasize the need for a better trial wavefunction for ph-AFQMC in simulating strongly correlated systems. With the 54-electron and 114-electron UEG models, we stress the potential utility of RHF+ph-AFQMC for simulating dense solids.
Coefficients of Gaussian Polynomials Modulo $N$

Let $\left[{n \atop k}\right]_q$ be a $q$-binomial coefficient. Stanley conjectured that the function $f_{k,R}(n) = \left|\left\{\alpha : [q^{\alpha}] \left[{n \atop k}\right]_q \equiv R \pmod{N}\right\}\right|$ is quasi-polynomial for $N$ prime. We prove this for any integer $N$ and obtain an expression for the generating function $F_{k,R}(x)$ for $f_{k,R}(n)$.
Emergent unitarity from the amplituhedron

We present a proof of perturbative unitarity for planar $$ \mathcal{N} $$ = 4 SYM, following from the geometry of the amplituhedron. This proof is valid for amplitudes of arbitrary multiplicity n, loop order L and MHV degree k.