cssi/SciSciGPT-SciSciNet huggingface dataset:
Adiabatic Elimination in Quantum Stochastic Models

We consider a physical system with a coupling to bosonic reservoirs via a quantum stochastic differential equation. We study the limit of this model as the coupling strength tends to infinity. We show that in this limit the solution to the quantum stochastic differential equation converges strongly to the solution of a limit quantum stochastic differential equation. In the limiting dynamics the excited states are removed and the ground states couple directly to the reservoirs.
A Parameter Space Exploration of Galaxy Cluster Mergers. II. Effects of Magnetic Fields

The hot intracluster plasma in clusters of galaxies is weakly magnetized. Mergers between clusters produce gas compression and motions which can increase the magnetic field strength. In this work, we perform high-resolution non-radiative magnetohydrodynamics simulations of binary galaxy cluster mergers with magnetic fields, to examine the effects of these motions on the magnetic field configuration and strength, as well as the effect of the field on the gas itself. Our simulations sample a parameter space of initial mass ratios and impact parameters. During the first core passage of mergers, the magnetic energy increases via gas compression. After this, shear flows produce temporary, Mpc-scale, strong-field "filament" structures. Lastly, magnetic fields grow stronger by turbulence. Field amplification is most effective for low mass ratio mergers, but mergers with a large impact parameter can increase the magnetic energy more via shearing motions. The amplification of the magnetic field is most effective in between the first two core passages of each cluster merger. After the second core passage, the magnetic energy in this region gradually decreases. In general, the transfer of energy from gas motions to the magnetic field is not significant enough to have a substantial effect on gas mixing and the subsequent increase in entropy which occurs in cluster cores as a result. In the absence of radiative cooling, this results in an overall decrease of the magnetic field strength in cluster cores. In these regions, the final magnetic field is isotropic, while it can be significantly tangential at larger radii.
Equivariant dendroidal sets

We extend the Cisinski–Moerdijk–Weiss theory of ∞ –operads to the equivariant setting to obtain a notion of G - ∞ –operads that encode “equivariant operads with norm maps” up to homotopy. At the root of this work is the identification of a suitable category of G –trees together with a notion of G –inner horns capable of encoding the compositions of norm maps. Additionally, we follow Blumberg and Hill by constructing suitable variants associated to each of the indexing systems featured in their work.
Kalman filter based tracker study for lepton flavor violation experiments

A tracking detector is proposed for lepton flavor violation experiments (μ → e conversion, μ → e+γ, μ → 3e) consisting of identical chambers which can be reconfigured to meet the requirements for all three experiments. A pattern recognition and track reconstruction procedure based on the Kalman filter technique is presented for this detector. The pattern recognition proceeds in two stages. At the first stage only hit straw tube center coordinates, without drift time information, are used to reduce the background to a manageable level. At the second stage the drift time information is incorporated and a deterministic annealing filter is applied to reach the final level of background suppression. The final track momentum reconstruction is provided by a combinatorial drop filter which is effective in hit-to-track assignment. The momentum resolution of the tracker in measuring monochromatic leptons is found to be σp = 0.17 and 0.26 MeV for the μ → e conversion and μ+ → e++γ processes, respectively. The tracker reconstruction resolution for the total scalar lepton momentum is σp = 0.33 MeV for the μ → 3e process. The obtained tracker resolutions allow an increase in sensitivity to the branching ratios for these processes by a few orders of magnitude over current experimental limits.
AN IMPUTATION-BASED APPROACH FOR PARAMETER ESTIMATION IN THE PRESENCE OF AMBIGUOUS CENSORING WITH APPLICATION IN INDUSTRIAL SUPPLY CHAIN

This paper describes a novel approach based on “proportional imputation” when identical units produced in a batch have random but independent installation and failure times. The current problem is motivated by a real life industrial production–delivery supply chain where identical units are shipped after production to a third party warehouse and then sold at a future date for possible installation. Due to practical limitations, at any given time point, the exact installation as well as the failure times are known for only those units which have failed within that time frame after the installation. Hence, in-house reliability engineers are presented with a very limited, as well as partial, data to estimate different model parameters related to installation and failure distributions. In reality, other units in the batch are generally not utilized due to lack of proper statistical methodology, leading to gross misspecification. In this paper we have introduced a likelihood based parametric and computationally efficient solution to overcome this problem.
Maximum a posteriori estimators as a limit of Bayes estimators

Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0–1 loss. In this paper, we provide a counterexample which shows that in general this claim is false. We then correct the claim that by providing a level-set condition for posterior densities such that the result holds. Since both estimators are defined in terms of optimization problems, the tools of variational analysis find a natural application to Bayesian point estimation.
Topological fermion condensates from anomalies

We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions be treated as Kahler-Dirac fields and the condensate arises from an anomaly associated with a U(1) global symmetry which is subsequently broken to a discrete subgroup. Remarkably the anomaly survives under discretization of the space which allows us to compute the condensate on an arbitrary triangulation. The results, being topological in character, should hold in a wide range of gravitationally coupled fermion theories both classical and quantum.
A Comparative Study of Feature Selection Methods for Stress Hotspot Classification in Materials

The first step in constructing a machine learning model is defining the features of the dataset that can be used for optimal learning. In this work, we discuss feature selection methods, which can be used to build better models, as well as achieve model interpretability. We applied these methods in the context of stress hotspot classification problem, to determine what microstructural characteristics can cause stress to build up in certain grains during uniaxial tensile deformation. The results show how some feature selection techniques are biased and demonstrate a preferred technique to get feature rankings for physical interpretations.
Calibration of the EDGES High-Band Receiver to Observe the Global 21-cm Signature from the Epoch of Reionization

The EDGES experiment strives to detect the the sky-average brightness temperature from the 21-cm line emitted during the Epoch of Reionization (EoR) in the redshift range 14 & z & 6. To probe this signal, EDGES conducts single-antenna measurements in the frequency range 100- 200 MHz from the Murchison Radioastronomy Observatory in Western Australia. In this paper we describe the current strategy for calibration of the EDGES instrument and, in particular, of its receiver. The calibration involves measuring accurately modeled passive and active noise sources connected to the receiver input in place of the antenna. We model relevant uncertainties that arise during receiver calibration and propagate them to the calibrated antenna temperature using a Monte Carlo approach. Calibration effects are isolated by assuming that the sky foregrounds and the antenna beam are perfectly known. We find that if five polynomial terms are used to account for calibration systematics, most of the calibration measurements conducted for EDGES produce residuals of 1 mK or less at 95% confidence. The largest residuals are due to uncertainty in the antenna and receiver reflection coefficients at levels below 20 mK when observing a low-foreground region. These residuals could be reduced by restricting the band to a smaller frequency range motivated by tighter reionization priors. They could also be reduced by 1) improving the accuracy in reflection measurements, especially their phase, 2) decreasing the changes with frequency of the antenna reflection phase, and 3) improving the impedance match at the antenna-receiver interface. Subject headings: early universe — cosmology: observations — methods: laboratory — methods: statistical
Complementation, local complementation, and switching in binary matroids

Abstract In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set V can be obtained from a complete graph on V via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. The last operation involves taking the complement in the neighbourhood of a vertex. In this paper, we consider natural generalizations of these operations for binary matroids and explore their behaviour. We characterize all binary matroids obtainable from the binary projective geometry of rank r under the operations of complementation and switching. Moreover, we show that not all binary matroids of rank at most r can be obtained from a projective geometry of rank r via a sequence of the three generalized operations. We introduce a fourth operation and show that, with this additional operation, we are able to obtain all binary matroids.
Error analysis in nuclear density functional theory

Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the Universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.
Thermodynamic Limit for Dipolar Media

We prove existence of a shape- and boundary-condition-independent thermodynamic limit for fluids and solids of identical particles with electric or magnetic dipole moments. Our result applies to fluids of hard-core particles, to dipolar soft spheres and Stockmayer fluids, to disordered solid composites, and to regular crystal lattices. In addition to their permanent dipole moments, particles may further polarize each other. Classical and quantum models are treated. Shape independence depends on the reduction in free energy accomplished by domain formation, so our proof applies only in the case of zero applied field. Existence of a thermodynamic limit implies texture formation in spontaneously magnetized liquids and disordered solids analogous to domain formation in crystalline solids.
Chondrules and nebular shocks

Beneath the fusion-encrusted surfaces of the most primitive stony meteorites lies not homogeneous rock, but a profusion of millimeter-sized igneous spheres. These chondrules, and their centimeter-sized counterparts, the calcium-aluminum-rich inclusions, comprise more than half of the volume fraction of chondritic meteorites. They are the oldest creations of the solar system. Their chemical composition matches that of the solar photosphere in all but the most volatile of elements, reflecting their condensation from the same pristine gas that formed the sun. In this invited editorial, we review the nebular shock wave model of Desch and Connolly (Meteoritics and Planetary Science 2002, 37, 183) that seeks to explain their origin. While the model succeeds in reproducing the unique petrological signatures of chondrules, the origin of the required shock waves in protoplanetary disks remains a mystery. Outstanding questions are summarized, with attention paid briefly to competing models.
ON DETERMINING THE SHAPE OF MATTER DISTRIBUTIONS

A basic property of objects, such as galaxies and halos that form in cosmological structure formation simulations, is their shape. Here, we critically investigate shape determination methods that are commonly used in the literature. It is found that using an enclosed integration volume and weight factors r −2 and r −2 ell (elliptical radius) for the contribution of each particle or volume element in the shape tensor leads to biased axis ratios and smoothing of details when calculating the local shape as a function of distance from the center. To determine the local shape of matter distributions as a function of distance for well-resolved objects (typically more than O(10 4 ) particles), we advocate a method that (1) uses an ellipsoidal shell (homoeoid) as an integration volume without any weight factors in the shape tensor and (2) removes subhalos.
AN INDEPENDENT ANALYSIS OF THE BROWN DWARF ATMOSPHERE MONITORING (BAM) DATA: LARGE-AMPLITUDE VARIABILITY IS RARE OUTSIDE THE L/T TRANSITION

Observations of variability can provide valuable information about the processes of cloud formation and dissipation in brown dwarf atmospheres. Here we report the results of an independent analysis of archival data from the Brown dwarf Atmosphere Monitoring (BAM) program. Time series data for 14 L and T dwarfs reported to be significantly variable over timescales of hours were analyzed. We confirm large-amplitude variability (amplitudes >2%) for 4 out of 13 targets and place upper limits of 0.7%-1.6% on variability in the remaining sample. For two targets we find evidence of weak variability at amplitudes of 1.3% and 1.6%. Based on our revised classification of variable objects in the BAM study, we find strong variability outside the L/T transition to be rare at near infrared wavelengths. From a combined sample of 81 L0-T9 dwarfs from the revised BAM sample and the variability survey of Radigan et al., we infer an overall observed frequency for large-amplitude variability outside the L/T transition of 3.2%, in contrast to 24% for L9-T3.5 spectral types. We conclude that while strong variability is not limited to the L/T transition, it occurs more frequently in this spectral type range, indicative of larger or more highly contrasting cloud features at these spectral types.
A comment on finite temperature correlations in integrable QFT

Abstract I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one-point functions of conserved quantities. I also argue that the proposal is not correct for two- (and higher-) point functions, and give some counterexamples to justify that claim.
Frequentist Consistency of Variational Bayes

A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular a...
Finding All $\epsilon$-Good Arms in Stochastic Bandits

The pure-exploration problem in stochastic multi-armed bandits aims to find one or more arms with the largest (or near largest) means. Examples include finding an {\epsilon}-good arm, best-arm identification, top-k arm identification, and finding all arms with means above a specified threshold. However, the problem of finding all {\epsilon}-good arms has been overlooked in past work, although arguably this may be the most natural objective in many applications. For example, a virologist may conduct preliminary laboratory experiments on a large candidate set of treatments and move all {\epsilon}-good treatments into more expensive clinical trials. Since the ultimate clinical efficacy is uncertain, it is important to identify all {\epsilon}-good candidates. Mathematically, the all-{\epsilon}-good arm identification problem presents significant new challenges and surprises that do not arise in the pure-exploration objectives studied in the past. We introduce two algorithms to overcome these and demonstrate their great empirical performance on a large-scale crowd-sourced dataset of 2.2M ratings collected by the New Yorker Caption Contest as well as a dataset testing hundreds of possible cancer drugs.
The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.
The Hopf algebra structure of multiple harmonic sums

Multiple harmonic sums appear in the perturbative computation of various quantities of interest in quantum field theory. In this article we introduce a class of Hopf algebras that describe the structure of such sums, and develop some of their properties that can be exploited in calculations.
A collision of subclusters in Abell 754

We present direct evidence of a collision of subclusters in the galaxy cluster Abell 754. Our comparison of new optical data and archival ROSAT PSPC X-ray data reveals three collision signatures predicted by n-body/hydrodynamical simulations of hierarchical cluster evolution. First, there is strong evidence of a nonhydrostatic process; neither of the two major clumps in the galaxy distribution lies on the off-center peak of the X-ray emission from the intracluster gas. Second, the peak of the X-ray emission is elongated perpendicular to the collision axis defined by connecting the centroids of the two galaxy clumps. Third, there is evidence of compression-heated gas; one of A754's two X-ray temperature components (Henry & Briel 1995) is among the hottest observed in any cluster and hotter than that inferred from the velocity dispersion of the associated galaxy clump. These signatures are consistent with the qualitative features of simulations (Evrard 1990a, b) in which two subclusters have collided in the plane of the sky during the last ~1 Gyr. The detection of such collisions is crucial for understanding both the dynamics of individual clusters and the underlying cosmology. First, for systems like A754, estimating the cluster X-ray mass from assumptions of hydrostatic equilibrium and isothermality is incorrect and may produce the discrepancies sometimes found between X-ray masses and those derived from gravitational lens models (Babul & Miralda-Escude 1994). Second, the fraction of nearby clusters in which subclusters have collided in the last ~1 Gyr is especially sensitive to the mean mass density parameter Ω0 (see Richstone, Loeb, & Turner 1992; Evrard et al. 1993; Lacey & Cole 1993). As we show for A754, we now have the means to identify recent collisions. With a large, well-defined cluster sample, it will be possible to place a new and powerful constraint on cosmological models.
Aspects of the synthesis of thin film superconducting infinite-layer nickelates

The recent observation of superconductivity in Nd0.8Sr0.2NiO2 calls for further investigation and optimization of the synthesis of this infinite-layer nickelate structure. Here, we present our current understanding of important aspects of the growth of the parent perovskite compound via pulsed laser deposition on SrTiO3 (001) substrates and the subsequent topotactic reduction. We find that to achieve single-crystalline, single-phase superconducting Nd0.8Sr0.2NiO2, it is essential that the precursor perovskite Nd0.8Sr0.2NiO3 thin film is stabilized with no visible impurity phases; in particular, a Ruddlesden–Popper-type secondary phase is often observed. We have further investigated the evolution of the soft-chemistry topotactic reduction conditions to realize full transformation to the infinite-layer structure with no film decomposition or formation of other phases. We find that capping the nickelate film with a subsequent SrTiO3 layer provides an epitaxial template to the top region of the nickelate film, much like the substrate. Thus, for currently optimized growth conditions, we can stabilize superconducting single-phase Nd0.8Sr0.2NiO2 (001) epitaxial thin films up to ∼10 nm.
Modeling of missing dynamical systems: deriving parametric models using a nonparametric framework

In this paper, we consider modeling missing dynamics with a nonparametric non-Markovian model, constructed using the theory of kernel embedding of conditional distributions on appropriate reproducing kernel Hilbert spaces (RKHS), equipped with orthonormal basis functions. Depending on the choice of the basis functions, the resulting closure model from this nonparametric modeling formulation is in the form of parametric model. This suggests that the success of various parametric modeling approaches that were proposed in various domains of applications can be understood through the RKHS representations. When the missing dynamical terms evolve faster than the relevant observable of interest, the proposed approach is consistent with the effective dynamics derived from the classical averaging theory. In the linear Gaussian case without the time-scale gap, we will show that the proposed non-Markovian model with a very long memory yields an accurate estimation of the nontrivial autocovariance function for the relevant variable of the full dynamics. The supporting numerical results on instructive nonlinear dynamics show that the proposed approach is able to replicate high-dimensional missing dynamical terms on problems with and without the separation of temporal scales.
Discovery of Three Pulsars from a Galactic Center Pulsar Population

We report the discovery of three pulsars whose large dispersion measures (DMs) and angular proximity to Sgr A* indicate the existence of a Galactic center population of neutron stars. The relatively long periods (0.98-1.48 s) most likely reflect strong selection against short-period pulsars from radio-wave scattering at the observation frequency of 2 GHz used in our survey with the Green Bank Telescope. One object (PSR J1746–2850I) has a characteristic spindown age of only 13 kyr along with a high surface magnetic field ~4 × 1013 G. It and a second object found in the same telescope pointing, PSR J1746–2850II (which has the highest known DM among pulsars), may have originated from recent star formation in the Arches or Quintuplet clusters given their angular locations. Along with a third object, PSR J1745–2910, and two similar high-dispersion, long-period pulsars reported by Johnston et al., the five objects found so far are 10-15 arcmin from Sgr A*, consistent with there being a large pulsar population in the Galactic center, most of whose members are undetectable in relatively low-frequency surveys because of pulse broadening from the same scattering volume that angularly broadens Sgr A* and OH/IR masers.
How accurately can we age-date solar-type dwarfs using activity/rotation diagnostics?

It is well established that activity and rotation diminishes during the life of sun-like main sequence (~F7-K2V) stars. Indeed, the evolution of rotation and activity among these stars appears to be so deterministic that their rotation/activity diagnostics are often utilized as estimators of stellar age. A primary motivation for the recent interest in improving the ages of solar-type field dwarfs is in understanding the evolution of debris disks and planetary systems. Reliable isochronal age-dating for field, solar-type main sequence stars is very difficult given the observational uncertainties and multi-Gyr timescales for significant structural evolution. Observationally, significant databases of activity/rotation diagnostics exist for field solar-type field dwarfs (mainly from chromospheric and X-ray activity surveys). But how well can we empirically age-date solar-type field stars using activity/rotation diagnostics? Here I summarize some recent results for F7-K2 dwarfs from an analysis by Mamajek & Hillenbrand (2008), including an improved “gyrochronology” [Period(color, age)] calibration, improved chromospheric (R′HK) and X-ray (log(LX/Lbol)) activity vs. rotation (via Rossby number) relations, and a chromospheric vs. X-ray activity relation that spans four orders of magnitude in log(LX/Lbol). Combining these relations, one can produce predicted chromospheric and X-ray activity isochrones as a function of color and age for solar type dwarfs.
The Number of Surfaces of Fixed Genus in an Alternating Link Complement

Let $L$ be a prime alternating link with $n$ crossings. We show that for each fixed $g$, the number of genus $g$ incompressible surfaces in the complement of $L$ is bounded by a polynomial in $n$. Previous bounds were exponential in $n$.
A Proper Motion Survey Using the First Sky Pass of NEOWISE-Reactivation Data

The Wide-field Infrared Survey Explorer (WISE) was reactivated in December of 2013 (NEOWISE) to search for potentially hazardous near-Earth objects. We have conducted a survey using the first sky pass of NEOWISE data and the AllWISE catalog to identify nearby stars and brown dwarfs with large proper motions ($\mu_{\rm total}$ $\gtrsim$ 250 mas yr$^{-1}$). A total of 20,548 high proper motion objects were identified, 1,006 of which are new discoveries. This survey has uncovered a significantly larger sample of fainter objects (W2 $\gtrsim$13 mag) than the previous WISE motion surveys of Luhman (2014a) and Kirkpatrick et al. (2014). Many of these objects are predicted to be new L and T dwarfs based on near- and mid-infrared colors. Using estimated spectral types along with distance estimates, we have identified several objects likely belonging to the nearby Solar neighborhood (d $<$ 25 pc). We have followed up 19 of these new discoveries with near-infrared or optical spectroscopy, focusing on potentially nearby objects, objects with the latest predicted spectral types, and potential late-type subdwarfs. This subset includes 6 M dwarfs, 5 of which are likely subdwarfs, as well as 8 L dwarfs and 5 T dwarfs, many of which have blue near-infrared colors. As an additional supplement, we provide 2MASS and AllWISE positions and photometry for every object found in our search, as well as 2MASS/AllWISE calculated proper motions.
Self-duality and the Supersymmetric KdV Hierarchy

We show how the supersymmetric KdV equation can be obtained from the self-duality condition on Yang-Mills fields in four dimensions associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of SUSY KdV equations as well as the s-KdV equations from such a condition. We formulate the SUSY KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self-duality condition in four dimensions can also lead to these equations.
Abelian and Non-Abelian Statistics in the Coherent State Representation

Fractional quantum-Hall states can host anyons -- elementary excitations that do not obey the quantum-mechanical rules followed by either fermions or bosons. That makes them fundamentally fascinating, but also technically challenging to tackle. Showing a new way to deal with anyons theoretically, two researchers from Washington University succeed in working out the rules so far unknown for the anyons in a notoriously difficult state.
Data Assimilation and Online Optimization With Performance Guarantees

This article considers a class of real-time stochastic optimization problems dependent on an unknown probability distribution. In the considered scenario, data are streaming frequently while trying to reach a decision. Thus, we aim to devise a procedure that incorporates samples (data) of the distribution sequentially and adjusts decisions accordingly. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm ( OnDA Algorithm) for this purpose. This algorithm guarantees out-of-sample performance of decisions with high probability, and gradually improves the quality of the decisions by incorporating the streaming data. We show that the OnDA Algorithm converges under a sufficiently slow data streaming rate, and provide a criteria for its termination after certain number of data have been collected. Simulations illustrate the results.
Cross-Layer Design of Automotive Systems

Editor’s notes: This article presents multiple cross-layer methods to ensure security as well as functional correctness of automotive systems. These approaches tie together multiple abstraction layers, going all the way from vehicular networks responsible for vehicle-to-vehicle and vehicle-to-infrastructure communication, to in-vehicle hardware/software architectures. — Samarjit Chakraborty, University of North Carolina at Chapel Hill
Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)

Explicit solutions of the cubic Fermat equation are constructed in ring class fields Ωf, with conductor f prime to 3, of any imaginary quadratic field K whose discriminant satisfies dK ≡ 1 (mod 3), in terms of the Dedekind η-function. As K and f vary, the set of coordinates of all solutions is shown to be the exact set of periodic points of a single algebraic function and its inverse defined on natural subsets of the maximal unramified, algebraic extension K3 of the 3-adic field ℚ3. This is used to give a dynamical proof of a class number relation of Deuring. These solutions are then used to give an unconditional proof of part of Aigner’s conjecture: the cubic Fermat equation has a nontrivial solution in K = ℚ(−d) if dK ≡ 1 (mod 3) and the class number h(K) is not divisible by 3. If 3 | h(K), congruence conditions for the trace of specific elements of Ωf are exhibited which imply the existence of a point of infinite order in Fer3(K).
Linear Hypothesis Testing in Dense High-Dimensional Linear Models

AbstractWe propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis. Providing asymptotically valid methods for testing general linear functions of the regression parameters in high-dimensions is extremely challenging - especially without making restrictive or unverifiable assumptions on the number of non-zero elements. We propose to test the moment conditions related to the newly designed restructured regression, where the inputs are transformed and augmented features. These new features incorporate the structure of the null hypothesis directly. The test statistics are constructed in such a way that lack of sparsity in the original model parameter does not present a problem for the theoretical justification of our procedures. We establish asymptotically exact control on Type I error without imposing any sparsity assumptions on mode...
Semiclassical transition probabilities for interacting oscillators

Semiclassical transition probabilities characterize transfer of energy between “hard” and “soft” modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities. Solutions are found numerically for a system of two interacting quartic oscillators. In the double-well case, we find numerical evidence that certain regular minkowskian trajectories have approximate stopping points or, equivalently, are approximately periodic. This property leads to estimates of tunneling excitation probabilities in that system and suggests that similar estimates may be possible in other systems with tunneling.
IN SITU MEASUREMENTS OF THE SIZE AND DENSITY OF TITAN AEROSOL ANALOGS

The organic haze produced from complex CH4/N2 chemistry in the atmosphere of Titan plays an important role in processes that occur in the atmosphere and on its surface. The haze particles act as condensation nuclei and are therefore involved in Titan's methane hydrological cycle. They also may behave like sediment on Titan's surface and participate in both fluvial and aeolian processes. Models that seek to understand these processes require information about the physical properties of the particles including their size and density. Although measurements obtained by Cassini-Huygens have placed constraints on the size of the haze particles, their densities remain unknown. We have conducted a series of Titan atmosphere simulation experiments and measured the size, number density, and particle density of Titan aerosol analogs, or tholins, for CH4 concentrations from 0.01% to 10% using two different energy sources, spark discharge and UV. We find that the densities currently in use by many Titan models are higher than the measured densities of our tholins.
Algorithmic detection and description of hyperbolic structures on closed 3{manifolds with solvable word problem

We outline a rigorous algorithm, rst suggested by Casson, for determining whether a closed orientable 3-manifold M is hyperbolic, and to compute the hyperbolic structure, if one exists. The algorithm requires that a procedure has been given to solve the word problem in 1M .
A queueing model with independent arrivals, and its fluid and diffusion limits

We study a queueing model with ordered arrivals, which can be called the $$\varDelta _{(i)}/GI/1$$Δ(i)/GI/1 queue. Here, customers from a fixed, finite, population independently sample a time to arrive from some given distribution $$F$$F, and enter the queue in order of the sampled arrival times. Thus, the arrival times are order statistics, and the inter-arrival times are differences of consecutive order statistics. They are served by a single server with independent and identically distributed service times, with general service distribution $$G$$G. The discrete event model is analytically intractable. Thus, we develop fluid and diffusion limits for the performance metrics of the queue. The fluid limit of the queue length is observed to be a reflection of a `fluid netput' process, while the diffusion limit is observed to be a function of a Brownian motion and a Brownian bridge process or `diffusion netput' process. The diffusion limit can be seen as being reflected through the directional derivative of the Skorokhod regulator of the fluid netput process in the direction of the diffusion netput process. We also observe what may be interpreted as a sample path Little's Law. Sample path analysis reveals various operating regimes where the diffusion limit switches between a free diffusion, a reflected diffusion process, and the zero process, with possible discontinuities during regime switches. The weak convergence results are established in the $$M_1$$M1 topology.
Inverse transport problems in quantitative PAT for molecular imaging

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography (PAT) with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in [Ren-Zhao, SIAM J. Imag. Sci., 2013] on the same problem but in the diffusive regime.
Asymptotic Distribution of Quasi-Normal Modes for Kerr–de Sitter Black Holes

We establish a Bohr–Sommerfeld type condition for quasi-normal modes of a slowly rotating Kerr–de Sitter black hole, providing their full asymptotic description in any strip of fixed width. In particular, we observe a Zeeman-like splitting of the high multiplicity modes at a = 0 (Schwarzschild–de Sitter), once spherical symmetry is broken. The numerical results presented in Appendix B show that the asymptotics are in fact accurate at very low energies and agree with the numerical results established by other methods in the physics literature. We also prove that solutions of the wave equation can be asymptotically expanded in terms of quasi-normal modes; this confirms the validity of the interpretation of their real parts as frequencies of oscillations, and imaginary parts as decay rates of gravitational waves.
COULOMB BLOCKADE OSCILLATIONS OF CONDUCTANCE AT FINITE ENERGY LEVEL SPACING IN A QUANTUM DOT

We find an analytical expression for the conductance of a single electron transistor in the regime when temperature, level spacing and charging energy of a grain are all of the same order. We consider the model of equidistant energy levels in a grain in the sequential tunneling approximation. In the case of spinless electrons, our theory describes transport through a dot in the quantum Hall regime. In the case of spin-½ electrons, we analyze the line shape of a peak, shift in the position of the peak's maximum as a function of temperature and the values of the conductance in the odd and even valleys.
Monopoles and vortices in the SU(2) positive plaquette model

Abstract We study the heavy quark potential in the SU(2) positive plaquette model using monopoles in the maximum abelian gauge, and vortices. Monopoles give a quantitative description of the string tension. Vortices approximately reproduce the entire heavy quark potential.
Disorder chaos in the Sherrington–Kirkpatrick model with external field

We consider a spin system obtained by coupling two distinct Sherrington–Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the overlap under the corresponding Gibbs measure is essentially concentrated at a single value. In the absence of external field, this statement was first confirmed by Chatterjee [Disorder chaos and multiple valleys in spin glasses (2009) Preprint]. In the present paper, using Guerra’s replica symmetry breaking bound, we prove that the SK model is also chaotic in the presence of the external field and the position of the overlap is determined by an equation related to Guerra’s bound and the Parisi measure.
3D integrated superconducting qubits

As the field of quantum computing advances from the few-qubit stage to larger-scale processors, qubit addressability and extensibility will necessitate the use of 3D integration and packaging. While 3D integration is well-developed for commercial electronics, relatively little work has been performed to determine its compatibility with high-coherence solid-state qubits. Of particular concern, qubit coherence times can be suppressed by the requisite processing steps and close proximity of another chip. In this work, we use a flip-chip process to bond a chip with superconducting flux qubits to another chip containing structures for qubit readout and control. We demonstrate that high qubit coherence (T 1, T 2,echo > 20 μs) is maintained in a flip-chip geometry in the presence of galvanic, capacitive, and inductive coupling between the chips. Superconducting qubits are a leading technology for realizing a quantum computer. To date, experiments have demonstrated control of up to ten qubits using interconnects that laterally address the qubits from the edge of a chip. Extending to larger numbers, however, will require utilizing the third dimension to avoid interconnect crowding and enable control and readout of all qubits in a two-dimensional array. Danna Rosenberg and a team led by William D. Oliver at MIT Lincoln Laboratory and MIT campus have developed a 3D design for efficiently addressing large numbers of qubits, comprising a stack of three bonded chips, each of which performs a different function. The team performed a proof-of-principle experiment using two bonded chips, demonstrating off-chip control and read out of a qubit without significantly impacting the quality of the qubit performance. This demonstration is an important step towards the 3D integration required to build larger-scale devices for quantum information processing.
Development of readout interconnections for the Si-W calorimeter of SiD

The SiD collaboration is developing a Si-W sampling electromagnetic calorimeter, with anticipated application for the International Linear Collider. Assembling the modules for such a detector will involve special bonding technologies for the interconnections, especially for attaching a silicon detector wafer to a flex cable readout bus. We review the interconnect technologies involved, including oxidation removal processes, pad surface preparation, solder ball selection and placement, and bond quality assurance. Our results show that solder ball bonding is a promising technique for the Si-W ECAL, and unresolved issues are being addressed.
Signature of Collision of Magnetic Flux Tubes in the Quiet Solar Photosphere

Collision of the magnetic flux tubes in the Quiet Sun was proposed as one of the possible sources for the heating of the solar atmosphere (Furusawa and Sakai, 2000). The solar photosphere was observed using the New Solar Telescope ad Big Bear Solar Observatory. In TiO spectral line at 705.68 nm we approached resolution of 0.1 00 . The horizontal plasma wave was observed spreading from the larger bright point. Shorty after this wave an increase in the oscillatory power appeared at the same location as the observed bright point. This behavior matches some of the results from the simulation of the collision of the two flux tubes with a weak current.
1/N EXPANSION AND PARTICLE SPECTRUM IN INDUCED QCD

We study the 1/N expansion in the recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation. In the first approximation the fluctuations of the density of eigenvalues of the scalar field are Gaussian, so that the scalar glueball spectrum is defined from the corresponding linear wave equation.
Schur-Agler class rational inner functions on the tridisk

We prove two results with regard to rational inner functions in the Schur-Agler class of the tridisk. Every rational inner function of degree (n,1,1) is in the Schur-Agler class, and every rational inner function of degree (n,m,1) is in the Schur-Agler class after multiplication by a monomial of sufficiently high degree.
Cluster and Feature Modeling from Combinatorial Stochastic Processes

One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, or partitioning, where each data point is modeled as being associated with one and only one of some collection of groups called clusters or partition blocks. Underlying these Bayesian nonparametric models are a set of interrelated stochastic processes, most notably the Dirichlet process and the Chinese restaurant process. In this paper we provide a formal development of an analogous problem, called feature modeling, for associating data points with arbitrary nonnegative integer numbers of groups, now called features or topics. We review the existing combinatorial stochastic process representations for the clustering problem and develop analogous representations for the feature modeling problem. These representations include the beta process and the Indian buffet process as well as new representations that provide insight into the connections between these processes. We thereby bring the same level of completeness to the treatment of Bayesian nonparametric feature modeling that has previously been achieved for Bayesian nonparametric clustering.
Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes

We prove that the cohomology ring of a finite-dimensional restricted Lie superalgebra over a field of characteristic $p > 2$ is a finitely-generated algebra. Our proof makes essential use of the explicit projective resolution of the trivial module constructed by J. Peter May for any graded restricted Lie algebra. We then prove that the cohomological finite generation problem for finite supergroup schemes over fields of odd characteristic reduces to the existence of certain conjectured universal extension classes for the general linear supergroup $GL(m|n)$ that are similar to the universal extension classes for $GL_n$ exhibited by Friedlander and Suslin.
Copper Waveguide Cavities With Reduced Surface Loss for Coupling to Superconducting Qubits

Significant improvements in superconducting qubit coherence times have been achieved recently with 3-D microwave waveguide cavities coupled to transmon qubits. While many of the measurements in this direction have utilized superconducting aluminum cavities, other recent work has involved qubits coupled to copper cavities with coherence times approaching 0.1 ms. The copper provides a good path for thermalizing the cavity walls and qubit chip, although the substantial cavity loss makes conventional dispersive qubit measurements challenging. We are exploring various approaches for improving the quality factor of 3-D copper cavities, including electropolishing and coating with superconducting layers of tin. We have characterized these cavities on multiple cooldowns and found tin plating to be robust. In addition, we have performed coherence measurements on transmon qubits in these cavities and observed promising performance.
Multi-Stage Pre-training for Low-Resource Domain Adaptation.

Transfer learning techniques are particularly useful for NLP tasks where a sizable amount of high-quality annotated data is difficult to obtain. Current approaches directly adapt a pretrained language model (LM) on in-domain text before fine-tuning to downstream tasks. We show that extending the vocabulary of the LM with domain-specific terms leads to further gains. To a bigger effect, we utilize structure in the unlabeled data to create auxiliary synthetic tasks, which helps the LM transfer to downstream tasks. We apply these approaches incrementally on a pretrained Roberta-large LM and show considerable performance gain on three tasks in the IT domain: Extractive Reading Comprehension, Document Ranking and Duplicate Question Detection.
Infinitely many hyperbolic Coxeter groups through dimension 19

We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space Hn for every n≤19 (resp. n≤6). When n=7 or 8, they may be taken to be nonarithmetic. Furthermore, for 2≤n≤19, with the possible exceptions n=16 and 17, the number of essentially distinct Coxeter groups in Hn with noncompact fundamental domain of volume≤V grows at least exponentially with respect to V. The same result holds for cocompact groups for n≤6. The technique is a doubling trick and variations on it; getting the most out of the method requires some work with the Leech lattice.