cssi/SciSciGPT-SciSciNet huggingface dataset:
Higher-derivative operators and effective field theory for general scalar-tensor theories

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.
Semiconductor probes of light dark matter

Abstract Dark matter with mass below about a GeV is essentially unobservable in conventional direct detection experiments. However, newly proposed technology will allow the detection of single electron events in semiconductor materials with significantly lowered thresholds. This would allow detection of dark matter as light as an MeV in mass. Compared to other detection technologies, semiconductors allow enhanced sensitivity because of their low ionization energy around an eV. Such detectors would be particularly sensitive to dark matter with electric and magnetic dipole moments, with a reach many orders of magnitude beyond current bounds. Observable dipole moment interactions can be generated by new particles with masses as great as ∼10 3 TeV, providing a window to scales beyond the reach of current colliders.
The Mass Function of Low-Mass Halo Stars: Limits on Baryonic Halo Dark Matter

We derive mass functions (MF) for halo red dwarfs (the faintest hydrogen burning stars), and then we extrapolate to place limits on the total mass of halo brown dwarfs (stars not quite massive enough to burn hydrogen). The mass functions are obtained from the luminosity function of a sample of 114 local halo stars in the US Naval Observatory parallax survey (Dahn et al.). We use stellar models of Alexander et al., and we make varying assumptions about metallicity, as well as possible unresolved binaries in the sample. We find that the MF for halo red dwarfs cannot rise more quickly than 1 m-2 as one approaches the hydrogen burning limit. Using recent results from star formation theory, we extrapolate the MF into the brown dwarf regime. We see that likely extrapolations imply that the total mass of brown dwarfs in the halo is less than ~3% of the local mass density of the halo (~0.3% for the more realistic models we consider). Our limits apply to brown dwarfs in the halo that come from the same stellar population as the red dwarfs.
Eleven-dimensional Lorentz symmetry from SUSY quantum mechanics

The supermembrane in light-cone gauge gives rise to a supersymmetric quantum mechanics system with SU(N) gauge symmetry when the group of area preserving diffeomorphisms is suitably regulated. de Wit, Marquard and Nicolai showed how eleven-dimensional Lorentz generators can be constructed from these degrees of freedom at the classical level. In this paper, these considerations are extended to the quantum level and it is shown the algebra closes to leading nontrivial order at large N. A proposal is made for extending these results to Matrix theory by realizing longitudinal boosts as large N renormalization group transformations.
Planar diagrams for local invariants of graphs in surfaces

In order to apply quantum topology methods to nonplanar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. These virtual graphs are...
Approximately counting embeddings into random graphs

Let H be a graph, and let CH(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating CH(G). Previous results cover only a few specific instances of this general problem, for example the case when H has degree at most one (the monomer-dimer problem). In this paper we present the first general subcase of the subgraph isomorphism counting problem, which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labelling of the vertices such that every edge is between vertices with different labels, and for every vertex all neighbours with a higher label have identical labels. The labelling implicitly generates a sequence of bipartite graphs, which permits us to break the problem of counting embeddings of large subgraphs into that of counting embeddings of small subgraphs. Using this method, we present a simple randomized algorithm for the counting problem. For all decomposable graphs H and all graphs G, the algorithm is an unbiased estimator. Furthermore, for all graphs H having a decomposition where each of the bipartite graphs generated is small and almost all graphs G, the algorithm is a fully polynomial randomized approximation scheme.We show that the graph classes of H for which we obtain a fully polynomial randomized approximation scheme for almost all G includes graphs of degree at most two, bounded-degree forests, bounded-width grid graphs, subdivision of bounded-degree graphs, and major subclasses of outerplanar graphs, series-parallel graphs and planar graphs of large girth, whereas unbounded-width grid graphs are excluded. Moreover, our general technique can easily be applied to proving many more similar results.
Self-assembly of Artificial Microtubules.

Understanding the complex self-assembly of biomacromolecules is a major outstanding question. Microtubules are one example of a biopolymer that possesses characteristics quite distinct from standard synthetic polymers that are derived from its hierarchical structure. In order to understand how to design and build artificial polymers that possess features similar to those of microtubules, we have initially studied the self-assembly of model monomers into a tubule geometry. Our model monomer has a wedge shape with lateral and vertical binding sites that are designed to form tubules. We used molecular dynamics simulations to study the assembly process for a range of binding site interaction strengths. In addition to determining the optimal regime for obtaining tubules, we have calculated a diagram of the structures that form over a wide range of interaction strengths. Unexpectedly, we find that the helical tubules form, even though the monomer geometry is designed for nonhelical tubules. We present the detailed dynamics of the tubule self-assembly process and show that the interaction strengths must be in a limited range to allow rearrangement within clusters. We extended previous theoretical methods to treat our system and to calculate the boundaries between different structures in the diagram.
Connectivity in secure wireless sensor networks under transmission constraints

In wireless sensor networks (WSNs), the Eschenauer-Gligor (EG) key pre-distribution scheme is a widely recognized way to secure communications. Although connectivity properties of secure WSNs with the EG scheme have been extensively investigated, few results address physical transmission constraints. These constraints reflect real-world implementations of WSNs in which two sensors have to be within a certain distance from each other to communicate. In this paper, we present zero-one laws for connectivity in WSNs employing the EG scheme under transmission constraints. These laws help specify the critical transmission ranges for connectivity. Our analytical findings are confirmed via numerical experiments. In addition to secure WSNs, our theoretical results are also applied to frequency hopping in wireless networks.
Light front quantization

More than twenty years after quantum chromodynamics (QCD) was introduced as a microscopic theory of strong interactions, very little is known about its solutions. At least in principle, it should be possible to describe the interaction of nucleons with external probes using quark and gluon degrees of freedom on the basis of QCD. So far, however, the extreme complexity of this theory has slowed any progress in this direction considerably. To investigate QCD further this paper investigates the following topics: Canonical Quantization; The Light-Front Vacuum; Perturbative Renormalization; and Nonperturbative Calculations.
Critical Phenomena in Exponential Random Graphs

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating function for the limiting expectations of all thermodynamic observables. We derive the full phase diagram for a large family of 3-parameter exponential random graph models with attraction and show that they all consist of a first order surface phase transition bordered by a second order critical curve.
Before the Bang

While inflation has been an extremely successful cosmological paradigm, almost certainly something have had to have happened before it began. Can the pre-inflationary phase be of any theoretical or phenomenological significance? Could Quantum Gravity have played any interesting role in this story? These are some of the questions we want to explore in this essay written for the Gravity Research Foundation 2013 "Awards for Essays on Gravitation" competition.
From Observables and States to Hilbert Space and Back: A 2-Categorical Adjunction

Given a representation of a $$C^*$$ -algebra, thought of as an abstract collection of physical observables, together with a unit vector, one obtains a state on the algebra via restriction. We show that the Gelfand–Naimark–Segal (GNS) construction furnishes a left adjoint of this restriction. To properly formulate this adjoint, it must be viewed as a weak natural transformation, a 1-morphism in a suitable 2-category, rather than as a functor between categories. Weak naturality encodes the functoriality and the universal property of adjunctions encodes the characterizing features of the GNS construction. Mathematical definitions and results are accompanied by physical interpretations.
Bayesian approach for linear optics correction

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as ``likelihood functions'' and ``prior probability distributions.'' Under some assumptions, the least square algorithm and then the Jacobian matrix approach can be rederived. The coherence of the correction algorithm is ensured through specifying a self-consistent regularization coefficient to prevent overfitting. Optimal weights for different correction objectives are obtained based on their measurement noise level. A new technique has been developed to resolve degenerated quadrupole errors when observed at a few select beam position monitors (BPMs). A necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near orthogonal.
Hidden symmetries and commensurability of 2-bridge link complements

In this paper, we show that any non-arithmetic hyperbolic $2$-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic $2$-bridge link complement cannot irregularly cover a hyperbolic $3$-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of $3$-manifolds with non-trivial JSJ-decomposition and rank two fundamental groups. We also show that the only commensurable hyperbolic $2$-bridge link complements are the figure-eight knot complement and the $6_{2}^{2}$ link complement. Our work requires a careful analysis of the tilings of $\mathbb{R}^{2}$ that come from lifting the canonical triangulations of the cusps of hyperbolic $2$-bridge link complements.
Interplay between magnetism and superconductivity in iron-chalcogenide superconductors: crystal growth and characterizations

In this review, we present a summary of results on single crystal growth of two types of iron-chalcogenide superconductors, Fe1+yTe1?xSex (11), and AxFe2?ySe2 (A = K, Rb, Cs, Tl, Tl/K, Tl/Rb), using Bridgman, zone-melting, vapor self-transport and flux techniques. The superconducting and magnetic properties (the latter gained mainly from neutron scattering measurements) of these materials are reviewed to demonstrate the connection between magnetism and superconductivity. It will be shown that for the 11 system, while static magnetic order around the reciprocal lattice position (0.5,?0) competes with superconductivity, spin excitations centered around (0.5,?0.5) are closely coupled to the materials' superconductivity; this is made evident by the strong correlation between the spectral weight around (0.5,?0.5) and the superconducting volume fraction. The observation of a spin resonance below the superconducting temperature, Tc, and the magnetic-field dependence of the resonance emphasize the close interplay between spin excitations and superconductivity, similar to cuprate superconductors. In AxFe2?ySe2, superconductivity with Tc ~ 30?K borders an antiferromagnetic insulating phase; this is closer to the behavior observed in the cuprates but differs from that in other iron-based superconductors.
Mass accretion rates and histories of dark matter haloes

We use the extensive catalogue of dark matter haloes from the Millennium Simulation to investigate the statistics of the mass accretion histories (MAHs) and accretion rates of ∼500 000 haloes from redshift z = 0 to 6. We find only about 25 per cent of the haloes to have MAHs that are well described by a 1-parameter exponential form. For the rest of the haloes, between 20 per cent (Milky Way mass) and 50 per cent (cluster mass) experience late-time growth that is steeper than an exponential, whereas the remaining haloes show plateaued late-time growth that is shallower than an exponential. The haloes with slower late-time growth tend to reside in denser environments, suggesting that either tidal stripping or the 'hotter' dynamics are suppressing the accretion rate of dark matter on to these haloes. These deviations from exponential growth are well fit by introducing a second parameter: M(z) ∝ (1 + z) β e ―γz . The full distribution of β and γ as a function of halo mass is provided. From the analytic form of M(z), we obtain a simple formula for the mean accretion rate of dark matter, M, as a function of redshift and mass. At z = 0, this rate is 42 M ⊙ yr ―1 for 10 12 M ⊙ haloes, which corresponds to a mean baryon accretion rate of M b = 7 M ⊙ yr ―1 . This mean rate increases approximately as (1 + z) 1.5 at low z and (1 + z) 2.5 at high z, reaching M b = 27, 69 and 140 M ⊙ yr ―1 at z = 1, 2 and 3. The specific rate depends on halo mass weakly: M/M ∝ M 0.127 . Results for the broad distributions about the mean rates are also discussed.
Simulations of Ice Chemistry in Cometary Nuclei

The first computational model of solid-phase chemistry in cometary nuclear ices is presented. An astrochemical kinetics model, MAGICKAL, is adapted to trace the chemical evolution in multiple layers of cometary ice, over a representative period of 5 Gyr. Physical conditions are chosen appropriate for "cold storage" of the cometary nucleus in the outer Solar System, prior to any active phase. The chemistry is simulated at a selection of static temperatures in the range 5 - 60 K, while the ice is exposed to the interstellar radiation field, inducing a photo-chemistry in the outer ice layers that produces significant formation of complex organic molecules. A treatment for the chemistry resulting from cosmic-ray bombardment of the ices is also introduced into the model, along with a new formulation for low-temperature photo-chemistry. Production of simple and complex molecules to depth on the order of 10 m or more is achieved, with local fractional abundances comparable to observed values in many cases. The production of substantial amounts of O2 (and H2O2) is found, suggesting that long-term processing by high-energy cosmic rays of cometary ices in situ, over a period on the order of 1 Gyr, may be sufficient to explain the large observed abundances of O2, if the overall loss of material from the comet is limited to a depth on the order of 10 m. Entry into the inner solar system could produce a further enhancement in the molecular content of the nuclear ices that may be quantifiable using this modeling approach.
A Unified Gravity-Electroweak Model Based on a Generalized Yang-Mills Framework

Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg–Salam theory. The Yang–Mills framework is generalized to include spacetime translational group T(4), whose generators Tμ ( = ∂/∂xμ) do not have constant matrix representations. By gauging T(4) × SU(2) × U(1) in flat spacetime, we have a new tensor field ϕμν which universally couples to all particles and anti-particles with the same constant g, which has the dimension of length. In this unified model, the T(4) gauge symmetry dictates that all wave equations of fermions, massive bosons and the photon in flat spacetime reduce to a Hamilton–Jacobi equation with the same "effective Riemann metric tensor" in the geometric-optics limit. Consequently, the results are consistent with experiments. We demonstrated that the T(4) gravitational gauge field can be quantized in inertial frames.
A DATA-DRIVEN ANALYTIC MODEL FOR PROTON ACCELERATION BY LARGE-SCALE SOLAR CORONAL SHOCKS

We have recently studied the development of an eruptive filament-driven, large-scale off-limb coronal bright front (OCBF) in the low solar corona, using remote observations from the Solar Dynamics Observatory's Advanced Imaging Assembly EUV telescopes. In that study, we obtained high-temporal resolution estimates of the OCBF parameters regulating the efficiency of charged particle acceleration within the theoretical framework of diffusive shock acceleration (DSA). These parameters include the time-dependent front size, speed, and strength, as well as the upstream coronal magnetic field orientations with respect to the front's surface normal direction. Here we present an analytical particle acceleration model, specifically developed to incorporate the coronal shock/compressive front properties described above, derived from remote observations. We verify the model's performance through a grid of idealized case runs using input parameters typical for large-scale coronal shocks, and demonstrate that the results approach the expected DSA steady-state behavior. We then apply the model to the event of 2011 May 11 using the OCBF time-dependent parameters derived by Kozarev et al. We find that the compressive front likely produced energetic particles as low as 1.3 solar radii in the corona. Comparing the modeled and observed fluences near Earth, we also find that the bulk of the acceleration during this event must have occurred above 1.5 solar radii. With this study we have taken a first step in using direct observations of shocks and compressions in the innermost corona to predict the onsets and intensities of solar energetic particle events.
Regularity for parabolic integro-differential equations with very irregular kernels

We prove Holder regularity for a general class of parabolic integro-dierenti al equa- tions, which (strictly) includes many previous results. We present a proof which avoids the use of a convex envelop as well as give a new covering argument which is better suited to the frac- tional order setting. Our main result involves a class of kernels which may contain a singular measure, may vanish at some points, and are not required to be symmetric. This new generality of integro-dierenti al operators opens the door to further applications of the theory, including some regularization estimates for the Boltzmann equation.
Interstellar Silicon Depletion and the Ultraviolet Extinction

Spinning small silicate grains were recently invoked to account for the Galactic foreground anomalous microwave emission. These grains, if present, will absorb starlight in the far ultraviolet (UV). There is also renewed interest in attributing the enigmatic 2175 Angstrom interstellar extinction bump to small silicates. To probe the role of silicon in the UV extinction, we explore the relations between the amount of silicon required to be locked up in silicates [Si/H]_{dust} and the 2175 Angstrom bump or the far-UV extinction rise, based on an analysis of the extinction curves along 46 Galactic sightlines for which the gas-phase silicon abundance [Si/H]_{gas} is known. We derive [Si/H]_{dust} either from {[Si/H]_{ISM} - [Si/H]_{gas}} or from the Kramers-Kronig relation which relates the wavelength-integrated extinction to the total dust volume, where [Si/H]_{ISM} is the interstellar silicon reference abundance and taken to be that of proto-Sun or B stars. We also derive [Si/H]_{dust} from fitting the observed extinction curves with a mixture of amorphous silicates and graphitic grains. We find that in all three cases [Si/H]_{dust} shows no correlation with the 2175 Angstrom bump, while the carbon depletion [C/H]_{dust} tends to correlate with the 2175 Angstrom bump. This supports carbon grains instead of silicates as the possible carrier of the 2175 Angstrom bump. We also find that neither [Si/H]_{dust} nor [C/H]_{dust} alone correlates with the far-UV extinction, suggesting that the far-UV extinction is a combined effect of small carbon grains and silicates.
Level m stratifications of versal deformations of p-divisible groups

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $c,d,m$ be positive integers. Let $D$ be a $p$-divisible group of codimension $c$ and dimension $d$ over $k$. Let $\scrD$ be a versal deformation of $D$ over a smooth $k$-scheme $\scrA$ which is equidimensional of dimension $cd$. We show that there exists a reduced, locally closed subscheme $\grs_D(m)$ of $\scrA$ that has the following property: a point $y\in\scrA(k)$ belongs to $\grs_D(m)(k)$ if and only if $y^*(\scrD)[p^m]$ is isomorphic to $D[p^m]$. We prove that $\grs_D(m)$ is {\it regular and equidimensional} of {\it dimension} $cd-\dim(\pmb{\text{Aut}}(D[p^m]))$. We give a proof of {\it Traverso's formula} which for $m>>0$ computes the codimension of $\grs_D(m)$ in $\scrA$ (i.e., $\dim(\pmb{\text{Aut}}(D[p^m]))$) in terms of the Newton polygon of $D$. We also provide a criterion of when $\grs_D(m)$ satisfies the {\it purity property} (i.e., it is an affine $\scrA$-scheme). Similar results are proved for {\it quasi Shimura $p$-varieties of Hodge type} that generalize the special fibres of good integral models of Shimura varieties of Hodge type in unramified mixed characteristic $(0,p)$.
Present and future prospects for GRB standard candles

Following our previous work, we conclude that a GRB standard candle constructed from the Ghirlanda et al. power-law relation between the geometry-corrected energy (E_gamma) and the peak of the rest-frame prompt burst spectrum (E_p) is not yet cosmographically useful, despite holding some potential advantages over SNe Ia. This is due largely to the small sample of \~20 GRBs with the required measured redshifts, jet-breaks, and peak energies, and to the strong sensitivity of the goodness-of-fit of the power-law to input assumptions. The most important such finding concerns the sensitivity to the generally unknown density (and density profile), of the circumburst medium. Although the E_p-E_gamma relation is a highly significant correlation over many cosmologies, until the sample expands to include many low-z events, it will be most sensitive to Omega_M but essentially insensitive to Omega_Lambda and w, with some hope of constraining dw/dt with high-z GRB data alone. The relation clearly represents a significant improvement in the search for an empirical GRB standard candle, but is further hindered by an unknown physical basis for the relation, the lack of a low-z training set to calibrate the relation in a cosmology-independent way, and several major potential systematic uncertainties and selection effects. Until these concerns are addressed, a larger sample is acquired, and attempts are made to marginalize or perform Monte Carlo simulations over the unknown density distribution, we urge caution concerning claims of the utility of GRBs for cosmography and especially the attempts to combine GRBs with SNe Ia.
Learning to Plan and Realize Separately for Open-Ended Dialogue Systems

Achieving true human-like ability to conduct a conversation remains an elusive goal for open-ended dialogue systems. We posit this is because extant approaches towards natural language generation (NLG) are typically construed as end-to-end architectures that do not adequately model human generation processes. To investigate, we decouple generation into two separate phases: planning and realization. In the planning phase, we train two planners to generate plans for response utterances. The realization phase uses response plans to produce an appropriate response. Through rigorous evaluations, both automated and human, we demonstrate that decoupling the process into planning and realization performs better than an end-to-end approach.
The Nature of Carbon Dioxide Bearing Ices in Quiescent Molecular Clouds

The properties of the ices that form in dense molecular clouds represent an important set of initial conditions in the evolution of interstellar and preplanetary matter in regions of active star formation. Of the various spectral features available for study, the bending mode of solid CO{sub 2} near 15 {mu}m has proven to be a particularly sensitive probe of physical conditions, especially temperature. We present new observations of this absorption feature in the spectrum of Q21-1, a background field star located behind a dark filament in the Cocoon Nebula (IC 5146). We show the profile of the feature to be consistent with a two-component (polar + nonpolar) model for the ices, based on spectra of laboratory analogs with temperatures in the range 10-20 K. The polar component accounts for {approx}85% of the CO{sub 2} in the line of sight. We compare for the first time 15 {mu}m profiles in three widely separated dark clouds (Taurus, Serpens, and IC 5146), and show that they are indistinguishable to within observational scatter. Systematic differences in the observed CO{sub 2}/H{sub 2}O ratio in the three clouds have little or no effect on the 15 {mu}m profile. The abundance of elemental oxygen in the icesmore » appears to be a unifying factor, displaying consistent behavior in the three clouds. We conclude that the ice formation process is robust and uniformly efficient, notwithstanding compositional variations arising from differences in how the O is distributed between the primary species (H{sub 2}O, CO{sub 2}, and CO) in the ices.« less
Radio Transients from Gamma-Ray Bursters

The rapid time variability of gamma-ray bursts implies the sources are very compact, and the peak luminosities are so high that some matter must be ejected at ultrarelativistic speeds. The very large Lorentz factors of the bulk flow are also indicated by the very broad and hard spectra. It is natural to expect that when the relativistic ejecta interact with the interstellar matter, a strong synchrotron radio emission is generated, as is the case with supernova remnants and radio galaxies. We estimate that the strongest gamma-ray bursts may be followed by radio transients with peak fluxes as high as 20 mJy. The time of peak radio emission depends on the distance scale; it is less than a minute if the bursts are in the galactic halo, and about a week if the bursts are at cosmological distances
Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifolds

In this note we prove two existence theorems for the Einstein constraint equations on asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with restrictions on the size of the transverse-traceless data and the non-gravitational field data, while the second assumes a near-CMC condition, with no other restrictions.
Shape invariance in phase space

Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the implications of the supersymmetric quantum mechanics and shape invariance techniques to the phase space formalism. We show that shape invariance induces a new set of relations between the Wigner functions of the system, that allows for their direct calculation, once we know one of them. The simple harmonic oscillator and the Morse potential are solved as examples.
Conditional proof of the Boltzmann-Sinai ergodic hypothesis

We consider the system of N (≥ 2) elastically colliding hard balls of masses m 1,…,m N and radius r on the flat unit torus $\mathbb{T}^{\nu}$ , ν≥2. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i.e. the full hyperbolicity and ergodicity of such systems for every selection (m 1,…,m N ;r) of the external parameters, provided that almost every singular orbit is geometrically hyperbolic (sufficient), i.e. the so called Chernov-Sinai Ansatz is true. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis.
Accelerated Distributed Nesterov Gradient Descent

This paper considers the distributed optimization problem over a network, where the objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. We develop an accelerated distributed Nesterov gradient descent method. When the objective function is convex and $L$ -smooth, we show that it achieves a $O(\frac{1}{t^{1.4-\epsilon }})$ convergence rate for all $\epsilon \in (0,1.4)$ . We also show the convergence rate can be improved to $O(\frac{1}{t^2})$ if the objective function is a composition of a linear map and a strongly convex and smooth function. When the objective function is $\mu$ -strongly convex and $L$ -smooth, we show that it achieves a linear convergence rate of $O([ 1 - C (\frac{\mu }{L})^{5/7} ]^t)$ , where $\frac{L}{\mu }$ is the condition number of the objective, and $C>0$ is some constant that does not depend on $\frac{L}{\mu }$ .
Kepler-1661 b: A Neptune-sized Kepler Transiting Circumbinary Planet around a Grazing Eclipsing Binary

We report the discovery of a Neptune-size (R_p = 3.87 +/- 0.06 R_Earth) transiting circumbinary planet, Kepler-1661 b, found in the Kepler photometry. The planet has a period of ~175 days and its orbit precesses with a period of only 35 years. The precession causes the alignment of the orbital planes to vary, and the planet is in a transiting configuration only ~7% of the time as seen from Earth. As with several other Kepler circumbinary planets, Kepler-1661 b orbits close to the stability radius, and is near the (hot) edge of habitable zone. The planet orbits a single-lined, grazing eclipsing binary, containing a 0.84 M_Sun and 0.26 M_Sun pair of stars in a mildly eccentric (e=0.11), 28.2-day orbit. The system is fairly young, with an estimated age of ~1-3 Gyrs, and exhibits significant starspot modulations. The grazing-eclipse configuration means the system is very sensitive to changes in the binary inclination, which manifests itself as a change in the eclipse depth. The starspots contaminate the eclipse photometry, but not in the usual way of inducing spurious eclipse timing variations. Rather, the starspots alter the normalization of the light curve, and hence the eclipse depths. This can lead to spurious eclipse depth variations, which are then incorrectly ascribed to binary orbital precession.
Resolutions of p–stratifolds with isolated singularities

Recently M. Kreck introduced a class of stratied spaces called p-stratifolds (Kr3). He dened and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we study a very special case of resolutions, so called optimal resolutions, for p-stratifolds with isolated singularities. We give necessary and sucient conditions for existence and analyze their classication.
Lattice gauge theory: A retrospective

Abstract I discuss some of the historical circumstances that drove us to use the lattice as a non-perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles. I wrap up with some challenges for the future.
Can the Existence of Dark Energy BE Directly Detected

Over the last decade, astronomical observations show that the acceleration of the expansion of the universe is greater than expected from our understanding of conventional general relativity, the mass density of the visible universe, the size of the visible universe and other astronomical measurements. The additional expansion has been attributed to a variety of phenomenon that have been given the general name of dark energy. Dark energy in the universe seems to comprise a majority of the energy in the visible universe amounting to about three times the total mass energy. But locally the dark energy density is very small. However it is not zero. In this paper I describe the work of others and myself on the question of whether dark energy density can be directly detected. This is a work-in-progress and I have no answer at present.
Not Judging a User by Their Cover: Understanding Harm in Multi-Modal Processing within Social Media Research

Social media has shaken the foundations of our society, unlikely as it may seem. Many of the popular tools used to moderate harmful digital content, however, have received widespread criticism from both the academic community and the public sphere for middling performance and lack of accountability. Though social media research is thought to center primarily on natural language processing, we demonstrate the need for the community to understand multimedia processing and its unique ethical considerations. Specifically, we identify statistical differences in the performance of Amazon Turk (MTurk) annotators when different modalities of information are provided and discuss the patterns of harm that arise from crowd-sourced human demographic prediction. Finally, we discuss the consequences of those biases through auditing the performance of a toxicity detector called Perspective API on the language of Twitter users across a variety of demographic categories.
A uniform area law for the entanglement of eigenstates in the disordered XY chain

We consider the isotropic or anisotropic XY spin chain in the presence of a transversal random magnetic field, with parameters given by random variables. It is shown that eigenfunction correlator localization of the corresponding effective one-particle Hamiltonian implies a uniform area law bound in expectation for the bipartite entanglement entropy of all eigenstates of the XY chain, i.e., a form of many-body localization at all energies. Here, entanglement with respect to arbitrary connected subchains of the chain can be considered. Applications where the required eigenfunction correlator bounds are known include the isotropic XY chain in random field as well as the anisotropic chain in strong or strongly disordered random field.
Image Classification Using Quantum Inference on the D-Wave 2X

We use a quantum annealing D-Wave 2X computer to obtain solutions to NP-hard sparse coding problems. To reduce the dimensionality of the sparse coding problem to fit on the quantum D-Wave 2X hardware, we passed downsampled MNIST images through a bottleneck autoencoder. To establish a benchmark for classification performance on this reduced dimensional data set, we built two deep convolutional neural networks (DCNNs). The first DCNN used an AlexNet-like architecture and the second a state-of-the-art residual network (RESNET)model, both implemented in TensorFlow. The two DCNNs yielded classification scores of 94.54 ± 0.7% and 98.8 ± 0.1%, respectively. As a control, we showed that both DCNN architectures produced near-state-of-the-art classification performance $(\sim99\%)$ on the original MNIST images. To obtain a set of optimized features for inferring sparse representations of the reduced dimensional MNIST dataset, we imprinted on a random set of 47 image patches followed by an off-line unsupervised learning algorithm using stochastic gradient descent to optimize for sparse coding. Our single-layer of sparse coding matched the stride and patch size of the first convolutional layer of the AlexNet-like DCNN and contained 47 fully-connected features, 47 being the maximum number of dictionary elements that could be embedded onto the D-Wave 2X hardware. When the sparse representations inferred by the D-Wave 2X were passed to a linear support vector machine, we obtained a classification score of 95.68%. We found that the classification performance supported by quantum inference was maximal at an optimal level of sparsity corresponding to a critical value of the sparsity/reconstruction error trade-off parameter that previous work has associated with a second order phase transition, an observation supported by a free energy analysis of D-Wave energy states. We mimicked a transfer learning protocol by feeding the D-Wave representations into a multilayer perceptron (MLP), yielding 98.48% classification performance. The classification performance supported by a single-layer of quantum inference was superior to that supported by a classical matching pursuit algorithm set to the same level of sparsity. Whereas the classification performance of both DCNNs declined as the number of training examples was reduced, the classification performance supported by quantum inference was insensitive to the number of training examples. We thus conclude that quantum inference supports classification of reduced dimensional MNIST images exceeding that of a size-matched AlexNet-like DCNN and nearly equivalent to a state-of-the-art RESNET DCNN.
Symplectic semiclassical wave packet dynamics

The paper gives a symplectic-geometric account of semiclassical Gaussian wave packet dynamics. We employ geometric techniques to 'strip away' the symplectic structure behind the time-dependent Schrodinger equation and incorporate it into semiclassical wave packet dynamics. We show that the Gaussian wave packet dynamics is a Hamiltonian system with respect to the symplectic structure, apply the theory of symplectic reduction and reconstruction to the dynamics, and discuss dynamic and geometric phases in semiclassical mechanics. A simple harmonic oscillator example is worked out to illustrate the results. We show that the reduced semiclassical harmonic oscillator dynamics is completely integrable by finding the action–angle coordinates for the system, and calculate the associated dynamic and geometric phases explicitly. We also propose an asymptotic approximation of the potential term that provides a practical semiclassical correction term to the approximation by Heller. Numerical results for a simple one-dimensional example show that the semiclassical correction term realizes a semiclassical tunneling.
Magneto-transport in MoS2: phase coherence, spin-orbit scattering, and the hall factor.

We have characterized phase coherence length, spin–orbit scattering length, and the Hall factor in n-type MoS2 2D crystals via weak localization measurements and Hall-effect measurements. Weak localization measurements reveal a phase coherence length of ∼50 nm at T = 400 mK for a few-layer MoS2 film, decreasing as T–1/2 with increased temperatures. Weak localization measurements also allow us, for the first time without optical techniques, to estimate the spin–orbit scattering length to be 430 nm, pointing to the potential of MoS2 for spintronics applications. Via Hall-effect measurements, we observe a low-temperature Hall mobility of 311 cm2/(V s) at T = 1 K, which decreases as a power law with a characteristic exponent γ = 1.5 from 10 to 60 K. At room temperature, we observe Hall mobility of 24 cm2/(V s). By determining the Hall factor for MoS2 to be 1.35 at T = 1 K and 2.4 at room temperature, we observe drift mobility of 420 and 56 cm2/(V s) at T = 1 K and room temperature, respectively.
Curriculum Learning in Deep Neural Networks for Financial Forecasting

For any financial organization, computing accurate quarterly forecasts for various products is one of the most critical operations. As the granularity at which forecasts are needed increases, traditional statistical time series models may not scale well. We apply deep neural networks in the forecasting domain by experimenting with techniques from Natural Language Processing (Encoder-Decoder LSTMs) and Computer Vision (Dilated CNNs), as well as incorporating transfer learning. A novel contribution of this paper is the application of curriculum learning to neural network models built for time series forecasting. We illustrate the performance of our models using Microsoft’s revenue data corresponding to Enterprise, and Small, Medium & Corporate products, spanning approximately 60 regions across the globe for 8 different business segments, and totaling in the order of tens of billions of USD. We compare our models’ performance to the ensemble model (of traditional statistics and machine learning) currently being used by Microsoft Finance. Using this in-production model as a baseline, our experiments yield an approximately 30% improvement overall in accuracy on test data. We find that our curriculum learning LSTM-based model performs best, which shows that one can implement our proposed methods without overfitting on medium-sized data.
Bergman Kernels of Elementary Reinhardt Domains

We study the Bergman kernel of certain domains in $\mathbb{C}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational function of the coordinates. For some other such domains, we show that the kernel is not a rational function. For a general elementary Reinhardt domain, we obtain a representation of the kernel as an infinite series.
Generalized persistence diagrams

We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category. We call this the type $${\mathcal {A}}$$ persistence diagram of a persistence module. If the category is also abelian, then we define a second type $${\mathcal {B}}$$ persistence diagram. In addition, we show that both diagrams are stable to all sufficiently small perturbations of the module. The type $${\mathcal {B}}$$ persistence diagram carries less information than the type $${\mathcal {A}}$$ persistence diagram, but it enjoys a stronger stability theorem.
Physical Origin of Transient Negative Capacitance in a Ferroelectric Capacitor

The unusual transient negative differential capacitance (NC) of a resistor--ferroelectric (FE) capacitor circuit is of keen interest for use in next-generation transistors, but a clear physical picture and theoretical framework are needed to interpret experiments. The authors show both numerically and analytically that transient NC comes from the mismatch of free charge and polarization in the capacitor during polarization switching, and a procedure to experimentally determine the viscosity coefficient in Landau theory is provided. These results should have real impact on metrology and device physics involving the NC effect.
Continental Classroom's TV course in probability and statistics

Continental classroom is a sequence of television courses broadcast by The Na tional Broadcasting Company over a nationwide network. Its first course was in physics, its second in chemistry, the third in mathematics, and the fourth in American government. So many heads and hands developed and fostered this idea of a national television course that I could not name them all here, even if I knew them^t Learning Resources Institute was in charge of arrangements for the course Contemporary Mathematics, broadcast first in 1960-61 over about 175 stations. Such a large-scale operation costs money, and contributions from foundations and corporations make the courses possible.2 The national teachers have been chosen with the cooperation of societies or or ganizations representing the discipline concerned. For example, the mathematics teachers were chosen with the help of an advisory committee3 appointed by The Conference Board of the Mathematical Sciences. Individual colleges and universities make their own enrollments, charge their own fees, give and grade the examinations,
Optimal Robustness-Consistency Trade-offs for Learning-Augmented Online Algorithms

We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when predictions are accurate and maintains worst-case guarantees. Such algorithms have been studied in a recent line of works due to Lykouris and Vassilvitskii (ICML '18) and Purohit et al (NeurIPS '18). They provide robustness-consistency trade-offs for a variety of online problems. However, they leave open the question of whether these trade-offs are tight, i.e., to what extent to such trade-offs are necessary. In this paper, we provide the first set of non-trivial lower bounds for competitive analysis using machine-learned predictions. We focus on the classic problems of ski-rental and non-clairvoyant scheduling and provide optimal trade-offs in various settings.
Supermanifolds, rigid manifolds and mirror symmetry

Abstract By providing a general correspondence between Landau-Ginzburg orbifolds and non-linear sigma models, we find that the elusive mirror of a rigid manifold is actually a supermanifold. We also discuss when sigma models with super-target spaces are conformally invariant and describe their chiral rings. Both supermanifolds with and without Kahler moduli are considered. This work leads us to conclude that mirror symmetry should be viewed as a relation among super-varieties rather than bosonic varieties.
Analytical shock solutions at large and small Prandtl number

Exact one-dimensional solutions to the equations of fluid dynamics are derived in the and limits (where is the Prandtl number). The solutions are analogous to the solution discovered by Becker and analytically capture the profile of shock fronts in ideal gases. The large- solution is very similar to Becker’s solution, differing only by a scale factor. The small- solution is qualitatively different, with an embedded isothermal shock occurring above a critical Mach number. Solutions are derived for constant viscosity and conductivity as well as for the case in which conduction is provided by a radiation field. For a completely general density- and temperature-dependent viscosity and conductivity, the system of equations in all three limits can be reduced to quadrature. The maximum error in the analytical solutions when compared to a numerical integration of the finite- equations is as and as .