cssi/SciSciGPT-SciSciNet huggingface dataset:
MODEL-INDEPENDENT STELLAR AND PLANETARY MASSES FROM MULTI-TRANSITING EXOPLANETARY SYSTEMS

Precise exoplanet characterization requires precise classification of exoplanet host stars. The masses of host stars are commonly estimated by comparing their spectra to those predicted by stellar evolution models. However, spectroscopically determined properties are difficult to measure accurately for stars that are substantially different from the Sun, such as M-dwarfs and evolved stars. Here, we propose a new method to dynamically measure the masses of transiting planets near mean-motion resonances and their host stars by combining observations of transit timing variations with radial velocity (RV) measurements. We derive expressions to analytically determine the mass of each member of the system and demonstrate the technique on the Kepler-18 system. We compare these analytic results to numerical simulations and find that the two are consistent. We identify eight systems for which our technique could be applied if follow-up RV measurements are collected. We conclude that this analysis would be optimal for systems discovered by next-generation missions similar to TESS or PLATO, which will target bright stars that are amenable to efficient RV follow-up.
Derivative-free optimization methods

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.
The Impact of Complex and Informed Adversarial Behavior in Graphical Coordination Games

How does system-level information impact the ability of an adversary to degrade performance in a networked control system? How does the complexity of an adversary's strategy affect its ability to degrade performance? This article focuses on these questions in the context of graphical coordination games where an adversary can influence a given fraction of the agents in the system, and the agents follow log-linear learning, a well-known distributed learning algorithm. Focusing on a class of homogeneous ring graphs of various connectivity, we begin by demonstrating that minimally connected ring graphs are the most susceptible to adversarial influence. We then proceed to characterize how both the sophistication of the attack strategies (static versus dynamic) and the informational awareness about the network structure can be leveraged by an adversary to degrade system performance. Focusing on the set of adversarial policies that induce stochastically stable states, our findings demonstrate that the relative importance between sophistication and information changes with the influencing power of the adversary. In particular, sophistication far outweighs informational awareness with regards to degrading system-level damage when the adversary's influence power is relatively weak. However, the opposite is true when an adversary's influence power is more substantial.
Representations Distinguished by Pairs of Exceptional Representations and a Conjecture of Savin

We study representations of GL(n) appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series representations in terms of their inducing data. In particular, we complete the proof of a conjecture of Savin, relating distinguished spherical representations to the image of the tautological lift from a suitable classical group.
Quantum Q systems: from cluster algebras to quantum current algebras

This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the $$A_r$$ quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593–2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra $$U_{\sqrt{q}}({\mathfrak {n}}[u,u^{-1}])\subset U_{\sqrt{q}}(\widehat{{\mathfrak {sl}}}_2)$$ , in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97–152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
Universal characteristic factors and Furstenberg averages

Let X=(X^0,\mu,T) be an ergodic measure preserving system. For a natural number k we consider the averages (*) 1/N \sum_{n=1}^N \prod_{j=1}^k f_j(T^{n a_j}x) where the functions f_j are bounded, and a_j are integers. A factor of X is characteristic for averaging schemes of length k (or k-characteristic) if for any non zero distinct integers a_1,...,a_k, the limiting L^2(\mu) behavior of the averages in (*) is unaltered if we first project the functions f_j onto the factor. A factor of X is a k-universal characteristic factor (k-u.c.f)} if it is a k-characteristic factor, and a factor of any k-characteristic factor. We show that there exists a unique k-u.c.f, and it has a structure of a (k-1)-step nilsystem, more specifically an inverse limit of (k-1)-step nilflows. Using this we show that the averages in (*) converge in L^2(\mu). This provides an alternative proof to the one given by Host and Kra in 2002.
The survival of the core fundamental plane against galactic mergers

The basic dimensional properties of the centers of elliptical galaxies, such as length scale, luminosity, and velocity dispersion, lie on a fundamental plane similar to that of elliptical galaxies as a whole. The orientation of this plane, and the distribution of core parameters within it, point to a strong correlation of core density with either core or total luminosity, and indicate that low-luminosity ellipticals are much denser than high-luminosity galaxies (Hubble Space Telescope data suggest that this relationship may be as steep as ρc∝L−2). In addition, low-luminosity ellipticals have a much smaller length scale than their high-luminosity counterparts. Since we think that small galaxies are occasionally accreted by big ones, the high density of these galaxies and their likely durability against the time-varying tidal field of the bigger ones suggests that they will survive substantially intact in the cores of larger galaxies and would be easily visible. Their presence would destroy the observed correlation. Motivated by this apparent inconsistency between an observed fact and a simple physical argument, we have developed an effective simulation method and applied it to the problem of the accretion of very dense secondary companions by tenuous primaries. We have studied the accretion of objects of varying luminosity ratios, with sizes and densities drawn from the fundamental plane under the assumption that the mass distribution in the central parts of the galaxies follows the light. The results indicate that in mergers with mass ratios greater than 10, chosen with an appropriate central density dependence on luminosity, the smaller object is only stripped down to the highest density encountered in the primary during the accretion process. Thus, the form of the core fundamental plane suggests that the mass distribution in galaxy centers is different from the light distribution, or that an understanding of secondary survival requires more than the dynamics of visible stars.
Improved bounds on the epidemic threshold of exact SIS models on complex networks

The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λ max (A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Lunar laser ranging: the millimeter challenge

Lunar laser ranging has provided many of the best tests of gravitation since the first Apollo astronauts landed on the Moon. The march to higher precision continues to this day, now entering the millimeter regime, and promising continued improvement in scientific results. This review introduces key aspects of the technique, details the motivations, observables, and results for a variety of science objectives, summarizes the current state of the art, highlights new developments in the field, describes the modeling challenges, and looks to the future of the enterprise.
Surface tension of flowing soap films

The surface tension of flowing soap films is measured with respect to the film thickness and the concentration of soap solution. We perform this measurement by measuring the curvature of the nylon wires that bound the soap film channel and use the measured curvature to parametrize the relation between the surface tension and the tension of the wire. We find that the surface tension of our soap films increases when the film is relatively thin or is made of soap solution of low concentration; otherwise, it approaches an asymptotic value of . A simple adsorption model with only two parameters describes our observations reasonably well. With our measurements, we are also able to estimate the Gibbs elasticity of our soap film.
The Imprint of Lithium Recombination on the Microwave Background Anisotropies

Following the 2001 paper of Loeb, we explore the imprint of the resonant 6708 A line opacity of neutral lithium on the temperature and polarization anisotropies of the cosmic microwave background (CMB) at observed wavelengths of 250-350 μm (0.9-1.2 THz). We show that if lithium recombines in the redshift range of z = 400-500 as expected, then the standard CMB temperature and polarization anisotropies would be significantly modified in this wavelength band. The lithium signal may be difficult to separate from the contamination by the far-infrared background and galactic foregrounds. We show that in polarization, the signal could be comparable to the expected polarization anisotropies of the far-infrared background on subdegree angular scales (l 100). Detection of the predicted signal can be used to infer the primordial abundance of lithium, and to probe structure in the universe at z ~ 500.
The Balmer Wavelength Range of BP Tauri

We have analyzed all the observations of BP Tauri taken by the International Ultraviolet Explorer (IUE) in the low-resolution (Δλ ~ 6 A), long-wavelength (λ = 1850-3350 A) range. This data set contains 61 spectra. We observe variability in the ultraviolet continuum of Δmcont. ~ 1 mag and variability in the Mg II line flux of Δm ~ 0.8 mag. Moreover, these spectra do not show any correlation between the continuum flux and the Mg II line flux, thus resolving a standing controversy in the literature concerning the origin of the Mg II line flux. There is no correlation between the color temperature of the UV continuum and the average value of its flux. Using models of the accretion process recently developed by other authors, we obtain energy fluxes, accretion spot sizes, and accretion rates from the IUE observations of BP Tauri. We find average energy fluxes of 5.0 × 1011 ergs cm-2 s- 1, average spot sizes of 4.4 × 10-3 times the stellar surface, and average accretion rates of 1.6 × 10-8 M☉ yr-1. Our analysis shows that the particle energy flux and the UV flux in the stellar surface are proportional to each other. Most strikingly, we observe a correlation between accretion rate and spot size, with the spot size increasing as the square of the accretion rate. Based on the results of a simulation, we conclude that geometrical effects (i.e., the varying inclination of the spot with respect to the observer) are not enough to account for this effect. Current models of the accretion process fail to reproduce such an effect, suggesting the need of using more realistic descriptions of the stellar field when treating magnetospheric accretion. There may also be an unmodeled efficiency factor that determines how matter is loaded into the field lines. Nondipole fields, geometry, oblique shocks, and the possibility of "limb brightening" should be taken into account when creating models and explaining the results of observations of T Tauri stars.
Aging near rough and smooth boundaries in colloidal glasses

We use a confocal microscope to study the aging of a bidisperse colloidal glass near rough and smooth boundaries. Near smooth boundaries, the particles form layers, and particle motion is dramatically slower near the boundary as compared to the bulk. Near rough boundaries, the layers nearly vanish, and particle motion is nearly identical to that of the bulk. The gradient in dynamics near the boundaries is demonstrated to be a function of the gradient in structure for both types of boundaries. Our observations show that wall-induced layer structures strongly influence aging.
Hyperbolic Structures on groups

For every group $G$, we introduce the set of hyperbolic structures on $G$, denoted $\mathcal{H}(G)$, which consists of equivalence classes of (possibly infinite) generating sets of $G$ such that the corresponding Cayley graph is hyperbolic; two generating sets of $G$ are equivalent if the corresponding word metrics on $G$ are bi-Lipschitz equivalent. Alternatively, one can define hyperbolic structures in terms of cobounded $G$-actions on hyperbolic spaces. We are especially interested in the subset $\mathcal{AH}(G)\subseteq \mathcal{H}(G)$ of acylindrically hyperbolic structures on $G$, i.e., hyperbolic structures corresponding to acylindrical actions. Elements of $\mathcal{H}(G)$ can be ordered in a natural way according to the amount of information they provide about the group $G$. The main goal of this paper is to initiate the study of the posets $\mathcal{H}(G)$ and $\mathcal{AH}(G)$ for various groups $G$. We discuss basic properties of these posets such as cardinality and existence of extremal elements, obtain several results about hyperbolic structures induced from hyperbolically embedded subgroups of $G$, and study to what extent a hyperbolic structure is determined by the set of loxodromic elements and their translation lengths.
Localized deformation for initial data sets with the dominant energy condition

We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condition. By establishing the local surjectivity theorem, we can promote the dominant energy condition to the strict inequality by compactly supported variations and obtain new gluing results with the dominant energy condition. The proof of local surjectivity is a modification of the earlier work for the usual constraint map by Corvino and Schoen (J Differ Geom 73(2):185–217, 2006) and by Chruściel and Delay (Mem Soc Math Fr (NS) 94:vi+103, 2003), with some refined analysis.
Homogeneous Analysis of Hot Earths: Masses, Sizes, and Compositions

Terrestrial planets have been found orbiting Sun-like stars with extremely short periods --- some as short as 4 hours. These "ultra-short-period planets" or "hot Earths" are so strongly irradiated that any initial H/He atmosphere has probably been lost to photoevaporation. As such, the sample of hot Earths may give us a glimpse at the rocky cores that are often enshrouded by thick H/He envelopes on wider-orbiting planets. However, the mass and radius measurements of hot Earths have been derived from a hodgepodge of different modeling approaches, and include several cases of contradictory results. Here, we perform a homogeneous analysis of the complete sample of 11 known hot Earths with an insolation exceeding 650 times that of the Earth. We combine all available data for each planet, incorporate parallax information from {\it Gaia} to improve the stellar and planetary parameters, and use Gaussian Process regression to account for correlated noise in the radial-velocity data. The homogeneous analysis leads to a smaller dispersion in the apparent composition of hot Earths, although there does still appear to be some intrinsic dispersion. Most of the planets are consistent with an Earth-like composition (35\% iron and 65\% rock), but two planets (K2-141b and K2-229b) show evidence for a higher iron fraction, and one planet (55\,Cnc\,e) has either a very low iron fraction or an envelope of low-density volatiles. All of the planets are less massive than 8\,$M_\oplus$, despite the selection bias towards more massive planets, suggesting that 8\,$M_\oplus$ is the critical mass for runaway accretion.
Data Sustainability and Reuse Pathways of Natural Resources and Environmental Scientists

This article presents a multifarious examination of natural resources and environmental scientists' adventures navigating the policy change toward open access and cultural shift in data management,...
CONGRUENCES AMONG POWER SERIES COEFFICIENTS OF MODULAR FORMS

Many authors have investigated the congruence relations among the coefficients of power series expansions of modular forms f in modular functions t. In a recent paper, R. Osburn and B. Sahu examine several power series expansions and prove that the coefficients exhibit congruence relations similar to the congruences satisfied by the Apery numbers associated with the irrationality of ζ(3). We show that many of the examples of Osburn and Sahu are members of infinite families.
Standard parabolic subsets of highest weight modules

In this paper we study certain fundamental and distinguished subsets of weights of an arbitrary highest weight module over a complex semisimple Lie algebra. These sets ${\rm wt}_J \mathbb{V}^\lambda$ are defined for each highest weight module $\mathbb{V}^\lambda$ and each subset $J$ of simple roots; we term them "standard parabolic subsets of weights". It is shown that for any highest weight module, the sets of simple roots whose corresponding standard parabolic subsets of weights are equal form intervals in the poset of subsets of the set of simple roots under containment. Moreover, we provide closed-form expressions for the maximum and minimum elements of the aforementioned intervals for all highest weight modules $\mathbb{V}^\lambda$ over semisimple Lie algebras $\mathfrak{g}$. Surprisingly, these formulas only require the Dynkin diagram of $\mathfrak{g}$ and the integrability data of $\mathbb{V}^\lambda$. As a consequence, we extend classical work by Satake, Borel-Tits, Vinberg, and Casselman, as well as recent variants by Cellini-Marietti to all highest weight modules. We further compute the dimension, stabilizer, and vertex set of standard parabolic faces of highest weight modules, and show that they are completely determined by the aforementioned closed-form expressions. We also compute the $f$-polynomial and a minimal half-space representation of the convex hull of the set of weights. These results were recently shown for the adjoint representation of a simple Lie algebra, but analogues remain unknown for any other finite- or infinite-dimensional highest weight module. Our analysis is uniform and type-free, across all semisimple Lie algebras and for arbitrary highest weight modules.
Unconfirmed Near-Earth Objects

We studied the Near-Earth Asteroid (NEA) candidates posted on the Minor Planet Center's Near-Earth Object Confirmation Page (NEOCP) between years 2013 and 2016. Out of more than 17000 NEA candidates, while the majority became either new discoveries or were associated with previously known objects, about 11% were unable to be followed-up or confirmed. We further demonstrate that of the unconfirmed candidates, 926 ± 50 are likely to be NEAs, representing 18% of discovered NEAs in that period. Only 11% (~93) of the unconfirmed NEA candidates were large (having absolute magnitude H < 22). To identify the reasons why these NEAs were not recovered, we analyzed those from the most prolific asteroid surveys: Pan-STARRS, the Catalina Sky Survey, the Dark Energy Survey, and the Space Surveillance Telescope. We examined the influence of plane-of-sky positions and rates of motion, brightnesses, submission delays, and computed absolute magnitudes, as well as correlations with the phase of the moon and seasonal effects. We find that delayed submission of newly discovered NEA candidate to the NEOCP drove a large fraction of the unconfirmed NEA candidates. A high rate of motion was another significant contributing factor. We suggest that prompt submission of suspected NEA discoveries and rapid response to fast-moving targets and targets with fast growing ephemeris uncertainty would allow better coordination among dedicated follow-up observers, decrease the number of unconfirmed NEA candidates, and increase the discovery rate of NEAs.
THE COMPACTNESS OF PRESUPERNOVA STELLAR CORES

The success or failure of the neutrino-transport mechanism for producing a supernova in an evolved massive star is known to be sensitive not only to the mass of the iron core that collapses, but also to the density gradient in the silicon and oxygen shells surrounding that core. Here we study the systematics of a presupernova core's 'compactness' as a function of the mass of the star and the physics used in its calculation. Fine-meshed surveys of presupernova evolution are calculated for stars from 15 to 65 M {sub ☉}. The metallicity and the efficiency of semiconvection and overshoot mixing are both varied and bare carbon-oxygen cores are explored as well as full hydrogenic stars. Two different codes, KEPLER and MESA, are used for the study. A complex interplay of carbon and oxygen burning, especially in shells, can cause rapid variations in the compactness for stars of very nearly the same mass. On larger scales, the distribution of compactness with main sequence mass is found to be robustly non-monotonic, implying islands of 'explodabilty,' particularly around 8-20 M {sub ☉} and 25-30 M {sub ☉}. The carbon-oxygen (CO) core mass of a presupernova star is a better, (though still ambiguous) discriminantmore » of its core structure than the main sequence mass.« less
A Lower Bound on the Partition Function for a Strictly Neutral Charge-Symmetric System

A lower bound on the grand partition function of a classical charge-symmetric system is adapted to the neutral grand canonical ensemble, in which the system is constrained to have zero total charge. This constraint permits us to consider two-body potentials that are only conditionally positive definite.
Dualities of 5d gauge theories from S-duality

We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained by adding matter to both sides of a more primitive duality. This allows us to define the notion of irreducible dualities which cannot be obtained from more primitive dualities. More general dualities then are obtained by adding matter to both sides of an irreducible duality. The geometric method described in this paper allows us to systematically construct irreducible dualities. As an application, we explicitly determine a special class of irreducible dualities classified by removal and addition of edges into a Dynkin diagram. This class of dualities vastly generalizes many of the known 5d dualities in the literature.
Experiments on the fragmentation of a buoyant liquid volume in another liquid

We present experiments on the instability and fragmentation of volumes of heavier liquids released into lighter immiscible liquids. We focus on the regime defined by small Ohnesorge numbers, density ratios of the order of one, and variable Weber numbers. The observed stages in the fragmentation process include deformation of the released fluid by either Rayleigh–Taylor instability (RTI) or vortex ring roll-up and destabilization, formation of filamentary structures, capillary instability, and drop formation. At low and intermediate Weber numbers, a wide variety of fragmentation regimes is identified. Those regimes depend on early deformations, which mainly result from a competition between the growth of RTI and the roll-up of a vortex ring. At high Weber numbers, turbulent vortex ring formation is observed. We have adapted the standard theory of turbulent entrainment to buoyant vortex rings with initial momentum. We find consistency between this theory and our experiments, indicating that the concept of turbulent entrainment is valid for non-dispersed immiscible fluids at large Weber and Reynolds numbers.
Classical zero-knowledge arguments for quantum computations

We show that every language in BQP admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol builds upon two recent results: a computational zero-knowledge proof system for languages in QMA, with a quantum verifier, introduced by Broadbent et al. (FOCS 2016), and an argument system for languages in BQP, with a classical verifier, introduced by Mahadev (FOCS 2018).
High-contrast Demonstration of an Apodized Vortex Coronagraph

High contrast imaging is the primary path to the direct detection and characterization of Earth-like planets around solar-type stars; a cleverly designed internal coronagraph suppresses the light from the star, revealing the elusive circumstellar companions. However, future large-aperture telescopes ($>$4~m in diameter) will likely have segmented primary mirrors, which causes additional diffraction of unwanted stellar light. Here we present the first high contrast laboratory demonstration of an apodized vortex coronagraph (AVC), in which an apodizer is placed upstream of a vortex focal plane mask to improve its performance with a segmented aperture. The gray-scale apodization is numerically optimized to yield a better sensitivity to faint companions assuming an aperture shape similar to the LUVOIR-B concept. Using wavefront sensing and control over a one-sided dark hole, we achieve a raw contrast of $2\times10^{-8}$ in monochromatic light at 775~nm, and a raw contrast of $4\times10^{-8}$ in a 10\% bandwidth. These results open the path to a new family of coronagraph designs, optimally suited for next-generation segmented space telescopes.
Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets

The Kepler Mission has discovered thousands of planets with radii <4 R_⨁, paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-to-Neptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-to-one relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass–radius relationship (M–R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M–R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M–R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that M/M_⨁ = 2.7(R/R_⨁)^(1.3), a scatter in mass of 1.9M_⨁, and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M–R relation for the sample of RV-measured transiting sub-Neptunes (R pl < 4 R_⨁). More broadly, this work provides a framework for further analyses of the M–R relation and its probable dependencies on period and stellar properties.
Long-time asymptotics of non-degenerate non-linear diffusion equations

We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We motivate these types of equations using Einstein’s random walk paradigm, leading to a partial differential equation in non-divergence form. On the other hand, using conservation principles leads to a partial differential equation in divergence form. A transformation is derived to handle both cases. Then, a maximum principle (on both an unbounded and a bounded domain) is proved in order to obtain bounds above and below for the time-evolution of the solutions to the non-linear diffusion problem. Specifically, these bounds are based on the fundamental solution of the linear problem (the so-called Aronson’s Green function). Having thus sandwiched the long-time asymptotics of solutions to the non-linear problems between two fundamental solutions of the linear problem, we prove that, unlike the case of degenerate diffusion, a non-degenerate diffusion equation’s solution converges onto the linear diffusion solution at long times. Select numerical examples support the mathematical theorems and illustrate the convergence process. Our results have implications on how to interpret asymptotic scalings of potentially anomalous diffusion processes (such as in the flow of particulate materials) that have been discussed in the applied physics literature.
The Virasoro vertex algebra and factorization algebras on Riemann surfaces

This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello–Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta–gamma system using the method of effective BV quantization.
Dominant shear bands observed in amorphous ZrCuAl nanowires under simulated compression

We observed the formation of dominant shear bands in model ZrCuAl metallic glass (MG) nanowires (18-nm-long) in molecular dynamics simulations, which implies size-independent incipient plasticity in MG materials. The MG nanowires were prepared using the simulated casting technique to ensure proper relaxation of sample surfaces. Under uniaxial compression, shear bands initiate at the surfaces and lead to reduced icosahedral short-range order. The shear band formation is sensitive to sample thermal history, which calls for careful consideration of sample preparation effects in both experimental and numerical studies of size effect in MG samples.
Twenty five years of asymptotic freedom

Abstract On the occasion of the 25th anniversary of Asymptotic Freedom I describe the discovery of Asymptotic Freedom and the emergence of QCD.
Spectroscopic Follow-up of Discoveries from the NEOWISE Proper Motion Survey

We present low-resolution near-infrared spectra of discoveries from an all-sky proper motion search conducted using multi-epoch data from the Wide-field Infrared Survey Explorer. Using the data from NEOWISE, along with the AllWISE catalog, Schneider et al. (2016) conducted an all-sky proper motion survey to search for nearby objects with high proper motions. Here, we present a follow-up spectroscopic survey of 65 of their discoveries, which focused primarily on potentially nearby objects (d L7), and subdwarf candidates. We found 31 new M dwarfs, 18 new L dwarfs, and 11 new T dwarfs. Of these, 13 are subdwarfs, including one new sdL1 and two new sdL7s. Eleven of these discovereies, with spectral types ranging from M7 to T7 (including one subdwarf) are predicted to be within 25 pc, adding to the number of known objects in the solar neighborhood. We also discovered three new early-type T subdwarf candidates, one sdT1, one sdT2, and one sdT3, which would increase the number of known early-type T subdwarfs from two to five.
Efficient Dielectric Metasurface Collimating Lenses for Mid-Infrared Quantum Cascade Lasers

Light emitted from single-mode semiconductor lasers generally has large divergence angles, and high numerical aperture lenses are required for beam collimation. Visible and near infrared lasers are collimated using aspheric glass or plastic lenses, yet collimation of mid-infrared quantum cascade lasers typically requires more costly aspheric lenses made of germanium, chalcogenide compounds, or other infrared-transparent materials. Here we report mid-infrared dielectric metasurface flat lenses that efficiently collimate the output beam of single-mode quantum cascade lasers. The metasurface lenses are composed of amorphous silicon posts on a flat sapphire substrate and can be fabricated at low cost using a single step conventional UV binary lithography. Mid-infrared radiation from a 4.8 μm distributed-feedback quantum cascade laser is collimated using a polarization insensitive metasurface lens with 0.86 numerical aperture and 79% transmission efficiency. The collimated beam has a half divergence angle of 0.36° and beam quality factor of M2=1.02.
PROPER MOTION AND TIMING OF TWO UNUSUAL PULSARS: CALVERA AND 1E 1207.4—5209

Using pairs of images from the Chandra High Resolution Camera we examine the proper motion of the central compact object (CCO) 1E 1207.4−5209 in the supernova remnant (SNR) PKS 1209−51/52, and the unusual pulsar Calvera that is possibly a CCO descendant. For 1E 1207.4−5209, an insignificant proper motion of mas yr−1 is measured, corresponding to a corrected tangential velocity of km s−1 at the distance of 2 kpc. This proves that the previously noted large offset of the pulsar from the apparent geometric center of the SNR is not due to high proper motion; evidently the symmetry of the remnant does not indicate its center of expansion. Calvera has a marginally significant proper motion of mas yr−1, corresponding to km s−1 for a hypothetical distance of 0.3 kpc. Notably, its vector is away from the Galactic plane, although its high Galactic latitude of may be more a consequence of its proximity than its velocity. We also provide updated timing solutions for each pulsar. Spanning 14.5 years, the ephemeris of 1E 1207.4−5209 has a small and steady frequency derivative that, because of the negligible proper motion, requires no kinematic correction. The derived surface dipole magnetic field strength of 1E 1207.4−5209 thus remains G. Calvera has G, intermediate between those of ordinary young pulsars and CCOs, suggesting that it may be on a trajectory of field growth that could account for the absence of descendants in the neighborhood of CCOs in the diagram.
MEASURING THE DIRECTION AND ANGULAR VELOCITY OF A BLACK HOLE ACCRETION DISK VIA LAGGED INTERFEROMETRIC COVARIANCE

We show that interferometry can be applied to study irregular, rapidly rotating structures, as are expected in the turbulent accretion flow near a black hole. Specifically, we analyze the lagged covariance between interferometric baselines of similar lengths but slightly different orientations. For a flow viewed close to face-on, we demonstrate that the peak in the lagged covariance indicates the direction and angular velocity of the emission pattern from the flow. Even for moderately inclined flows, the covariance robustly estimates the flow direction, although the estimated angular velocity can be significantly biased. Importantly, measuring the direction of the flow as clockwise or counterclockwise on the sky breaks a degeneracy in accretion disk inclinations when analyzing time-averaged images alone. We explore the potential efficacy of our technique using three-dimensional, general relativistic magnetohydrodynamic (GRMHD) simulations, and we highlight several baseline pairs for the Event Horizon Telescope (EHT) that are well-suited to this application. These results indicate that the EHT may be capable of estimating the direction and angular velocity of the emitting material near Sagittarius A*, and they suggest that a rotating flow may even be utilized to improve imaging capabilities.
Quantum deformation of planar amplitudes

In maximally supersymmetric four-dimensional gauge theories planar on-shell diagrams are closely related to the positive Grassmannian and the cell decomposition of it into the union of so called positroid cells. (This was proven by N. Arkani-Hamed, J. Bourjaily, F. Cachazo, A. Goncharov, A. Postnikov, and J. Trnka.) We establish that volume forms on positroids used to express scattering amplitudes can be q-deformed to Hochschild homology classes of corresponding quantum algebras. The planar amplitudes are represented as sums of contributions of some set of positroid cells; we quantize these contributions. In classical limit our considerations allow us to obtain explicit formulas for contributions of positroid cells to scattering amplitudes.
Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). We implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.
Analysis of 2 + 1 diffusive–dispersive PDE arising in river braiding

We present local existence and uniqueness results for the following 2 + 1 diffusive–dispersive equation due to P. Hall arising in modelling of river braiding: \begin{equation*} u_{yyt} - \gamma u_{xxx} -\alpha u_{yyyy} - \beta u_{yy} + \left ( u^2 \right )_{xyy} = 0 \end{equation*} for (x,y) ∈ [0, 2π] × [0, π], t > 0, with boundary condition u y =0=u yyy at y=0 and y=π and 2π periodicity in x, using a contraction mapping argument in a Bourgain-type space T s,b . We also show that the energy ∥u(·, ·, t)∥2 L 2 and cumulative dissipation ∫0 t ∥u y (·, ·, s)∥ L 2 2 dt are globally controlled in time t.
A SPECTROSCOPIC SURVEY OF MASSIVE STARS IN M31 AND M33

We describe our spectroscopic follow-up to the Local Group Galaxy Survey (LGGS) photometry of M31 and M33. We have obtained new spectroscopy of 1895 stars, allowing us to classify 1496 of them for the first time. Our study has identified many foreground stars, and established membership for hundreds of early- and mid-type supergiants. We have also found 9 new candidate Luminous Blue Variables and a previously unrecognized Wolf-Rayet star. We republish the LGGS M31 and M33 catalogs with improved coordinates and including spectroscopy from the literature and our new results. The spectroscopy in this paper is responsible for the vast majority of the stellar classifications in these two nearby spiral neighbors. The most luminous (and hence massive) of the stars in our sample are early-type B supergiants, as expected; the more massive O stars will be fainter visually, and thus mostly remain unobserved so far. The majority of the unevolved stars in our sample are in the 20-40Mo range.
Synchronization of Kuramoto oscillators in dense networks

We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let G = (V, E) be a connected graph and denotes its adjacency matrix. Let the function be given by This function has a global maximum when θi = θ for all 1 ≤ i ≤ n. It is known that if every vertex is connected to at least μ(n − 1) other vertices for μ sufficiently large, then every local maximum is global. Taylor proved this for μ ≥ 0.9395 and Ling, Xu & Bandeira improved this to μ ≥ 0.7929. We give a slight improvement to μ ≥ 0.7889. Townsend, Stillman & Strogatz suggested that the critical value might be μc = 0.75.
Random Heegaard splittings

Consider a random walk on the mapping class group, and let w n be the location of the random walk at time n. A random Heegaard splitting M(w n ) is a 3-manifold obtained by using w n as the gluing map between two handlebodies. We show that the joint distribution of (w n , w n −1 ) is asymptotically independent, and converges to the product of the harmonic and reflected harmonic measures defined by the random walk. We use this to show that the translation length of w n acting on the curve complex, and the distance between the disk sets of M(w n ) in the curve complex, grows linearly in n. In particular, this implies that a random Heegaard splitting is hyperbolic with asymptotic probability 1.
Directions in orbits of geometrically finite hyperbolic subgroups

We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case with two recent infinite-volume exceptions by Zhang for Apollonian circle packings and certain Schottky groups. Our results hold for general Zariski dense, non-elementary, geometrically finite subgroups in any dimension. Unlike in the lattice case orbits of geometrically finite subgroups do not necessarily equidistribute on the whole boundary of hyperbolic space. But rather they may equidistribute on a fractal subset. Understanding the behavior of these orbits near the boundary is central to Patterson–Sullivan theory and much further work. Our theorem characterises the higher order spatial statistics and thus addresses a very natural question. As a motivating example our work applies to sphere packings (in any dimension) which are invariant under the action of such discrete subgroups. At the end of the paper we show how this statistical characterization can be used to prove convergence of moments and to write down the limiting formula for the two-point correlation function and nearest neighbor distribution. Moreover we establish a formula for the 2 dimensional limiting gap distribution (and cumulative gap distribution) which also applies in the lattice case.
Drosophila Activin signaling promotes muscle growth through InR/dTORC1 dependent and independent processes.

The Myostatin/Activin branch of the TGFβ superfamily acts as a negative regulator of vertebrate skeletal muscle size, in part, through downregulation of insulin/IGF-1 signaling. Surprisingly, recent studies in Drosophila indicate that motoneuron derived Activin signaling acts as a positive regulator of muscle size. Here we demonstrate that Drosophila Activin signaling promotes growth of the muscle cells along all three axes; width, thickness and length. Activin signaling positively regulates the InR/dTORC1 pathway and the level of Mhc, an essential sarcomeric protein, via increased Pdk1 and Akt1 expression. Enhancing InR/dTORC1 signaling in the muscle of Activin pathway mutants restores Mhc levels close to wild-type, but only increases muscle width. In contrast, hyperactivation of the Activin pathway in muscles increases overall larval body and muscle fiber length even when Mhc levels were lowered by suppression of dTORC1. Together, these results indicate that the Drosophila Activin pathway regulates larval muscle geometry and body size via promoting InR/dTORC1-dependent Mhc production and the differential assembly of sarcomeric components into either pre-existing or new sarcomeric units depending on the balance of InR/dTORC1 and Activin signals.