cssi/SciSciGPT-SciSciNet huggingface dataset:
Perspective acceleration and gravitational redshift. Measuring masses of individual white dwarfs using Gaia + SIM astrometry

According to current plans, the SIM/NASA mission will be launched just after the end of operations for the Gaia/ESA mission. This is a new situation which enables long term astrometric projects that could not be achieved by either mission alone. Using the well-known perspective acceleration effect on astrometric measurements, the true heliocentric radial velocity of a nearby star can be measured with great precision if the time baseline of the astrometric measurements is long enough. Since white dwarfs are compact objects, the gravitational redshift can be quite large (40–80 km/s), and is the predominant source of any shift in wavelength. The mismatch of the true radial velocity with the spectroscopic shift thus leads to a direct measure of the Mass–Radius relation for such objects. Using available catalog information about the known nearby white dwarfs, we estimate how many masses/gravitational redshift measurements can be obtained with an accuracy better than 2%. Nearby white dwarfs are relatively faint objects (10 < V < 15), which can be easily observed by both missions. We also briefly discuss how the presence of a long period planet can mask the astrometric signal of perspective acceleration.
The Connection between Galaxies and Dark Matter Structures in the Local Universe

We provide new constraints on the connection between galaxies in the local universe, identified by the Sloan Digital Sky Survey, and dark matter halos and their constituent substructures in the ?-cold dark matter model using WMAP7 cosmological parameters. Predictions for the abundance and clustering properties of dark matter halos, and the relationship between dark matter hosts and substructures, are based on a high-resolution cosmological simulation, the Bolshoi simulation. We associate galaxies with dark matter halos and subhalos using subhalo abundance matching, and perform a comprehensive analysis which investigates the underlying assumptions of this technique including (1) which halo property is most closely associated with galaxy stellar masses and luminosities, (2) how much scatter is in this relationship, and (3) how much subhalos can be stripped before their galaxies are destroyed. The models are jointly constrained by new measurements of the projected two-point galaxy clustering and the observed conditional stellar mass function of galaxies in groups. We find that an abundance matching model that associates galaxies with the peak circular velocity of their halos is in good agreement with the data, when scatter of 0.20 ? 0.03?dex in stellar mass at a given peak velocity is included. This confirms the theoretical expectation that the stellar mass of galaxies is tightly correlated with the potential wells of their dark matter halos before they are impacted by larger structures. The data put tight constraints on the satellite fraction of galaxies as a function of galaxy stellar mass and on the scatter between halo and galaxy properties, and rule out several alternative abundance matching models that have been considered. This will yield important constraints for galaxy formation models, and also provides encouraging indications that the galaxy-halo connection can be modeled with sufficient fidelity for future precision studies of the dark universe.
Application of the trend filtering algorithm for photometric time series data

Detecting transient light curves (e.g., transiting planets) requires high-precision data, and thus it is important to effectively filter systematic trends affecting ground-based wide-field surveys. We apply an implementation of the Trend Filtering Algorithm (TFA) to the 2MASS calibration catalog and select Palomar Transient Factory (PTF) photometric time series data. TFA is successful at reducing the overall dispersion of light curves, however, it may over-filter intrinsic variables and increase "instantaneous" dispersion when a template set is not judiciously chosen. In an attempt to rectify these issues we modify the original TFA from the literature by including measurement uncertainties in its computation, including ancillary data correlated with noise, and algorithmically selecting a template set using clustering algorithms as suggested by various authors. This approach may be particularly useful for appropriately accounting for variable photometric precision surveys and/or combined data sets. In summary, our contributions are to provide a MATLAB software implementation of TFA and a number of modifications tested on synthetics and real data, summarize the performance of TFA and various modifications on real ground-based data sets (2MASS and PTF), and assess the efficacy of TFA and modifications using synthetic light curve tests consisting of transiting and sinusoidal variables. While the transiting variables test indicates that these modifications confer no advantage to transit detection, the sinusoidal variables test indicates potential improvements in detection accuracy.
The initial value problem in Lagrangian drift kinetic theory

Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model’s initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, ‘renormalized’ variational approach to drift kinetic theory that manifestly respects the parent model’s initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual ‘field particle’ Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.
Topological edge modes by smart patterning

We study identical coupled mechanical resonators whose collective dynamics are fully determined by the patterns in which they are arranged. In this work, we call a system topological if (1) boundary resonant modes fully fill all existing spectral gaps whenever the system is halved, and (2) if the boundary spectrum cannot be removed or gapped by any boundary condition. We demonstrate that such topological characteristics can be induced solely through patterning, in a manner entirely independent of the structure of the resonators and the details of the couplings. The existence of such patterns is proven using $K$ theory and exemplified using an experimental platform based on magnetically coupled spinners. Topological metamaterials built on these principles can be easily engineered at any scale, providing a practical platform for applications and devices.
Planets in Other Universes: Habitability constraints on density fluctuations and galactic structure

Motivated by the possibility that different versions of the laws of physics could be realized within other universes, this paper delineates the galactic structure parameters that allow for habitable planets and revisits constraints on the amplitude Q of the primordial density fluctuations. Previous work indicates that large values of Q lead to galaxies so dense that planetary orbits cannot survive long enough for life to develop. Small values of Q lead to delayed star formation, loosely bound galaxies, and compromised heavy element retention. This work generalizes previous treatments in the following directions: [A] We consider models for the internal structure of the galaxies, including a range of stellar densities, and find the fraction of the resulting galactic real estate that allows for stable, long-lived planetary orbits. [B] For high velocity encounters, we perform a large ensemble of numerical simulations to estimate cross sections for the disruption of planetary orbits due to interactions with passing stars. [C] We consider the background radiation fields produced by the galaxies: if a galaxy is too compact, the night sky seen from a potentially habitable planet can provide more power than the host star. [D] One consequence of intense galactic background radiation fields is that some portion of the galaxy, denoted as the Galactic Habitable Zone, will provide the right flux levels to support habitable planets for essentially any planetary orbit including freely floating bodies (but excluding close-in planets). As the value of Q increases, the fraction of stars in a galaxy that allow for (traditional) habitable planets decreases due to both orbital disruption and the intense background radiation. However, the outer parts of the galaxy always allow for habitable planets, so that the value of Q does not have a well-defined upper limit (due to scattering or radiation constraints). Moreover, some Galactic Habitable Zones are large enough to support more potentially habitable planets than the galaxies found in our universe. These results suggest that the possibilities for habitability in other universes are somewhat more favorable and far more diverse than previously imagined.
Hawking radiation inside a Schwarzschild black hole

The boundary of any observer’s spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer’s spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law character of the Hawking radiation, coupled with conservation of energy–momentum, the trace anomaly, and the familiar behavior of Hawking radiation far from the black hole, leads to a complete description of the quantum energy–momentum inside a Schwarzschild black hole. The quantum energy–momentum near the singularity diverges as $$r^{-6}$$ , and consists of relativistic Hawking radiation and negative energy vacuum in the ratio $$3 : -\,2$$ . The classical back reaction of the quantum energy–momentum on the geometry, calculated using the Einstein equations, serves merely to exacerbate the singularity. All the results are consistent with traditional calculations of the quantum energy–momentum in 1 + 1 spacetime dimensions.
Many-body quantum dynamics slows down at low density

We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.
Your actions tell where you are: Uncovering Twitter users in a metropolitan area

Twitter is an extremely popular social networking platform. Most Twitter users do not disclose their locations due to privacy concerns. Although inferring the location of an individual Twitter user has been extensively studied, it is still missing to effectively find the majority of the users in a specific geographical area without scanning the whole Twittersphere, and obtaining these users will result in both positive and negative significance. In this paper, we propose LocInfer, a novel and lightweight system to tackle this problem. LocInfer explores the fact that user communications in Twitter exhibit strong geographic locality, which we validate through large-scale datasets. Based on the experiments from four representative metropolitan areas in U.S., LocInfer can discover on average 86.6% of the users with 73.2% accuracy in each area by only checking a small set of candidate users. We also present a countermeasure to the users highly sensitive to location privacy and show its efficacy by simulations.
Earths in Other Solar Systems' N-body Simulations: The Role of Orbital Damping in Reproducing the Kepler Planetary Systems

The population of exoplanetary systems detected by Kepler provides opportunities to refine our understanding of planet formation. Unraveling the conditions needed to produce the observed exoplanets will sallow us to make informed predictions as to where habitable worlds exist within the galaxy. In this paper, we examine using N-body simulations how the properties of planetary systems are determined during the final stages of assembly. While accretion is a chaotic process, trends in the ensemble properties of planetary systems provide a memory of the initial distribution of solid mass around a star prior to accretion. We also use EPOS, the Exoplanet Population Observation Simulator, to account for detection biases and show that different accretion scenarios can be distinguished from observations of the Kepler systems. We show that the period of the innermost planet, the ratio of orbital periods of adjacent planets, and masses of the planets are determined by the total mass and radial distribution of embryos and planetesimals at the beginning of accretion. In general, some amount of orbital damping, either via planetesimals or gas, during accretion is needed to match the whole population of exoplanets. Surprisingly, all simulated planetary systems have planets that are similar in size, showing that the "peas in a pod" pattern can be consistent with both a giant impact scenario and a planet migration scenario. The inclusion of material at distances larger than what Kepler observes has a profound impact on the observed planetary architectures, and thus on the formation and delivery of volatiles to possible habitable worlds.
A Duality Framework for Stochastic Optimal Control of Complex Systems

We address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For practical situations with constraints consistent to those studied here, our results imply that the Pareto control policy may be of value when we seek to derive online the optimal control policy in complex systems.
Stacking fault energy prediction for austenitic steels: thermodynamic modeling vs. machine learning

Stacking fault energy (SFE) is of the most critical microstructure attribute for controlling the deformation mechanism and optimizing mechanical properties of austenitic steels, while there are no accurate and straightforward computational tools for modeling it. In this work, we applied both thermodynamic modeling and machine learning to predict the stacking fault energy (SFE) for more than 300 austenitic steels. The comparison indicates a high need of improving low-temperature CALPHAD (CALculation of PHAse Diagrams) databases and interfacial energy prediction to enhance thermodynamic model reliability. The ensembled machine learning algorithms provide a more reliable prediction compared with thermodynamic and empirical models. Based on the statistical analysis of experimental results, only Ni and Fe have a moderate monotonic influence on SFE, while many other elements exhibit a complex effect that their influence on SFE may change with the alloy composition.
Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence

A new theoretical analysis combines a decades-old exact approach to turbulence with Einstein's theory of relativity to develop a framework for turbulence in relativistic fluids, such as those found near supermassive black holes or even in the gravitational field itself. (Image credit: X-ray: NASA/CXC/CfA/R.Kraft et al.; Submillimeter: MPIfR/ESO/APEX/A.Weiss et al.; Optical: ESO/WFI)
Intersections and joins of free groups

Let F be a free group. If H and K are subgroups of F , we let H ∨K = 〈H,K〉 denote the join of H and K. We study the relationship between the rank of H ∩K and that of H ∨K for a pair of finitely generated subgroups H and K of F . In particular, we have the following particular case of the Hanna Neumann Conjecture, which has also been obtained by L. Louder [6] using his machinery for folding graphs of spaces [7, 8, 9]. For detailed discussions of the Hanna Neumann Conjecture, see [11, 12, 13, 16, 4, 3]. Theorem 1 (Kent, Louder). Let H and K be nontrivial finitely generated subgroups of a free group of ranks h and k, respectively. If rank(H ∨K)−1≥ h+ k−1 2 then
FINDING ROCKY ASTEROIDS AROUND WHITE DWARFS BY THEIR PERIODIC THERMAL EMISSION

Since white dwarfs (WDs) are small, the contrast between the thermal emission of an orbiting object and a WD is dramatically enhanced compared to a main-sequence host. Furthermore, rocky objects much smaller than the moon have no atmospheres and are tidally locked to the WD. We show that this leads to temperature contrasts between their day and night side of the order of unity that should lead to temporal variations in infrared flux over an orbital period of ~0.2 to ~2 days. Ground-based telescopes could detect objects with a mass as small as 1% of the lunar mass ML around Sirius B with a few hours of exposure. The James Webb Space Telescope may be able to detect objects as small as 10–3 ML around most nearby WDs. The tightest constraints will typically be placed on 12,000 K WDs, whose Roche zone coincides with the dust sublimation zone. Constraining the abundance of minor planets around WDs as a function of their surface temperatures (and therefore age) provides a novel probe for the physics of planetary formation.
Approximate universal relations among tidal parameters for neutron star binaries

One of largest uncertainties in nuclear physics is the relation between the pressure and density of supranuclear matter: the equation of state. Some of this uncertainty may be removed through future gravitational wave observations of neutron star binaries by extracting the tidal deformabilities (or Love numbers) of neutron stars. Previous studies showed that only a certain combination of the individual deformabilities of each body (chirp tidal deformability) can be measured with second-generation gravitational wave interferometers, such as Adv. LIGO, due to correlations between the individual deformabilities. To overcome this, we search for approximately universal (or equation-of-state independent) relations between two combinations of the individual tidal deformabilities, such that once one of them has been measured, the other can be automatically obtained and the individual ones decoupled through these relations. We find an approximately universal relation between the symmetric and the anti-symmetric combination of the individual tidal deformabilities that is equation-of-state-insensitive to $20\%$ for binaries with masses less than $1.7M_\odot$. We show that these relations can be used to eliminate a combination of the tidal parameters from the list of model parameters, thus breaking degeneracies and improving the accuracy in parameter estimation. A simple study shows that the universal relations can improve the accuracy in the extraction of the symmetric combination of tidal parameters by as much as an order of magnitude, making the overall accuracy in the extraction of this parameter slightly better than that of the chirp tidal deformability. These new universal relations and the improved measurement accuracy on tidal parameters not only are important to astrophysics and nuclear physics, but also impact our ability to probe extreme gravity with gravitational waves and cosmology.
Mind the Gap: Is the Too Big to Fail Problem Resolved?

The faintness of satellite systems in galaxy groups has contributed to the widely discussed "missing satellite" and "too big to fail" issues. Using techniques based on Tremaine & Richstone (1977), we show that there is no problem with the luminosity function computed from modern codes per se, but that the gap between first and second brightest systems is too big {\it given} the luminosity function, that the same large gap is found in modern, large scale baryonic $\Lambda$CDM simulations such as EAGLE and IllustrisTNG, is even greater in dark matter only simulations, and finally, that this is most likely due to gravitationally induced merging caused by classical dynamical friction. Quantitatively the gap is larger in the computed simulations than in the randomized ones by $1.79 \pm 1.04$, $1.51 \pm 0.93$, $3.43 \pm 1.44$ and $3.33 \pm 1.35$ magnitudes in the EAGLE, IllustrisTNG, and dark matter only simulations of EAGLE and IllustrisTNG respectively. Furthermore the anomalous gaps in the simulated systems are even larger than in the real data by over half a magnitude and are still larger in the dark matter only simulations. Briefly stated, $\Lambda$CDM does not have a problem with an absence of "too big to fail" galaxies. Statistically significant large gaps between first and second brightest galaxies are to be expected.
Pixel Color Magnitude Diagrams for Semi-resolved Stellar Populations: The Star Formation History of Regions within the Disk and Bulge of M31

The analysis of stellar populations has, by and large, been developed for two limiting cases: spatially-resolved stellar populations in the color-magnitude diagram, and integrated light observations of distant systems. In between these two extremes lies the semi-resolved regime, which encompasses a rich and relatively unexplored realm of observational phenomena. Here we develop the concept of pixel color magnitude diagrams (pCMDs) as a powerful technique for analyzing stellar populations in the semi-resolved regime. pCMDs show the distribution of imaging data in the plane of pixel luminosity vs. pixel color. A key feature of pCMDs is that they are sensitive to all stars, including both the evolved giants and the unevolved main sequence stars. An important variable in this regime is the mean number of stars per pixel, $N_{\rm pix}$. Simulated pCMDs demonstrate a strong sensitivity to the star formation history (SFH) and allow one to break degeneracies between age, metallicity and dust based on two filter data for values of $N_{\rm pix}$ up to at least $10^4$. We extract pCMDs from Hubble Space Telescope (HST) optical imaging of M31 and derive non-parametric SFHs from $10^6$ yr to $10^{10}$ yr for both the crowded disk and bulge regions (where $N_{\rm pix}\approx30-10^3$). From analyzing a small region of the disk we find a non-parametric SFH that is smooth and consistent with an exponential decay timescale of 4 Gyr. The bulge SFH is also smooth and consistent with a 2 Gyr decay timescale. pCMDs will likely play an important role in maximizing the science returns from next generation ground and space-based facilities.
Recent Progress on Developments and Characterization of Hybrid CMOS X-ray Detectors

Future space-based X-ray telescope missions are likely to have significantly increased demands on detector read out rates due to increased collection area, and there will be a desire to minimize radiation damage in the interests of maintaining spectral resolution. While CCDs have met the requirements of past missions, active pixel sensors are likely to be a standard choice for some future missions due to their inherent radiation hardness and fast, flexible read-out architecture. One form of active pixel sensor is the hybrid CMOS sensor. In a joint program of Penn State University and Teledyne Imaging Sensors, hybrid CMOS sensors have been developed for use as X-ray detectors. Results of this development effort and tests of fabricated detectors will be presented, along with potential applications for future missions.
Decidable Synthesis of Programs with Uninterpreted Functions

We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a restriction called coherence that was recently identified to yield decidable verification. We formulate a powerful grammar-restricted (syntax-guided) synthesis problem for coherent uninterpreted programs, and we show the problem to be decidable, identify its precise complexity, and also study several variants of the problem.
A high-precision mechanical absolute-rotation sensor.

We have developed a mechanical absolute-rotation sensor capable of resolving ground rotation angle of less than 1 nrad / Hz above 30 mHz and 0.2 nrad / Hz above 100 mHz about a single horizontal axis. The device consists of a meter-scale beam balance, suspended by a pair of flexures, with a resonance frequency of 10.8 mHz. The center of mass is located 3 μm above the pivot, giving an excellent horizontal displacement rejection of better than 3 × 10−5 rad/m. The angle of the beam is read out optically using a high-sensitivity autocollimator. We have also built a tiltmeter with better than 1 nrad / Hz sensitivity above 30 mHz. Co-located measurements using the two instruments allowed us to distinguish between background rotation signal at low frequencies and intrinsic instrument noise. The rotation sensor is useful for rotational seismology and for rejecting background rotation signal from seismometers in experiments demanding high levels of seismic isolation, such as Advanced Laser Interferometer Gravitational-wave Observatory.
The number of convex tilings of the sphere by triangles, squares, or hexagons

A tiling of the sphere by triangles, squares, or hexagons is convex if every vertex has at most 6, 4, or 3 polygons adjacent to it, respectively. Assigning an appropriate weight to any tiling, our main result is explicit formulas for the weighted number of convex tilings with a given number of tiles. To prove these formulas, we build on work of Thurston, who showed that the convex triangulations correspond to orbits of vectors of positive norm in a Hermitian lattice $\Lambda\subset \mathbb{C}^{1,9}$. First, we extend this result to convex square- and hexagon-tilings. Then, we explicitly compute the relevant lattice $\Lambda$. Next, we integrate the Siegel theta function for $\Lambda$ to produce a modular form whose Fourier coefficients encode the weighted number of tilings. Finally, we determine the formulas using finite-dimensionality of spaces of modular forms.
Radiation fields for nanoscale systems

For a group of charged particles obeying quantum mechanics interacting with an electromagnetic field, the charge and current density in a pure state of the system are expressed with the many-body wave function of the state. Using these as sources, the microscopic Maxwell equations can be written down for any given pure state of a many-body system. By employing semi-classical radiation theory with these sources, the microscopic Maxwell equations can be used to compute the strong radiation fields produced by interacting charged quantal particles. For a charged quantal particle, three radiation fields involve only the vector potential $\mathbf{A}$. This is another example demonstrating the observability of vector potential. Five radiation fields are perpendicular to the canonical momentum of a single charged particle. For a group of charged particles, a new type of radiation field is predicted to be perpendicular to $\mathbf{A}(\mathbf{x}_{j},t)\times \lbrack\nabla\times(\nabla_{j}\Psi^{\prime})]$, where $\Psi^{'}$ is the many-body wave function. This kind of radiation does not exist for a single charged particle. The macroscopic Maxwell equations are derived from the corresponding microscopic equations for a pure state by the Russakoff-Robinson procedure which requires only a spatial coarse graining. Because the sources of fields are also the responses of a system to an external field, one also has to give up the temporal coarse graining of the current density which is often supposed to be critical in the kinetic approach of conductivity.
RoomShift: Room-scale Dynamic Haptics for VR with Furniture-moving Swarm Robots

RoomShift is a room-scale dynamic haptic environment for virtual reality, using a small swarm of robots that can move furniture. RoomShift consists of nine shape-changing robots: Roombas with mechanical scissor lifts. These robots drive beneath a piece of furniture to lift, move and place it. By augmenting virtual scenes with physical objects, users can sit on, lean against, place and otherwise interact with furniture with their whole body; just as in the real world. When the virtual scene changes or users navigate within it, the swarm of robots dynamically reconfigures the physical environment to match the virtual content. We describe the hardware and software implementation, applications in virtual tours and architectural design and interaction techniques.
Analytic Solution of a Delay Differential Equation Arising in Cost Functionals for Systems With Distributed Delays

The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e., Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a delay-free auxiliary ordinary differential equation system with algebraically coupled split-boundary conditions, which characterizes the solutions of the delay differential equation and is used for solution synthesis. A spectral property of the time-delay system yields a necessary and sufficient condition for existence and uniqueness of solutions to the auxiliary system, equivalently the delay differential equation. The result is a tractable analytic solution framework to the delay differential equation.
DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY

We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for establishing the symmetry and Schur positivity of quasisymmetric functions.
The Atiyah–Hitchin bracket and the open Toda lattice

Abstract The dynamics of the finite nonperiodic Toda lattice is an isospectral deformation of the finite three-diagonal Jacobi matrix. It is known since the work of Stieltjes that such matrices are in one-to-one correspondence with their Weyl functions. These are rational functions mapping the upper half-plane into itself. We consider representations of the Weyl functions as a quotient of two polynomials and exponential representation. We establish a connection between these representations and recently developed algebraic-geometrical approach to the inverse problem for Jacobi matrix. The space of rational functions has natural Poisson structure discovered by Atiyah and Hitchin. We show that an invariance of the AH structure under linear-fractional transformations leads to two systems of canonical coordinates and two families of commuting Hamiltonians. We establish a relation of one of these systems with Jacobi elliptic coordinates.
Interfacial magnetic anisotropy from a 3-dimensional Rashba substrate

We study the magnetic anisotropy which arises at the interface between a thin film ferromagnet and a 3-d Rashba material. We use a tight-binding model to describe the bilayer, and the 3-d Rashba material characterized by the spin-orbit strength α and the direction of broken bulk inversion symmetry n. We find an in-plane uniaxial anisotropy in the z×n direction, where z is the interface normal. For realistic values of α, the uniaxial anisotropy is of a similar order of magnitude as the bulk magnetocrystalline anisotropy. Evaluating the uniaxial anisotropy for a simplified model in 1-d shows that for small band filling, the in-plane easy axis anisotropy scales as α4 and results from a twisted exchange interaction between the spins in the 3-d Rashba material and the ferromagnet. For a ferroelectric 3-d Rashba material, n can be controlled with an electric field, and we propose that the interfacial magnetic anisotropy could provide a mechanism for electrical control of the magnetic orientation.
Tests for tau's charged-current structure

Abstract The Lorentz structure of the tau lepton's charged-current can almost be completely determined by use of stage-two spin-correlation functions for the {ϱ − , ϱ + } and {a 1 − , a 1 + } decay modes. It is possible to test for “( V − A ) + something” structure in the J charged lepton current, so as to boundthe scales Λ for “new physics” such as arising from tau weak magnetism, weak electricity and/or second-class currents. In practice, only limited information can be obtained from the τ → πν channels.
On the discovery of social roles in large scale social systems

The social role of a participant in a social system is a label conceptualizing the circumstances under which she interacts within it. They may be used as a theoretical tool that explains why and how users participate in an online social system. Social role analysis also serves practical purposes, such as reducing the structure of complex systems to relationships among roles rather than alters, and enabling a comparison of social systems that emerge in similar contexts. This article presents a data-driven approach for the discovery of social roles in large scale social systems. Motivated by an analysis of the present art, the method discovers roles by the conditional triad censuses of user ego-networks, which is a promising tool because they capture the degree to which basic social forces push upon a user to interact with others. Clusters of censuses, inferred from samples of large scale network carefully chosen to preserve local structural properties, define the social roles. The promise of the method is demonstrated by discussing and discovering the roles that emerge in both Facebook and Wikipedia. The article concludes with a discussion of the challenges and future opportunities in the discovery of social roles in large social systems.
F theory, geometric engineering and N=1 dualities

Abstract We consider geometric engineering of N = 1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold. By bringing 3-branes near 7-branes we engineer N = 1 supersymmetric SU(Nc) gauge theory with Nf flavors in the fundamental. We identify the Higgs branch of this system with the instanton moduli space on the compact four-dimensional space of the 7-brane world-volume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane world-volume can generate superpotential for Nf = Nc − 1 as well as lead to quantum corrections to the moduli space for Nf = Nc. Finally we argue that Seiberg's duality for N = 1 supersymmetric QCD may be mapped to T-duality exchanging 7-branes with 3-branes.
Critical Magnetic Field Strengths for Solar Coronal Plumes in Quiet Regions and Coronal Holes

Coronal plumes are bright magnetic funnels found in quiet regions (QRs) and coronal holes (CHs). They extend high into the solar corona and last from hours to days. The heating processes of plumes involve dynamics of the magnetic field at their base, but the processes themselves remain mysterious. Recent observations suggest that plume heating is a consequence of magnetic flux cancellation and/or convergence at the plume base. These studies suggest that the base flux in plumes is of mixed polarity, either obvious or hidden in Solar Dynamics Observatory (SDO)/HMI data, but do not quantify it. To investigate the magnetic origins of plume heating, we select 10 unipolar network flux concentrations, four in CHs, four in QRs, and two that do not form a plume, and track plume luminosity in SDO/AIA 171 A images along with the base flux in SDO/HMI magnetograms, over each flux concentration's lifetime. We find that plume heating is triggered when convergence of the base flux surpasses a field strength of ~200–600 G. The luminosity of both QR and CH plumes respond similarly to the field in the plume base, suggesting that the two have a common formation mechanism. Our examples of non-plume-forming flux concentrations, reaching field strengths of 200 G for a similar number of pixels as for a couple of our plumes, suggest that a critical field might be necessary to form a plume but is not sufficient for it, thus advocating for other mechanisms, e.g., flux cancellation due to hidden opposite-polarity field, at play.
Cavallo's multiplier for in situ generation of high voltage

A classic electrostatic induction machine, Cavallo's multiplier, is suggested for in situ production of very high voltage in cryogenic environments. The device is suitable for generating a large electrostatic field under conditions of very small load current. Operation of the Cavallo multiplier is analyzed, with quantitative description in terms of mutual capacitances between electrodes in the system. A demonstration apparatus was constructed, and measured voltages are compared to predictions based on measured capacitances in the system. The simplicity of the Cavallo multiplier makes it amenable to electrostatic analysis using finite element software, and electrode shapes can be optimized to take advantage of a high dielectric strength medium such as liquid helium. A design study is presented for a Cavallo multiplier in a large-scale, cryogenic experiment to measure the neutron electric dipole moment.
Geodesics of Random Riemannian Metrics

We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the view of the particle, we show that the law of its observed environment is absolutely continuous with respect to the law of the random metric, and we provide an explicit form for its Radon–Nikodym derivative. We use this result to prove a “local Markov property” along an unbounded geodesic, demonstrating that it eventually encounters any type of geometric phenomenon. We also develop in this paper some general results on conditional Gaussian measures. Our Main Theorem states that a geodesic chosen with random initial conditions (chosen independently of the metric) is almost surely not minimizing. To demonstrate this, we show that a minimizing geodesic is guaranteed to eventually pass over a certain “bump surface,” which locally has constant positive curvature. By using Jacobi fields, we show that this is sufficient to destabilize the minimizing property.
Universally optimal distribution of points on spheres

We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m distances between distinct points in it and it is a spherical (2m-1)-design. We prove that every sharp configuration minimizes potential energy for all completely monotonic potential functions. Examples include the minimal vectors of the E_8 and Leech lattices. We also prove the same result for the vertices of the 600-cell, which do not form a sharp configuration. For most known cases, we prove that they are the unique global minima for energy, as long as the potential function is strictly completely monotonic. For certain potential functions, some of these configurations were previously analyzed by Yudin, Kolushov, and Andreev; we build on their techniques. We also generalize our results to other compact two-point homogeneous spaces, and we conclude with an extension to Euclidean space.
IS SUBDIFFUSIONAL TRANSPORT SLOWER THAN NORMAL

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale of strong viscoelastic correlations τ. The subdiffusive transport regime emerges transiently for t < τ. However, the transport becomes asymptotically normal for t ≫ τ. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e., anomalously slow, in time, 〈δx(t)〉 ∝ Ftα, 〈δx2(t)〉 ∝ tα, 0 < α <1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales.
Dynamical Evolution, Light Curves, and Spectra of Spherical and Collimated Gamma-Ray Burst Remnants

We present an analytical approach to the dynamical evolution of fireballs or axisymmetric jets expanding into an external medium, with application to gamma-ray burst remnants. This method leads to numerical calculations of fireball dynamics that are computationally faster than hydrodynamic simulations. It is also a very flexible approach that can easily be extended to include more complex situations, such as a continuous injection of energy at the reverse shock and the sideways expansion in nonspherical ejecta. Some features of the numerical results for the remnant dynamical evolution are discussed and compared with the analytical results. We find that the ratio of the observer time at which the jet half-angle reaches twice its initial value to the time at which the light cone becomes wider than the jet is substantially smaller than predicted analytically. The effects that arise from the remnant's curvature and thickness further reduce this ratio, such that the afterglow light-curve break that is due to the remnant's finite angular extent overlaps the weaker break that is due to the jet's sideways expansion. An analysis of the effects of the curvature and thickness of the remnant on the afterglow light curves shows that these effects are important and should be taken into account for accurate calculations of the afterglow emission.
ASTROBIOLOGICAL EFFECTS OF GAMMA-RAY BURSTS IN THE MILKY WAY GALAXY

A planet having protective ozone within the collimated beam of a Gamma Ray Burst (GRB) may suffer ozone depletion, potentially causing a mass extinction event to existing life on a planet's surface and oceans. We model the dangers of long GRBs to planets in the Milky Way and utilize a static statistical model of the Galaxy that matches major observable properties, such as the inside-out star formation history, metallicity evolution, and 3-dimensional stellar number density distribution. The GRB formation rate is a function of both the star formation history and metallicity; however, the extent to which chemical evolution reduces the GRB rate over time in the Milky Way is still an open question. Therefore, we compare the damaging effects of GRBs to biospheres in the Milky Way using two models. One model generates GRBs as a function of the inside-out star formation history. The other model follows the star formation history, but generates GRB progenitors as a function of metallicity, thereby favoring metal-poor host regions of the Galaxy over time. If the GRB rate only follows the star formation history, the majority of the GRBs occur in the inner Galaxy. However, if GRB progenitors are constrained to low metallicity environments, then GRBs only form in the metal-poor outskirts at recent epochs. Interestingly, over the past 1 Gyr, the surface density of stars (and their corresponding planets) that survive a GRB is still greatest in the inner galaxy in both models. The present day danger of long GRBs to life at the solar radius ($R_\odot=8$ kpc) is low. We find that at least $\sim$65% of stars survive a GRB over the past 1 Gyr. Furthermore, when the GRB rate was expected to have been enhanced at higher redshifts, such as $z\gtrsim0.5$, our results suggest that a large fraction of planets would have survived these lethal GRB events.
Noncommutative Bennett and Rosenthal inequalities

In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and Pinelis, Utev for commutative random variables. We also present new best constants in Rosenthal’s inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg and Tao.
REALISTIC MODELING OF LOCAL DYNAMO PROCESSES ON THE SUN

Magnetic fields are usually observed in the quiet Sun as small-scale elements that cover the entire solar surface (the “salt-and-pepper” patterns in line-of-sight magnetograms). By using 3D radiative MHD numerical simulations, we find that these fields result from a local dynamo action in the top layers of the convection zone, where extremely weak “seed” magnetic fields (e.g., from a 10{sup −6} G) can locally grow above the mean equipartition field to a stronger than 2000 G field localized in magnetic structures. Our results reveal that the magnetic flux is predominantly generated in regions of small-scale helical downflows. We find that the local dynamo action takes place mostly in a shallow, about 500 km deep, subsurface layer, from which the generated field is transported into the deeper layers by convective downdrafts. We demonstrate that the observed dominance of vertical magnetic fields at the photosphere and horizontal fields above the photosphere can be explained by small-scale magnetic loops produced by the dynamo. Such small-scale loops play an important role in the structure and dynamics of the solar atmosphere and their detection in observations is critical for understanding the local dynamo action on the Sun.
Demonstration of ultra-broadband single-mode and single-polarization operation in T-Guides

Silica-based anchored-membrane waveguides (T-Guides) are fabricated and characterized from the visible to infrared with streak imaging. It is numerically shown that the T-Guides can have wideband single-mode and single-polarization (SMSP) properties over a span of 2.6 octaves. Experimentally, a polarization-dependent loss difference of up to 89±19 dB/cm is measured between orthogonal polarizations and a record SMSP window of >1.27 octaves is observed, limited only by the available measurement equipment. These measurements make a strong case for T-Guides for SMSP photonics, particularly in high-index materials such as those in our previous demonstration on silicon.