cssi/SciSciGPT-SciSciNet huggingface dataset:
Limitations of holography

By studying global AdS using different foliations, global and Rindler-AdS, we show that there are two different asymptotic Fefferman–Graham expansions possible and thus two different definitions of "boundaries". We demonstrate that imposing boundary conditions on the two boundaries is not mutually compatible even when these boundaries are pushed to infinity. Thus, these two procedures define two genuinely distinct theories that we call global-CFT and Rindler-CFT. We show that the Rindler-CFT is not the same as the theory one gets by "Rindlerizing the global-CFT" described in hep-th/9804085. We conjecture that the Rindler theory is incapable of capturing the dynamics inside the horizon and discuss its implications for the BTZ-CFT duality proposed in hep-th/0106112.
Polynomial Splitting Measures and Cohomology of the Pure Braid Group

We study for each n a one-parameter family of complex-valued measures on the symmetric group $$S_n$$ , which interpolate the probability of a monic, degree n, square-free polynomial in $$\mathbb {F}_q[x]$$ having a given factorization type. For a fixed factorization type, indexed by a partition $$\lambda $$ of n, the measure is known to be a Laurent polynomial. We express the coefficients of this polynomial in terms of characters associated to $$S_n$$ -subrepresentations of the cohomology of the pure braid group $$H^{\bullet }(P_n, \mathbb {Q})$$ . We deduce that the splitting measures for all parameter values $$z= -\frac{1}{m}$$ (resp. $$z= \frac{1}{m}$$ ), after rescaling, are characters of $$S_n$$ -representations (resp. virtual $$S_n$$ -representations).
Investigation of a Vorticity-preserving Scheme for the Euler Equations

We investigate the vorticity-preserving properties of the compressible, second-order residual-based scheme, "RBV2." The scheme has been extensively tested on hydrodynamical problems, and has been shown to exhibit remarkably accurate results on the propagation of inviscid compressible vortices, airfoil-vortex interactions on a curvilinear mesh, vortex mergers in an astrophysical accretion disk, and the establishment of a two-dimensional inverse cascade in high-resolution turbulent simulations. Here, we demonstrate that RBV2 sustains the analytic solution for a one-dimensional shear flow. We assess the fidelity by which the algorithm maintains a skewed shear flow, and present convergence tests to quantify the magnitude of the expected numerical dispersion. We propose an adjustment to the dissipation in the algorithm that retains the vorticity-preserving qualities, and accurately incorporates external body forces, and demonstrate that it indefinitely maintains a steady-state hydrostatic equilibrium between a generic acceleration and a density gradient. We present a novel numerical assessment of vorticity preservation for discrete wavenumber, vortical modes of discrete wavenumber up to the Nyquist wavenumber. We apply this assessment to RBV2 in order to quantify the extent to which the scheme preserves vorticity for the full Euler equations. We find that RBV2 perfectly preserves vorticity for modes with symmetric wavenumbers, i.e., k x = k y , and that the error increases with asymmetry. We simulate the dynamical interaction of vortices in a protoplanetary disk to demonstrate the utility of the updated scheme for rendering astrophysical flows replete with vortices and turbulence. We conclude that RBV2 is a competitive treatment for evolving vorticity-dominated astrophysical flows, with minimal dissipation.
Betti numbers and stability for configuration spaces via factorization homology

Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold $M$, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology of $M$. By locating the homology of each configuration space within the Chevalley-Eilenberg complex of this Lie algebra, we extend theorems of Bodigheimer-Cohen-Taylor and Felix-Thomas and give a new, combinatorial proof of the homological stability results of Church and Randal-Williams. Our method lends itself to explicit calculations, examples of which we include.
A Chandra X-Ray Study of the Globular Cluster M80

We report our analysis of a Chandra X-ray observation of the rich globular cluster M80, in which we detect some 19 sources to a limiting 0.5-2.5 keV X-ray luminosity of 7*10^30 ergs/s within the half-mass radius. X-ray spectra indicate that two of these sources are quiescent low-mass X-ray binaries (qLMXBs) containing neutron stars. We identify five sources as probable cataclysmic variables (CVs), one of which seems to be heavily absorbed, implying high inclination. The brightest CV may be the X-ray counterpart of Nova 1860 T Sco. The concentration of the X-ray sources within the cluster core implies an average mass of 1.2+/-0.2 Msun, consistent with the binary nature of these systems and very similar to the radial distribution of the blue stragglers in this cluster. The X-ray and blue straggler source populations in M80 are compared to those in the similar globular cluster 47 Tuc.
Reduced strength and extent of dynamic heterogeneity in a strong glass former as compared to fragile glass formers.

We examined dynamic heterogeneity in a model tetrahedral network glass-forming liquid. We used four-point correlation functions to extract dynamic correlation lengths ξ4a(t) and susceptibilities χ4a(t) corresponding to structural relaxation on two length scales a. One length scale corresponds to structural relaxation at nearest neighbor distances and the other corresponds to relaxation of the tetrahedral structure. We find that the dynamic correlation length ξ4a grows much slower with increasing relaxation time than for model fragile glass formers. We also find that χ4a∼(ξ4a)z for a range of temperatures, but z < 3 at the lowest temperatures examined in this study. However, we do find evidence that the temperature where Stokes-Einstein violation begins marks a temperature where there is a change in the character of dynamically heterogeneous regions. Throughout the paper, we contrast the structure and dynamics of a strong glass former with that of a representative fragile glass former.
Non-gaussianities from perturbing recombination

We approximately compute the bispectrum induced on the CMB temperature by fluctuations in the standard recombination epoch. Of all the second order sources that can induce non-Gaussianity during recombination, we concentrate on those proportional to the perturbation in the free electron density, which is about a factor of 5 larger than the other first order perturbations. This term induces some non-Gaussianity by delaying the time of recombination and by changing the photon diffusion scale. We find that the signal is not scale invariant, peaked on squeezed triangles with the smaller multipole around the scale of the first acoustic peak, and that its size corresponds to an effective fNL −3.5, which could be marginally detected by Planck if both temperature and polarization are measured.
An effective formalism for testing extensions to General Relativity with gravitational waves

The recent direct observation of gravitational waves (GW) from merging black holes opens up the possibility of exploring the theory of gravity in the strong regime at an unprecedented level. It is therefore interesting to explore which extensions to General Relativity (GR) could be detected. We construct an Effective Field Theory (EFT) satisfying the following requirements. It is testable with GW observations; it is consistent with other experiments, including short distance tests of GR; it agrees with widely accepted principles of physics, such as locality, causality and unitarity; and it does not involve new light degrees of freedom. The most general theory satisfying these requirements corresponds to adding to the GR Lagrangian operators constructed out of powers of the Riemann tensor, suppressed by a scale comparable to the curvature of the observed merging binaries. The presence of these operators modifies the gravitational potential between the compact objects, as well as their effective mass and current quadrupoles, ultimately correcting the waveform of the emitted GW.
The use of intellectual property protection mechanisms by publicly supported firms

Technology-based firms use intellectual property protection mechanisms (IPPMs) to appropriate the returns to their research investments. The empirical literature has generally focused on the use of...
Progress in Weakly Coupled String Phenomenology

The weakly coupled vacuum of E8 ⊗ E8 heterotic string theory remains an attractive scenario for particle physics. The particle spectrum and the issue of dilaton stabilization are reviewed. A specific model for hidden sector condensation and supersymmetry breaking, that respects known constraints from string theory, is described, and its phenomenological and cosmological implications are discussed.
Coexistence for a multitype contact process with seasons.

We introduce a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into seasons called alternately season 1 and season 2. We prove that there is an open set of the parameters for which both species can coexist when their dispersal range is large enough. Numerical simulations also suggest that three species can coexist in the presence of two seasons. This contrasts with the long-term behavior of the time-homogeneous multitype contact process for which the species with the higher birth rate outcompetes the other species when the death rates are equal.
Almost commuting self-adjoint matrices --- the real and self-dual cases

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.
Gravitational wave sources: reflections and echoes

The recent detection of gravitational waves has generated interest in alternatives to the black hole interpretation of sources. A subset of such alternatives involves a prediction of gravitational wave ‘echoes’. We consider two aspects of possible echoes: first, general features of echoes coming from spacetime reflecting conditions. We find that the detailed nature of such echoes does not bear any clear relationship to quasi-normal frequencies. Second, we point out the pitfalls in the analysis of local reflecting ‘walls’ near the horizon of rapidly rotating black holes.
Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space

We prove Homological Mirror Symmetry for a smooth $$d$$ -dimensional Calabi–Yau hypersurface in projective space, for any $$d \ge 3$$ (for example, $$d=3$$ is the quintic threefold). The main techniques involved in the proof are: the construction of an immersed Lagrangian sphere in the ‘ $$d$$ -dimensional pair of pants’; the introduction of the ‘relative Fukaya category’, and an understanding of its grading structure; a description of the behaviour of this category with respect to branched covers (via an ‘orbifold’ Fukaya category); a Morse–Bott model for the relative Fukaya category that allows one to make explicit computations; and the introduction of certain graded categories of matrix factorizations mirror to the relative Fukaya category.
Radiative corrections to masses and couplings in universal extra dimensions

Models with an orbifolded universal extra dimension receive important loop-induced corrections to the masses and couplings of Kaluza-Klein (KK) particles. The dominant contributions stem from so-called boundary terms which violate KK number. Previously, only the parts of these boundary terms proportional to ln(ΛR) have been computed, where R is the radius of the extra dimension and Λ is cut-off scale. However, for typical values of ΛR ∼ 10 · · · 50, the logarithms are not particularly large and non-logarithmic contributions may be numerically important. In this paper, these remaining finite terms are computed and their phenomenological impact is discussed. It is shown that the finite terms have a significant impact on the KK mass spectrum. Furthermore, one finds new KK-number violating interactions that do not depend on ln(ΛR) but nevertheless are non-zero. These lead to new production and decay channels for level-2 KK particles at colliders.
Conformal invariance and the metrication of the fundamental forces

We revisit Weyl’s metrication (geometrization) of electromagnetism. We show that by making Weyl’s proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion, we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang–Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.
A RAY-TRACING ALGORITHM FOR SPINNING COMPACT OBJECT SPACETIMES WITH ARBITRARY QUADRUPOLE MOMENTS. II. NEUTRON STARS

A moderately spinning neutron star acquires an oblate shape and a spacetime with a significant quadrupole moment. These two properties affect its apparent surface area for an observer at infinity, as well as the light curve arising from a hot spot on its surface. In this paper, we develop a ray-tracing algorithm to calculate the apparent surface areas of moderately spinning neutron stars making use of the Hartle-Thorne metric. This analytic metric allows us to calculate various observables of the neutron star in a way that depends only on its macroscopic properties and not on the details of its equation of state. We use this algorithm to calculate the changes in the apparent surface area, which could play a role in measurements of neutron-star radii and, therefore, in constraining their equation of state. We show that whether a spinning neutron star appears larger or smaller than its non-rotating counterpart depends primarily on its equatorial radius. For neutron stars with radii ~10 km, the corrections to the Schwarzschild spacetime cause the apparent surface area to increase with spin frequency. In contrast, for neutron stars with radii ~15 km, the oblateness of the star dominates the spacetime corrections and causes the apparent surface area to decrease with increasing spin frequency. In all cases, the change in the apparent geometric surface area for the range of observed spin frequencies is 5% and hence only a small source of error in the measurement of neutron-star radii.
A Fast Approach to Creative Telescoping

In this note we reinvestigate the task of computing creative telescoping relations in differential–difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute several ideas of how to make an implementation of this approach reasonably fast and provide such an implementation. A selection of examples shows that it can be superior to existing methods by a large factor.
Holomorphic shadows in the eyes of model theory

We define a subset of an almost complex manifold (M, J) to be a holomorphic shadow if it is the image of a J-holomorphic map from a compact complex manifold. Notice that a J-holomorphic curve is a holomorphic shadow, and so is a complex subvariety of a compact complex manifold. We show that under some conditions on an almost complex structure J on a manifold M, the holomorphic shadows in the Cartesian products of (M, J) form a Zariski-type structure. Checking this leads to non-trivial geometric questions and results. We then apply the work of Hrushovski and Zilber on Zariski-type structures. We also restate results of Gromov and McDuff on J-holomorphic curves in symplectic geometry in the language of shadows structures.
Adaptive reinforcement learning through evolving self-modifying neural networks

The adaptive learning capabilities seen in biological neural networks are largely a product of the self-modifying behavior emerging from online plastic changes in synaptic connectivity. Current methods in Reinforcement Learning (RL) only adjust to new interactions after reflection over a specified time interval, preventing the emergence of online adaptivity. Recent work addressing this by endowing artificial neural networks with neuromodulated plasticity have been shown to improve performance on simple RL tasks trained using backpropagation, but have yet to scale up to larger problems. Here we study the problem of meta-learning in a challenging quadruped domain, where each leg of the quadruped has a chance of becoming unusable, requiring the agent to adapt by continuing locomotion with the remaining limbs. Results demonstrate that agents evolved using self-modifying plastic networks are more capable of adapting to complex meta-learning learning tasks, even outperforming the same network updated using gradient-based algorithms while taking less time to train.
Quantum gravity effects at a black hole horizon

Abstract Quantum fluctuations in the background geometry of a black hole are shown to affect the propagation of matter states falling into the black hole in a foliation that corresponds to observations purely outside the horizon. A state that starts as a Minkowski vacuum at past null infinity gets entangled with the gravity sector, so that close to the horizon it can be represented by a statistical ensemble of orthogonal states. We construct an operator connecting the different states and comment on the possible physical meaning of the above construction. The induced energy-momentum tensor of these states is computed in the neighbourhood of the horizon, and it is found that energy-momentum fluctuations become large in the region where the bulk of the Hawking radiation is produced. The background spacetime as seen by an outside observer may be drastically altered in this region, and an outside observer should see significant interactions between the infalling matter and the outgoing Hawking radiation. The boundary of the region of strong quantum gravitational effects is given by a time-like hypersurface of constant Schwarzschild radius r one Planck unit away from the horizon. This boundary hypersurface is an example of a stretched horizon.
Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

Three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: ...
SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. III. PARTICLE DIFFUSION

We use large hybrid (kinetic-protons-fluid-electrons) simulations to investigate the transport of energetic particles in self-consistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed that ion acceleration may be very efficient (up to 10%-20% in energy), and outlined how the streaming of energetic particles amplifies the upstream magnetic field. Here, we measure particle diffusion around shocks with different strengths, finding that the mean free path for pitch-angle scattering of energetic ions is comparable with their gyroradii calculated in the self-generated turbulence. For moderately strong shocks, magnetic field amplification proceeds in the quasi-linear regime, and particles diffuse according to the self-generated diffusion coefficient, i.e., the scattering rate depends only on the amount of energy in modes with wavelengths comparable with the particle gyroradius. For very strong shocks, instead, the magnetic field is amplified up to non-linear levels, with most of the energy in modes with wavelengths comparable to the gyroradii of highest-energy ions, and energetic particles experience Bohm-like diffusion in the amplified field. We also show how enhanced diffusion facilitates the return of energetic particles to the shock, thereby determining the maximum energy that can be achieved in a given time via diffusive shock acceleration. The parameterizationmore » of the diffusion coefficient that we derive can be used to introduce self-consistent microphysics into large-scale models of cosmic ray acceleration in astrophysical sources, such as supernova remnants and clusters of galaxies.« less
Embedding realistic surveys in simulations through volume remapping

Connecting cosmological simulations to real-world observational programs is often complicated by a mismatch in geometry: while surveys often cover highly irregular cosmological volumes, simulations are customarily performed in a periodic cube. We describe a technique to remap this cube into elongated box-like shapes that are more useful for many applications. The remappings are one-to-one, volume-preserving, keep local structures intact, and involve minimal computational overhead.
Derivation of the Hall and extended magnetohydrodynamics brackets

There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this paper, we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously. As an important step in this process, we exhibit each theory's two advected fluxes (in analogy to ideal MHD's advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Lie-dragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the Euler-Lagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones.
Surface Composition of (99942) Apophis

On 2029 April 13, near-Earth asteroid (NEA) (99942) Apophis will pass at a distance of ~6 Earth radii from Earth. This event will provide researchers with a unique opportunity to study the effects of tidal forces experienced by an asteroid during a close encounter with a terrestrial planet. Binzel et al. predicted that close flybys of terrestrial planets by NEAs would cause resurfacing of their regolith due to seismic shaking. In this work, we present the best pre-encounter near-infrared spectra of Apophis obtained so far. These new data were obtained during the 2013 apparition using the NASA Infrared Telescope Facility (IRTF). We found that our spectral data is consistent with previous observations by Binzel et al. but with a much higher signal-to-noise ratio. Spectral band parameters were extracted from the spectra and were used to determine the composition of the asteroid. Using a naive Bayes classifier, we computed the likelihood of Apophis being an LL chondrite to be >99% based on mol% of Fa versus Fs. Using the same method, we estimated a probability of 89% for Apophis being an LL chondrite based on ol/(ol+px) and Fs. The results from the dynamical model indicate that the most likely source region for Apophis is the ν 6 resonance in the inner main belt. Data presented in this study (especially Band I depth) could serve as a baseline to verify seismic shaking during the 2029 encounter.
Topological Field Theory and Computing with Instantons

It is well known that dynamical systems may be employed as computing machines. However, not all dynamical systems offer particular advantages compared to the standard paradigm of computation, in regard to efficiency and scalability. Recently, it was suggested that a new type of machines, named digital –hence scalable– memcomputing machines (DMMs), that employ non-linear dynamical systems with memory, can solve complex Boolean problems efficiently. This result was derived using functional analysis without, however, providing a clear understanding of which physical features make DMMs such an efficient computational tool. Here, we show, using recently proposed topological field theory of dynamical systems, that the solution search by DMMs is a composite instanton. This process effectively breaks the topological supersymmetry common to all dynamical systems, including DMMs. The emergent long-range order – a collective dynamical behavior– allows logic gates of the machines to correlate arbitrarily far away from each other, despite their non-quantum character. We exemplify these results with the solution of prime factorization, but the conclusions generalize to DMMs applied to any other Boolean problem.
The Force Singularity for Partially Immersed Parallel Plates

In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine some unusual details of the exotic behavior that can occur at the singular configuration separating infinite rise from infinite descent of the fluid between the plates, as the plates approach each other. In connection with this singular behavior, we present also some new estimates on meniscus height details.
Motivic Hilbert zeta functions of curves are rational

The motivic Hilbert zeta function of a variety . In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.
Complete families of linearly non-degenerate rational curves

We prove that every complete family of linearly non-degenerate rational curves of degree e > 2 in Pn has at most n−1 moduli. For e = 2 we prove that such a family has at most n moduli. The general method involves exhibiting a map from the base of a family X to the Grassmannian of e-planes in Pn and analyzing the resulting map on cohomology. Department of Mathematics, Columbia University, New York, NY 10025, U.S.A. e-mail: deland@math.columbia.edu Received by the editors September 12, 2008; revised November 16, 2008. Published electronically March 5, 2011. AMS subject classification: 14N05, 14H10. 1
CheckDP: An Automated and Integrated Approach for Proving Differential Privacy or Finding Precise Counterexamples

We propose CheckDP, an automated and integrated approach for proving or disproving claims that a mechanism is differentially private. CheckDP can find counterexamples for mechanisms with subtle bugs for which prior counterexample generators have failed. Furthermore, it was able to automatically generate proofs for correct mechanisms for which no formal verification was reported before. CheckDP is built on static program analysis, allowing it to be more efficient and precise in catching infrequent events than sampling based counterexample generators (which run mechanisms hundreds of thousands of times to estimate their output distribution). Moreover, its sound approach also allows automatic verification of correct mechanisms. When evaluated on standard benchmarks and newer privacy mechanisms, CheckDP generates proofs (for correct mechanisms) and counterexamples (for incorrect mechanisms) within 70 seconds without any false positives or false negatives.
An explicit model for the homotopy theory of finite-type Lie $n$–algebras

Lie n–algebras are the L∞ analogs of chain Lie algebras from rational homotopy theory. Henriques showed that finite-type Lie n–algebras can be integrated to produce certain simplicial Banach manifolds, known as Lie ∞–groups, via a smooth analog of Sullivan’s realization functor. We provide an explicit proof that the category of finite-type Lie n–algebras and (weak) L∞–morphisms admits the structure of a category of fibrant objects (CFO) for a homotopy theory. Roughly speaking, this CFO structure can be thought of as the transfer of the classical projective CFO structure on nonnegatively graded chain complexes via the tangent functor. In particular, the weak equivalences are precisely the L∞–quasi-isomorphisms. Along the way, we give explicit constructions for pullbacks and factorizations of L∞–morphisms between finite-type Lie n–algebras. We also analyze Postnikov towers and Maurer–Cartan/deformation functors associated to such Lie n–algebras. The main application of this work is our joint paper with C Zhu (1127–1219), which characterizes the compatibility of Henriques’ integration functor with the homotopy theory of Lie n–algebras and that of Lie ∞–groups.
Exact expressions for double descent and implicit regularization via surrogate random design

Double descent refers to the phase transition that is exhibited by the generalization error of unregularized learning models when varying the ratio between the number of parameters and the number of training samples. The recent success of highly over-parameterized machine learning models such as deep neural networks has motivated a theoretical analysis of the double descent phenomenon in classical models such as linear regression which can also generalize well in the over-parameterized regime. We provide the first exact non-asymptotic expressions for double descent of the minimum norm linear estimator. Our approach involves constructing a special determinantal point process which we call surrogate random design, to replace the standard i.i.d. design of the training sample. This surrogate design admits exact expressions for the mean squared error of the estimator while preserving the key properties of the standard design. We also establish an exact implicit regularization result for over-parameterized training samples. In particular, we show that, for the surrogate design, the implicit bias of the unregularized minimum norm estimator precisely corresponds to solving a ridge-regularized least squares problem on the population distribution. In our analysis we introduce a new mathematical tool of independent interest: the class of random matrices for which determinant commutes with expectation.
Tracing the Hercules stream around the Galaxy

It has been proposed that the Hercules stream, a group of co-moving stars in the solar neighborhood offset from the bulk of the velocity distribution, is the result of resonant interactions between stars in the outer disk and the Galactic bar. So far it has only been seen in the immediate solar neighborhood, but the resonance model makes a prediction over a large fraction of the Galactic disk. I predict the distribution of stellar velocities and the changing Hercules feature in this distribution as a function of location in the Galactic disk in a simple model for the Galaxy and the bar that produces the observed Hercules stream. The Hercules feature is expected to be strong enough to be unambiguously detected in the distribution of line-of-sight velocities in selected directions. I identify quantitatively the most promising lines of sight for detection in line-of-sight velocities using the Kullback-Leibler divergence between the predictions of the resonance model and an axisymmetric model; these directions are at 250? l 290?. The predictions presented here are only weakly affected by distance uncertainties, assumptions about the distribution function in the stellar disk, and the details of the Galactic potential including the effect of spiral structure. Gaia and future spectroscopic surveys of the Galactic disk such as APOGEE and HERMES will be able to robustly test the origin of the Hercules stream and constrain the properties of the Galactic bar.
The Riemannian L 2 topology on the manifold of Riemannian metrics

We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate the topology on the manifold of metrics induced by the distance function of the L 2 Riemannian metric—so-called because it induces an L 2 topology on each tangent space. It turns out that this topology on the tangent spaces gives rise to an L 1-type topology on the manifold of metrics itself. We study this new topology and its completion, which agrees homeomorphically with the completion of the L 2 metric. We also give a user-friendly criterion for convergence (with respect to the L 2 metric) in the manifold of metrics.
Feedback motion planning under non-Gaussian uncertainty and non-convex state constraints

Planning under process and measurement uncertainties is a challenging problem. In its most general form, it can be modeled as a Partially Observed Markov Decision Process (POMDP) problem. However POMDPs are generally difficult to solve when the underlying spaces are continuous, particularly when beliefs are non-Gaussian, and the difficulty is further exacerbated when there are also non-convex constraints on states. Existing algorithms to address such challenging POMDPs are expensive in terms of computation and memory. In this paper, we provide a feedback policy in non-Gaussian belief space by solving a convex program for common non-linear observation models. The solution involves a Receding Horizon Control strategy using particle filters for the non-Gaussian belief representation. We develop a way of capturing non-convex constraints in the state space and adapt the optimization to incorporate such constraints, as well. A key advantage of this method is that it does not introduce additional variables in the optimization problem and is therefore more scalable than existing constrained problems in belief space. We demonstrate the performance of the method on different scenarios.
Error propagation dynamics of PIV-based pressure field calculations: How well does the pressure Poisson solver perform inherently?

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.
Van der Waals Universality in Homonuclear Atom-Dimer Elastic Collisions

The universal aspects of atom-dimer elastic collisions are investigated within the framework of Faddeev equations. The two-body interactions between the neutral atoms are approximated by the separable potential approach. Our analysis considers a pure van der Waals potential tail as well as soft-core van der Waals interactions permitting us in this manner to address the universally general features of atom-dimer resonant spectra. In particular, we show that the atom-dimer resonances are solely associated with the excited Efimov states. Furthermore, the positions of the corresponding resonances for a soft-core potentials with more than 5 bound states are in good agreement with the corresponding results from an infinitely deep pure van der Waals tail potential.
Stability and the gauge problem in non-perturbative cosmology

In this paper, we describe the first steps towards fully non-perturbative cosmology. We explain why the conventional methods used by cosmologists based on the ADM formulation are generally inadequate for this purpose and why it is advantageous instead to adapt the harmonic formulation pioneered and utilized in mathematical and numerical relativity. Here we focus on using this approach to evaluating the linear mode stability in homogeneous and nearly homogeneous backgrounds and devising a valid scheme and diagnostics for numerical computation. We also briefly touch on the relevance of these methods for extracting cosmological observables from non-perturbative simulations.
Off-policy Policy Evaluation For Sequential Decisions Under Unobserved Confounding

When observed decisions depend only on observed features, off-policy policy evaluation (OPE) methods for sequential decision making problems can estimate the performance of evaluation policies before deploying them. This assumption is frequently violated due to unobserved confounders, unrecorded variables that impact both the decisions and their outcomes. We assess robustness of OPE methods under unobserved confounding by developing worst-case bounds on the performance of an evaluation policy. When unobserved confounders can affect every decision in an episode, we demonstrate that even small amounts of per-decision confounding can heavily bias OPE methods. Fortunately, in a number of important settings found in healthcare, policy-making, operations, and technology, unobserved confounders may primarily affect only one of the many decisions made. Under this less pessimistic model of one-decision confounding, we propose an efficient loss-minimization-based procedure for computing worst-case bounds, and prove its statistical consistency. On two simulated healthcare examples---management of sepsis patients and developmental interventions for autistic children---where this is a reasonable model of confounding, we demonstrate that our method invalidates non-robust results and provides meaningful certificates of robustness, allowing reliable selection of policies even under unobserved confounding.
Candidate Tidal Dwarf Galaxies in Arp 305: Lessons on Dwarf Detachment and Globular Cluster Formation

To search for Tidal Dwarf Galaxies (TDGs) and to study star formation (SF) in tidal features, we are conducting a large UV imaging survey of interacting galaxies selected from the Arp (1996) Atlas using the Galaxy Evolution Explorer (GALEX) telescope. As part of that study, we present a GALEX UV and Sloan Digital Sky Survey and SARA optical study of the gas-rich interacting galaxy pair Arp 305 (NGC 4016/7). The GALEX UV data reveal much extended diffuse UV emission and SF outside the disks. This includes a luminous star-forming region between the two galaxies, and a number of such regions in tidal tails. We have identified 45 young star-forming clumps in Arp 305, including several TDG candidates. By comparing the UV and optical colors to population synthesis models, we determined that the clumps are very young, with several having ages ~6 Myr. We do not find many intermediate age clumps in spite of the fact that the last closest encounter was about 300 Myr ago. We have used a smooth particle hydrodynamics code to model the interaction and determine the fate of the star clusters and candidate TDGs.
Laminar free shear layer modification using localized periodic heating

The application of local periodic heating for control of a spatially developing shear layer downstream of a finite-thickness splitter plate is examined by numerically solving the two-dimensional Navier–Stokes equations. At the trailing edge of the plate, an oscillatory heat flux boundary condition is prescribed as the thermal forcing input to the shear layer. The thermal forcing introduces a low level of oscillatory surface vorticity flux and baroclinic vorticity at the actuation frequency in the vicinity of the trailing edge. The vortical perturbations produced can independently excite the fundamental instability that accounts for shear layer roll-up as well as the subharmonic instability that encourages the vortex pairing process farther downstream. We demonstrate that the nonlinear dynamics of a spatially developing shear layer can be modified by local oscillatory heat flux as a control input. We believe that this study provides a basic foundation for flow control using thermal-energy-deposition-based actuators such as thermophones and plasma actuators.
Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

The drawdown process of a one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown precedes a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are applied to address problems in risk analysis and for option pricing of the drawdown process. Finally, we present examples of Brownian motion with drift and three-dimensional Bessel processes, where we prove an identity in law.
High-Speed Bullet Ejections during the AGB to Planetary Nebula Transition: HST Observations of the Carbon Star, V Hydrae

The well-studied carbon star, V Hya, showing evidence for high-speed, collimated outflows and dense equatorial structures, is a key object in the study of the poorly understood transition of AGB stars into aspherical planetary nebulae. Using the Space Telescope Imaging Spectrograph instrument on board the Hubble Space Telescope, we have obtained high spatial-resolution long-slit optical spectra of V Hya that show high-velocity emission in [S ii] and [Fe ii] lines. Our data set, spanning three epochs spaced apart by a year during each of two periods (in 2002–2004 and 2011–2013), shows that V Hya ejects high-speed (~200–250 ) bullets once every ~8.5 years. The ejection axis flip–flops around a roughly eastern direction, both in and perpendicular to the sky-plane, and the radial velocities of the ejecta also vary in concert between low and high values. We propose a model in which the bullet ejection is associated with the periastron passage of a binary companion in an eccentric orbit around V Hya with an orbital period of ~8.5 years. The flip–flop phenomenon is likely the result of collimated ejection from an accretion disk (produced by gravitational capture of material from the primary) that is warped and precessing, and/or that has a magnetic field that is misaligned with that of the companion or the primary star. We show how a previously observed 17 year period in V Hya's light-cycle can also be explained in our model. Additionally, we describe how the model proposed here can be extended to account for multipolar nebulae.
Constraining the Solar Galactic Reflex Velocity using Gaia Observations of the Sagittarius Stream

Because of its particular orientation around the Galaxy - i.e., in a plane nearly perpendicular to the Galactic plane and containing both the Sun and Galactic center - the Sagittarius (Sgr) stream provides a powerful means by which to measure the solar reflex velocity, and thereby infer the velocity of the Local Standard of Rest (LSR), in a way that is independent of assumptions about the solar Galactocentric distance. Moreover, the solar reflex velocity with respect to the stream is projected almost entirely into the proper motion component of Sgr stream stars perpendicular to the Sgr plane, which makes the inferred velocity relatively immune to most Sgr model assumptions. Using Gaia DR2 proper motions of ~2,000 stars identified to be Sgr stream candidates in concert with the Law and Majewski (2010) Sgr N-body models (which provide a good match to the Gaia observations) we constrain the solar reflex velocity induced by its orbital motion around the Galaxy to be $\Theta_{\odot} = 253 \pm 6$ km/s. Assuming a solar peculiar motion in the direction of orbital rotation of 12 km/s, and an LSR velocity of 12 km/s with respect to the local circular speed, the implied circular speed of the Milky Way at the solar circle is $229 \pm 6$ km/s.
Mining Persistent Activity in Continually Evolving Networks

Frequent pattern mining is a key area of study that gives insights into the structure and dynamics of evolving networks, such as social or road networks. However, not only does a network evolve, but often the way that it evolves, itself evolves. Thus, knowing, in addition to patterns' frequencies, for how long and how regularly they have occurred-i.e., their persistence-can add to our understanding of evolving networks. In this work, we propose the problem of mining activity that persists through time in continually evolving networks-i.e., activity that repeatedly and consistently occurs. We extend the notion of temporal motifs to capture activity among specific nodes, in what we call activity snippets, which are small sequences of edge-updates that reoccur. We propose axioms and properties that a measure of persistence should satisfy, and develop such a persistence measure. We also propose PENminer, an efficient framework for mining activity snippets' Persistence in Evolving Networks, and design both offline and streaming algorithms. We apply PENminer to numerous real, large-scale evolving networks and edge streams, and find activity that is surprisingly regular over a long period of time, but too infrequent to be discovered by aggregate count alone, and bursts of activity exposed by their lack of persistence. Our findings with PENminer include neighborhoods in NYC where taxi traffic persisted through Hurricane Sandy, the opening of new bike-stations, characteristics of social network users, and more. Moreover, we use PENminer towards identifying anomalies in multiple networks, outperforming baselines at identifying subtle anomalies by 9.8-48% in AUC.
The AST/RO Survey of the Galactic Center Region. I. The Inner 3 Degrees

We present fully-sampled maps of 461GHz CO J = 4 → 3, 807GHz CO J = 7 → 6, and 492GHz [C I] 3 P1 → 3 P0 emission from the inner 3 degrees of the Galactic Center region taken with the Antarctic Submillimeter Telescope and Remote Observatory (AST/RO) in 2001–2002. The data cover −1. ◦ 3 70 K) at cloud edges to low values (<50 K) in the interiors. Typical gas pressures in the Galactic Center gas are n(H2) � Tkin ∼ 10 5.2 Kcm −3 . We present an (l, b) map of molecular hydrogen column density derived from our LVG results.
Finite Horizon Adaptive Optimal Distributed Power Allocation for Enhanced Cognitive Radio Network in the Presence of Channel Uncertainties

In this paper, novel enhanced Cognitive Radio Network (CRN) is considered by using power control where secondary users (SUs) are allowed to use wireless resources of the primary users (PUs) when PUs are deactivated, but also allow SUs to coexist with PUs while PUs are activated by managing interference caused from SUs to PUs. Therefore, a novel finite horizon adaptive optimal distributed power allocation (FH-AODPA) scheme is proposed by incorporating the effect of channel uncertainties for enhanced CRN in the presence of wireless channel uncertainties under two cases. In Case 1, proposed scheme can force the Signal-to-interference (SIR)of the SUs to converge to a higher target value for increasing network throughput when PU’s are not communicating within finite horizon. Once PUs are activated as in the Case 2, proposed scheme cannot only force the SIR’s of PUs to converge to a higher target SIR, but also force the SIR’s of SUs to converge to a lower value for regulating their interference to Pus during finite time period. In order to mitigate the attenuation of SIR’s due to channel uncertainties the proposed novel FH-AODPA allows the SIR’s of both PUs’ and SUs’ to converge to a desired target SIR while minimizing the energy consumption within finite horizon. Simulation results illustrate that this novel FH-AODPA scheme can converge much faster and cost less energy than others by adapting to the channel variations optimally.