cssi/SciSciGPT-SciSciNet huggingface dataset:
Supervised Fitting of Geometric Primitives to 3D Point Clouds

Fitting geometric primitives to 3D point cloud data bridges a gap between low-level digitized 3D data and high-level structural information on the underlying 3D shapes. As such, it enables many downstream applications in 3D data processing. For a long time, RANSAC-based methods have been the gold standard for such primitive fitting problems, but they require careful per-input parameter tuning and thus do not scale well for large datasets with diverse shapes. In this work, we introduce Supervised Primitive Fitting Network (SPFN), an end-to-end neural network that can robustly detect a varying number of primitives at different scales without any user control. The network is supervised using ground truth primitive surfaces and primitive membership for the input points. Instead of directly predicting the primitives, our architecture first predicts per-point properties and then uses a differential model estimation module to compute the primitive type and parameters. We evaluate our approach on a novel benchmark of ANSI 3D mechanical component models and demonstrate a significant improvement over both the state-of-the-art RANSAC-based methods and the direct neural prediction.
Helicity in superfluids: Existence and the classical limit

The analog of hydrodynamic helicity in superfluids is zero for all flows. A semiclassical limit is found in the link and writhe of bundles of superfluid vortices. Numerical simulations show that the dynamics of semiclassical helicity closely resemble those seen in experiments in viscous fluids.
Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems

Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on certain parameters of interest. These parameters may represent neuronal activity in a human brain, frequencies of electromagnetic waves, fluorescent probes in a cell, or magnetic relaxation times of biological tissues. Separable nonlinear inverse problems can be reformulated as underdetermined sparse-recovery problems, and solved using convex programming. This approach has had empirical success in a variety of domains, from geophysics to medical imaging, but lacks a theoretical justification. In particular, compressed-sensing theory does not apply, because the measurement operators are deterministic and violate incoherence conditions such as the restricted-isometry property. Our main contribution is a theory for sparse recovery adapted to deterministic settings. We show that convex programming succeeds in recovering the parameters of interest, as long as their values are sufficiently distinct with respect to the correlation structure of the measurement operator. The theoretical results are illustrated through numerical experiments for two applications: heat-source localization and estimation of brain activity from electroencephalography data.
Aspects of nucleation on curved and flat surfaces.

We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calculations in the plane and on the sphere. Using an isoperimetric inequality from the differential geometry literature and a theorem on the inequality’s saturation, we show how geometry informs the critical droplet size and shape. This inequality establishes a “mean field” result for nucleated droplets. We then study the effects of fluctuations on the interfaces of droplets in two dimensions, treating the droplet interface as a fluctuating line. We emphasize that care is needed in deriving the line curvature energy from the Landau-Ginzburg energy functional and in interpreting the scalings of the nucleation rate with the size of the droplet. We end with a comparison of nucleation in the plane and on a sphere.
Azumaya objects in triangulated bicategories

We introduce the notion of Azumaya object in general homotopy-theoretic settings. We give a self-contained account of Azumaya objects and Brauer groups in bicategorical contexts, generalizing the Brauer group of a commutative ring. We go on to describe triangulated bicategories and prove a characterization theorem for Azumaya objects therein. This theory applies to give a homotopical Brauer group for derived categories of rings and ring spectra. We show that the homotopical Brauer group of an Eilenberg–Mac Lane spectrum is isomorphic to the homotopical Brauer group of its underlying commutative ring. We also discuss tilting theory as an application of invertibility in triangulated bicategories.
The near field refractor

Abstract We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces separating two homogeneous media with different refractive indices that refract radiation emanating from the origin into a target domain contained in an n − 1 dimensional hypersurface. The input and output energy are prescribed. This implies the existence of lenses focusing radiation in a prescribed manner.
On the de gregorio modification of the constantin-lax-majda model

We study a modification due to De Gregorio of the Constantin–Lax–Majda (CLM) model $${\omega_{t}}$$ = $${\omega H\omega}$$ on the unit circle. The De Gregorio equation is $${\omega_{t} +u\omega_{x}-{u}_{x}\omega = 0, {u}_{x} = H\omega }$$ . In contrast with the CLM model, numerical simulations suggest that the solutions of the De Gregorio model with smooth initial data exist globally for all time, and generically converge to equilibria when $${t \rightarrow \pm \infty}$$ , in a way resembling inviscid damping. We prove that such behavior takes place near a manifold of equilibria.
DISCOVERY of A CLOSE PAIR of FAINT DWARF GALAXIES in the HALO of CENTAURUS A

As part of the Panoramic Imaging Survey of Centaurus and Sculptor (PISCeS), we report the discovery of a pair of faint dwarf galaxies (CenA-MM-Dw1 and CenA-MM-Dw2) at a projected distance of ∼90 kpc from the nearby elliptical galaxy NGC 5128 (CenA). We measure a tip of the red giant branch distance to each dwarf, finding D = 3.63 ± 0.41 Mpc for CenA-MM-Dw1 and D = 3.60 ± 0.41 Mpc for CenA-MM-Dw2, both of which are consistent with the distance to NGC 5128. A qualitative analysis of the color-magnitude diagrams indicates stellar populations consisting of an old, metal-poor red giant branch (≳12 Gyr, [Fe/H] ∼ –1.7 to –1.9). In addition, CenA-MM-Dw1 seems to host an intermediate-age population as indicated by its candidate asymptotic giant branch stars. The derived luminosities (M{sub V} = –10.9 ± 0.3 for CenA-MM-Dw1 and –8.4 ± 0.6 for CenA-MM-Dw2) and half-light radii (r{sub h} = 1.4 ± 0.04 kpc for CenA-MM-Dw1 and 0.36 ± 0.08 kpc for CenA-MM-Dw2) are consistent with those of Local Group dwarfs. CenA-MM-Dw1's low central surface brightness (μ {sub V,} {sub 0} = 27.3 ± 0.1 mag arcsec{sup –2}) places it among the faintest and most extended M31 satellites. Most intriguingly, CenA-MM-Dw1 and CenA-MM-Dw2 have a projected separation of only 3 arcmin (∼3 kpc): wemore » are possibly observing the first, faint satellite of a satellite in an external group of galaxies.« less
Renormalization and matching for the Collins-Soper kernel from lattice QCD

The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI′/MOM) scheme, as well as the conversion factor from the RI′/MOM-renormalized quasi-TMDPDF to the $$ \overline{\mathrm{MS}} $$ scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.
Carrier transport in films of alkyl-ligand-terminated silicon nanocrystals

Silicon nanocrystals (Si NCs) have shown great promise for electroluminescent and photoluminescent applications. In order to optimize the properties of Si NC devices, however, electronic transport in Si NC films needs to be thoroughly understood. Here we present a systematic study of the temperature and electric field dependence of conductivity in films of alkyl-ligand-terminated Si NCs, which to date have shown the highest potential for device applications. Our measurements suggest that the conductivity is limited by the ionization of rare NCs containing donor impurities. At low bias, this ionization is thermally activated, with an ionization energy equal to twice the NC charging energy. As the bias is increased, the ionization energy is reduced by the electric field, as determined by the Poole–Frenkel effect. At large bias and sufficiently low temperature, we observe cold ionization of electrons from donor-containing NCs, with a characteristic tunneling length of about 1 nm. The temperature- and electri...
GASEOUS MEAN OPACITIES FOR GIANT PLANET AND ULTRACOOL DWARF ATMOSPHERES OVER A RANGE OF METALLICITIES AND TEMPERATURES

We present new calculations of Rosseland and Planck gaseous mean opacities relevant to the atmospheres of giant planets and ultracool dwarfs. Such calculations are used in modeling the atmospheres, interiors, formation, and evolution of these objects. Our calculations are an expansion of those presented in Freedman et al. to include lower pressures, finer temperature resolution, and also the higher metallicities most relevant for giant planet atmospheres. Calculations span 1 μbar to 300 bar, and 75-4000 K, in a nearly square grid. Opacities at metallicities from solar to 50 times solar abundances are calculated. We also provide an analytic fit to the Rosseland mean opacities over the grid in pressure, temperature, and metallicity. In addition to computing mean opacities at these local temperatures, we also calculate them with weighting functions up to 7000 K, to simulate the mean opacities for incident stellar intensities, rather than locally thermally emitted intensities. The chemical equilibrium calculations account for the settling of condensates in a gravitational field and are applicable to cloud-free giant planet and ultracool dwarf atmospheres, but not circumstellar disks. We provide our extensive opacity tables for public use.
What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation

Deep learning algorithms are well-known to have a propensity for fitting the training data very well and often fit even outliers and mislabeled data points. Such fitting requires memorization of training data labels, a phenomenon that has attracted significant research interest but has not been given a compelling explanation so far. A recent work of Feldman (2019) proposes a theoretical explanation for this phenomenon based on a combination of two insights. First, natural image and data distributions are (informally) known to be long-tailed, that is have a significant fraction of rare and atypical examples. Second, in a simple theoretical model such memorization is necessary for achieving close-to-optimal generalization error when the data distribution is long-tailed. However, no direct empirical evidence for this explanation or even an approach for obtaining such evidence were given. In this work we design experiments to test the key ideas in this theory. The experiments require estimation of the influence of each training example on the accuracy at each test example as well as memorization values of training examples. Estimating these quantities directly is computationally prohibitive but we show that closely-related subsampled influence and memorization values can be estimated much more efficiently. Our experiments demonstrate the significant benefits of memorization for generalization on several standard benchmarks. They also provide quantitative and visually compelling evidence for the theory put forth in (Feldman, 2019).
A Unified Microscopic-Macroscopic Monte Carlo Simulation of Gas-grain Chemistry in Cold Dense Interstellar Clouds

For the first time, we report a unified microscopic-macroscopic Monte Carlo simulation of gas-grain chemistry in cold interstellar clouds in which both the gas-phase and the grain-surface chemistry are simulated by a stochastic technique. The surface chemistry is simulated with a microscopic Monte Carlo method in which the chemistry occurs on an initially flat surface. The surface chemical network consists of 29 reactions initiated by the accreting species H, O, C, and CO. Four different models are run with diverse but homogeneous physical conditions including temperature, gas density, and diffusion-barrier-to-desorption energy ratio. As time increases, icy interstellar mantles begin to grow. Our approach allows us to determine the morphology of the ice, layer by layer, as a function of time, and to ascertain the environment or environments for individual molecules. Our calculated abundances can be compared with observations of ices and gas-phase species, as well as the results of other models.
On a new class of tempered stable distributions: moments and regular variation

We extend the class of tempered stable distributions, which were first introduced in Rosinski (2007). Our new class allows for more structure and more variety of the tail behaviors. We discuss various subclasses and the relations between them. To characterize the possible tails, we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs.
3D string theory and Umbral moonshine

The simplest string theory compactifications to 3D with 16 supercharges—the heterotic string on T 7, and type II strings on —are related by U-duality, and share a moduli space of vacua parametrized by . One can think of this as the moduli space of even, self-dual 32-dimensional lattices with signature (8,24). At 24 special points in moduli space, the lattice splits as . can be the Leech lattice or any of 23 Niemeier lattices, while is the E 8 root lattice. We show that starting from this observation, one can find a precise connection between the Umbral groups and type IIA string theory on K3. This may provide a natural physical starting point for understanding Mathieu and Umbral moonshine. The maximal unbroken subgroups of Umbral groups in 6D (or any other limit) are those obtained by starting at the associated Niemeier point and moving in moduli space while preserving the largest possible subgroup of the Umbral group. To illustrate the action of these symmetries on BPS states, we discuss the computation of certain protected four-derivative terms in the effective field theory, and recover facts about the spectrum and symmetry representations of 1/2-BPS states.
ACE bounds; SEMs with equilibrium conditions

Discussion of "Instrumental Variables: An Econometrician's Perspective" by Guido W. Imbens [arXiv:1410.0163].
A Generalization of Quantum Statistics

We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.
A quantum-inspired classical algorithm for recommendation systems

We give a classical analogue to Kerenidis and Prakash’s quantum recommendation system, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning. Our main result is an algorithm that, given an m × n matrix in a data structure supporting certain l2-norm sampling operations, outputs an l2-norm sample from a rank-k approximation of that matrix in time O(poly(k)log(mn)), only polynomially slower than the quantum algorithm. As a consequence, Kerenidis and Prakash’s algorithm does not in fact give an exponential speedup over classical algorithms. Further, under strong input assumptions, the classical recommendation system resulting from our algorithm produces recommendations exponentially faster than previous classical systems, which run in time linear in m and n. The main insight of this work is the use of simple routines to manipulate l2-norm sampling distributions, which play the role of quantum superpositions in the classical setting. This correspondence indicates a potentially fruitful framework for formally comparing quantum machine learning algorithms to classical machine learning algorithms.
Polymer Nanofibers with Outstanding Thermal Conductivity and Thermal Stability: Fundamental Linkage between Molecular Characteristics and Macroscopic Thermal Properties

Polymer nanofibers with high thermal conductivities and outstanding thermal stabilities are highly desirable in heat transfer-critical applications such as thermal management, heat exchangers, and energy storage. In this work, we unlock the fundamental relations between the thermal conductivity and thermal stability of polymer nanofibers and their molecular characteristics by studying the temperature-induced phase transitions and thermal transport of a series of polymer nanofibers. Ten different polymer nanofibers with systematically chosen molecular structures are studied using large-scale molecular dynamics simulations. We found that high thermal conductivity and good thermal stability can be achieved in polymers with rigid backbones, exemplified by π-conjugated polymers, due to suppressed segmental rotations and large phonon group velocities. The low probability of segmental rotation not only prevents temperature-induced phase transition but also enables long phonon mean free paths due to reduced disor...
Dusty Star Forming Galaxies at High Redshift

Abstract Far-infrared and submillimeter wavelength surveys have now established the important role of dusty, star-forming galaxies (DSFGs) in the assembly of stellar mass and the evolution of massive galaxies in the Universe. The brightest of these galaxies have infrared luminosities in excess of 10 13 L ⊙ with implied star-formation rates of thousands of solar masses per year. They represent the most intense starbursts in the Universe, yet many are completely optically obscured. Their easy detection at submm wavelengths is due to dust heated by ultraviolet radiation of newly forming stars. When summed up, all of the dusty, star-forming galaxies in the Universe produce an infrared radiation field that has an equal energy density as the direct starlight emission from all galaxies visible at ultraviolet and optical wavelengths. The bulk of this infrared extragalactic background light emanates from galaxies as diverse as gas-rich disks to mergers of intense starbursting galaxies. Major advances in far-infrared instrumentation in recent years, both space-based and ground-based, has led to the detection of nearly a million DSFGs, yet our understanding of the underlying astrophysics that govern the start and end of the dusty starburst phase is still in nascent stage. This review is aimed at summarizing the current status of DSFG studies, focusing especially on the detailed characterization of the best-understood subset (submillimeter galaxies, who were summarized in the last review of this field over a decade ago, Blain et al., 2002), but also the selection and characterization of more recently discovered DSFG populations. We review DSFG population statistics, their physical properties including dust, gas and stellar contents, their environments, and current theoretical models related to the formation and evolution of these galaxies.
Stellar Binaries Incident on Supermassive Black Hole Binaries: Implications for Double Tidal Disruption Events, Calcium-rich Transients, and Hypervelocity Stars

We analyze the outcome of the interaction between a stellar binary and a supermassive black hole binary (SMBHB) by performing a large number of gravitational scattering experiments. Most of the encounters result in either the ejection of an intact binary or the ejection of two individual stars following the tidal breakup of the binary. However, tidal disruption events (TDEs) and mergers constitute a few percent of the outcomes, and double, temporally distinct TDEs (i.e., separated by at least one orbit of the supermassive black hole binary) occur at the percent level. We also demonstrate that the properties of the ejected binaries are significantly altered through the interaction with the SMBHB, and their large eccentricities increase the merger rate and could lead to gravitational-wave inspirals far from the nucleus of the host galaxy. We discuss our results in the context of observed tidal disruption events, hypervelocity stars, and remote supernovae, such as calcium-rich transients.
X-ray diffraction from shock-loaded polycrystals.

X-ray diffraction was demonstrated from shock-compressed polycrystalline metals on nanosecond time scales. Laser ablation was used to induce shock waves in polycrystalline foils of Be, 25–125μm thick. A second laser pulse was used to generate a plasma x-ray source by irradiation of a Ti foil. The x-ray source was collimated to produce a beam of controllable diameter, which was directed at the Be sample. X-rays were diffracted from the sample, and detected using films and x-ray streak cameras. The diffraction angle was observed to change with shock pressure. The diffraction angles were consistent with the uniaxial (elastic) and isotropic (plastic) compressions expected for the loading conditions used. Polycrystalline diffraction will be used to measure the response of the crystal lattice to high shock pressures and through phase changes.
Diffraction limited focusing and routing of gap plasmons by a metal-dielectric-metal lens

Passive optical elements can play key roles in photonic applications such as plasmonic integrated circuits. Here we experimentally demonstrate passive gap-plasmon focusing and routing in two-dimensions. This is accomplished using a high numerical-aperture metal-dielectric-metal lens incorporated into a planar-waveguide device. Fabrication via metal sputtering, oxide deposition, electron- and focused-ion- beam lithography, and argon ion-milling is reported on in detail. Diffraction-limited focusing is optically characterized by sampling out-coupled light with a microscope. The measured focal distance and full-width-half-maximum spot size agree well with the calculated lens performance. The surface plasmon polariton propagation length is measured by sampling light from multiple out-coupler slits.
Energy Flow Networks: Deep Sets for Particle Jets

A key question for machine learning approaches in particle physics is how to best represent and learn from collider events. As an event is intrinsically a variable-length unordered set of particles, we build upon recent machine learning efforts to learn directly from sets of features or “point clouds”. Adapting and specializing the “Deep Sets” framework to particle physics, we introduce Energy Flow Networks, which respect infrared and collinear safety by construction. We also develop Particle Flow Networks, which allow for general energy dependence and the inclusion of additional particle-level information such as charge and flavor. These networks feature a per-particle internal (latent) representation, and summing over all particles yields an overall event-level latent representation. We show how this latent space decomposition unifies existing event representations based on detector images and radiation moments. To demonstrate the power and simplicity of this set-based approach, we apply these networks to the collider task of discriminating quark jets from gluon jets, finding similar or improved performance compared to existing methods. We also show how the learned event representation can be directly visualized, providing insight into the inner workings of the model. These architectures lend themselves to efficiently processing and analyzing events for a wide variety of tasks at the Large Hadron Collider. Implementations and examples of our architectures are available online in our EnergyFlow package.
Spectroscopic infrared extinction mapping as a probe of grain growth in IRDCs

We present spectroscopic tests of MIR to FIR extinction laws in IRDC G028.36+00.07, a potential site of massive star and star cluster formation. Lim & Tan developed methods of FIR extinction mapping of this source using Spitzer-MIPS 24 μm and Herschel-PACS 70 μm images, and by comparing to MIR Spitzer-IRAC 3–8 μm extinction maps, found tentative evidence for grain growth in the highest mass surface density regions. Here we present results of spectroscopic infrared extinction mapping using Spitzer-IRS (14–38 μm) data of the same Infrared dark cloud (IRDC). These methods allow us to first measure the SED of the diffuse Galactic interstellar medium that is in the foreground of the IRDC. We then carry out our primary investigation of measuring the MIR to FIR opacity law and searching for potential variations as a function of mass surface density within the IRDC. We find relatively flat, featureless MIR–FIR opacity laws that lack the ~12 and ~35 μm features associated with the thick water ice mantle models of Ossenkopf & Henning. Their thin ice mantle models and the coagulating aggregate dust models of Ormel et al. are a generally better match to the observed opacity laws. We also find evidence for generally flatter MIR to FIR extinction laws as mass surface density increases, strengthening the evidence for grain and ice mantle growth in higher density regions.
Improved Point-source Detection in Crowded Fields Using Probabilistic Cataloging

Cataloging is challenging in crowded fields because sources are extremely covariant with their neighbors and blending makes even the number of sources ambiguous. We present the first optical probabilistic catalog, cataloging a crowded (~0.1 sources per pixel brighter than 22nd magnitude in F606W) Sloan Digital Sky Survey r band image from M2. Probabilistic cataloging returns an ensemble of catalogs inferred from the image and thus can capture source-source covariance and deblending ambiguities. By comparing to a traditional catalog of the same image and a Hubble Space Telescope catalog of the same region, we show that our catalog ensemble better recovers sources from the image. It goes more than a magnitude deeper than the traditional catalog while having a lower false discovery rate brighter than 20th magnitude. We also present an algorithm for reducing this catalog ensemble to a condensed catalog that is similar to a traditional catalog, except it explicitly marginalizes over source-source covariances and nuisance parameters. We show that this condensed catalog has a similar completeness and false discovery rate to the catalog ensemble. Future telescopes will be more sensitive, and thus more of their images will be crowded. Probabilistic cataloging performs better than existing software in crowded fields and so should be considered when creating photometric pipelines in the Large Synoptic Survey Telescope era.
Algebraic motion of vertically displacing plasmas

The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating...
The contact homology of Legendrian knots with maximal Thurston-Bennequin invariant

The Chekanov–Eliashberg invariant [2,4], which assigns to each Legendrian knot K a differential graded algebra (Ch(K), ∂) over F = Z/2Z, has been a powerful tool for classifying Legendrian knots in the standard contact S3. The closely related characteristic algebra C(K) was defined by Ng [13] to be the quotient of Ch(K) by the two-sided ideal 〈Im(∂)〉; if two knots K and K ′ are Legendrian isotopic, then we can add some free generators to C(K) and C(K ′) to make them isomorphic. Both of these invariants only provide information about nondestabilizable knots: if K is a stabilized knot, then both the Legendrian contact homology H∗(Ch(K)) and the characteristic algebra C(K) vanish. For an introduction to Legendrian knots, see [6]. Shonkwiler and Vela-Vick [20] gave the first examples of Legendrian knots with nonvanishing contact homology which do not have maximal Thurston– Bennequin invariant, representing the knot types m(10161) and m(10145). Conversely, there are conjecturally nondestabilizable knots of type m(10139), 10161, and m(12n242) with nonmaximal tb and vanishing contact homology [3, 20]. On the other hand, it is an open question whether there is a Legendrian knot K for which tb(K) is maximal but the contact homology of K vanishes. We will answer this question and show that it is not determined solely by the classical invariants tb and r of K:
Hilbert schemes of 8 points

The Hilbert scheme Hnd of n points in Ad contains an irreducible component Rnd which generically represents n distinct points in Ad. We show that when n is at most 8, the Hilbert scheme Hnd is reducible if and only if n=8 and d≥4. In the simplest case of reducibility, the component R84⊂H84 is defined by a single explicit equation, which serves as a criterion for deciding whether a given ideal is a limit of distinct points. To understand the components of the Hilbert scheme, we study the closed subschemes of Hnd which parametrize those ideals which are homogeneous and have a fixed Hilbert function. These subschemes are a special case of multigraded Hilbert schemes, and we describe their components when the colength is at most 8. In particular, we show that the scheme corresponding to the Hilbert function (1,3,2,1) is the minimal reducible example.
Attacker Control and Impact for Confidentiality and Integrity

Language-based information flow methods offer a principled way to enforce strong security properties, but enforcing noninterference is too inflexible for realistic applications. Security-typed languages have therefore introduced declassification mechanisms for relaxing confidentiality policies, and endorsement mechanisms for relaxing integrity policies. However, a continuing challenge has been to define what security is guaranteed when such mechanisms are used. This paper presents a new semantic framework for expressing security policies for declassification and endorsement in a language-based setting. The key insight is that security can be characterized in terms of the influence that declassification and endorsement allow to the attacker. The new framework introduces two notions of security to describe the influence of the attacker. Attacker control defines what the attacker is able to learn from observable effects of this code; attacker impact captures the attacker's influence on trusted locations. This approach yields novel security conditions for checked endorsements and robust integrity. The framework is flexible enough to recover and to improve on the previously introduced notions of robustness and qualified robustness. Further, the new security conditions can be soundly enforced by a security type system. The applicability and enforcement of the new policies is illustrated through various examples, including data sanitization and authentication.
Topological partition function and string-string duality

Abstract Evidence for string/string-duality can be given not only by matching the vector couplings but also by matching the gravitational couplings. In this note this is shown in the rank three example, the closest stringy analog of the Seiberg/Witten-setup, which is related to the Calabi-Yau WP 1,1,2,2,6 4 (12). I provide an exact analytical verification of a relation checked by coefficient comparison to fourth order by Kaplunovsky, Louis and Theisen.
Symmetrization of principal minors and cycle-sums

We solve the Symmetrized Principal Minor Assignment Problem, that is we show how to determine if for a given vector there is an matrix that has all principal minors equal to . We use a special isomorphism (a non-linear change of coordinates to cycle-sums) that simplifies computation and reveals hidden structure. We use the symmetries that preserve symmetrized principal minors and cycle-sums to treat three cases: symmetric, skew-symmetric and general square matrices. We describe the matrices that have such symmetrized principal minors as well as the ideal of relations among symmetrized principal minors / cycle-sums. We also connect the resulting algebraic varieties of symmetrized principal minors to tangential and secant varieties, and Eulerian polynomials.
Content-Based Cognitive Interference Control for City Monitoring Applications in the Urban IoT

In the Urban Internet of Things (IoT), devices and systems are interconnected at the city scale to provide innovative services to the citizens. However, the traffic generated by the sensing and processing systems may overload local access networks. A coexistence problem arises where concurrent applications mutually interfere and compete for available resources. This effect is further aggravated by the multiple scales involved and heterogeneity of the networks supporting the urban IoT. One of the main contributions of this paper is the introduction of the notion of content- oriented cognitive interference control in heterogeneous local access networks supporting computing and data processing in the urban IoT. A network scenario where multiple communication technologies, such as Device-to- Device and Long Term Evolution (LTE), is considered. The focus of the present paper is on city monitoring applications, where a video data stream generated by a camera system is remotely processed to detect objects. The cognitive network paradigm is extended to dynamically shape the interference pattern generated by concurrent data streams and induce a packet loss trajectory compatible with video processing algorithms. Numerical results show that the proposed cognitive transmission strategy enables a significant throughput increase of interfering applications for a target accuracy of the monitoring application.
A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields

In 2014, Flynn and the second author bounded the average number of components of the functional graphs of polynomials of fixed degree over a finite field. When the fixed degree was large (relative to the size of the finite field), their lower bound matched Kruskal's asymptotic for random functional graphs. However, when the fixed degree was small, they were unable to match Krusal's bound, since they could not (Lagrange) interpolate cycles in functional graphs of length greater than the fixed degree. In our work, we introduce a heuristic for approximating the average number of such cycles of any length. This heuristic is, roughly, that for sets of edges in a functional graph, the quality of being a cycle and the quality of being interpolable are "uncorrelated enough". We prove that this heuristic implies that the average number of components of the functional graphs of polynomials of fixed degree over a finite field is within a bounded constant of Kruskal's bound. We also analyze some numerical data comparing implications of this heuristic to some component counts of functional graphs of polynomials over finite fields.
ORIGIN OF THE DENSE CORE MASS FUNCTION IN CONTRACTING FILAMENTS

Mass functions of starless dense cores (CMFs) may arise from contraction and dispersal of core-forming filaments. In an illustrative model, a filament contracts radially by self-gravity, increasing the mass of its cores. During this contraction, FUV photoevaporation and ablation by shocks and winds disperse filament gas and limit core growth. The stopping times of core growth are described by a waiting-time distribution. The initial filament column density profile and the resulting CMF each match recent Herschel observations in detail. Then low-mass cores have short growth ages and arise from the innermost filament gas, while massive cores have long growth ages and draw from more extended filament gas. The model fits the initial density profile and CMF best for mean core density 2 × 104 cm–3 and filament dispersal timescale 0.5 Myr. Then the typical core mass, radius, mean column density, and contraction speed are respectively 0.8 solar masses, 0.06 pc, 6 × 1021 cm–2, and 0.07 km s–1, also in accord with observed values.
A hybrid advection scheme for conserving angular momentum on a refined Cartesian mesh

We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable nonaxisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios and on quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows such as accretion disks and mass-transferring binary systems.
On the Submillimeter Opacity of Protoplanetary Disks

Solid particles with the composition of interstellar dust and power-law size distribution dn/da ∝ a-p (for a ≤ amax with amax 3λ and 3 < p < 4) will have submillimeter opacity spectral index β(λ) ≡ d ln κ/d ln ν ≈ (p - 3)βISM, where βISM ≈ 1.7 is the opacity spectral index of interstellar dust material in the Rayleigh limit. For the power-law index p ≈ 3.5, which characterizes interstellar dust and may apply for particles growing by agglomeration in protoplanetary disks, grain growth to sizes a 3 mm will result in β(1 mm) 1. Grain growth can naturally account for β ≈ 1 observed for protoplanetary disks, provided that amax 3λ.
Magnificent Four with Colors

We study the rank N magnificent four theory, which is the supersymmetric localization of U(N) super-Yang–Mills theory with matter (a super-group U(N|N) gauge theory) on a Calabi–Yau fourfold. Our theory contains the higher rank Donaldson–Thomas theory of threefolds. We conjecture an explicit formula for the partition function $${\mathcal {Z}}$$, and report on the performed checks. The partition function $${\mathcal {Z}}$$ has a free field representation. Surprisingly, it depends on the Coulomb and mass parameters in a simple way. We also clarify the definition of the instanton measure.
Frequency stability characterization of a broadband fiber Fabry-Pérot interferometer

An optical etalon illuminated by a white light source provides a broadband comb-like spectrum that can be employed as a calibration source for astronomical spectrographs in radial velocity (RV) surveys for extrasolar planets. For this application the frequency stability of the etalon is critical, as its transmission spectrum is susceptible to frequency fluctuations due to changes in cavity temperature, optical power and input polarization. In this paper we present a laser frequency comb measurement technique to characterize the frequency stability of a custom-designed fiber Fabry-Perot interferometer (FFP). Simultaneously probing the stability of two etalon resonance modes, we assess both the absolute stability of the etalon and the long-term stability of the cavity dispersion. We measure mode positions with MHz precision, which corresponds to splitting the FFP resonances by a part in 500 and to RV precision of ≈ 1 m s−1. We address limiting systematic effects, including the presence of parasitic etalons, that need to be overcome to push the metrology of this system to the equivalent RV precision of 10 cm s−1. Our results demonstrate a means to characterize environmentally-driven perturbations of etalon resonance modes across broad spectral bandwidths, as well as motivate the benefits and challenges of FFPs as spectrograph calibrators.
Enhancement of NEST capabilities for simulating low-energy recoils in liquid xenon

The Noble Element Simulation Technique (NEST) is an extensive collection of models explaining both the scintillation light and ionization yields of noble elements as a function of particle type (nuclear recoils, electron recoils, alphas), electric field, and incident energy or energy loss (dE/dx). It is packaged as C++ code for Geant4 that implements said models, overriding the default model which does not account for certain complexities, such as the reduction in yields for nuclear recoils (NR) compared to electron recoils (ER). We present here improvements to the existing NEST models and updates to the code which make the package even more realistic and turn it into a more full-fledged Monte Carlo simulation. All available liquid xenon data on NR and ER to date have been taken into consideration in arriving at the current models. Furthermore, NEST addresses the question of the magnitude of the light and charge yields of nuclear recoils, including their electric field dependence, thereby helping to understand the capabilities of liquid xenon detectors for detection or exclusion of a low-mass dark matter WIMP.
Hidden functional relation in large-N quark–monopole system at finite temperature

Abstract The quark–monopole potential is computed at finite temperature in the context of AdS / CFT correspondence. It is found that the potential is invariant under g →1/ g and U T → U T / g . As in the quark–quark case there exists a maximum separation between quark and monopole, and L -dependence of the potential exhibits a bifurcation behavior. We find a functional relation dE QM Reg /dL= 1/E (1,0) Reg (U 0 ) 2 + 1/E (0,1) Reg (U 0 ) 2 −1/2 which is responsible for the bifurcation. The remarkable property of this relation is that it makes a relation between physical quantities defined at the AdS boundary through a quantity defined at the bulk. The physical implication of this relation for the existence of the extra dimension is speculated.
Fermionic Glauber Operators and Quark Reggeization

We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the t-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in |t|/s relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as qq → gg and qq → γγ. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the 3 color channel, as well as the leading logarithmic BFKL equation. Results in the 6 and 15 color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.
Unified Field Theory from Enlarged Transformation Group. The Consistent Hamiltonian

A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group enlargement was accomplished by including those transformations to anholonomic coordinates under which conservation laws are covariant statements. Field equations have been obtained from a variational principle which is invariant under the larger group. These field equations imply the validity of the Einstein equations of general relativity with a stress-energy tensor that is just what one expects for the electroweak field and associated currents. In this paper, as a first step toward quantization, a consistent Hamiltonian for the theory is obtained. Some concluding remarks are given concerning the need for further development of the theory. These remarks include discussion of a possible method for extending the theory to include the strong interaction.
GRB ASTROPHYSICS IN THE SWIFT ERA AND BEYOND

Gamma-ray Bursts (GRBs) are relativistic cosmological beacons of transient high energy radiation whose afterglows span the electromagnetic spectrum. Theoretical expectations of correlated neutrino emission position GRBs at an astrophysical nexus for a metamorphosis in our understanding of the Cosmos. This new dawn in the era of experimental (particle) astrophysics and cosmology is afforded by current facilities enabling the novel astronomy of high energy neutrinos, in concert with unprecedented electromagnetic coverage. In that regard, GRBs represent a compelling scientific theme that may facilitate fundamental breakthroughs in the context of Swift, Fermi and IceCube. Scientific synergy will be achieved by leveraging the combined sensitivity of contemporaneous ground-based and satellite observatories, thus optimizing their collective discovery potential. Hence, the advent of GRB multi-messenger astronomy may cement an explicit connection to fundamental physics, via nascent cosmic windows, throughout the next decade.