cssi/SciSciGPT-SciSciNet huggingface dataset:
Partial duals of plane graphs, separability and the graphs of knots

There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedded graph represents a link diagram. Furthermore, although a Tait graph describes a unique link diagram, the same embedded graph can represent many different link diagrams. One is then led to ask which embedded graphs represent link diagrams, and how link diagrams presented by the same embedded graphs are related to one another. Here we answer these questions by characterizing the class of embedded graphs that represent link diagrams, and then using this characterization to find a move that relates all of the link diagrams that are presented by the same set of embedded graphs.
Grain Destruction in a Supernova Remnant Shock Wave

Dust grains are sputtered away in the hot gas behind shock fronts in supernova remnants (SNRs), gradually enriching the gas phase with refractory elements. We have measured emission in C IV λ1550 from C atoms sputtered from dust in the gas behind a non-radiative shock wave in the northern Cygnus Loop. Overall, the intensity observed behind the shock agrees approximately with predictions from model calculations that match the Spitzer 24 μm and the X-ray intensity profiles. Thus, these observations confirm the overall picture of dust destruction in SNR shocks and the sputtering rates used in models. However, there is a discrepancy in that the C IV intensity 10'' behind the shock is too high compared with the intensities at the shock and 25'' behind it. Variations in the density, hydrogen neutral fraction, and the dust properties over parsec scales in the pre-shock medium limit our ability to test dust destruction models in detail.
F -signature exists

Suppose R is a d-dimensional reduced F-finite Noetherian local ring with prime characteristic p>0 and perfect residue field. Let \(R^{1/p^{e}}\) be the ring of pe-th roots of elements of R for e∈ℕ, and let ae denote the maximal rank of a free R-module appearing in a direct sum decomposition of \(R^{1/p^{e}}\). We show the existence of the limit \(s(R) := \lim_{e \to\infty} \frac{a_{e}}{p^{ed}}\), called the F-signature of R. This invariant—which can be extended to all local rings in prime characteristic—was first formally defined by C. Huneke and G. Leuschke (in Math. Ann. 324(2), 391–404, 2002) and has previously been shown to exist only in special cases. The proof of our main result is based on the development of certain uniform Hilbert-Kunz estimates of independent interest. Additionally, we analyze the behavior of the F-signature under finite ring extensions and recover explicit formulae for the F-signatures of arbitrary finite quotient singularities.
Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory

We develop an microscopic model of the M-theory Schwarzschild black hole using the Banks-Fischler-Shenker-Susskind Matrix formulation of quantum gravity. The underlying dynamics is known to be chaotic, which allows us to use methods from Random Matrix Theory and non-equilibrium statistical mechanics to propose a coarse-grained bottom-up picture of the event horizon — and the associated Hawking evaporation phenomenon. The analysis is possible due to a hierarchy between the various timescales at work. Event horizon physics is found to be non-local at the Planck scale, and we demonstrate how non-unitary physics and information loss arise from the process of averaging over the chaotic unitary dynamics. Most interestingly, we correlate the onset of non-unitarity with the emergence of spacetime geometry outside the horizon. We also write a mean field action for the evolution of qubits — represented by polarization states of supergravity modes. This evolution is shown to have similarities to a recent toy model of black hole evaporation proposed by Osuga and Page — a model aimed at developing a plausible no-firewall scenario.
Supersymmetric Two-Boson Equation, its Reductions and the Nonstandard Supersymmetric KP Hierarchy

In this paper, we review various properties of the supersymmetric Two-Boson (sTB) system. We discuss the equation and its nonstandard Lax representation. We construct the local conserved charges as well as the Hamiltonian structures of the system, and show how this system leads to various other known supersymmetric integrable models under appropriate field redefinition. We discuss the sTB and the supersymmetric nonlinear Schrodinger (sNLS) equations as constrained, nonstandard supersymmetric Kadomtsev-Petviashvili (sKP) systems and note that the nonstandard sKP systems naturally unify all the KP and mKP flows while leading to a new integrable supersymmetrization of the KP equation. We construct the nonlocal conserved charges associated with the sTB system and show that the algebra of charges corresponds to a graded, cubic algebra. Also, we note that the sTB system has a hidden supersymmetry making it an N=2 extended supersymmetric system.
The structure factor of primes

Although the prime numbers are deterministic, they can be viewed, by some measures, as pseudo-random numbers. In this article, we numerically study the pair statistics of the primes using statistical–mechanical methods, particularly the structure factor in an interval with M large, and L/M smaller than unity. We show that the structure factor of the prime-number configurations in such intervals exhibits well-defined Bragg-like peaks along with a small 'diffuse' contribution. This indicates that primes are appreciably more correlated and ordered than previously thought. Our numerical results definitively suggest an explicit formula for the locations and heights of the peaks. This formula predicts infinitely many peaks in any non-zero interval, similar to the behavior of quasicrystals. However, primes differ from quasicrystals in that the ratio between the location of any two predicted peaks is rational. We also show numerically that the diffuse part decays slowly as M and L increases. This suggests that the diffuse part vanishes in an appropriate infinite-system-size limit.
SMAUG: End-to-End Full-Stack Simulation Infrastructure for Deep Learning Workloads

In recent years, there has been tremendous advances in hardware acceleration of deep neural networks. However, most of the research has focused on optimizing accelerator microarchitecture for higher performance and energy efficiency on a per-layer basis. We find that for overall single-batch inference latency, the accelerator may only make up 25–40%, with the rest spent on data movement and in the deep learning software framework. Thus far, it has been very difficult to study end-to-end DNN performance during early stage design (before RTL is available), because there are no existing DNN frameworks that support end-to-end simulation with easy custom hardware accelerator integration. To address this gap in research infrastructure, we present SMAUG, the first DNN framework that is purpose-built for simulation of end-to-end deep learning applications. SMAUG offers researchers a wide range of capabilities for evaluating DNN workloads, from diverse network topologies to easy accelerator modeling and SoC integration. To demonstrate the power and value of SMAUG, we present case studies that show how we can optimize overall performance and energy efficiency for up to 1.8×–5× speedup over a baseline system, without changing any part of the accelerator microarchitecture, as well as show how SMAUG can tune an SoC for a camera-powered deep learning pipeline.
On Kauffman bracket skein modules of marked 3-manifolds and the Chebyshev-Frobenius homomorphism

We study the skein algebras of marked surfaces and the skein modules of marked 3–manifolds. Muller showed that skein algebras of totally marked surfaces may be embedded in easy-to-study algebras known as quantum tori. We first extend Muller’s result to permit marked surfaces with unmarked boundary components. The addition of unmarked components allows us to develop a surgery theory which enables us to extend the Chebyshev homomorphism of Bonahon and Wong between skein algebras of unmarked surfaces to a “Chebyshev–Frobenius homomorphism” between skein modules of marked 3–manifolds. We show that the image of the Chebyshev–Frobenius homomorphism is either transparent or skew-transparent. In addition, we make use of the Muller algebra method to calculate the center of the skein algebra of a marked surface when the quantum parameter is not a root of unity.
Organizing volumes of right-angled hyperbolic polyhedra

This article defines a pair of combinatorial operations on the combinatorial structure of compact right-angled hyperbolic polyhedra in dimension three called decomposition and edge surgery. It is shown that these operations simplify the combinatorics of such a polyhedron, while keeping it within the class of right-angled objects, until it is a disjoint union of Lobell polyhedra, a class of polyhedra which generalizes the dodecahedron. Furthermore, these combinatorial operations are shown to have geometric realizations which are volume decreasing. This allows for an organization of the volumes of right-angled hyperbolic polyhedra and allows, in particular, the determination of the polyhedra with smallest and second smallest volumes. 51M10, 57M50; 52B99
Methane, Carbon Monoxide, and Ammonia in Brown Dwarfs and Self-Luminous Giant Planets

We address disequilibrium abundances of some simple molecules in the atmospheres of solar composition brown dwarfs and self-luminous extrasolar giant planets using a kinetics-based one-dimensional atmospheric chemistry model. Our approach is to use the full kinetics model to survey the parameter space with effective temperatures between 500 K and 1100 K. In all of these worlds, equilibrium chemistry favors CH{sub 4} over CO in the parts of the atmosphere that can be seen from Earth, but in most disequilibrium favors CO. The small surface gravity of a planet strongly discriminates against CH{sub 4} when compared to an otherwise comparable brown dwarf. If vertical mixing is like Jupiter's, the transition from methane to CO occurs at 500 K in a planet. Sluggish vertical mixing can raise this to 600 K, but clouds or more vigorous vertical mixing could lower this to 400 K. The comparable thresholds in brown dwarfs are 1100 ± 100 K. Ammonia is also sensitive to gravity, but, unlike CH{sub 4}/CO, the NH{sub 3}/N{sub 2} ratio is insensitive to mixing, which makes NH{sub 3} a potential proxy for gravity. HCN may become interesting in high-gravity brown dwarfs with very strong vertical mixing. Detailed analysis of the CO-CH{sub 4}more » reaction network reveals that the bottleneck to CO hydrogenation goes through methanol, in partial agreement with previous work. Simple, easy to use quenching relations are derived by fitting to the complete chemistry of the full ensemble of models. These relations are valid for determining CO, CH{sub 4}, NH{sub 3}, HCN, and CO{sub 2} abundances in the range of self-luminous worlds we have studied, but may not apply if atmospheres are strongly heated at high altitudes by processes not considered here (e.g., wave breaking).« less
Investigating surface loss effects in superconducting transmon qubits

Superconducting qubits are sensitive to a variety of loss mechanisms including dielectric loss from interfaces. By changing the physical footprint of the qubit, it is possible to modulate sensitivity to surface loss. Here, we show a systematic study of planar superconducting transmons of differing physical footprints to optimize the qubit design for maximum coherence. We find that qubits with small footprints are limited by surface loss and that qubits with large footprints are limited by other loss mechanisms, which are currently not understood.
An auxiliary-field quantum Monte Carlo study of the chromium dimer

The chromium dimer (Cr2) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve (PEC), is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present an accurate calculation of the PEC and ground state properties of Cr2, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set limit are then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.
Hadron Properties and Dyson-Schwinger Equations

Abstract An overview of the theory and phenomenology of hadrons and QCD is provided from a Dyson–Schwinger equation viewpoint. Following a discussion of the definition and realization of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the U A ( 1 ) problem, and calculated masses of the lightest J = 0 , 1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln -weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution.
Some generalizations of Schur functors

The theory of Schur functors provides a powerful and elegant approach to the representation theory of GL_n - at least to the so-called polynomial representations - especially to questions about how the theory varies with n. We develop parallel theories that apply to other classical groups and to non-polynomial representations of GL_n. These theories can also be viewed as linear analogs of the theory of FI-modules.
Simple and Approximately Optimal Pricing for Proportional Complementarities

We study a new model of complementary valuations, which we call "proportional complementarities.'' In contrast to common models, such as hypergraphic valuations, in our model, we do not assume that the extra value derived from owning a set of items is independent of the buyer's base valuations for the items. Instead, we model the complementarities as proportional to the buyer's base valuations, and these proportionalities are known market parameters. Our goal is to design a simple pricing scheme that, for a single buyer with proportional complementarities, yields approximately optimal revenue. We define a new class of mechanisms where some number of items are given away for free, and the remaining items are sold separately at inflated prices. We find that the better of such a mechanism and selling the grand bundle earns a 12-approximation to the optimal revenue for pairwise proportional complementarities. This confirms the intuition that items should not be sold completely separately in the presence of complementarities. In the more general case, a buyer has a maximum of proportional positive hypergraphic valuations, where a hyperedge in a given hypergraph describes the boost to the buyer's value for item i given by owning any set of items T in addition. The maximum-out-degree of such a hypergraph is d, and k is the positive rank of the hypergraph. For valuations given by these parameters, our simple pricing scheme is an O(min{d,k})-approximation.
The Equation of State of Hot, Dense Matter and Neutron Stars

Recent developments in the theory of pure neutron matter and experiments concerning the symmetry energy of nuclear matter, coupled with recent measurements of high-mass neutron stars, now allow for relatively tight constraints on the equation of state of dense matter. We review how these constraints are formulated and describe the implications they have for neutron stars and core-collapse supernovae. We also examine thermal properties of dense matter, which are important for supernovae and neutron star mergers, but which cannot be nearly as well constrained at this time by experiment. In addition, we consider the role of the equation of state in medium-energy heavy-ion collisions.
On the Three-Dimensional Central Moment Lattice Boltzmann Method

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-implicit and second-order, with the implicitness subsequently removed by means of a transformation. As a result, the approach is frame-invariant by construction and its emergent dynamics describing fully 3D fluid motion in the presence of force fields is Galilean invariant. Numerical experiments for a set of benchmark problems demonstrate its accuracy.
N$$^*$$ Experiments and Their Impact on Strong QCD Physics

I give a brief report on experimental studies of the spectrum and the structure of the excited states of the nucleon and what we learn about their internal structure. The focus is on the effort to obtain a more complete picture of the light-quark baryon excitation spectrum employing electromagnetic beams, and on the study of the transition form factors and helicity amplitudes an their dependence on the size of the four-momentum transfer $$Q^2$$ , especially on some of the most prominent resonances. These were obtained in pion and eta electroproduction experiments off proton targets.
A mechanism for balancing accuracy and scope in cross-machine black-box GPU performance modeling

The ability to model, analyze, and predict execution time of computations is an important building block that supports numerous efforts, such as load balancing, benchmarking, job scheduling, develo...
A Callias-Type Index Theorem with Degenerate Potentials

A generalization of Callias’ index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index obtained depends on the choice of a family of Fredholm extensions, though as in the classical version it depends only on the data at infinity.
Self-homodyne-enabled generation of indistinguishable photons

The rapid generation of non-classical light serves as the foundation for exploring quantum optics and developing applications such as secure communications or the generation of NOON states. While strongly coupled quantum dot-photonic crystal resonator systems have great potential as non-classical light sources due to their promise of tailored output statistics, the generation of indistinguishable photons has been obscured due to the strongly dissipative nature of such systems. Here, we demonstrate that the recently discovered self-homodyne suppression technique can be used to overcome this limitation and tune the quantum statistics of transmitted light, achieving indistinguishable photon emission competitive with state-of-the-art metrics. Furthermore, our nanocavity-based platform directly lends itself to scalable on-chip architectures for quantum information.
Benchmarking Geant4 for Simulating Galactic Cosmic Ray Interactions Within Planetary Bodies

Galactic cosmic rays undergo complex nuclear interactions with nuclei within planetary bodies that have little to no atmosphere. Radiation transport simulations are a key tool used in understanding the neutron and gamma-ray albedo coming from these interactions and tracing these signals back to geochemical composition of the target. We study the validity of the code Geant4 for simulating such interactions by comparing simulation results to data from the Apollo 17 Lunar Neutron Probe Experiment. Different assumptions regarding the physics are explored to demonstrate how these impact the Geant4 simulation results. In general, all of the Geant4 results over-predict the data, however, certain physics lists perform better than others. In addition, we show that results from the radiation transport code MCNP6 are similar to those obtained using Geant4.
Revised Supernova Rates from the IfA Deep Survey

The IfA Deep Survey uncovered ~ 130 thermonuclear supernova (TN SN, i.e., Type Ia) candidates at redshifts from z = 0.1 out to beyond z = 1. The TN SN explosion rates derived from these data have been controversial, conflicting with evidence emerging from other surveys. This work revisits the IfA Deep Survey to re-evaluate the photometric evidence. Applying the SOFT program to the light curves of all SN candidates, we derive new classification grades and redshift estimates. We find a volumetric rate for z ~ 0.5 that is substantially smaller than the originally published values, bringing the revised IfA Deep rate into good agreement with other surveys. With our improved photometric analysis techniques, we are able to confidently extend the rate measurements to higher redshifts and we find a steadily increasing TN SN rate, with no indication of a peak out to z = 1.05.
The Mass of The Product of Spheres

Any compact manifold with positive scalar curvature has an associated asymptotically flat metric constructed using the Green’s function of the conformal Laplacian, and the mass of this metric is an important geometric invariant. An explicit expression for the mass of the product of spheres S2 × S2, both with the same Gaussian curvature, is given. Expressions for the masses of the quotient spaces G(2, 4), and \({\mathbb{RP}^2 \times \mathbb{RP}^2}\) are also given. The values of these masses arise in a construction of critical metrics on certain 4-manifolds; applications to this problem will also be discussed.
Effects of microwave irradiation on multiwalled carbon nanotubes of different diameters

We have studied the visible and infrared radiation emitted by multiwalled carbon nanotubes (MWCNTs) of different diameters when exposed to 2.45-GHz microwaves. A comparison of the spectra suggests that MWCNTs with larger diameters emit radiation of greater intensity than those with smaller diameters. Furthermore, the MWCNTs continue to emit visible and infrared radiation over the course of several microwave-irradiation cycles, with no degradation in the intensity of the emitted radiation. A comparison of Raman D- to G-band peak-intensity ratios reveals that microwave-irradiation did not significantly impact the MWCNTs’ defect densities. The results of our experiments suggest that MWCNTs may have the potential for use in lighting technologies and that ohmic heating caused by the polarization of the MWCNTs in the microwave field is likely responsible for the observed emissions of visible and infrared radiation.
Anamorphic transformation and its application to time–bandwidth compression

A general method for compressing the modulation time–bandwidth product of analog signals is introduced. As one of its applications, this physics-based signal grooming, performed in the analog domain, allows a conventional digitizer to sample and digitize the analog signal with variable resolution. The net result is that frequency components that were beyond the digitizer bandwidth can now be captured and, at the same time, the total digital data size is reduced. This compression is lossless and is achieved through a feature selective reshaping of the signal’s complex field, performed in the analog domain prior to sampling. Our method is inspired by operation of Fovea centralis in the human eye and by anamorphic transformation in visual arts. The proposed transform can also be performed in the digital domain as a data compression algorithm to alleviate the storage and transmission bottlenecks associated with “big data.”
Exact results and soft breaking masses in supersymmetric gauge theory

Abstract We give an explicit formalism connecting softly broken supersymmetric gauge theories (with QCD as one limit) to N = 2 and N = 1 supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged N = 1 model. The functional forms of effective lagrangian terms resulting from soft supersymmetry breaking are constrained by the symmetries of the enlarged model, although not well enough to fully determine the vacuum structure of generic softly broken models. Nevertheless, by perturbing the exact N = 1 model results with sufficiently small soft breaking masses, we show that there exist nonsupersymmetric models that exhibit monopole condensation and confinement in the same modes as the N = 1 case.
Observing Exoplanets with High-Dispersion Coronagraphy. II. Demonstration of an Active Single-Mode Fiber Injection Unit

High-dispersion coronagraphy (HDC) optimally combines high contrast imaging techniques such as adaptive optics/wavefront control plus coronagraphy to high spectral resolution spectroscopy. HDC is a critical pathway towards fully characterizing exoplanet atmospheres across a broad range of masses from giant gaseous planets down to Earth-like planets. In addition to determining the molecular composition of exoplanet atmospheres, HDC also enables Doppler mapping of atmosphere inhomogeneities (temperature, clouds, wind), as well as precise measurements of exoplanet rotational velocities. Here, we demonstrate an innovative concept for injecting the directly-imaged planet light into a single-mode fiber, linking a high-contrast adaptively-corrected coronagraph to a high-resolution spectrograph (diffraction-limited or not). Our laboratory demonstration includes three key milestones: close-to-theoretical injection efficiency, accurate pointing and tracking, on-fiber coherent modulation and speckle nulling of spurious starlight signal coupling into the fiber. Using the extreme modal selectivity of single-mode fibers, we also demonstrated speckle suppression gains that outperform conventional image-based speckle nulling by at least two orders of magnitude.
Automatic continuity for homeomorphism groups and applications

Let M be a compact manifold, possibly with boundary. We show that the group of homeomorphisms of M has the automatic continuity property: any homomorphism from Homeo(M) to any separable group is necessarily continuous. This answers a question of C Rosendal. If N ⊂ M is a submanifold, the group of homeomorphisms of M that preserve N also has this property. Various applications of automatic continuity are discussed, including applications to the topology and structure of groups of germs of homeomorphisms. In an appendix with Frederic Le Roux we also show, using related techniques, that the group of germs at a point of homeomorphisms of ℝn is strongly uniformly simple.
Groups with decidable word problem that do not embed in groups with decidable conjugacy problem

We show the existence of finitely presented torsion-free groups with decidable word problem that cannot be embedded in any finitely generated group with decidable conjugacy problem. This answers a well-known question of Collins from the early 1970’s.
Weakly coupled oscillators in a slowly varying world

We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the method to an all-to-all network and show that there is a waxing and waning of synchrony of modulated neurons.
Numerical simulation of magnetized jet creation using a hollow ring of laser beams

Three dimensional FLASH magneto-hydrodynamic modeling is carried out to interpret the OMEGA laser experiments of strongly magnetized, highly collimated jets driven by a ring of 20 OMEGA beams. The predicted optical Thomson scattering spectra and proton images are in good agreement with a subset of the experimental data. Magnetic fields generated via the Biermann battery term are amplified at the boundary between the core and the surrounding of the jet. The simulation predicts multiple axially aligned magnetic flux ropes with an alternating poloidal component. Future applications of the hollow ring configuration in laboratory astrophysics are discussed.Three dimensional FLASH magneto-hydrodynamic modeling is carried out to interpret the OMEGA laser experiments of strongly magnetized, highly collimated jets driven by a ring of 20 OMEGA beams. The predicted optical Thomson scattering spectra and proton images are in good agreement with a subset of the experimental data. Magnetic fields generated via the Biermann battery term are amplified at the boundary between the core and the surrounding of the jet. The simulation predicts multiple axially aligned magnetic flux ropes with an alternating poloidal component. Future applications of the hollow ring configuration in laboratory astrophysics are discussed.
Toward a Nordhaus–Gaddum inequality for the number of dominating sets

A dominating set in a graph G is a set S of vertices such that every vertex of G is either in S or is adjacent to a vertex in S. Nordhaus–Gaddum inequalities relate a graph G to its complement G¯. In this spirit Wagner proved that any graph G on n vertices satisfies ∂(G)+∂(G¯)≥2n, where ∂(G) is the number of dominating sets in a graph G. In the same paper he commented that proving an upper bound for ∂(G)+∂(G¯) among all graphs on n vertices seems to be much more difficult. Here we prove an upper bound on ∂(G)+∂(G¯) and prove that any graph maximizing this sum has minimum degree at least ⌊n∕2⌋−2 and maximum degree at most ⌈n∕2⌉+1. We conjecture that the complete balanced bipartite graph maximizes ∂(G)+∂(G¯) and have verified this computationally for all graphs on at most 10 vertices.
Application of Discrete Light-Cone Quantization to Yukawa Theory in Four Dimensions

The numerical technique of discrete light-cone quantization (DLCQ) is applied to a single-fermion truncation of Yukawa theory in four dimensions. The truncated theory is regulated by three Pauli-Villars bosons, which are introduced directly in the DLCQ Fock-state basis. A special form of the Lanczos diagonalization algorithm is used to handle the indefinite metric. Renormalization is done nonperturbatively.
On quantum potential dynamics

Non-relativistic de Broglie–Bohm theory describes particles moving under the guidance of the wave function. In de Broglieʼs original formulation, the particle dynamics is given by a first-order differential equation. In Bohmʼs reformulation, it is given by Newtonʼs law of motion with an extra potential that depends on the wave function—the quantum potential—together with a constraint on the possible velocities. It was recently argued, mainly by numerical simulations, that relaxing this velocity constraint leads to a physically untenable theory. We provide further evidence for this by showing that for various wave functions the particles tend to escape the wave packet. In particular, we show that for a central classical potential and bound energy eigenstates the particle motion is often unbounded. This work seems particularly relevant for ways of simulating wave function evolution based on Bohmʼs formulation of the de Broglie–Bohm theory. Namely, the simulations may become unstable due to deviations from the velocity constraint.
Resonances for Obstacles in Hyperbolic Space

We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound $${ {\rm Im} \lambda \leq - \frac12 }$$ , which is optimal in dimension 2. In odd dimensions we also show that $${ {\rm Im} \lambda \leq - \frac{\mu}{\rho} }$$ for a universal constant $${\mu}$$ , where $${ \rho }$$ is the radius of a ball containing the obstacle; this gives an improvement for small obstacles. In dimensions 3 and higher the proofs follow the classical vector field approach of Morawetz, while in dimension 2 we obtain our bound by working with spaces coming from general relativity. We also show that in odd dimensions resonances of small obstacles are close, in a suitable sense, to Euclidean resonances.
Triple Scissor Extender: A 6-DOF lifting and positioning robot

We present a novel 6 DOF robotic mechanism for reaching high ceilings and positioning an end-effector. The end-effector is supported with three scissor mechanisms that extend towards the ceiling with 6 independent linear actuators moving the base ends of the individual scissors. The top point of each scissor is connected to one of three ball joints located at the three vertices of the top triangular plate holding the end-effector. Coordinated motion of the 6 linear actuators at the base allows the end-effector to reach an arbitrary position with an arbitrary orientation. The design concept of the Triple Scissor Extender is presented, followed by kinematic modeling and analysis of the the Inverse Jacobian relating actuator velocities to the end-effector velocities. The Inverse Jacobian eigenvalues are determined for diverse configurations in order to characterize the kinematic properties. A proof-of-concept prototype has been designed and built. The Inverse Jacobian for use in differential control is evaluated through experiments.
Employee Volunteer Programs are Associated with Firm-Level Benefits and CEO Incentives: Data on the Ethical Dilemma of Corporate Social Responsibility Activities

Ethical dilemmas arise when one must decide between conflicting ethical imperatives. One potential ethical dilemma is a manager’s decision of whether to engage in corporate social responsibility (CSR) activities. This decision could pit the ethical imperative of honoring unwritten obligations to society against the ethical imperative of honoring contractual obligations to the firm. However, CSR activities might only be a minor ethical dilemma or none at all if they simultaneously benefit the firm and society. To examine this I test the association between future-period employee productivity and current-period use of one type of CSR activity: employee volunteer programs. I use a unique sample of 1428 firm-years, hand-collected from sustainability reports of 373 firms. I find evidence that the current-period use of an employee volunteer program has a positive association with future-period employee productivity (moderated by the firm’s current-period employee productivity). I find this result in future periods up to 6 years after a firm uses an employee volunteer program. I also find a positive association between incentives that focus CEOs’ attention on long-term firm outcomes and more extensive employee volunteer programs (also moderated by current-period employee productivity).
Computationally efficient deep neural network for computed tomography image reconstruction

Purpose Deep neural network-based image reconstruction has demonstrated promising performance in medical imaging for undersampled and low-dose scenarios. However, it requires large amount of memory and extensive time for the training. It is especially challenging to train the reconstruction networks for three-dimensional computed tomography (CT) because of the high resolution of CT images. The purpose of this work is to reduce the memory and time consumption of the training of the reconstruction networks for CT to make it practical for current hardware, while maintaining the quality of the reconstructed images. Methods We unrolled the proximal gradient descent algorithm for iterative image reconstruction to finite iterations and replaced the terms related to the penalty function with trainable convolutional neural networks (CNN). The network was trained greedily iteration by iteration in the image domain on patches, which requires reasonable amount of memory and time on mainstream graphics processing unit (GPU). To overcome the local-minimum problem caused by greedy learning, we used deep UNet as the CNN and incorporated separable quadratic surrogate with ordered subsets for data fidelity, so that the solution could escape from easy local minimums and achieve better image quality. Results The proposed method achieved comparable image quality with state-of-the-art neural network for CT image reconstruction on two-dimensional (2D) sparse-view and limited-angle problems on the low-dose CT challenge dataset. The difference in root-mean-square-error (RMSE) and structural similarity index (SSIM) was within [-0.23,0.47] HU and [0,0.001], respectively, with 95% confidence level. For three-dimensional (3D) image reconstruction with ordinary-size CT volume, the proposed method only needed 2 GB graphics processing unit (GPU) memory and 0.45 s per training iteration as minimum requirement, whereas existing methods may require 417 GB and 31 min. The proposed method achieved improved performance compared to total variation- and dictionary learning-based iterative reconstruction for both 2D and 3D problems. Conclusions We proposed a training-time computationally efficient neural network for CT image reconstruction. The proposed method achieved comparable image quality with state-of-the-art neural network for CT reconstruction, with significantly reduced memory and time requirement during training. The proposed method is applicable to 3D image reconstruction problems such as cone-beam CT and tomosynthesis on mainstream GPUs.
A dynamic programming approach to the Parisi functional

G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional using stochastic dynamic programing and semi-linear PDE. We give a derivation of important properties of the Parisi PDE avoiding the use of Ruelle Probability Cascades and Cole-Hopf transformations. As an application, we give a simple proof of the strict convexity of the Parisi functional, which was recently proved by Auffinger and Chen in [2].
Real-space study of the optical absorption in alternative phases of silicon

We introduce a real-space approach to understand the relationship between optical absorption and crystal structure. We apply this approach to alternative phases of silicon, with a focus on the ${\mathrm{Si}}_{20}$ crystal phase as a case study. We find that about 83% of the changes in the calculated low-energy absorption in ${\mathrm{Si}}_{20}$ as compared to Si in the diamond structure can be attributed to reducing the differences between the on-site energies of the bonding and antibonding orbitals as well as increasing the hopping integrals for specific Si-Si bonds.
Towards an Achievable Performance for the Loop Nests

Numerous code optimization techniques, including loop nest optimizations, have been developed over the last four decades. Loop optimization techniques transform loop nests to improve the performance of the code on a target architecture, including exposing parallelism. Finding and evaluating an optimal, semantic-preserving sequence of transformations is a complex problem. The sequence is guided using heuristics and/or analytical models and there is no way of knowing how close it gets to optimal performance or if there is any headroom for improvement.
Damping enhancement in coherent ferrite-insulating-paramagnet bilayers

Author(s): Wisser, JJ; Grutter, AJ; Gilbert, DA; N'Diaye, AT; Klewe, C; Shafer, P; Arenholz, E; Suzuki, Y; Emori, S | Abstract: High-quality epitaxial ferrites, such as low-damping MgAl-ferrite (MAFO), are promising nanoscale building blocks for all-oxide heterostructures driven by pure spin current. However, the impact of oxide interfaces on spin dynamics in such heterostructures remains an open question. Here, we investigate the spin dynamics and chemical and magnetic depth profiles of 15-nm-thick MAFO coherently interfaced with an isostructural 1-8-nm-thick overlayer of paramagnetic CoCr2O4 (CCO) as an all-oxide model system. Compared to MAFO without an overlayer, effective Gilbert damping in MAFO/CCO is enhanced by a factor of g3, irrespective of the CCO overlayer thickness. We attribute this damping enhancement to spin scattering at the approximately 1-nm-thick chemically disordered layer at the MAFO-CCO interface, rather than spin pumping or proximity-induced magnetism. Our results indicate that damping in ferrite-based heterostructures is strongly influenced by interfacial chemical disorder, even if the thickness of the disordered layer is a small fraction of the ferrite thickness.
Minimax rates for estimating the dimension of a manifold

Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be estimated. We characterize the statistical difficulty of this problem by deriving upper and lower bounds on the minimax rate for estimating the dimension. First, we consider the problem of testing the hypothesis that the support of the data-generating probability distribution is a well-behaved manifold of intrinsic dimension $d_1$ versus the alternative that it is of dimension $d_2$, with $d_{1}<d_{2}$. With an i.i.d. sample of size $n$, we provide an upper bound on the probability of choosing the wrong dimension of $O\left( n^{-\left(d_{2}/d_{1}-1-\epsilon\right)n} \right)$, where $\epsilon$ is an arbitrarily small positive number. The proof is based on bounding the length of the traveling salesman path through the data points. We also demonstrate a lower bound of $\Omega \left( n^{-(2d_{2}-2d_{1}+\epsilon)n} \right)$, by applying Le Cam's lemma with a specific set of $d_{1}$-dimensional probability distributions. We then extend these results to get minimax rates for estimating the dimension of well-behaved manifolds. We obtain an upper bound of order $O \left( n^{-(\frac{1}{m-1}-\epsilon)n} \right)$ and a lower bound of order $\Omega \left( n^{-(2+\epsilon)n} \right)$, where $m$ is the embedding dimension.
Novel jet observables from machine learning

Previous studies have demonstrated the utility and applicability of machine learning techniques to jet physics. In this paper, we construct new observables for the discrimination of jets from different originating particles exclusively from information identified by the machine. The approach we propose is to first organize information in the jet by resolved phase space and determine the effective N -body phase space at which discrimination power saturates. This then allows for the construction of a discrimination observable from the N -body phase space coordinates. A general form of this observable can be expressed with numerous parameters that are chosen so that the observable maximizes the signal vs. background likelihood. Here, we illustrate this technique applied to discrimination of $$ H\to b\overline{b} $$ decays from massive $$ g\to b\overline{b} $$ splittings. We show that for a simple parametrization, we can construct an observable that has discrimination power comparable to, or better than, widely-used observables motivated from theory considerations. For the case of jets on which modified mass-drop tagger grooming is applied, the observable that the machine learns is essentially the angle of the dominant gluon emission off of the $$ b\overline{b} $$ pair.
Obtaining genus 2 Heegaard splittings from Dehn surgery

Let K be a hyperbolic knot in S and suppose that some Dehn surgery on K with distance at least 3 from the meridian yields a 3–manifold M of Heegaard genus 2 . We show that if M does not contain an embedded Dyck’s surface (the closed nonorientable surface of Euler characteristic 1), then the knot dual to the surgery is either 0–bridge or 1–bridge with respect to a genus 2 Heegaard splitting of M . In the case that M does contain an embedded Dyck’s surface, we obtain similar results. As a corollary, if M does not contain an incompressible genus 2 surface, then the tunnel number of K is at most 2 .
A Resolved Millimeter Emission Belt in the AU Mic Debris Disk

We present imaging observations at 1.3 mm of the debris disk surrounding the nearby M-type flare star AU Mic with beam size 3'' (30 AU) from the Submillimeter Array. These data reveal a belt of thermal dust emission surrounding the star with the same edge-on geometry as the more extended scattered light disk detected at optical wavelengths. Simple modeling indicates a central radius of ~35 AU for the emission belt. This location is consistent with the reservoir of planetesimals previously invoked to explain the shape of the scattered light surface brightness profile through size-dependent dust dynamics. The identification of this belt further strengthens the kinship between the debris disks around AU Mic and its more massive sister star β Pic, members of the same ~10 Myr old moving group.
HD/H2 AS A PROBE OF THE ROLES OF GAS, DUST, LIGHT, METALLICITY, AND COSMIC RAYS IN PROMOTING THE GROWTH OF MOLECULAR HYDROGEN IN THE DIFFUSE INTERSTELLAR MEDIUM

We modeled recent observations of UV absorption of HD and in the Milky Way and toward damped/subdamped Ly? systems at z = 0.18 and z >1.7. N(HD)/N() ratios reflect the separate self-shieldings of HD and and the coupling introduced by deuteration chemistry. Locally, observations are explained by diffuse molecular gas with 16 cm?3 n(H) 128 cm?3 if the cosmic-ray ionization rate per H nucleus ? H ?=2 ? 10?16 s?1, as inferred from H3 + and OH+. The dominant influence on N(HD)/N() is the cosmic-ray ionization rate with a much weaker downward dependence on n(H) at solar metallicity, but dust extinction can drive N(HD) higher as with N(). At z > 1.7, N(HD) is comparable to the Galaxy but with 10 times smaller N() and somewhat smaller N()/N(H I). Comparison of our Galaxy with the Magellanic Clouds shows that smaller /H is expected at subsolar metallicity, and we show by modeling that HD/ increases with density at low metallicity, opposite to the Milky Way. Observations of HD would be explained with higher n(H) at low metallicity, but high-z systems have high HD/ at metallicity 0.04 Z 2 solar. In parallel, we trace dust extinction and self-shielding effects. The abrupt transition to /H 1%-10% occurs mostly from self-shielding, although it is assisted by extinction for n(H) 16 cm?3. Interior fractions are substantially increased by dust extinction below 32 cm?3. At smaller n(H), ? H , small increases in triggered by dust extinction can trigger abrupt increases in N(HD).