cssi/SciSciGPT-SciSciNet huggingface dataset:
Injectivity of satellite operators in knot concordance

Let P be a knot in a solid torus, K a knot in 3-space and P(K) the satellite knot of K with pattern P. This defines an operator on the set of knot types and induces a satellite operator P:C--> C on the set of smooth concordance classes of knots. There has been considerable interest in whether certain such functions are injective. For example, it is a famous open problem whether the Whitehead double operator is weakly injective (an operator is called weakly injective if P(K)=P(0) implies K=0 where 0 is the class of the trivial knot). We prove that, modulo the smooth 4-dimensional Poincare Conjecture, any strong winding number one satellite operator is injective on C. More precisely, if P has strong winding number one and P(K)=P(J), then K is smoothly concordant to J in S^3 x [0,1] equipped with a possibly exotic smooth structure. We also prove that any strong winding number one operator is injective on the topological knot concordance group. If P(0) is unknotted then strong winding number one is the same as (ordinary) winding number one. More generally we show that any satellite operator with non-zero winding number n induces an injective function on the set of Z[1/n]-concordance classes of knots. We extend some of our results to links.
Optimizing surface defects for atomic-scale electronics: Si dangling bonds

Surface defects created and probed with scanning tunneling microscopes are a promising platform for atomic-scale electronics and quantum information technology applications. Using first-principles calculations we demonstrate how to engineer dangling bond (DB) defects on hydrogenated Si(100) surfaces, which give rise to isolated impurity states that can be used in atomic-scale devices. In particular, we show that sample thickness and biaxial strain can serve as control parameters to design the electronic properties of DB defects. While in thick Si samples the neutral DB state is resonant with bulk valence bands, ultrathin samples (1--2 nm) lead to an isolated impurity state in the gap; similar behavior is seen for DB pairs and DB wires. Strain further isolates the DB from the valence band, with the response to strain heavily dependent on sample thickness. These findings suggest new methods for tuning the properties of defects on surfaces for electronic and quantum information applications. Finally, we present a consistent and unifying interpretation of many results presented in the literature for DB defects on hydrogenated silicon surfaces, rationalizing apparent discrepancies between different experiments and simulations.
An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection.

Abstract Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright–Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known partial differential equations. For a multi-allelic model with general diploid selection, various theoretical results exist on representations of the transition density, but finding an explicit formula has remained a difficult problem. In this paper, a technique recently developed for a diallelic model is extended to find an explicit transition density for an arbitrary number of alleles, under a general diploid selection model with recurrent parent-independent mutation. Specifically, the method finds the eigenvalues and eigenfunctions of the generator associated with the multi-allelic diffusion, thus yielding an accurate spectral representation of the transition density. Furthermore, this approach allows for efficient, accurate computation of various other quantities of interest, including the normalizing constant of the stationary distribution and the rate of convergence to this distribution.
Interaction between gravitational radiation and electromagnetic radiation

In this review paper, we investigate the connection between gravity and electromagnetism from Faraday to the present day. The particular focus is on the connection between gravitational and electro...
A composite axion from a supersymmetric product group

A global U(1)PQ symmetry is protected from gravitational effects in the s-confining SU(N)k product group theory with $$ A + 4Q+N\overline{Q} $$ matter. If the SU(4) family symmetry is gauged and an appropriate tree-level superpotential is added, then the dynamically generated superpotential spontaneously breaks SU(4) × U(1)PQ → SU(3)c and produces a QCD axion. Small values of the CP -violating θ parameter are then possible without any fine-tuning, as long as the product group is suitably large. By introducing a second copy of the s-confining SU(N) product group also coupled to the gauged SU(4), we find that values as small as N = 7 are consistent with $$ \overline{\theta}<1{0}^{-10} $$ , even under the pessimistic assumption that the dominant contribution to the axion quality is at tree level.
Nambu-Goldstone modes and diffuse deformations in elastic shells

I consider the shape of a deformed elastic shell. Using the fact that the lowest-energy, small deformations are along infinitesimal isometries of the shell's mid-surface, I describe a class of weakly stretching deformations for thin shells based on the Nambu–Goldstone modes associated with those isometries. The main result is an effective theory to describe the diffuse deformations of thin shells that incorporate stretching and bending energies. The theory recovers previous results for the propagation of a “pinch” on a cylinder. A cone, on the other hand, has two length scales governing the persistence of a pinch: one governing the relaxation of the pinch that scales with thickness as a −1/2 power and one that scales with thickness above which deformations again become isometric. These lengths meet at a critical thickness below which low energy deformations again become nearly isometric.
Accelerating quantum optics experiments with statistical learning

Quantum optics experiments, involving the measurement of low-probability photon events, are known to be extremely time-consuming. We present a methodology for accelerating such experiments using physically motivated ansatzes together with simple statistical learning techniques such as Bayesian maximum a posteriori estimation based on few-shot data. We show that it is possible to reconstruct time-dependent data using a small number of detected photons, allowing for fast estimates in under a minute and providing a one-to-two order of magnitude speed-up in data acquisition time. We test our approach using real experimental data to retrieve the second order intensity correlation function, G ( 2 ) ( τ ), as a function of time delay τ between detector counts, for thermal light as well as anti-bunched light emitted by a quantum dot driven by periodic laser pulses. The proposed methodology has a wide range of applicability and has the potential to impact the scientific discovery process across a multitude of domains.
On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley’s measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley’s measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley’s measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size. Three dependence structures are studied: the intraclass (IC) and serially correlated (SC) normal models, and order statistics. For IC and SC models, the information about the mean parameter decreases and the predictive information increases with the correlation, but the joint information is not monotone and has a unique minimum. Compensation of the loss of parameter information due to dependence requires larger samples. For the order statistics, the joint information exceeds Lindley’s measure by an amount which does not depend on the prior or the model for the data, but it is not monotone in the sample size and has a unique maximum.
A CFT Perspective on Gravitational Dressing and Bulk Locality

We revisit the construction of local bulk operators in AdS/CFT with special focus on gravitational dressing and its consequences for bulk locality. Specializing to 2+1-dimensions, we investigate these issues via the proposed identification between bulk operators and cross-cap boundary states. We obtain explicit expressions for correlation functions of bulk fields with boundary stress tensor insertions, and find that they are free of non-local branch cuts but do have non-local poles. We recover the HKLL recipe for restoring bulk locality for interacting fields as the outcome of a natural CFT crossing condition. We show that, in a suitable gauge, the cross-cap states solve the bulk wave equation for general background geometries, and satisfy a conformal Ward identity analo-gous to a soft graviton theorem. Virasoro symmetry, the large N conformal bootstrap and the uniformization theorem all play a key role in our derivations.
Enhanced light extraction in tunnel junction-enabled top emitting UV LEDs

The efficiency of ultraviolet (UV) light-emitting diodes (LEDs) is critically limited by absorption losses in p-type and metal layers. In this work, surface-roughening-based light extraction structures were combined with tunneling-based top-layer contacts to achieve highly efficient top-side light extraction in UV LEDs. By using self-assembled Ni nanoclusters as an etch mask, the top surface-roughened LEDs were found to enhance the external quantum efficiency by over 40% for UV LEDs with a peak emission wavelength of 326 nm. The method described here can be used for fabricating highly efficient UV LEDs without the need for complex manufacturing techniques such as flip chip bonding.
A possible gravitational lens in the Hubble Deep Field South

We model an apparent gravitational lens system HDFS 2232509-603243 in the Hubble Deep Field South. The system consists of a blue V=25 mag arc separated by 09 from a red V=22 mag elliptical galaxy. A mass distribution that follows the observed light distribution with a constant mass-to-light ratio can fit the arc component positions if external shear is added. A good fit is also obtained with simple parameterized models, and all the models predict a fourth image that is fainter than the detection limit. The inferred mass-to-light ratio is ~15 in solar units if the lens is at z=0.6. The lens models predict a velocity dispersion of ~280 km s-1 that could be confirmed with spectroscopy.
Sparse Array DFT Beamformers for Wideband Sources

Sparse arrays are popular for performance optimization while keeping the hardware and computational costs down. In this paper, we consider sparse arrays design method for wideband source operating in a wideband jamming environment. Maximizing the signal-to-interference plus noise ratio (MaxSINR) is adopted as an optimization objective for wideband beamforming. Sparse array design problem is formulated in the DFT domain to process the source as parallel narrowband sources. The problem is formulated as quadratically constraint quadratic program (QCQP) alongside the weighted mixed $l_{1-\infty}$ -norm squared penalization of the beamformer weight vector. The semidefinite relaxation (SDR) of QCQP promotes sparse solutions by iteratively re-weighting beamformer based on previous iteration. It is shown that the DFT approach reduces the computational cost considerably as compared to the delay line approach, while efficiently utilizing the degrees of freedom to harness the maximum output SINR offered by the given array aperture.
On Compact Riemannian Manifolds with Convex Boundary and Ricci Curvature Bounded from Below

We propose to study positive harmonic functions satisfying a nonlinear Neuman condition on a compact Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary. A precise conjecture is formulated. We discuss its implications and present some partial results. Related questions are discussed for compact Riemannian manifolds with positive Ricci curvature and convex boundary.
Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics

In the spirit of the fewest switches surface hopping, the frozen Gaussian approximation with surface hopping (FGA-SH) method samples a path integral representation of the non-adiabatic dynamics in the semiclassical regime. An improved sampling scheme is developed in this work for FGA-SH based on birth and death branching processes. The algorithm is validated for the standard test examples of non-adiabatic dynamics.
Tempered Hermite process

A tempered Hermite process modifies the power law kernel in the time domain representation of a Hermite process by multiplying an exponential tempering factor $\lambda>0$ such that the process is well defined for Hurst parameter $H>\frac{1}{2}$. A~tempered Hermite process is the weak convergence limit of a certain discrete chaos process.
Speed trajectory planning at signalized intersections using sequential convex optimization

An algorithm is developed to optimize vehicle speed trajectory over multiple signalized intersections with known traffic signal information to minimize fuel consumption and travel time, and to meet ride comfort requirements using sequential convex optimization method. A comparison between the proposed method and dynamic programming is carried out to verify its optimality. In addition, vehicle motion during turning is studied because of its significant effect on fuel consumption and travel time.
Helicity Methods for High Multiplicity Subleading Soft and Collinear Limits

The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity variables in collinear limits with consistency relations derived from the soft collinear effective theory, we show how to efficiently extract the subleading power leading logarithms of N-jet event shape observables directly from known spinor-helicity amplitudes. At subleading power, we observe the presence of power law singularities arising solely from the expansion of the amplitudes, which for hadron collider event shapes lead to the presence of derivatives of parton distributions. The techniques introduced here can be used to efficiently compute the power corrections for N-jettiness subtractions for processes involving jets at the LHC.
Classifying Camina groups: A theorem of Dark and Scoppola

Recall that a group G is a Camina group if every nonlinear irreducible character of G vanishes on GnG 0 . Dark and Scoppola classified the Camina groups that can occur. We present a different proof of this classification using Theorem 2, which strengthens a result of Isaacs on Camina pairs. Theorem 2 is of independent interest.
The Frank–Lieb approach to sharp Sobolev inequalities

Frank and Lieb gave a new, rearrangement-free, proof of the sharp Hardy–Littlewood–Sobolev inequalities by exploiting their conformal covariance. Using this they gave new proofs of sharp Sobolev in...
Spitzer IRS Observations of the XA Region in the Cygnus Loop Supernova Remnant

We report on spectra of two positions in the XA region of the Cygnus Loop supernova remnant obtained with the InfraRed Spectrograph on the Spitzer Space Telescope. The spectra span the 10-35 μm wavelength range, which contains a number of collisionally excited forbidden lines. These data are supplemented by optical spectra obtained at the Whipple Observatory and an archival UV spectrum from the International Ultraviolet Explorer. Coverage from the UV through the IR provides tests of shock wave models and tight constraints on model parameters. Only lines from high ionization species are detected in the spectrum of a filament on the edge of the remnant. The filament traces a 180 km s{sup –1} shock that has just begun to cool, and the oxygen to neon abundance ratio lies in the normal range found for Galactic H II regions. Lines from both high and low ionization species are detected in the spectrum of the cusp of a shock-cloud interaction, which lies within the remnant boundary. The spectrum of the cusp region is matched by a shock of about 150 km s{sup –1} that has cooled and begun to recombine. The post-shock region has a swept-up column density of about 1.3 ×more » 10{sup 18} cm{sup –2}, and the gas has reached a temperature of 7000-8000 K. The spectrum of the Cusp indicates that roughly half of the refractory silicon and iron atoms have been liberated from the grains. Dust emission is not detected at either position.« less
A Lower Bound on Blowup Rates for the 3D Incompressible Euler Equation and a Single Exponential Beale-Kato-Majda Type Estimate

We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in \({H^{s}(\mathbb {R}^3)}\) , for \({s>\frac{5}{2}}\) . Instead of double exponential estimates of Beale-Kato-Majda type, we obtain a single exponential bound on \({\|u(t)\|_{H^s}}\) involving the length parameter introduced by Constantin in (SIAM Rev. 36(1):73–98, 1994). In particular, we derive lower bounds on the blowup rate of such solutions.
On the Kinematic Origin of the Luminosity-Pulse Lag Relationship in Gamma-ray Bursts

This Letter presents an interpretation based on gamma-ray burst source kinematics for the relationship found by Norris et al. between peak luminosity and energy-dependent pulse lag. I argue that the correlation should instead be between number luminosity and pulse lag. This interpretation improves the least-squares fit of this correlation for the known bursts by 25% or more. It also suggests a distance estimation scheme. I propose that this relationship is due to the variation in line-of-sight velocity among bursts. This interpretation allows one to speculate on the range of gamma-ray burst expansion velocities or the size of their jet opening angles.
Near-infrared K and L' Flux Ratios in Six Lensed Quasars

We examine the wavelength dependence of flux ratios for six gravitationally lensed quasars using K and L' images obtained at the Gemini North 8 m telescope. We select lenses with source redshifts z{sub s} < 2.8 so that K-band images probe rest-frame optical emission from accretion disks, while L'-band images probe rest-frame near-infrared flux emitted (in part) from the more extended surrounding torus. Since the observations correspond to different source sizes, the K and L' flux ratios are sensitive to structure on different scales and may be useful for studying small structure in the lens galaxies. Four of the six lenses show differences between K and L' flux ratios. In HE 0435-1223, SDSS 0246-0825, and HE 2149-2745, the differences may be attributable to known microlensing and/or intrinsic variability. In SDSS 0806+2006, the wavelength dependence is not easily attributed to known variations and may indicate the presence of substructure. By contrast, in Q0142-100 and SBS 0909+523 the K and L' flux ratios are consistent within the uncertainties. We discuss the utility of the current data for studying chromatic effects related to microlensing, dust extinction, and dark matter substructure.
Habitable Zones of Post-Main Sequence Stars

Once a star leaves the main sequence and becomes a red giant, its Habitable Zone (HZ) moves outward, promoting detectable habitable conditions at larger orbital distances. We use a one-dimensional radiative-convective climate and stellar evolutionary models to calculate post-MS HZ distances for a grid of stars from 3,700K to 10,000K (~M1 to A5 stellar types) for different stellar metallicities. The post-MS HZ limits are comparable to the distances of known directly imaged planets. We model the stellar as well as planetary atmospheric mass loss during the Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) phases for super-Moons to super-Earths. A planet can stay between 200 million years up to 9 Gyr in the post-MS HZ for our hottest and coldest grid stars, respectively, assuming solar metallicity. These numbers increase for increased stellar metallicity. Total atmospheric erosion only occurs for planets in close-in orbits. The post-MS HZ orbital distances are within detection capabilities of direct imaging techniques.
The Stellar Initial Mass Function in Early-type Galaxies from Absorption Line Spectroscopy. I. Data and Empirical Trends

The strength of gravity-sensitive absorption lines in the integrated light of old stellar populations is one of the few direct probes of the stellar initial mass function (IMF) outside of the Milky Way. Owing to the advent of fully depleted CCDs with little or no fringing it has recently become possible to obtain accurate measurements of these features. Here, we present spectra covering the wavelength ranges 0.35-0.55 ?m and 0.72-1.03 ?m for the bulge of M31 and 34 early-type galaxies from the SAURON sample, obtained with the Low Resolution Imaging Spectrometer on Keck. The signal-to-noise ratio is 200 ??1 out to 1 ?m, which is sufficient to measure gravity-sensitive features for individual galaxies and to determine how they depend on other properties of the galaxies. Combining the new data with previously obtained spectra for globular clusters in M31 and the most massive elliptical galaxies in the Virgo cluster, we find that the dwarf-sensitive Na I ?8183, 8195 doublet and the FeH ?9916 Wing-Ford band increase systematically with velocity dispersion, while the giant-sensitive Ca II ?8498, 8542, 8662 triplet decreases with dispersion. These trends are consistent with a varying IMF, such that galaxies with deeper potential wells have more dwarf-enriched mass functions. In a companion paper, we use a comprehensive stellar population synthesis model to demonstrate that IMF effects can be separated from age and abundance variations and quantify the IMF variation among early-type galaxies.
CHERN–SIMONS THEORY, EXACTLY SOLVABLE MODELS AND FREE FERMIONS AT FINITE TEMPERATURE

We show that matrix models in Chern–Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian model and the Calogero model. We compute the corresponding Hamiltonians, ground-state wave functions and ground-state energies and point out that the models can be interpreted as quasi-1D Coulomb plasmas. We also study the relationship between Chern–Simons theory on S3 and a system of N one-dimensional fermions at finite temperature with harmonic confinement. In particular, we show that the Chern–Simons partition function can be described by the density matrix of the free fermions in a very particular, crystalline, configuration. For this, we both use the Brownian motion and the matrix model description of Chern–Simons theory and find several common features with c = 1 theory at finite temperature. Finally, using the exactly solvable model result, we show that the finite temperature effect can be described with a specific two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at large separations.
GEOMETRICALLY RELATING MOMENTUM CUT-OFF AND DIMENSIONAL REGULARIZATION

The β function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the β functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.
Studying the Evolution of Warm Dust Encircling BD +20 307 Using SOFIA

The small class of known stars with unusually warm, dusty debris disks is a key sample to probe in order to understand cascade models and the extreme collisions that likely lead to the final configurations of planetary systems. Because of its extreme dustiness and small radius, the disk of BD +20 307 has a short predicted collision time and is therefore an interesting target in which to look for changes in dust quantity and composition over time. To compare with previous ground and Spitzer Space Telescope data, Stratospheric Observatory for Infrared Astronomy (SOFIA) photometry and spectroscopy were obtained. The system's 8.8–12.5 μm infrared emission increased by 10 ± 2% over nine years between the SOFIA and earlier Spitzer measurements. In addition to an overall increase in infrared excess, there is a suggestion of a greater increase in flux at shorter wavelengths (less than 10.6 μm) compared to longer wavelengths (greater than 10.6 μm). Steady-state collisional cascade models cannot explain the increase in BD +20 307's disk flux over such short timescales. A catastrophic collision between planetary-scale bodies is still the most likely origin for the system's extreme dust; however, the cause for its recent variation requires further investigation.
VIBRATION SPECTRA OF THE m-TREE FRACTAL

We introduce a family of post-critically finite fractal trees indexed by the number of branches they possess. Then we produce a Laplacian operator on graph approximations to these fractals and use spectral decimation to describe the spectrum of the Laplacian on these trees. Lastly we consider the behavior of the spectrum as the number of branches increases.
Lifting matroid divisors on tropical curves

Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves realizing this bound might only exist over certain characteristics or over certain fields of definition. Our examples also apply to the theory of metrized complexes and weighted graphs. These examples arise by relating the lifting problem to matroid realizability. We also give a proof of Mnev universality with explicit bounds on the size of the matroid, which may be of independent interest.
A Tight Uniform Continuity Bound for Equivocation

We prove a tight uniform continuity bound for the conditional Shannon entropy of discrete finitely supported random variables in terms of total variation distance.
An Interdisciplinary Review of Music Performance Analysis

A musical performance renders an acoustic realization of a musical score or other representation of a composition. Different performances of the same composition may vary in terms of performance parameters such as timing or dynamics, and these variations may have a major impact on how a listener perceives the music. The analysis of music performance has traditionally been a peripheral topic for the MIR research community, where often a single audio recording is used as representative of a musical work. This paper surveys the field of Music Performance Analysis (MPA) from several perspectives including the measurement of performance parameters, the relation of those parameters to the actions and intentions of a performer or perceptual effects on a listener, and finally the assessment of musical performance. This paper also discusses MPA as it relates to MIR, pointing out opportunities for collaboration and future research in both areas.
A Bayesian approach for parameter estimation and prediction using a computationally intensive model

Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model , where θ denotes the uncertain, best input setting. Hence the statistical model is of the form where accounts for measurement, and possibly other, error sources. When nonlinearity is present in , the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model . This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. We also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.
Analysis of multi-cell downlink cooperation with a constrained spatial model

Multi-cell cooperation (MCC) mitigates intercell interference and improves throughput at the cell edge. This paper considers a cooperative downlink, whereby cell-edge mobiles are served by multiple cooperative base stations. The cooperating base stations transmit identical signals over paths with non-identical path losses, and the receiving mobile performs diversity combining. The analysis in this paper is driven by a new expression for the conditional outage probability when signals arriving over different paths are combined in the presence of noise and interference, where the conditioning is with respect to the network topology and shadowing. The channel model accounts for path loss, shadowing, and Nakagami fading, and the Nakagami fading parameters do not need to be identical for all paths. To study performance over a wide class of network topologies, a random spatial model is adopted, and performance is found by statistically characterizing the rates provided on the downlinks. To model realistic networks, the model requires a minimum separation among base stations. Having adopted a realistic model and an accurate analysis, the paper proceeds to determine performance under several resource-allocation policies and provides insight regarding how the cell edge should be defined.
The dynamical diquark model: first numerical results

We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schrodinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.
Localization for Random Block Operators Related to the XY Spin Chain

We study a class of random block operators which appear as effective one-particle Hamiltonians for the anisotropic XY quantum spin chain in an exterior magnetic field given by an array of i.i.d. random variables. For arbitrary non-trivial single-site distribution of the magnetic field, we prove dynamical localization of these operators at non-zero energy.
Maximum of the Characteristic Polynomial of Random Unitary Matrices

It was recently conjectured by Fyodorov, Hiary and Keating that the maximum of the characteristic polynomial on the unit circle of a \({N\times N}\) random unitary matrix sampled from the Haar measure grows like \({CN/({\rm log} N)^{3/4}}\) for some random variable C. In this paper, we verify the leading order of this conjecture, that is, we prove that with high probability the maximum lies in the range \({[N^{1 - \varepsilon},N^{1 + \varepsilon}]}\), for arbitrarily small \({\varepsilon}\).
Leibniz seminorms and best approximation from C * -subalgebras

We show that if B is a C *-subalgebra of a C *-algebra A such that B contains a bounded approximate identity for A , and if L is the pull-back to A of the quotient norm on A/B , then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C *-algebra by elements of a unital C *-subalgebra.
One-dimensional weak localization of electrons in a single InAs nanowire.

We report on low temperature (2−30K) electron transport and magneto-transport measurements of a chemically synthesized InAs nanowire. Both the temperature, T, and transverse magnetic field dependences of the nanowire conductance are consistent with the functional forms predicted in one-dimensional (1D) weak localization theory. By fitting the magneto-conductance data to theory, the phase coherence length of electrons is determined to be tens of nanometers with a T−1/3 dependence. Moreover, as the electron density is increased by a gate voltage, the magneto-conductance shows a possible signature of suppression of weak localization in multiple 1D subbands.
Portable device to determine particle asymmetry parameter

Accurate characterization of the asymmetry parameter g is of crucial importance for radiative transfer calculations. Here, we present a portable light scattering (PLS) device designed for in situ, real-time, and contact-free measurements of the particle phase function. The integration time is 20ms for each measurement. Using this device, we measured g values for laboratory-generated brown (organic) carbon aerosol and soot, and commercially available Arizona Road Dust. For the three types of aerosol, the g values were 0.664 ± 0.002, 0.506 ± 0.004, and 0.701 ± 0.020, respectively. The smallest angle our PLS device approaches is 0.7°, which is an order of magnitude smaller than that of commercial nephelometers, thus facilitating more accurate determination of g.
Rook theory of the finite general linear group

Matrices over a finite field having fixed rank and restricted support are a natural q-analog of rook placements on a board, even though their enumeration is known to yield nonpolynomial answers in ...
Photonic microwave generation with high-power photodiodes

We utilized and characterized high-power, high-linearity modified unitraveling carrier (MUTC) photodiodes for low-phase-noise photonic microwave generation based on optical frequency division (OFD). When illuminated with picosecond pulses from a repetition-rate-multiplied gigahertz Ti:sapphire modelocked laser, the photodiodes can achieve a 10 GHz signal power of +14 dBm. Using these diodes, we generated a 10 GHz microwave tone with less than 500 attoseconds absolute integrated timing jitter (1 Hz–10 MHz) and a phase noise floor of −177 dBc/Hz.We also characterized the electrical response, amplitude-to-phase conversion, saturation, and residual noise of the MUTC photodiodes.
Disentangling AGN and Star Formation in Soft X-Rays

We have explored the interplay of star formation and active galactic nucleus (AGN) activity in soft X-rays (0.5-2 keV) in two samples of Seyfert 2 galaxies (Sy2s). Using a combination of low-resolution CCD spectra from Chandra and XMM-Newton, we modeled the soft emission of 34 Sy2s using power-law and thermal models. For the 11 sources with high signal-to-noise Chandra imaging of the diffuse host galaxy emission, we estimate the luminosity due to star formation by removing the AGN, fitting the residual emission. The AGN and star formation contributions to the soft X-ray luminosity (i.e., L(sub x,AGN) and L(sub x,SF)) for the remaining 24 Sy2s were estimated from the power-law and thermal luminosities derived from spectral fitting. These luminosities were scaled based on a template derived from XSINGS analysis of normal star-forming galaxies. To account for errors in the luminosities derived from spectral fitting and the spread in the scaling factor, we estimated L(sub x,AGN) and L(sub x,SF))from Monte Carlo simulations. These simulated luminosities agree with L(sub x,AGN) and L(sub x,SF) derived from Chandra imaging analysis within a 3sigma confidence level. Using the infrared [Ne ii]12.8 micron and [O iv]26 micron lines as a proxy of star formation and AGN activity, respectively, we independently disentangle the contributions of these two processes to the total soft X-ray emission. This decomposition generally agrees with L(sub x,SF) and L(sub x,AGN) at the 3 sigma level. In the absence of resolvable nuclear emission, our decomposition method provides a reasonable estimate of emission due to star formation in galaxies hosting type 2 AGNs.
On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections

Pole-skipping is a recently discovered signature of many-body quantum chaos in collective energy dynamics. It establishes a precise connection between resummed, all-order hydrodynamics and the underlying microscopic chaos. In this paper, we demonstrate the existence of pole-skipping in holographic conformal field theories with higher-derivative gravity duals. In particular, we first consider Einstein-Hilbert gravity deformed by curvature-squared (R2) corrections and then type IIB supergravity theory with the α′ 3R4 term, where α′ is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order 1/Nc corrections (with Nc being the number of colours of the dual gauge group) and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet theory, pole-skipping turns out to be valid non-perturbatively in the Gauss-Bonnet coupling. The α′ 3R4 deformation enables us to study perturbative inverse ’t Hooft coupling corrections (α′ 3 ∼ 1/λ3/2) in SU(Nc), $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory with infinite Nc. While the maximal Lyapunov exponent characterising quantum chaos remains uncorrected, the butterfly velocity is shown to depend both on Nc and the coupling. Several implications of the relation between hydrodynamics and chaos are discussed, including an intriguing similarity between the dependence of the butterfly velocity and the ratio of shear viscosity to entropy density on stringy corrections.
Modeling a Nanocantilever-Based Biosensor Using a Stochastically Perturbed Harmonic Oscillator

Nanoscale biosensors are devices designed to detect analytes by combining biological components and physicochemical detectors. A well-known design of these sensors involves the implementation of nanocantilevers. These microscopic diving boards are coated with binding probes that have an affinity for a particular amino acid, enzyme or protein in living organisms. When these probes attract target particles, such as biomolecules, the binding of these particles changes the vibrating frequency of the cantilever. This process is random in nature and produces fluctuations in the frequency and damping of the cantilever. In this paper, we studied the effect of these fluctuations using a stochastically perturbed, classical harmonic oscillator.
Perspectives in cosmology

The new standard cosmology, based on the theory of inflation, has very impressive observational support. I review some outstanding problems of the new cosmology and the global view of the universe – the multiverse – that it suggests. I focus in particular on prospects for further observational tests of inflation and of the multiverse.
QCD EVOLUTION BY FINITE ELEMENT METHODS

A simple, new method for solving the Q2 evolution of parton distributions in perturbative QCD using cubic splines is described and applied to the evolution of non-singlet quark distributions.
Self-shrinkers with second fundamental form of constant length

We give a new and simple proof of a result of Ding and Xin, which states that any smooth complete self-shrinker in with the second fundamental form of constant length must be a generalised cylinder for some . Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions.
Provably adaptive reinforcement learning in metric spaces

We study reinforcement learning in continuous state and action spaces endowed with a metric. We provide a refined analysis of the algorithm of Sinclair, Banerjee, and Yu (2019) and show that its regret scales with the zooming dimension of the instance. This parameter, which originates in the bandit literature, captures the size of the subsets of near optimal actions and is always smaller than the covering dimension used in previous analyses. As such, our results are the first provably adaptive guarantees for reinforcement learning in metric spaces.
The non-convex geometry of low-rank matrix optimization

This work considers two popular minimization problems: (i) the minimization of a general convex function $f(\mathbf{X})$ with the domain being positive semi-definite matrices; (ii) the minimization of a general convex function $f(\mathbf{X})$ regularized by the matrix nuclear norm $\|\mathbf{X}\|_*$ with the domain being general matrices. Despite their optimal statistical performance in the literature, these two optimization problems have a high computational complexity even when solved using tailored fast convex solvers. To develop faster and more scalable algorithms, we follow the proposal of Burer and Monteiro to factor the low-rank variable $\mathbf{X} = \mathbf{U}\mathbf{U}^\top $ (for semi-definite matrices) or $\mathbf{X}=\mathbf{U}\mathbf{V}^\top $ (for general matrices) and also replace the nuclear norm $\|\mathbf{X}\|_*$ with $(\|\mathbf{U}\|_F^2+\|\mathbf{V}\|_F^2)/2$. In spite of the non-convexity of the resulting factored formulations, we prove that each critical point either corresponds to the global optimum of the original convex problems or is a strict saddle where the Hessian matrix has a strictly negative eigenvalue. Such a nice geometric structure of the factored formulations allows many local search algorithms to find a global optimizer even with random initializations.
Minimal immersions of closed surfaces in hyperbolic three-manifolds

We study minimal immersions of closed surfaces (of genus g ≥ 2) in hyperbolic three-manifolds, with prescribed data (σ, tα), where σ is a conformal structure on a topological surface S, and αdz2 is a holomorphic quadratic differential on the surface (S, σ). We show that, for each \({t \in (0,\tau_0)}\) for some τ0 > 0, depending only on (σ, α), there are at least two minimal immersions of closed surface of prescribed second fundamental form Re(tα) in the conformal structure σ. Moreover, for t sufficiently large, there exists no such minimal immersion. Asymptotically, as t → 0, the principal curvatures of one minimal immersion tend to zero, while the intrinsic curvatures of the other blow up in magnitude.
Scaling properties of evolutionary paths in a biophysical model of protein adaptation

The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and alphabet. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape that describes how proteins evolve new binding interactions while maintaining their folding stability. We combine the scaling relations with numerical calculations for coarse-grained protein sequences to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.
Thermal expansion in dispersion-bound molecular crystals

We explore how anharmonicity, nuclear quantum effects (NQE), many-body dispersion interactions, and Pauli repulsion influence thermal properties of dispersion-bound molecular crystals. Accounting for anharmonicity with ab initio molecular dynamics yields cell parameters accurate to within $2%$ of experiment for a set of pyridinelike molecular crystals at finite temperatures and pressures. From the experimental thermal expansion curve, we find that pyridine-I has a Debye temperature just above its melting point, indicating sizable NQE across the entire crystalline range of stability. We find that NQE lead to a substantial volume increase in pyridine-I $(\ensuremath{\approx}40$% more than classical thermal expansion at 153 K) and attribute this to intermolecular Pauli repulsion promoted by intramolecular quantum fluctuations. When predicting delicate properties such as the thermal expansivity, we show that many-body dispersion interactions and more sophisticated density functional approximations improve the accuracy of the theoretical model.
A locally preferred structure characterises all dynamical regimes of a supercooled liquid

Recent experimental results suggest that metallic liquids universally exhibit a high-temperature dynamical crossover, which is correlated with the glass transition temperature (). We demonstrate, using molecular dynamics results for , that this temperature, , is linked with cooperative atomic rearrangements that produce domains of connected icosahedra. Supercooling to a new characteristic temperature, , is shown to produce higher order cooperative rearrangements amongst connected icosahedra, which manifests as the formation of large Zr-rich connected domains that possess macroscopic proportions of the liquid’s icosahedra. This coincides with the decoupling of atomic diffusivities, large-scale domain fluctuations and the onset of glassy dynamics in the liquid. These extensive domains then abruptly stabilise above and eventually percolate before the glass is formed. All characteristic temperatures (, and ) are thus connected by successive manifestations of the structural cooperativity that begins at .