ShantanuT01/DACTYL-Pretraining huggingface dataset:
An affine transport equation was used recently to study properties of angular momentum and gravitational-wave memory effects in general relativity. In this paper, we investigate local properties of this transport equation in greater detail. Associated with this transport equation is a map between the tangent spaces at two points on a curve. This map consists of a homogeneous (linear) part given by the parallel transport map along the curve plus an inhomogeneous part, which is related to the development of a curve in a manifold into an affine tangent space. For closed curves, the affine transport equation defines a "generalized holonomy" that takes the form of an affine map on the tangent space. We explore the local properties of this generalized holonomy by using covariant bitensor methods to compute the generalized holonomy around geodesic polygon loops. We focus on triangles and "parallelogramoids" with sides formed from geodesic segments. For small loops, we recover the well-known result for the leading-order linear holonomy ($\sim$ Riemann $\times$ area), and we derive the leading-order inhomogeneous part of the generalized holonomy ($\sim$ Riemann $\times$ area$^{3/2}$). Our bitensor methods let us naturally compute higher-order corrections to these leading results. These corrections reveal the form of the finite-size effects that enter into the holonomy for larger loops; they could also provide quantitative errors on the leading-order results for finite loops.
Supernova remnants are believed to be the main sites where Galactic cosmic rays originate. This scenario, however, fails to explain some of the features observed in the cosmic-ray spectrum. Microquasars have been proposed as additional candidates, because their non-thermal emission indicates the existence of efficient particle acceleration mechanisms in their jets. A promising scenario envisages the production of relativistic neutrons in the jets, that decay outside the system injecting relativistic protons to the surroundings. The first investigations of this scenario suggest that microquasars might be fairly alternative cosmic-ray sources.   We aim at assessing the role played by the degree of collimation of the jet on the cosmic-ray energetics in the neutron-carrier scenario, as well as the properties of the emission region. Our goals are to explain the Galactic component of the observed proton cosmic-ray spectrum at energies higher than $\sim 10$ GeV and to relate the mentioned jet properties with the power and spectral index of the produced cosmic rays. We find that collimated jets, with compact acceleration regions close to the jet base, are very efficient sources that could deliver a fraction of up to $\sim 0.01$ of their relativistic proton luminosity into cosmic rays. Collimation is the most significant feature regarding efficiency; a well collimated jet might be $\sim 4$ orders of magnitude more efficient than a poorly collimated one. The main feature of the presented mechanism is the production of a spectrum with a steeper spectral index ($\sim 2.3$ at energies up to $\sim 10$ TeV) than in the supernova scenario, and closer to what is observed. The predictions of our model may be used to infer the total contribution of the population of Galactic microquasars to the cosmic ray population, and therefore to quantitatively assess their significance as cosmic-ray sources.
The thermopower in a two-dimensional semimetal existing in HgTe quantum wells 18-21 nm thick has been studied experimentally and theoretically for the first time. It has been found theoretically and experimentally that the thermopower has two components - diffusion and phonon drag and that the second component is several times larger than the first. It has been concluded that the electron-hole scattering plays an important role in both mechanisms of the thermopower.
We investigate the effect of a single microlens on Stokes parameters.   Semi-analytical formulae of the microlensed Stokes parameters are derived. The formulae not only reduce the double integrals in the estimations of those quantities but can also be approximated to a useful form in the bypass case. By using our formulation, we show that a combination of polarimetric data with photometric data enables us to estimate not only the finite source effect but also the direction of the microlens motion.
We study Active Galactic Nucleus (AGN) activity in the fossil galaxy cluster, RX J1416.4+2315. Radio observations were carried out using Giant Metrewave Radio Telescope (GMRT) at two frequencies, 1420 MHz and 610 MHz. A weak radio lobe that extends from the central nucleus is detected in 610 MHz map. Assuming the radio lobe originated from the central AGN, we show the energy injection into the Inter Galactic Medium (IGM) is only sufficient to heat up the central 50 kpc within the cluster core, while the cooling radius is larger ( $\sim$ 130 kpc). In the hardness ratio map, three low energy cavities have been identified. No radio emission is detected for these regions. We evaluated the power required to inflate the cavities and showed that the total energy budget is sufficient to offset the radiative cooling. We showed that the initial conditions would change the results remarkably. Furthermore, efficiency of Bondi accretion to power the AGN has been estimated.
We investigate the phase space of parameters in the Pati-Salam model derived in the context of D-branes scenarios, requiring low energy string scale. We find that a non-supersymmetric version complies with a string scale as low as 10 TeV, while in the supersymmetric version the string scale raises up to ~2 x 10^7 TeV. The limited energy region for RGE running demands a large tan(beta) in order to have experimentally acceptable masses for the top and bottom quarks.
We prove that for any given positive integer $\ell$ there are infinitely many imaginary quadratic fields with 2-class group of type $(2,2^\ell)$, and provide a lower bound for the number of such groups with bounded discriminant for $\ell\ge2$. This work is based on a related result for cyclic 2-class groups by Dominguez, Miller and Wong, and our proof proceeds similarly. Our proof requires introducing congruence conditions into Perelli's result on Goldbach numbers represented by polynomials, which we establitish in some generality.
A plethora of deep learning models have been developed for the task of Alzheimer's disease classification from brain MRI scans. Many of these models report high performance, achieving three-class classification accuracy of up to 95%. However, it is common for these studies to draw performance comparisons between models that are trained on different subsets of a dataset or use varying imaging preprocessing techniques, making it difficult to objectively assess model performance. Furthermore, many of these works do not provide details such as hyperparameters, the specific MRI scans used, or their source code, making it difficult to replicate their experiments. To address these concerns, we present a comprehensive study of some of the deep learning methods and architectures on the full set of images available from ADNI. We find that, (1) classification using 3D models gives an improvement of 1% in our setup, at the cost of significantly longer training time and more computation power, (2) with our dataset, pre-training yields minimal ($<0.5\%$) improvement in model performance, (3) most popular convolutional neural network models yield similar performance when compared to each other. Lastly, we briefly compare the effects of two image preprocessing programs: FreeSurfer and Clinica, and find that the spatially normalized and segmented outputs from Clinica increased the accuracy of model prediction from 63% to 89% when compared to FreeSurfer images.
NaSt1 (aka Wolf-Rayet 122) is a peculiar emission-line star embedded in an extended nebula of [N II] emission with a compact dusty core. This object was characterized by Crowther & Smith (1999) as a Wolf-Rayet (WR) star cloaked in an opaque nebula of CNO-processed material, perhaps analogous to Eta Car and its Homunculus nebula, albeit with a hotter central source. To discern the morphology of the [N II] nebula we performed narrowband imaging using the Hubble Space Telescope and Wide-field Camera 3. The images reveal that the nebula has a disk-like geometry tilted 12 degrees from edge-on, composed of a bright central ellipsoid surrounded by a larger clumpy ring. Ground-based spectroscopy reveals radial velocity structure (~10 km/s) near the outer portions of the nebula's major axis, which is likely to be the imprint of outflowing gas. Near-infrared adaptive-optics imaging with Magellan AO has resolved a compact ellipsoid of Ks-band emission aligned with the larger [N II] nebula, which we suspect is the result of scattered He I line emission (2.06 um). Observations with the Chandra X-ray Observatory have revealed an X-ray point source at the core of the nebula that is heavily absorbed at energies <1 keV and has properties consistent with WR stars and colliding-wind binaries. We suggest that NaSt1 is a WR binary embedded in an equatorial outflow that formed as the result of non-conservative mass transfer. NaSt1 thus appears to be a rare and important example of a stripped-envelope WR forming through binary interaction, caught in the brief Roche-lobe overflow phase.
We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.
[Abridged] Radio galaxies and quasars are among the largest and most powerful single objects known and are believed to have had a significant impact on the evolving Universe and its large scale structure. We explore the intrinsic and extrinsic properties of the population of FRII objects (kinetic luminosities, lifetimes, and the central densities of their environments). In particular, the radio and kinetic luminosity functions of FRIIs are investigated using the complete, flux limited radio catalogues of 3CRR and Best et al. We construct multidimensional Monte Carlo simulations using semi-analytical models of FRII radio source growth to create artificial samples of radio galaxies. Unlike previous studies, we compare radio luminosity functions found with both the observed and simulated data to explore the fundamental source parameters. We allow the source physical properties to co-evolve with redshift, and we find that all the investigated parameters most likely undergo cosmological evolution. Strikingly, we find that the break in the kinetic luminosity function must undergo redshift evolution of at least (1+z)^3. The fundamental parameters are strongly degenerate, and independent constraints are necessary to draw more precise conclusions. We use the estimated kinetic luminosity functions to set constraints on the duty cycles of these powerful radio sources. A comparison of the duty cycles of powerful FRIIs with those determined from radiative luminosities of AGN of comparable black hole mass suggests a transition in behaviour from high to low redshifts, corresponding to either a drop in the typical black hole mass of powerful FRIIs at low redshifts, or a transition to a kinetically-dominated, radiatively-inefficient FRII population.
The anisotropic electronic structure responsible for the antiferromagnetic transition in CeRu$_2$Al$_{10}$ at the unusually high temperature of $T_0$ = 28 K was studied using optical conductivity spectra, Ce 3d X-ray photoemission spectra, and band calculation. It was found that the electronic structure in the $ac$ plane is that of a Kondo semiconductor, whereas that along the b axis has a nesting below 32 K (slightly higher than $T_0$). These characteristics are the same as those of CeOs$_2$Al$_{10}$ [S. Kimura {\it et al.}, Phys. Rev. Lett. 106, 056404 (2011).]. The $c$-$f$ hybridization intensities between the conduction and $4f$ electrons of CeRu$_2$Al$_{10}$ and CeOs$_2$Al$_{10}$ are weaker than that of CeFe$_2$Al$_{10}$, showing no magnetic ordering. These results suggest that the electronic structure with one-dimensional weak $c$-$f$ hybridization along the b axis combined with two-dimensional strong hybridization in the $ac$ plane causes charge-density wave (CDW) instability, and the CDW state then induces magnetic ordering.
The renormalization of the effective QCD-Hamiltonian theory for the quark-antiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed point-Hamiltonian brings the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of the renormalized effective QCD-Hamiltonian comes from the pion mass and radius, for a given constituent quark mass. The 1s and excited 2s states of $\bar u q$ are calculated as a function of the mass of the quark $q$ being s, c or b, and compared to the experimental values.
In this paper we contribute a simple yet effective approach for estimating 3D poses of multiple people from multi-view images. Our proposed coarse-to-fine pipeline first aggregates noisy 2D observations from multiple camera views into 3D space and then associates them into individual instances based on a confidence-aware majority voting technique. The final pose estimates are attained from a novel optimization scheme which links high-confidence multi-view 2D observations and 3D joint candidates. Moreover, a statistical parametric body model such as SMPL is leveraged as a regularizing prior for these 3D joint candidates. Specifically, both 3D poses and SMPL parameters are optimized jointly in an alternating fashion. Here the parametric models help in correcting implausible 3D pose estimates and filling in missing joint detections while updated 3D poses in turn guide obtaining better SMPL estimations. By linking 2D and 3D observations, our method is both accurate and generalizes to different data sources because it better decouples the final 3D pose from the inter-person constellation and is more robust to noisy 2D detections. We systematically evaluate our method on public datasets and achieve state-of-the-art performance. The code and video will be available on the project page: https://ait.ethz.ch/projects/2021/multi-human-pose/.
We conduct intensity mapping to probe for extended diffuse Ly$\alpha$ emission around Ly$\alpha$ emitters (LAEs) at $z\sim2-7$, exploiting very deep ($\sim26$ mag at $5\sigma$) and large-area ($\sim4.5$ deg$^2$) Subaru/Hyper Suprime-Cam narrow-band (NB) images and large LAE catalogs consisting of a total of 1781 LAEs at $z=2.2$, $3.3$, $5.7$, and $6.6$ obtained by the HSC-SSP SILVERRUSH and CHORUS projects. We calculate the spatial correlations of these LAEs with $\sim1-2$ billion pixel flux values of the NB images, deriving the average Ly$\alpha$ surface brightness (${\rm SB_{Ly\alpha}}$) radial profiles around the LAEs. By carefully estimating systematics such as fluctuations of sky background and point spread functions, we detect diffuse Ly$\alpha$ emission ($\sim10^{-20}-10^{-19}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$) at $100-1000$ comoving kpc around $z=3.3$ LAEs at the $4.1\sigma$ level and tentatively ($\sim2\sigma$) at the other redshifts, beyond the virial radius of a dark-matter halo with a mass of $10^{11}\ M_\odot$. While the observed ${\rm SB_{Ly\alpha}}$ profiles have similar amplitudes at $z=2.2-6.6$ within the uncertainties, the intrinsic ${\rm SB_{Ly\alpha}}$ profiles (corrected for the cosmological dimming effect) increase toward high redshifts. This trend may be explained by increasing hydrogen gas density due to the evolution of the cosmic volume. Comparisons with theoretical models suggest that extended Ly$\alpha$ emission around a LAE is powered by resonantly scattered Ly$\alpha$ photons in the CGM and IGM that originates from the inner part of the LAE, and/or neighboring galaxies around the LAE.
Here we investigate the canonical Gaussian map for higher multiple coverings of curves, the case of double coverings being completely understood thanks to previous work by Duflot. In particular, we prove that every smooth curve can be covered with degree not too high by a smooth curve having arbitrarily large genus and surjective canonical Gaussian map. As a consequence, we recover an asymptotic version of a recent result by Ciliberto and Lopez and we address the Arbarello subvariety in the moduli space of curves.
This article presents a coupling approach for the approximation of iterated stochastic integrals of length three. The generation of such integrals is the central problem of higher-order pathwise approximations for SDEs, which still lacks a satisfactory answer due to the restriction of dimensionality and computational load. Here we start from the Fourier representation of the triple stochastic integral and investigate the global behaviour of the joint density of the representation. Finally in the main result we give a coupling in the quadratic Vaserstein distance.
The "broad iron spectral features" are often seen in X-ray spectra of Active Galactic Nuclei (AGN) and black-hole binaries (BHB). These features may be explained either by the "relativistic disc reflection" scenario or the "partial covering" scenario: It is hardly possible to determine which model is valid from time-averaged spectral analysis. Thus, X-ray spectral variability has been investigated to constrain spectral models. To that end, it is crucial to study iron structure of BHBs in detail at short time-scales, which is, for the first time, made possible with the Parallel-sum clocking (P-sum) mode of XIS detectors on board Suzaku. This observational mode has a time-resolution of 7.8~ms as well as a CCD energy-resolution. We have carried out systematic calibration of the P-sum mode, and investigated spectral variability of the BHB GRS 1915+105. Consequently, we found that the spectral variability of GRS 1915+105 does not show iron features at sub-seconds. This is totally different from variability of AGN such as 1H0707--495, where the variation amplitude significantly drops at the iron K-energy band. This difference can be naturally explained in the framework of the "partial covering" scenario.
We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.
We use a recent sample of 49 galaxies to show that there is a proportionality relation between the black hole mass M_BH and the quantity \mu =M_G*\sigma /c, where M_G is mass of the spheroidal stellar component and \sigma is the stellar velocity dispersion. \mu is called the momentum parameter and the ratio is M_BH/\mu ~3.3. This result is applied to the penetrating-jet feedback model which argues that the correlation that holds is with a momentum-like parameter, although this feedback mechanism is based on energy balance.
In \cite{S}, Shyr derived an analogue of Dirichlet's class number formula for arithmetic Tori. We use this formula to derive a Brauer-Siegel formula for Tori, relating the Discriminant of a torus to the product of its regulator and class number. We apply this formula to derive asymptotics and lower bounds for Galois orbits of CM points in the Siegel modular variety $A_{g,1}$. Specifically, we ask that the sizes of these orbits grows like a power of Discriminant of the underlying endomorphism algebra. We prove this unconditionally in the case $g\leq 5$, and for all $g$ under the Generalized Riemann Hypothesis for CM fields. Along the way we derive a general transfer principle for torsion in ideal class groups of number fields.
We investigate the magnetic properties of three Mn$_6$ single molecule magnets by means of inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The experimental data reveal that small structural distortions of the molecular geometry produce a significant effect on the energy level diagram and therefore on the magnetic properties of the molecule. We show that the giant spin model completely fails to describe the spin level structure of the ground spin multiplets. We analyze theoretically the spin Hamiltonian for the low spin Mn$_6$ molecule (S=4) and we show that the excited $S$ multiplets play a key role in determining the effective energy barrier for the magnetization reversal, in analogy to what was previously found for the two high spin Mn6 (S=12) molecules [S. Carretta et al., Phys. Rev. Lett. 100, 157203 (2008)].
The overall coefficient of the two-loop 4-particle amplitude in superstring theory is determined by making use of the factorization and unitarity. To accomplish this we computed in detail all the relevant tree and one-loop amplitudes involved and determined their overall coefficients in a consistent way.
An 'induced restriction' of a simple binary matroid $M$ is a restriction $M|F$, where $F$ is a flat of $M$. We consider the class $\mathcal{M}$ of all simple binary matroids $M$ containing neither a free matroid on three elements (which we call a 'claw'), nor a Fano plane as an induced restriction. We give an exact structure theorem for this class; two of its consequences are that the matroids in $\mathcal{M}$ have unbounded critical number, while the matroids in $\mathcal{M}$ not containing the clique $M(K_5)$ as an induced restriction have critical number at most $2$.
We consider an extension of the Ramanujan series with a variable $x$. If we let $x=x_0$, we call the resulting series: "Ramanujan series with the shift $x_0$". Then, we relate these shifted series to some $q$-series and solve the case of level $4$ with the shift $x_0=1/2$. Finally, we indicate a possible way towards proving some patterns observed by the author corresponding to the levels $\ell=1, 2, 3$ and the shift $x_0=1/2$.
We study the Clifford type inequality for a particular type of curves $C_{2,2,5}$, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macr\`i, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in $\mathbf{P}^4_{\mathbb C}$.
We investigate the variation of the string field action under changes of the string field vertices giving rise to different decompositions of the moduli spaces of Riemann surfaces. We establish that any such change in the string action arises from a field transformation canonical with respect to the Batalin-Vilkovisky (BV) antibracket, and find the explicit form of the generator of the infinitesimal transformations. Two theories using different decompositions of moduli space are shown to yield the same gauge fixed action upon use of different gauge fixing conditions. We also elaborate on recent work on the covariant BV formalism, and emphasize the necessity of a measure in the space of two dimensional field theories in order to extend a recent analysis of background independence to quantum string field theory.