ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we propose Deep Alignment Network (DAN), a robust face alignment method based on a deep neural network architecture. DAN consists of multiple stages, where each stage improves the locations of the facial landmarks estimated by the previous stage. Our method uses entire face images at all stages, contrary to the recently proposed face alignment methods that rely on local patches. This is possible thanks to the use of landmark heatmaps which provide visual information about landmark locations estimated at the previous stages of the algorithm. The use of entire face images rather than patches allows DAN to handle face images with large variation in head pose and difficult initializations. An extensive evaluation on two publicly available datasets shows that DAN reduces the state-of-the-art failure rate by up to 70%. Our method has also been submitted for evaluation as part of the Menpo challenge.
The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in electronic systems is quite challenging. We propose an electronic transport measurement scheme that both the charge amount and the spatial distribution of the TFC can be extracted from the differential conductance through a quantum dot coupled to the topological system being measured. For one-dimensional Su-Schrieffer-Heeger (SSH) model, both the $e/2$ charge of the TFC and its distribution can be verified. We also show that the Anderson disorder effect, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while has little effect on the one-dimensional SSH chain. Nonetheless, our measurement scheme can still work well for specific higher-order topological insulator materials, for instance, the $2e/3$ TFC in the breathing kagome model could be confirmed even in the presence of disorder effect.
During five ROSAT HRI observations in July 1995, a bright X-ray source (designated 1RXH J132519.8-430312) was detected 2.5' south-west of the nucleus of NGC 5128 (Centaurus A) at the outer regions of the elliptical galaxy. At that time it was the brightest point source in the ROSAT HRI field-of-view. All other ROSAT observations made before and after these observations show no trace of the source suggesting that this is a highly variable object. Chandra observations of Cen A made in September 1999 show a source at the ROSAT position which may be the quiescent counterpart of the transient. It is very probable that the transient is located in NGC 5128. Given the existence of a transient source that close to the direction of NGC 5128, all observations (at least in soft X-rays) of Cen A, with instruments of low spatial resolution, must take the presence and variability of this object into account.
In the present work we give a generalization of the hyperboloidal foliation method which allows us to remove the restriction on support of initial data in $\mathbb{R}^{1+1}$. Then we will make an application on a model system.
We present 10" to 18" images of four massive clusters of galaxies through the Sunyaev-Zel'dovich Effect (SZE). These measurements, made at 90~GHz with the MUSTANG receiver on the Green Bank Telescope (GBT), reveal pressure sub-structure to the intra-cluster medium (ICM) in three of the four systems. We identify the likely presence of a previously unknown weak shock-front in MACS0744+3927. By fitting the Rankine-Hugoniot density jump conditions in a complementary SZE/X-ray analysis, we infer a Mach number of M = 1.2^{+0.2}_{-0.2} and a shock-velocity of 1827^{+267}_{-195}~km/s. In RXJ1347-1145, we present a new reduction of previously reported data and confirm the presence of a south-east SZE enhancement with a significance of 13.9 sigma when smoothed to 18" resolution. This too is likely caused by shock-heated gas produced in a recent merger. In our highest redshift system, CL1226+3332, we detect sub-structure at a peak significance of 4.6 sigma in the form of a ridge oriented orthogonally to the vector connecting the main mass peak and a sub-clump revealed by weak lensing. We also conclude that the gas distribution is elongated in a south-west direction, consistent with a previously proposed merger scenario. The SZE image of the cool core cluster Abell 1835 is, in contrast, consistent with azimuthally symmetric signal only. This pilot study demonstrates the potential of high-resolution SZE images to complement X-ray data and probe the dynamics of galaxy clusters
Within the $\sigma-\omega$ model of coupled nucleon-meson systems, a generalized relativistic Lenard--Balescu--equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as flucuation effects. It contains all possible processes due to one meson exchange and special attention is kept to the off--shell character of the particles. As a new feature of many particle effects, processes are possible which can be interpreted as particle creation and annihilation due to in-medium one meson exchange. In-medium cross sections are obtained from the generalized derivation of collision integrals, which possess complete crossing symmetries.
This work presents an approach to evaluate the exact value of the fractal dimension of the cutting path $d^{CP}_f$ on hierarchical structures with finite order of ramification. This represents the first renormalization group treatment of the universality class of watersheds. By making use of the self-similar property, we show that $d^{CP}_f$ depends only on the average cutting path (CP) of the first generation of the structure. For the simplest Wheastone hierarchical lattice (WHL), we present a mathematical proof. For a larger WHL structure, the exact value of $d^{CP}_f$ is derived based on an computer algorithm that identifies the length of all possible CP's of the first generation.
The NASA space telescope Kepler has provided unprecedented time-series observations which have revolutionised the field of asteroseismology, i.e. the use of stellar oscillations to probe the interior of stars. The Kepler-data include observations of stars in open clusters, which are particularly interesting for asteroseismology. One of the clusters observed with Kepler is NGC 6811, which is the target of the present paper. However, apart from high-precision time-series observations, sounding the interiors of stars in open clusters by means of asteroseismology also requires accurate and precise atmospheric parameters as well as cluster membership indicators for the individual stars. We use medium-resolution (R~25,000) spectroscopic observations, and three independent analysis methods, to derive effective temperatures, surface gravities, metallicities, projected rotational velocities and radial velocities, for 15 stars in the field of the open cluster NGC 6811. We discover two double-lined and three single-lined spectroscopic binaries. Eight stars are classified as either certain or very probable cluster members, and three stars are classified as non-members. For four stars, cluster membership could not been assessed. Five of the observed stars are G-type giants which are located in the colour-magnitude diagram in the region of the red clump of the cluster. Two of these stars are surely identified as red clump stars for the first time. For those five stars, we provide chemical abundances of 31 elements. The mean radial-velocity of NGC 6811 is found to be +6.68$\pm$0.08 km s$^{-1}$ and the mean metallicity and overall abundance pattern are shown to be very close to solar with an exception of Ba which we find to be overabundant.
We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.
A method is presented for the reconstruction of both the background and signal in invariant-mass analyses for two-photon decays. The procedure does not make use of event mixing techniques and as such is based exclusively on an event-by-event analysis. Consequently, topological correlations of the event (e.g. jet structures) are automatically taken into account. By means of the decay process $\pi^{0} \to \gamma \gamma$ it will be demonstrated how the procedure allows for determination of the $\pi^{0}$ yield from the observed decay photons.
We present Atacama Large Millimeter Array (ALMA) observations of $^{12}$CO2$-$1 emission from circumstellar material around the massive star $\eta$~Carinae. These observations reveal new structural details about the cool equatorial torus located $\sim$4000 au from the star. The CO torus is not a complete azimuthal loop, but rather, is missing its near side, which appears to have been cleared away. The missing material matches the direction of apastron in the eccentric binary system, making it likely that $\eta$~Car's companion played an important role in disrupting portions of the torus soon after ejection. Molecular gas seen in ALMA data aligns well with the cool dust around $\eta$~Car previously observed in mid-infrared (IR) maps, whereas hot dust resides at the inner surface of the molecular torus. The CO also coincides with the spatial and velocity structure of near-IR H$_2$ emission. Together, these suggest that the CO torus seen by ALMA is actually the pinched waist of the Homunculus polar lobes, which glows brightly because it is close to the star and warmer than the poles. The near side of the torus appears to be a blowout, associated with fragmented equatorial ejecta. We discuss implications for the origin of various features northwest of the star. CO emission from the main torus implies a total gas mass in the range of 0.2-1 $M_{\odot}$ (possibly up to 5 $M_{\odot}$ or more, although with questionable assumptions). Deeper observations are needed to constrain CO emission from the cool polar lobes.
Motivated by the possible conflict between the Navarro-Frenk-White(NFW) model predictions for the dark matter contents of galactic systems and its correlation with baryonic surface density, we will explore an alternative paradigm for the description of dark matter halos. Such an alternative emerges from Tsallis' non-extensive thermodynamics applied to self-gravitating systems and leads to the so-called ``stellar polytrope'' (SP) model. We consider that this could be a better approach to real structures rather than the isothermal model, given the fact that the first one takes into account the non-extensivity of energy and entropy present in these type of systems characterized by long-range interactions. We compare a halo based on the Navarro-Frenk-White (NFW) and one which follows the SP description. Analyzing the dark matter contents estimated by means of global physical parameters of galactic disks, obtained from a sample of actual galaxies, with the ones of the unobserved dark matter halos, we conclude that the SP model is favored over the NFW model in such a comparison.
The faint stellar halos of galaxies contain key information about the oldest stars and the process of galaxy formation. A previous study of stacked SDSS images of disk galaxies has revealed a halo with an abnormally red r-i colour, seemingly inconsistent with our current understanding of stellar halos. Here, we investigate the statistical properties of the faint envelopes of low surface brightness disk galaxies to look for further support for a red excess. 1510 edge-on low surface brightness galaxies were selected from the SDSS Data Release 5, rescaled to the same apparent size, aligned and stacked. This procedure allows us to reach a surface brightness of mu_g ~ 31 mag arcsec^-2. After a careful assessment of instrumental light scattering effects, we derive median and average radial surface brightness and colour profiles in g,r and i. The sample is then divided into 3 subsamples according to g-r colour. All three samples exhibit a red colour excess in r-i in the thick disk/halo region. The halo colours of the full sample, g-r = 0.60+-0.15 and r-i = 0.80+-0.15, are found to be incompatible with the colours of any normal type of stellar population. The fact that no similar colour anomaly is seen at comparable surface brightness levels along the disk rules out a sky subtraction residual as the source of the extreme colours. A number of possible explanations for these abnormally red halos are discussed. We find that two different scenarios -- dust extinction of extragalactic background light and a stellar population with a very bottom-heavy initial mass function -- appear to be broadly consistent with our observations and with similar red excesses reported in the halos of other types of galaxies.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
The $\omega$-, $\rho$- and $\phi$-resonance production and their dileptonic decay in $\pi^- A$ reactions at 1.1 - 1.7 GeV/c are calculated within the intranuclear cascade (INC) approach. The invariant mass distribution of the dilepton pair for each resonance can be decomposed in two components which correspond to their decay 'inside' the target nucleus and in the vacuum, respectively. The first components are strongly distorted by the nuclear medium due to resonance-nucleon scattering and a possible mass shift at finite baryon density. These medium modifications are compared to background sources in the dilepton spectrum from $\pi N$ bremsstrahlung as well as the Dalitz decays of $\omega$ and $\eta$ mesons produced in the reaction. Detailed predictions for $\pi^- Pb$ reactions at 1.3 and 1.7 GeV/c are made within several momentum bins for the lepton pair.
In this work, we explain three beyond standard model (BSM) phenomena, namely neutrino masses, the baryon asymmetry of the Universe and Dark Matter, within a single model and in each explanation the right handed (RH) neutrinos play the prime role. Indeed by just introducing two RH neutrinos we can generate the neutrino masses by the Type-I seesaw mechanism. The baryon asymmetry of the Universe can arise from thermal leptogenesis from the decay of lightest RH neutrino before the decoupling of the electroweak sphaleron transitions, which redistribute the $ B-L $ number into a baryon number. At the same time, the decay of the RH neutrino can produce the Dark Matter (DM) as an asymmetric Dark Matter component. The source of CP violation in the two sectors is exactly the same, related to the complex couplings of the neutrinos. By determining the comoving number density for different values of the CP violation in the DM sector, we obtain a particular value of the DM mass after satisfying the relic density bound. We also give prediction for the DM direct detection (DD) in the near future by different ongoing DD experiments.
The parton distribution function for a b quark in the B meson (called the shape function) plays an important role in the analysis of the B -> X_s gamma and B -> X_u l nu data, and gives one of the dominant uncertainties in the determination of |Vub|. We introduce a new framework to treat the shape function, which consistently incorporates its renormalization group evolution and all constraints on its shape and moments in any short distance mass scheme. At the same time it allows a reliable treatment of the uncertainties. We develop an expansion in a suitable complete set of orthonormal basis functions, which provides a procedure for systematically controlling the uncertainties due to the unknown functional form of the shape function. This is a significant improvement over fits to model functions. Given any model for the shape function, our construction gives an orthonormal basis in which the model occurs as the first term, and corrections to it can be studied. We introduce a new short distance scheme, the "invisible scheme", for the kinetic energy matrix element, lambda_1. We obtain closed form results for the differential rates that incorporate perturbative corrections and a summations of logarithms at any order in perturbation theory, and present results using known next-to-next-to-leading order expressions. The experimental implementation of our framework is straightforward.
A much-studied system is the quasi-2D electron gas in image-potential bound states at the surface of helium and hydrogen. In this paper, we report on an analogous quasi-1D system: electrons bound by image-like polarization forces to the surface of a helium-coated carbon nanotube. The potential is computed from an electron-helium pseudopotential, plus a dynamic image term evaluated from a semi-classical model of the nanotube's response function. Predictions are made for the bound states and potential many-body properties of this novel electron gas for a specific choice of tube radius and film thickness.
We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of the branch and ramification locus have simple normal crossings.
The Lyman-alpha emitters found at z=4.5 and 5.7 by the Large Area Lyman Alpha (LALA) survey have high equivalent widths in the Lyman-alpha line. Such lines can be produced by narrow-lined active galactic nuclei (AGNs) or by stellar populations with a very high proportion of young, massive stars. To check for Type-II (i.e., narrow-lined) quasars, we obtained a deep X-ray image of 49 Lyman-alpha sources in a single field of the ACIS instrument on the Chandra X-ray Observatory. None of these sources were detected with a 3-sigma limiting X-ray luminosity of 2.9x10^{43} ergs/s. For comparison, the two known high redshift type-II quasars have luminosities of 4x10^{43} ergs/s before extinction correction. The sources remain undetected in stacked images of the 49 lyman-alpha sources (with 6.5 Mega-seconds effective Chandra on-axis exposure) at 3-sigma limits of 4.9x10^{42} ergs/s. The resulting X-ray to lyman-alpha ratio is about 4-24 times lower than the ratio for known type-II quasars, while the average Lyman-alpha luminosity of the LALA sample is in between the two type-II's. The cumulative X-ray to Lyman-alpha ratio limit is also below that of 90% of low-redshift Seyfert galaxies.
We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The probability for generating the NOON state with five phonons is over 0.15.
Using a recently-developed time-of-flight measurement technique with 1 ps time resolution and electron-energy spectroscopy, we developed a method to measure the longitudinal-optical-phonon emission rate of hot electrons travelling along a depleted edge of a quantum Hall bar. A comparison of the experimental results to a single-particle model implies that the main scattering mechanism involves a two-step process via intra-Landau-level transition. We show this scattering can be suppressed by controlling the edge potential profile, and a scattering length > 1 mm can be achieved, allowing the use of this system for scalable single-electron device applications.
We prove an incidence theorem for points and planes in the projective space $\mathbb P^3$ over any field $\mathbb F$, whose characteristic $p\neq 2.$ An incidence is viewed as an intersection along a line of a pair of two-planes from two canonical rulings of the Klein quadric. The Klein quadric can be traversed by a generic hyperplane, yielding a line-line incidence problem in a three-quadric, the Klein image of a regular line complex. This hyperplane can be chosen so that at most two lines meet. Hence, one can apply an algebraic theorem of Guth and Katz, with a constraint involving $p$ if $p>0$.   This yields a bound on the number of incidences between $m$ points and $n$ planes in $\mathbb P^3$, with $m\geq n$ as $$O\left(m\sqrt{n}+ m k\right),$$ where $k$ is the maximum number of collinear planes, provided that $n=O(p^2)$ if $p>0$. Examples show that this bound cannot be improved without additional assumptions.   This gives one a vehicle to establish geometric incidence estimates when $p>0$. For a non-collinear point set $S\subseteq \mathbb F^2$ and a non-degenerate symmetric or skew-symmetric bilinear form $\omega$, the number of distinct values of $\omega$ on pairs of points of $S$ is $\Omega\left[\min\left(|S|^{\frac{2}{3}},p\right)\right]$. This is also the best known bound over $\mathbb R$, where it follows from the Szemer\'edi-Trotter theorem. Also, a set $S\subseteq \mathbb F^3$, not supported in a single semi-isotropic plane contains a point, from which $\Omega\left[\min\left(|S|^{\frac{1}{2}},p\right)\right]$ distinct distances to other points of $S$ are attained.
Let $G=(V,E)$ be a graph. For some $\alpha$ with $0<\alpha \leq 1$, a subset $S$ of $V$ is said to be a $\alpha$-partial dominating set if $|N[S]|\geq \alpha |V|$. The size of a smallest such $S$ is called the $\alpha$-partial domination number and is denoted by $\mathsf{pd}_\alpha(G)$. In this paper, we introduce $\alpha$-partial domination number in a graph $G$ and study different bounds on the partial domination number of a graph $G$ with respect to its order, maximum degree, domination number etc., Moreover, $\alpha$-partial domination spectrum is introduced and Nordhaus-Gaddum bounds on the partial domination number are studied.
Directed transport in ratchets is determined by symmetry-breaking in a system out of equilibrium. A hallmark of rocking ratchets is current reversals: an increase in the rocking force changes the direction of the current. In this work for a bi-harmonically driven spatially symmetric rocking ratchet we show that a class of current reversal is precisely determined by symmetry-breaking, thus creating a link between dynamical and symmetry-breaking mechanisms.
We present a general Bayesian formalism for the definition of Figures of Merit (FoMs) quantifying the scientific return of a future experiment. We introduce two new FoMs for future experiments based on their model selection capabilities, called the decisiveness of the experiment and the expected strength of evidence. We illustrate these by considering dark energy probes, and compare the relative merits of stage II, III and IV dark energy probes. We find that probes based on supernovae and on weak lensing perform rather better on model selection tasks than is indicated by their Fisher matrix FoM as defined by the Dark Energy Task Force. We argue that our ability to optimize future experiments for dark energy model selection goals is limited by our current uncertainty over the models and their parameters, which is ignored in the usual Fisher matrix forecasts. Our approach gives a more realistic assessment of the capabilities of future probes and can be applied in a variety of situations.