ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using high spatial resolution HST WFC3 and ACS imaging of resolved stellar populations, we constrain the contribution of thermally-pulsing asymptotic giant branch (TP-AGB) stars and red helium burning (RHeB) stars to the 1.6 um near-infrared (NIR) luminosities of 23 nearby galaxies. The TP-AGB phase contributes as much as 17% of the integrated F160W flux, even when the red giant branch is well populated. The RHeB population contribution can match or even exceed the TP-AGB contribution, providing as much as 21% of the integrated F160W light. The NIR mass-to-light (M/L) ratio should therefore be expected to vary significantly due to fluctuations in the star formation rate over timescales from 25 Myr to several Gyr. We compare our observational results to predictions based on optically derived star formation histories and stellar population synthesis (SPS) models, including models based on the Padova isochrones (used in popular SPS programs). The SPS models generally reproduce the expected numbers of TP-AGB stars in the sample. The same SPS models, however, give a larger discrepancy in the F160W flux contribution from the TP-AGB stars, over-predicting the flux by a weighted mean factor of 2.3 +/-0.8. This larger offset is driven by the prediction of modest numbers of high luminosity TP-AGB stars at young (<300 Myrs) ages. The best-fit SPS models simultaneously tend to under-predict the numbers and fluxes of stars on the RHeB sequence, typically by a factor of 2.0+/-0.6 for galaxies with significant numbers of RHeBs. Coincidentally, over-prediction of the TP-AGB and under-prediction of the RHeBs result in a NIR M/L ratio largely unchanged for a rapid star formation rate. However, the NIR-to-optical flux ratio of galaxies could be significantly smaller than AGB-rich models would predict, an outcome that has been observed in some intermediate redshift post-starburst galaxies. (Abridged)
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the representation of the Linnik distribution as a normal scale mixture with the Mittag-Leffler mixing distribution. As a corollary, we obtain the known representation of the Linnik distribution as a scale mixture of Laplace distributions. Another corollary of the main representation is the theorem establishing that the distributions of random sums of independent identically distributed random variables with finite variances converge to the Linnik distribution under an appropriate normalization if and only if the distribution of the random number of summands under the same normalization converges to the Mittag-Leffler distribution.
We prove that analogues of the Hardy-Littlewood generalised twin prime conjecture for almost primes hold on average. Our main theorem establishes an asymptotic formula for the number of integers $n=p_1p_2 \leq X$ such that $n+h$ is a product of exactly two primes which holds for almost all $|h|\leq H$ with $\log^{19+\varepsilon}X\leq H\leq X^{1-\varepsilon}$, under a restriction on the size of one of the prime factors of $n$ and $n+h$. Additionally, we consider correlations $n,n+h$ where $n$ is a prime and $n+h$ has exactly two prime factors, establishing an asymptotic formula which holds for almost all $|h| \leq H$ with $X^{1/6+\varepsilon}\leq H\leq X^{1-\varepsilon}$.
We consider the holomorphic unramified mapping of two arbitrary finite bordered Riemann surfaces. Extending the map to the doubles $X_1$ and $X_2$ of Riemann surfaces we define the vector bundle on the second double as a direct image of the vector bundle on first double. %% We choose line bundles of half-order differentials $\Delta_1$ and $\Delta_2$ so that the vector bundle $V^{X_2}_{\chi_\ad} \otimes \Delta_2$ on $X_2$ would be the direct image of the vector bundle $V^{X_1}_{\chi_\ao} \otimes \Delta_1$. We then show that the Hardy spaces $H_{2, J_1(p)} (S_1,V_{\chi_\ao} \otimes \Delta_1)$ and $H_{2,J_2(p)} (S_2,V_{\chi_\ad} \otimes \Delta_2)$ are isometrically isomorphic. Proving that we construct an explicit isometric isomorphism and a matrix representation $\chi_\ad$ of the fundamental group $\piod(X_2, p_0)$ given a matrix representation $\chi_\ao$ of the fundamental group $\piod(X_1, p'_0)$. %% On the basis of the results of \cite{vin} and Theorem \ref{theorem_1} proven in the present work we then conjecture that there exists a covariant functor from the category ${\cal RH}$ of finite bordered surfaces with vector bundle and signature matrices to the category of Kre\u{\i}n spaces and isomorphisms which are ramified covering of Riemann surfaces.
The main goal of network pruning is imposing sparsity on the neural network by increasing the number of parameters with zero value in order to reduce the architecture size and the computational speedup. In most of the previous research works, sparsity is imposed stochastically without considering any prior knowledge of the weights distribution or other internal network characteristics. Enforcing too much sparsity may induce accuracy drop due to the fact that a lot of important elements might have been eliminated. In this paper, we propose Guided Attention for Sparsity Learning (GASL) to achieve (1) model compression by having less number of elements and speed-up; (2) prevent the accuracy drop by supervising the sparsity operation via a guided attention mechanism and (3) introduce a generic mechanism that can be adapted for any type of architecture; Our work is aimed at providing a framework based on interpretable attention mechanisms for imposing structured and non-structured sparsity in deep neural networks. For Cifar-100 experiments, we achieved the state-of-the-art sparsity level and 2.91x speedup with competitive accuracy compared to the best method. For MNIST and LeNet architecture we also achieved the highest sparsity and speedup level.
Using the theory of hyperkahler manifolds, we generalize the notion of Enriques surfaces to higher dimensions and construct several examples using group actions on Hilbert schemes of points or moduli spaces of stable sheaves.
Let f: X \to Z be a surjective morphism of smooth complex projective varieties with connected fibers. Suppose that L is a pseudo-effective divisor on X that is f-numerically trivial. We show that there is a divisor D on Z such that L is numerically equivalent to f^*D.
Ludendorff coronal flattening index of the Total Solar Eclipse (TSE) on March 9, 2016, was calculated at various distances in solar radius. As a result, we obtained the coronal flattening index $\left(\epsilon =a+b\right)$ at a distance of 2 solar radii is 0.16. The $24^{th}$ solar cycle phase based on the 2016 TSE event obtained -0.64 which showed the corona is pre-minimum type. Resulted coronal flattening index value gives a predicted maximum amplitude of the monthly sunspot number ($W_{max}$) for the $25^{th}$ solar cycle to be $70\pm65$. Therefore, the solar activity for $25^{th}$ solar cycle predicted to be lower than the current solar cycle, which has a maximum sunspot number value of 146 in February 2014
In this paper we revisit a singular bulk potential in the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. This singular potential, called Ball-Majumdar potential, is introduced in [3], and is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. Specifically, we establish blowup rates of both this singular potential and its gradient as Q approaches its physical boundary.
We study the greatest common divisor problem for torus invariant blowing-up morphisms of nonsingular toric Fano varieties. Our main result applies the theory of Okounkov bodies together with an arithmetic form of Cartan's Second Main theorem, which has been established by Ru and Vojta. It also builds on Silverman's geometric concept of greatest common divisor. As a special case of our results, we deduce a bound for the generalized greatest common divisor of pairs of nonzero algebraic numbers.
As a step towards a more realistic modeling of vibrations in single-molecule devices, we investigate the effects of charge-dependent vibrational frequencies and anharmonic potentials on electronic transport. For weak phonon relaxation, we find that in both cases vibrational steps split into a multitude of substeps. This effectively leads to a bias-dependent broadening of vibrational features in current-voltage and conductance characteristics, which provides a fingerprint of nonequilibrium vibrations whenever other broadening mechanisms are secondary. In the case of an asymmetric molecule-lead coupling, we observe that frequency differences can also cause negative differential conductance.
Mapping Mg II resonance emission scattered by galactic winds offers a means to determine the spatial extent and density of the warm outflow. Using Keck/LRIS spectroscopy, we have resolved scattered Mg II emission to the east of 32016857, a star-forming galaxy at z =0.9392 with an outflow. The Mg II emission from this galaxy exhibits a P-Cygni profile, extends further than both the continuum and [O II] emission along the eastern side of the slit, and has a constant Doppler shift along the slit which does not follow the velocity gradient of the nebular [O II] emission. Using the Sobolev approximation, we derive the density of Mg+ ions at a radius of 12 to 18 kpc in the outflow. We model the ionization correction and find that much of the outflowing Mg is in Mg++. We estimate that the total mass flux could be as large as 330 - 500 solar masses per year, with the largest uncertainties coming from the depletion of Mg onto grains and the clumpiness of the warm outflow. We show that confining the warm clouds with a hot wind reduces the estimated mass flux of the warm outflow and indicates amass-loading factor near unity in the warm phase alone. Based on the high blue luminosities that distinguish 32016857 and TKRS 4389, described by Rubin et al. 2011, from other galaxies with P-Cygni emission, we suggest that, as sensitivity to diffuse emission improves, scattering halos may prove to be a generic property of star-forming galaxies at intermediate redshifts.
We investigate the possibility of accounting for the observed anomalous velocities of stars in galaxies to be a result of a dynamic prescription for having a galaxy generate and prescribe its own inertial frame. It is demonstrated that within observational uncertainties, an overall rotation of an inertial frame dragged by a galaxy is a comfortable fit to the observed anomalous velocity curves. A case for looking for a natural law for prescribing an inertial frame by a mass distribution over a finite (galaxy size) range is made out.
(abridged) We present the discovery of two T dwarf binaries, 2MASS 1225-2739AB and 2MASS 1534-2952AB, identified in a sample of ten T dwarfs imaged with the Hubble Space Telescope Wide Field Planetary Camera 2. The separations of the two binary systems are 0{\farcs}282$\pm$0{\farcs}005 and 0{\farcs}065$\pm$0{\farcs}007, implying projected separations of 3.17$\pm$0.14 and 1.0$\pm$0.3 AU, respectively. The observed binary fraction of our HST sample, 20$^{+17}_{-7}$%, is consistent with results obtained for late-M and L field dwarfs, and implies a bias-corrected binary fraction of 9$^{+15}_{-4}$% for $a \gtrsim 1$ AU and $q \gtrsim 0.4$, significantly lower than the binary fractions of F--G and early-type M dwarf stars. Neither of the T binaries have separations $a \gtrsim 10$ AU, consistent with results from other brown dwarf binary searches. We conclude that tidal disruption by passing stars or Giant Molecular Clouds, which limits the extent of wide stellar binaries, plays no role in eliminating wide brown dwarf binaries, implying either disruption very early in the formation process (ages $\lesssim 1-10$ Myr) or a formation mechanism which precludes such systems. We find that the maximum binary separation in the brown dwarf regime appears to scale as M$_{total}^2$, a possible clue to the physical mechanism which restricts wide substellar systems.
We present a new approach for statistical inference on noise properties of CMB anisotropy data. We consider a Maximum Likelihood parametric estimator to recover the full dependence structure of the noise process. We also consider a semiparametric procedure which is only sensitive to the low frequency behavior of the noise spectral density. Both approaches are statistically robust and computationally convenient in the case of long memory noise, even under nonstationary circumstances. We show that noise properties can be consistently derived by such procedures without resorting to currently used iterative noise-signal methods. More importantly, we show that optimal (GLS) CMB maps can be obtained from the observed timestream with the only knowledge of the noise memory parameter, the outcome of our estimators.
With the aid of Ruppeiner thermodynamic metric defined on a two-dimensional phase space of dipolar ($m$) and quadrupolar ($q$) order parameters, we derive an expression for the Ricci scalar ($R$) in the isotropic Blume-Emery-Griffiths model. Temperature dependence of $R$ is investigated for various values of bilinear to biquadratic ratio ($r$). Its behavior near the continuous/discontinuous phase transition temperatures and a tricritical point is presented. It is found that in addition to the divergence singularity and finite jumps connected with the phase transitions there are field-dependent broad extrema in the Ricci scalar.
The availability of affordable 3D full body reconstruction systems has given rise to free-viewpoint video (FVV) of human shapes. Most existing solutions produce temporally uncorrelated point clouds or meshes with unknown point/vertex correspondences. Individually compressing each frame is ineffective and still yields to ultra-large data sizes. We present an end-to-end deep learning scheme to establish dense shape correspondences and subsequently compress the data. Our approach uses sparse set of "panoramic" depth maps or PDMs, each emulating an inward-viewing concentric mosaics. We then develop a learning-based technique to learn pixel-wise feature descriptors on PDMs. The results are fed into an autoencoder-based network for compression. Comprehensive experiments demonstrate our solution is robust and effective on both public and our newly captured datasets.
The edge-on, nearby spiral galaxy NGC5907 has long been used as the prototype of a ``non-interacting'' warped galaxy. We report here the discovery of two interactions with companion dwarf galaxies that substantially change this picture. First, a faint ring structure is discovered around this galaxy that is likely due to the tidal disruption of a companion dwarf spheroidal galaxy. The ring is elliptical in shape with the center of NGC5907 close to one of the ring's foci. This suggests the ring material is in orbit around NGC5907. No gaseous component to the ring has been detected either with deep H$\alpha$ images or in Very Large Array (VLA) HI 21-cm line maps. The visible material in the ring has an integrated luminosity <= 10^8 L_sun and its brightest part has a color R-I ~ 0.9. All of these properties are consistent with the ring being a tidally-disrupted dwarf spheroidal galaxy. Second, we find that NGC5907 has a dwarf companion galaxy, PGC54419, projected to be only 36.9 kpc from the center of NGC5907, close in radial velocity (\Delta V = 45 km s^{-1}) to the giant spiral galaxy. This dwarf is seen at the tip of the HI warp and in the direction of the warp. Hence, NGC5907 can no longer be considered ``non-interacting,'' but is obviously interacting with its dwarf companions much as the Milky Way interacts with its dwarf galaxies. These results, coupled with the finding by others that dwarf galaxies tend to be found around giant galaxies, suggest that tidal interaction with companions, even if containing a mere 1% of the mass of the parent galaxy, might be sufficient to excite the warps found in the disks of many large spiral galaxies.
We consider the search for the Higgs boson at a high-luminosity Fermilab Tevatron, an upgraded Tevatron of energy 3.5 TeV, and the CERN Large Hadron Collider, via $WH/ZH$ production followed by H -> bb~ and leptonic decay of the weak vector bosons. We show that each of these colliders can potentially observe the standard Higgs boson in the intermediate-mass range, 80 GeV <m_H < 120 GeV. This mode complements the search for and the study of the intermediate-mass Higgs boson via H -> \gamma\gamma at the LHC. In addition, it can potentially be used to observe the lightest Higgs scalar of the minimal supersymmetric model in a region of parameter space not accessible to CERN LEP II or the LHC (using h -> \gamma\gamma,ZZ^*).
We completely determine the intersection cohomology of the Satake compactifications of the moduli space of principally polarized abelian varieties in genera 2,3,4, except for the degree 10 intersection cohomology in genus 4. We also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the Satake compactification in these genera. As a byproduct we obtain in addition several results about the intersection cohomology of the link bundles involved.
By the first-principles electronic structure calculations, we have systematically studied the electronic structures of recently discovered extremely large magnetoresistance (XMR) materials LaSb and LaBi. We find that both LaSb and LaBi are semimetals with the electron and hole carriers in perfect balance. The calculated carrier densities in the order of $10^{20}$ cm$^{-3}$ are in good agreement with the experimental values, implying long mean free time of carriers and thus high carrier mobilities. With a semiclassical two-band model, the perfect charge compensation and high carrier mobilities naturally explain (i) the XMR observed in LaSb and LaBi; (ii) the non-saturating quadratic dependence of XMR on external magnetic field; and (iii) the resistivity plateau in the turn-on temperature behavior at very low temperatures. The explanation of these features without resorting to the topological effect indicates that they should be the common characteristics of all perfectly electron-hole compensated semimetals.
In this paper, we aim at tackling the problem of crowd counting in extremely high-density scenes, which contain hundreds, or even thousands of people. We begin by a comprehensive analysis of the most widely used density map-based methods, and demonstrate how easily existing methods are affected by the inhomogeneous density distribution problem, e.g., causing them to be sensitive to outliers, or be hard to optimized. We then present an extremely simple solution to the inhomogeneous density distribution problem, which can be intuitively summarized as extending the density map from 2D to 3D, with the extra dimension implicitly indicating the density level. Such solution can be implemented by a single Density-Aware Network, which is not only easy to train, but also can achieve the state-of-art performance on various challenging datasets.
We present the current status of ongoing searches for molecular hydrogen in high-redshift (1.8 < zabs <= 4.2) Damped Lyman-alpha systems (DLAs) capitalising on observations performed with the ESO Very Large Telescope (VLT) Ultraviolet and Visual Echelle Spectrograph (UVES). We identify 77 DLAs/strong sub-DLAs, with log N(HI) >= 20 and z_abs > 1.8, which have data that include redshifted H2 Lyman and/or Werner-band absorption lines. This sample of HI, H2 and metal line measurements, performed in an homogeneous manner, is more than twice as large as our previous sample (Ledoux et al. 2003) and considers every system in which searches for H2 could be completed so far, including all non-detections. H2 is detected in thirteen of the systems with molecular fractions of values between f=5x10^-7 and f=0.1, where f=2N(H2)/(2N(H2)+N(HI)). Upper limits are measured for the remaining 64 systems with detection limits of typically log N(H2)=14.3, corresponding to log f<-5. We find that about 35% of the DLAs with metallicities relative to solar [X/H]>=-1.3 (i.e., 1/20th solar), with X = Zn, S or Si, have molecular fractions log f>-4.5, while H2 is detected -- regardless of the molecular fraction -- in 50% of them. In contrast, only about 4% of the [X/H]<-1.3 DLAs have log f>-4.5. We show that the presence of H2 does not strongly depend on the total neutral hydrogen column density, although the probability of finding log f>-4.5 is higher for log N(HI)>=20.8 than below this limit (19% and 7% respectively). The overall H2 detection rate in log N(HI)>=20 DLAs is found to be about 16% (10% considering only log f>-4.5 detections) after correction for a slight bias towards large N(HI). [truncated]
In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers.   The material of this paper was presented in part at the 11th International Workshop for Young Mathematicians - NUMBER THEORY, Krak\'{o}w, 14th-20th september 2008.
What makes quantum information science a science? This paper explores the idea that quantum information science may offer a powerful approach to the study of complex quantum systems.
Diaconis and Griffiths (2014) study the multivariate Krawtchouk polynomials orthogonal on the multinomial distribution.   In this paper we derive the reproducing kernel orthogonal polynomials Q_n(x,y};N,p) on the multinomial distribution which are sums of products of orthonormal polynomials in x and y of fixed total degree n=0,1,.., N. sum_{n=0}^N rho^nQ_n(x,y);N,p) arises naturally from a probabilistic argument. An application to a multinomial goodness of fit test is developed, where the chi-squared test statistic is decomposed into orthogonal components which test the order of fit. A new duplication formula for the reproducing kernel polynomials in terms of the 1-dimensional Krawtchouk polynomials is derived. The duplication formula allows a Lancaster characterization of all reversible Markov chains with a multinomial stationary distribution whose eigenvectors are multivariate Krawtchouk polynomials and where eigenvalues are repeated within the same total degree. The \chi^2 cutoff time, and total variation cutoff time is investigated in such chains.   Emphasis throughout the paper is on a probabilistic understanding of the polynomials and their applications, particularly to Markov chains.
In Parrondo's games, the apparently paradoxical situation occurs where individually losing games combine to win. The basic formulation and definitions of Parrondo's games are described in Harmer et al.. These games have recently gained considerable attention as they are physically motivated and have been related to physical systems such as the Brownian ratchet, lattice gas automata and spin systems. Various authors have pointed outinterest in these games for areas as diverse as biogenesis, political models, small-world networks, economics and population genetics. In this chapter, we will first introduce the relevant properties of Markov transition operators and then introduce some terminology and visualisation techniques from the theory of dynamical systems. We will then use these tools, later in the chapter, to define and investigate some interesting properties of Parrondo's games.