ShantanuT01/DACTYL-Pretraining huggingface dataset:
For two $r$-graphs $\mathcal{T}$ and $\mathcal{H}$, let $\text{ex}_{r}(n,\mathcal{T},\mathcal{H})$ be the maximum number of copies of $\mathcal{T}$ in an $n$-vertex $\mathcal{H}$-free $r$-graph. The determination of Tur\'{a}n number $\text{ex}_{r}(n,\mathcal{T},\mathcal{H})$ has become the fundamental core problem in extremal graph theory ever since the pioneering work Tur\'{a}n's Theorem was published in $1941$. Although we have some rich results for the simple graph case, only sporadic results have been known for the hypergraph Tur\'{a}n problems. In this paper, we mainly focus on the function $\text{ex}_{r}(n,\mathcal{T},\mathcal{H})$ when $\mathcal{H}$ is one of two different hypergraph extensions of the complete bipartite graph $K_{s,t}$. The first extension is the complete bipartite $r$-graph $K_{s,t}^{(r)}$, which was introduced by Mubayi and Verstra\"{e}te~[J. Combin. Theory Ser. A, 106: 237--253, 2004]. Using the powerful random algebraic method, we show that if $s$ is sufficiently larger than $t$, then \[\text{ex}_{r}(n,\mathcal{T},K_{s,t}^{(r)})=\Omega(n^{v-\frac{e}{t}}),\] where $\mathcal{T}$ is an $r$-graph with $v$ vertices and $e$ edges. In particular, when $\mathcal{T}$ is an edge or some specified complete bipartite $r$-graph, we can determine their asymptotics.   The second important extension is the complete $r$-partite $r$-graph $K_{s_{1},s_{2},\ldots,s_{r}}^{(r)}$, which has been widely studied. When $r=3$, we provide an explicit construction giving \[\text{ex}_{3}(n,K_{2,2,7}^{(3)})\geqslant\frac{1}{27}n^{\frac{19}{7}}+o(n^{\frac{19}{7}}).\] Our construction is based on the Norm graph, and improves the lower bound $\Omega(n^{\frac{73}{27}})$ obtained by probabilistic method.
The stochastic models investigated in this paper describe the evolution of a set of $F_N$ identical balls scattered into $N$ urns connected by an underlying symmetrical graph with constant degree $h_N$. After some random amount of time {\em all the balls} of any urn are redistributed locally, among the $h_N$ urns of its neighborhood. The allocation of balls is done at random according to a set of weights which depend on the state of the system. The main original features of this context is that the cardinality $h_N$ of the range of interaction is not necessarily linear with respect to $N$ as in a classical mean-field context and, also, that the number of simultaneous jumps of the process is not bounded due to the redistribution of all balls of an urn at the same time. The approach relies on the analysis of the evolution of the local empirical distributions associated to the state of urns located in the neighborhood of a given urn. Under convenient conditions, by taking an appropriate Wasserstein distance and by establishing several technical estimates for local empirical distributions, we are able to prove mean-field convergence results.   When the load per node goes to infinity, a convergence result for the invariant distribution of the associated McKean-Vlasov process is obtained for several allocation policies. For the class of power of $d$ choices policies, we show that the associated invariant measure has an asymptotic finite support property under this regime. This result differs somewhat from the classical double exponential decay property usually encountered in the literature for power of $d$ choices policies.
The {\it concordance} cosmological model has been successfully tested throughout the last decades. Despite its successes, the fundamental nature of dark matter and dark energy is still unknown. Modifications of the gravitational action have been proposed as an alternative to these dark components. The straightforward modification of gravity is to generalize the action to a function, $f(R)$, of the scalar curvature. Thus one is able to describe the emergence and the evolution of the Large Scale Structure without any additional (unknown) dark component. In the weak field limit of the $f(R)$-gravity, a modified Newtonian gravitational potential arises. This gravitational potential accounts for an extra force, generally called fifth force, that produces a precession of the orbital motion even in the classic mechanical approach. We have shown that the orbits in the modified potential can be written as Keplerian orbits under some conditions on the strength and scale length of this extra force. Nevertheless, we have also shown that this extra term gives rise to the precession of the orbit. Thus, comparing our prediction with the measurements of the precession of some planetary motions, we have found that the strength of the fifth force must be in the range $[2.70-6.70]\times10^{-9}$ whit the characteristic scale length to fixed to the fiducial values of $\sim 5000$ AU.
Although well-known large-scale datasets, such as ImageNet, have driven image understanding forward, most of these datasets require extensive manual annotation and are thus not easily scalable. This limits the advancement of image understanding techniques. The impact of these large-scale datasets can be observed in almost every vision task and technique in the form of pre-training for initialization. In this work, we propose an easily scalable and self-supervised technique that can be used to pre-train any semantic RGB segmentation method. In particular, our pre-training approach makes use of automatically generated labels that can be obtained using depth sensors. These labels, denoted by HN-labels, represent different height and normal patches, which allow mining of local semantic information that is useful in the task of semantic RGB segmentation. We show how our proposed self-supervised pre-training with HN-labels can be used to replace ImageNet pre-training, while using 25x less images and without requiring any manual labeling. We pre-train a semantic segmentation network with our HN-labels, which resembles our final task more than pre-training on a less related task, e.g. classification with ImageNet. We evaluate on two datasets (NYUv2 and CamVid), and we show how the similarity in tasks is advantageous not only in speeding up the pre-training process, but also in achieving better final semantic segmentation accuracy than ImageNet pre-training
A comparison of the H1 data on the longitudinal structure function, $F_L$, at small $x$ with the predictions from the generalized vector dominance / color dipole picture (GVD/CDP) is presented. Using the set of parameters previously determined in the fits to the total cross section, $\sigma_{\gamma^* p}$, we find good agreement with the data for $F_L$. Scaling in $\eta = (Q^2 + m^2_0) / \Lambda^2 (W^2)$ is discussed in detail for the longitudinal and transverse photoabsorption cross sections.
For a sequence of identically distributed negatively associated random variables $\{X_n; n\geq 1\}$ with partial sums $S_n=\sum_{i=1}^nX_i, n\geq 1$, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form $$ \sum_{n \ge n_0} n^{r -2 -\frac{1}{pq}} a_n E(\max_{1 \le k \le n}|S_k|^{\frac{1}{q}} - \epsilon b_n^{\frac{1}{pq}})^+ < \infty $$ to hold where $r>1, q>0$ and either $n_0=1, 0<p<2, a_n=1, b_n=n$ or $n_0=3, p=2, a_n=(\log n)^{-\frac{1}{2q}}, b_n=n\log n$. These results extend results of Chow (1988) and Li and Sp\u{a}taru (2005) from the independent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.
Although galactic winds play a critical role in regulating galaxy formation, hydrodynamic cosmological simulations do not resolve the scales that govern the interaction between winds and the ambient circumgalactic medium (CGM). We implement the Physically Evolved Wind (PhEW) model of Huang et al. (2020) in the GIZMO hydrodynamics code and perform test cosmological simulations with different choices of model parameters and numerical resolution. PhEW adopts an explicit subgrid model that treats each wind particle as a collection of clouds that exchange mass, metals, and momentum with their surroundings and evaporate by conduction and hydrodynamic instabilities as calibrated on much higher resolution cloud scale simulations. In contrast to a conventional wind algorithm, we find that PhEW results are robust to numerical resolution and implementation details because the small scale interactions are defined by the model itself. Compared to conventional wind simulations with the same resolution, our PhEW simulations produce similar galaxy stellar mass functions at $z\geq 1$ but are in better agreement with low-redshift observations at $M_* < 10^{11}M_\odot$ because PhEW particles shed mass to the CGM before escaping low mass halos. PhEW radically alters the CGM metal distribution because PhEW particles disperse metals to the ambient medium as their clouds dissipate, producing a CGM metallicity distribution that is skewed but unimodal and is similar between cold and hot gas. While the temperature distributions and radial profiles of gaseous halos are similar in simulations with PhEW and conventional winds, these changes in metal distribution will affect their predicted UV/X-ray properties in absorption and emission.
An algorithm, based on Fourier decomposition of light curves, permitted to define a sample of 388 contact binaries with well observed light curves, periods shorter one day and with available V-I colors (the R-sample), from among 933 eclipsing binary systems in the OGLE variable-star catalog for 9 fields of Baade's Window. The sample of such systems which was visually classified by the OGLE project as EW-type binaries (the O-sample) is by 55% larger and consists of 604 stars. The algorithm prevents inclusion of RR Lyr and SX Phe stars which in visual classification might be mistakenly taken for contact binaries with periods equal to twice their pulsation periods. Determinations of distances for the contact systems, utilizing the M_I = M_I(log P, V-I) absolute-magnitude calibration and the map of reddening and extinction of Stanek (1996), indicate an approximately uniform distribution of contact binaries almost all the way to the Galactic Bulge, implying heights up to z = 420 - 450 pc. This distribution, as well as a tendency for the colors to be concentrated in the region normally occupied by old Turn-Off-Point stars, confirm the currently held opinion that contact binary systems belong to the old stellar population of the Galaxy. The apparent frequency estimated in the volume-limited sense, relative to nearby MS dwarfs to the distances of 2 and 3 kpc, is one contact system per about 250 - 300 stars; it is one contact system per 400 MS stars if M-dwarfs are included. The apparent density of contact systems is 7-10x10^-5 pc^-3.
We present a numerical model which allows us to study the Kelvin force probe microscopy response to the charge switching in quantum dots at various time scales. The model provides more insight into the behavior of frequency shift and dissipated energy under different scanning conditions measuring a temporarily charged quantum dot on surface. Namely, we analyze the dependence of the frequency shift, its fluctuation and of the dissipated energy, on the resonance frequency of tip and electron tunneling rates between tip - quantum dot and quantum dot - sample. We discuss two complementary approaches to simulating the charge dynamics, a stochastic and a deterministic one. In addition, we derive analytic formulas valid for small amplitudes, describing relations between the frequency shift, dissipated energy, and the characteristic rates driving the charging and discharging processes.
We previously reported anomalous fiber-optic gyroscope signals observed above rotating rings at temperatures close to liquid helium. Our results suggested that the liquid helium itself may be the source of our observed phenomenon. We constructed a new cryostat experiment that allows rotating a large quantity of liquid helium together with a superconducting niobium tube. The facility is built in such a way that our gyroscope can be placed directly in the center of rotation along the axis; however, the cryostat is built around the gyroscope to allow measuring without interference of helium liquid or gas. An anomalous signal was found of similar value compared to our previous measurements with a changed sign. As this measurement was done at a different location (center position) with respect to our old setup (top position), first hints for a possible field distribution of this phenomenon can be made. However, due to lower angular velocities used in this new setup so far, our measurement resolution was close to three times the resolution of our gyroscope and hence our data represent work in progress.
I discuss the dynamical interaction of galactic disks with the surrounding dark matter halos. In particular it is demonstrated that if the self-gravitating shearing sheet, a model of a patch of a galactic disk, is embedded in a live dark halo, this has a strong effect on the dynamics of density waves in the sheet. I describe how the density waves and the halo interact via halo particles either on orbits in resonance with the wave or on non-resonant orbits. Contrary to expectation the presence of the halo leads to a very considerable enhancement of the amplitudes of the density waves in the shearing sheet. This effect appears to be the equivalent of the recently reported enhanced growth of bars in numerically simulated stellar disks embedded in live dark halos. Finally I discuss the counterparts of the perturbations of the disk in the dark halo.
We show that there is a logarithmic algebraic space parameterizing logarithmic morphisms between fixed logarithmic schemes when those logarithmic schemes satisfy natural hypotheses. As a corollary, we obtain the algebraicity of the stack of stable logarithmic maps without restriction on the logarithmic structure of the target.
We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an all-electron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the k-point sampling. As numerical realizations of the GW approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequency-dependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.
In this paper, we propose a Text-Degradation Invariant Auto Encoder (Text-DIAE), a self-supervised model designed to tackle two tasks, text recognition (handwritten or scene-text) and document image enhancement. We start by employing a transformer-based architecture that incorporates three pretext tasks as learning objectives to be optimized during pre-training without the usage of labeled data. Each of the pretext objectives is specifically tailored for the final downstream tasks. We conduct several ablation experiments that confirm the design choice of the selected pretext tasks. Importantly, the proposed model does not exhibit limitations of previous state-of-the-art methods based on contrastive losses, while at the same time requiring substantially fewer data samples to converge. Finally, we demonstrate that our method surpasses the state-of-the-art in existing supervised and self-supervised settings in handwritten and scene text recognition and document image enhancement. Our code and trained models will be made publicly available at~\url{ http://Upon_Acceptance}.
We introduce a minimal model of small-world growing network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially with degree and average clustering coefficient $C={3/2}ln3-1\approx 0.6479$, which are in good agreement with the numerical simulations. We also prove that the increasing tendency of average path length of the considered network is a little slower than the logarithm of the network order $N$.
We report the Nernst effect (v) and thermoelectric power (S) data for the Ce2PdIn8 heavy-fermion compound. Both S and v behave anomalously at low temperatures: the thermopower shows a Kondo-like maximum at T = 37 K, while the Nernst coefficient becomes greatly enhanced and field dependent below T ~ 30 K. In the zero-T limit S/T and v/T diverge logarithmically, what is related to occurrence of the quantum critical point (QCP). Presented results suggest that the antiferromagnetic spin-density-wave scenario may be applicable to QCP in Ce2PdIn8.
We report on Rossi X-ray Timing Explorer observations of four type I X-ray bursters; namely 1E1724-3045, GS1826-238, SLX1735-269 and KS1731-260. The first three were in a low state (LS) whereas KS1731-260 was in a high state. The LS sources have very similar power spectra, displaying high frequency noise up to \~200 Hz. For KS1731-260, its power spectrum is dominated by noise at frequencies below 20 Hz. In addition a quasi-periodic oscillation at 1200 Hz is detected. The 1-200 keV LS spectra are all consistent with resulting from thermal Comptonization with an electron temperature (kTe) around 25-30 keV. For KS1731-260, the spectrum is also dominated by Comptonization, but with kTe around 3 keV and no significant hard X-ray emission. With the exception of GS1826-238, there is an underlying soft component. For all sources, we have detected an iron line at 6.4 keV. A reflection component is present in the spectra of GS1826-238 and SLX1735-269. We suggest a model in which the region of main energy release, where hard X-rays are produced would be an optically thin boundary layer merged with an Advection Dominated Accretion Flow (ADAF). The soft component observed probably represents the unscattered emission from the accretion disk of variable inner radius. When the accretion rate increases, the inner disk radius shrinks, the strength of the reflected component and associated iron line increase, and the Comptonization region cools off in response to an increased cooling flux from the accretion disk and from the reprocessed/reflected component. Finally, in the light of these observations, we discuss extensively the various criteria recently proposed to distinguish between non-quiescent accreting black holes and neutron stars.
Recent results presented at the International Cosmic Ray Conference in Beijing will be reviewed. Topics include HE2: "Muons and Neutrinos" and HE3: "Interactions, Particle Physics Aspects, Cosmology"
We obtain Musielak Orlicz bumps conditions on a pair of weights for the boundedness of Calder\'on Zygmund operators and their commutators between variable Lebesgue spaces with different weights. The symbols of the commutators belong to a wider class of functions. We also give Bloom type estimates for commutators of Calder\'on Zygmund and fractional integral operators in the variable Lebesgue context. The techniques involved in both type of results are related with the theory of sparse domination.
The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axial symmetry. The accuracy of the trial functions is tested for realistic pairing Hamiltonians and odd-odd N=Z nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. It is shown that the extended QCM approach is able to predict with high accuracy the energies of the lowest T=0 and T=1 states. The present calculations indicate that in these states the isovector and the isoscalar pairing correlations coexist together, with the former playing a dominant role.
From the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5), we extract a sample of 4594 galaxies at redshifts 0.02<z<0.03, complete down to a stellar mass of M=10^10 Msol. We quantify their structure (Sersic index), morphology (Sersic index + ``Bumpiness''), and local environment. We show that morphology and structure are intrinsically different galaxy properties, and we demonstrate that this is a physically relevant distinction by showing that these properties depend differently on galaxy mass and environment. Structure mainly depends on galaxy mass whereas morphology mainly depends on environment. This is driven by variations in star formation activity, as traced by color, which only weakly affects the structure of a galaxy but strongly affects its morphological appearance. The implication of our results is that the existence of the morphology-density relation is intrinsic and not just due to a combination of more fundamental, underlying relations. Our findings have consequences for high-redshift studies, which often use some measure of structure as a proxy for morphology. A direct comparison with local samples selected through visually classified morphologies may lead to biases in the inferred evolution of the morphological mix of the galaxy population, and misinterpretations in terms of how galaxy evolution depends on mass and environment.
Blue supergiant stars are known to display photometric and spectroscopic variability that is suggested to be linked to stellar pulsations. Pulsational activity in massive stars strongly depends on the star's evolutionary stage and is assumed to be connected with mass-loss episodes, the appearance of macroturbulent line broadening, and the formation of clumps in the wind. To investigate a possible interplay between pulsations and mass-loss, we carried out an observational campaign of the supergiant 55 Cyg over a period of five years to search for photospheric activity and cyclic mass-loss variability in the stellar wind. We modeled the H, He I, Si II and Si III lines using the nonlocal thermal equilibrium atmosphere code FASTWIND and derived the photospheric and wind parameters. In addition, we searched for variability in the intensity and radial velocity of photospheric lines and performed a moment analysis of the line profiles to derive frequencies and amplitudes of the variations. The Halpha line varies with time in both intensity and shape, displaying various types of profiles: P Cygni, pure emission, almost complete absence, and double or multiple peaked. The star undergoes episodes of variable mass-loss rates that change by a factor of 1.7-2 on different timescales. We also observe changes in the ionization rate of Si II and determine a multiperiodic oscillation in the He I absorption lines, with periods ranging from a few hours to 22.5 days. We interpret the photospheric line variations in terms of oscillations in p-, g-, and strange modes. We suggest that these pulsations can lead to phases of enhanced mass loss. Furthermore, they can mislead the determination of the stellar rotation. We classify the star as a post-red supergiant, belonging to the group of alpha Cyg variables.