ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use the Gu-Huang model for a special case when the universe is seven dimensional. In the core of extra dimension we place a modified Gidding-Strominger wormhole. This wormhole is separated by a thin wall from the extra dimensional space. The wormhole content is assumed to satisfy the adiabatic gas law. The wormhole pressure penetrates into the extra dimension. We then solve the Einstein equation assuming that the real universe and the extra dimension contains only inextendable fluid with negligible local pressure. We show the physical universe expands because the time dependent Hubble parameter is positive. Under certain condition the deacceleration parameter, $q_0$, is also positive. But the most significant outcome of our investigation is the fact that $q_0$ fluctuates. If we can detect by observation that the acceleration fluctuates, our model will be an alternative explanation without the help of dark energy. We could however link dark energy with work done by wormhole pressure.
We discuss the vacuum energy density and the cosmological constant of dS$_5$ brane world with a dilaton field. It is shown that a stable AdS$_4$ brane can be constructed and gravity localization can be realized. An explicit relation between the dS bulk cosmological constant and the brane cosmological constant is obtained. The discrete mass spectrum of the massive scalar field in the AdS$_4$ brane is used to acquire the relationship between the brane cosmological constant and the vacuum energy density. The vacuum energy density in the brane gotten by this method is in agreement with astronomical observations.
We describe explicitly all hyperelliptic limits of quadrics through smooth canonical curves of genus $g$ in ${\mathbb P}^{g-1}$. Also, we construct an open embedding of the blow up of a ${\rm PGL}_g$-bundle over the moduli space of curves of genus $g$ along the hyperelliptic locus into the blow up of the canonical Hilbert scheme of ${\mathbb P}^{g-1}$ along the closure of the locus of canonical ribbons, which are certain double thickenings of rational normal curves introduced and studied by Bayer and Eisenbud.
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise constant function is also reasonable in a case of using a quantum impedance approach.The dependence of an accuracy of numerical calculations on a number of cascads by which a real potential is represented was found. The method of including into a consideration of zero-range singular potentials was developed.
We study semi-classical multi-spin strings in the non-supersymmetric backgrounds of $AdS$ Black Hole and Witten's confining model. We consider constant radius strings with rotations along the isometries of the backgrounds. In the $AdS$ Black Hole, solutions exist only if there is a non-zero spin in the Black Hole part. In contrast with the $AdS$ background, we find solutions which although have no rotation in the $S^5$ part, have a regular $\lambda$ expansion in the expression for large energy. In the near-extremal $D_3$ and $D_4$ backgrounds, we find that strings have to be located on the confining wall. We also discuss the stability of solutions by considering the fluctuation Lagrangians.
We describe the decay out of a superdeformed band using the methods of reaction theory. Assuming that decay-out occurs due to equal coupling (on average) to a sea of equivalent chaotic normally deformed (ND) states, we calculate the average intraband decay intensity and show that it can be written as an ``optical'' background term plus a fluctuation term, in total analogy with average nuclear cross sections. We also calculate the variance in closed form. We investigate how these objects are modified when the decay to the ND states occurs via an ND doorway and the ND states' statistical properties are changed from chaotic to regular. We show that the average decay intensity depends on two dimensionless variables in the first case while in the second case, four variables enter the picture.
We consider an Information-Plus-Noise type matrix where the Information matrix is a spiked matrix. When some eigenvalues of the random matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the spikes. Note that, in an Appendix, we present alternative versions of the earlier results of Bai and Silverstein about the lack of eigenvalues outside the support of the deterministic equivalent measure and of Capitaine about the exact separation phenomenon, where we remove some technical assumptions.
The paper commented upon gives the impression that whether the gauged version of a sigma model gives rise to the original or the dual model depends on the choice of gauge fixing. It is demonstrated here that this is not so.
Measuring the distances to Galactic planetary nebulae (PNe) has been an intractable problem for many decades. We have now established a robust optical statistical distance indicator, the H$\alpha$ surface brightness- radius or S-r relation, which addresses this problem. We developed this relation from a critically evaluated sample of primary calibrating PNe. The robust nature of the method results from our revised calibrating distances with significantly reduced systematic uncertainties, and the recent availability of high-quality data, including updated nebular diameters and integrated H$\alpha$ fluxes. The S-r technique is simple in its application, requiring only an angular size, an integrated H\alpha\ flux, and the reddening to the PN. From these quantities, an intrinsic radius is calculated, which when combined with the angular size, yields the distance directly. Furthermore, we have found that optically thick PNe tend to populate the upper bound of the trend, while optically-thin PNe fall along the lower boundary in the S-r plane. This enables sub-trends to be developed which offer even better precision in the determination of distances, as good as 18 per cent in the case of optically-thin, high-excitation PNe. This is significantly better than any previous statistical indicator. We use this technique to create a catalogue of statistical distances for over 1100 Galactic PNe, the largest such compilation in the literature to date. Finally, in an appendix, we investigate both a set of transitional PNe and a range of PN mimics in the S-r plane, to demonstrate its use as a diagnostic tool. Interestingly, stellar ejecta around massive stars plot on a tight locus in S-r space with the potential to act as a separate distance indicator for these objects.
We have studied the influence of external pressure up to 1 GPa on the magnetic transitions of the orthorhombic Haldane-spin chain compound Tb2BaNiO5 an exotic multiferroic material. This parent compound is known to undergo N\'eel ordering at TN1= 63 K and another magnetic transition at TN2= 25K at which ferroelectricity sets in, however, without any change in the magnetic symmetry, but with only a sharp change in the canting angle of Tb 4f and Ni 3d magnetic moments. There is a subtle difference in the antiferromagnetic state above and below TN2, which is supported by the fact that there is a metamagnetic transition below TN2only (for 5 K, at about 60 kOe). We report here that, with the application of external pressure, there is an upward shift of TN1, while TN2 shifts towards lower temperatures. It is interesting that the two magnetic transitions in the same compound behave differently under pressure and the opposite behavior at TN2 is attributed to local distortion leading to ferroelectricity. The results are augmented by temperature dependent x-ray diffraction and positive chemical pressure studies. The chemical pressure caused by the isoelectronic doping at Ba site by Sr reduces both the transition temperatures. Clearly, the external pressure favors antiferromagnetic coupling (that is, leading to TN1 enhancement), whereas the chemical pressure reduces TN1, suggesting important role of the changes in local hybridization induced by doping on magnetism in this material.
We present far-UV HST/COS spectra of four nearby BL Lac Objects. BL Lac spectra are dominated by a smooth, power-law continuum which arises in a relativistic jet. However, the spectra are not necessarily featureless; weak, broad- and/or narrow-line emission is sometimes seen in high-quality optical spectra. We present detections of Lya emission in HST/COS spectra of Mrk421 (z=0.030) and PKS2005-489 (z=0.071) as well as an archival HST/GHRS observation of Mrk501 (z=0.0337). Archival HST/STIS observations of PKS2155-304 (z=0.116) show no Lya emission to a very low upper limit. Using the assumption that the broad-line region (BLR) clouds are asymmetrically placed around the AGN, we use these measured Lya emission features to constrain either the relativistic Gamma values for the ionizing continuum produced by the jet (in the ionization-bounded case) or the mass of warm gas (in the density-bounded case). While realistic Gamma values can be obtained for all four cases, the values for Mrk421 and PKS2155-304 are high enough to suggest that covering factors of broad-line-region clouds of ~1-2% might be required to provide consistency with earlier values of Doppler boosting and viewing angles suggested for this class of BL Lacs. This discrepancy also exists in the case of M87, where the amount of Doppler boosting in our direction is expected to be minimal, again suggestive of a small covering factor of broad-line-region clouds. If, as these small covering factors might suggest, the assumptions of a density-bounded model could be more correct, then the observed Lya luminosities require that BL\,Lac/FRI nuclei possess very little warm gas (10^-4 to 10^-5 Msun) as suggested by Guilbert, Fabian & McCray (1983). If these clouds are in pressure balance with a hotter (~10^6 K) gas, the BLR contains too little mass to power the AGN by accretion alone.
Relative ages for the globular cluster (GC) subpopulations in the Virgo giant elliptical galaxy M87 (NGC 4486) have been determined from Stroemgren photometry obtained with WFPC2 on board HST. Using a variety of population synthesis models, and assuming the GC mass at the turnover of the luminosity function is the same for both subpopulations, differential ages have been determined from the observed magnitudes at the turnover of the globular cluster luminosity function and from the mean color of each subpopulation. We measure an age difference between the two subpopulations of 0.2 +/- 1.5 (systematic) +/- 2 (random) Gyr, in the sense that the blue GCs are formally older. Thus, to within our measurement errors, the two subpopulations are found to be coeval. Combined with previous spectroscopic age determinations for M87 GCs, our results favor a picture in which the GCs associated with this galaxy are formed at high redshift, and within a period of a few Gyr.
The increasing entropy, large-scale isotropy and approximate flatness of the universe are considered in the context of signature change, which is a classical model of quantum tunnelling in quantum cosmology. The signature change hypothesis implies an initial inflationary epoch, the magnetic half of the Weyl curvature hypothesis, and a close analogue of the conformal singularity hypothesis. Adding the electric half of the Weyl curvature hypothesis yields, for a perfect fluid, only homogeneous and isotropic cosmologies. In the cosmological-constant case, the unique solution is the Vilenkin tunnelling solution, which gives a de Sitter cosmology.
We show that it is possible to build effective matter density power spectra in tomographic cosmic shear observations that exhibit the Baryonic Acoustic Oscillations (BAO) features once a nulling transformation has been applied to the data. The precision with which the amplitude and position of these features can be reconstructed is quantified in terms of sky coverage, intrinsic shape noise, median source redshift and number density of sources. BAO detection in Euclid or LSST like wide surveys will be possible with a modest signal-to-noise ratio. It would improve dramatically for slightly deeper surveys.
In an effort to probe the extent of variations in the interstellar ^7Li/^6Li ratio seen previously, ultra-high-resolution (R ~ 360,000), high signal-to-noise spectra of stars in the Perseus OB2 and Scorpius OB2 Associations were obtained. These measurements confirm our earlier findings of an interstellar ^7Li/^6Li ratio of about 2 toward o Per, the value predicted from models of Galactic cosmic ray spallation reactions. Observations of other nearby stars yield limits consistent with the isotopic ratio ~ 12 seen in carbonaceous chondrite meteorites. If this ratio originally represented the gas toward o Per, then to decrease the original isotope ratio to its current value an order of magnitude increase in the Li abundance is expected, but is not seen. The elemental K/Li ratio is not unusual, although Li and K are formed via different nucleosynthetic pathways. Several proposals to account for the low ^7Li/^6Li ratio were considered, but none seems satisfactory.   Analysis of the Li and K abundances from our survey highlighted two sight lines where depletion effects are prevalent. There is evidence for enhanced depletion toward X Per, since both abundances are lower by a factor of 4 when compared to other sight lines. Moreover, a smaller Li/H abundance is observed toward 20 Aql, but the K/H abundance is normal, suggesting enhanced Li depletion (relative to K) in this direction. Our results suggest that the ^7Li/^6Li ratio has not changed significantly during the last 4.5 billion years and that a ratio ~ 12 represents most gas in the solar neighborhood. In addition, there appears to be a constant stellar contribution of ^7Li, indicating that one or two processes dominate its production in the Galaxy.
We demonstrate using the classical density functional theory (DFT) model that an intermediate degree of mass localization in the amorphous state is essential for producing the boson peak. The localization length $\ell$ is identified from the width of the gaussian density profile in terms of which the inhomogeneous density n(x) of the solid is expressed in DFT. At a fixed average density, there exists a limiting value $\ell_0$ of $\ell$ signifying a minimum mass localization in the amorphous state. For more delocalized states ($\ell>\ell_0$) occurrence of boson peak is unfeasible.
The {\em Fibonacci cube} of dimension $n$, denoted as $\Gamma\_n$, is the subgraph of $n$-cube $Q\_n$ induced by vertices with no consecutive 1's. We study the maximum number of disjoint subgraphs in $\Gamma\_n$ isomorphic to $Q\_k$, and denote this number by $q\_k(n)$. We prove several recursive results for $q\_k(n)$, in particular we prove that $q\_{k}(n) = q\_{k-1}(n-2) + q\_{k}(n-3)$. We also prove a closed formula in which $q\_k(n)$ is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence $\{q\_{k}(n)\}\_{n=0}^{ \infty}$.
The study of CNO cycle involves the examination of the proton radiative capture, or the $(p,\gamma)$ reactions below 2 MeV. The astrophysical $\mathcal{S}$ factor characterizing the $(p,\gamma)$ reaction is usually reduced to the electric dipole transition $E1$ from the scattering state to the bound state. In this work, the partial scattering and the single-particle bound wave functions in the reduced matrix element of the transition are obtained from the single self-consistent mean-field potential deduced from the Skyrme Hartree-Fock calculation. The astrophysical $\mathcal{S}$ factors of the $(p,\gamma)$ reactions in the CNO cycle were successfully reproduced. The self-consistent Hartree-Fock calculation from the discrete to the continuum is a promising approach for the microscopic analysis of the nucleon-induced reactions in nuclear astrophysics.
We study the spatial decay of spin polarized hot carrier current in a spin-valve structure consisting of a semiconductor quantum wire flanked by half-metallic ferromagnetic contacts. The current decays because of D'yakonov-Perel' spin relaxation in the semiconductor caused by Rashba spin orbit interaction. The associated relaxation length is found to decrease with increasing lattice temperature (in the range 30-77 K) and exhibit a non-monotonic dependence on the electric field driving the current. The relaxation lengths are several tens of microns which are at least an order of magnitude larger than what has been theoretically calculated for two-dimensional structures at comparable temperatures, Rashba interaction strengths and electric fields. This improvement is a consequence of one-dimensional carrier confinement that does not necessarily suppress carrier scattering, but nevertheless suppresses D'yakonov-Perel' spin relaxation.
For a system at given temperature, with energy known as a function of a set of variables, we obtain the thermal fluctuation of the evolution of the variables by replacing the phase-space with a lattice and invoking the principle of detailed balance. Besides its simplicity, the asset of this method is that it enables us to obtain the Langevin equation when the phase-space is anisotropic and when the system is described by means of curvilinear coordinates. As an illustration, we apply our results to the Kramer--Watts-Tobin equation in superconductivity. The choice between the It\^{o} and the Stratonovich procedures is discussed.
Observations of the 297 s X-ray pulsar 1E1145.1-6141 with the Rossi X-Ray Timing Explorer have revealed its 14.4 d eccentric orbit around its B supergiant companion. The best-fit orbital elements are: P_orb = 14.365(2) d, a_x sin i=99.4(18) light-s, e=0.20(3). No eclipses are detected, indicating that the binary inclination is less than 55 deg.
We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement.
We investigate the gravitational form factors (GFFs) and the longitudinal momentum densities ($p^+$ densities) for proton in a light-front quark-diquark model. The light-front wave functions are constructed from the soft-wall AdS/QCD prediction. The contributions from both the scalar and the axial vector diquarks are considered here. The results are compared with the consequences of a parametrization of nucleon generalized parton distributions (GPDs) in the light of recent MRST measurements of parton distribution functions (PDFs) and a soft-wall AdS/QCD model. The spatial distribution of angular momentum for up and down quarks inside the nucleon has been presented. At the density level, we illustrate different definitions of angular momentum explicitly for an up and down quark in the light-front quark-diquark model inspired by AdS/QCD.
We introduce classes of edge-colourings of the complete graph -- that we call nice and beautiful -- and study how many heterochromatic spanning trees appear under such colourings. We prove that if the colouring is nice, there is at least a quadratic number of different heterochromatic trees; and if the colouring is beautiful there is an exponential number of different such trees.
Let F be a set system on [n] with all sets having k elements and every pair of sets intersecting. The celebrated theorem of Erdos-Ko-Rado from 1961 says that any such system has size at most ${n-1 \choose k-1}$. A natural question, which was asked by Ahlswede in 1980, is how many disjoint pairs must appear in a set system of larger size. Except for the case k=2, solved by Ahlswede and Katona, this problem has remained open for the last three decades.   In this paper, we determine the minimum number of disjoint pairs in small k-uniform families, thus confirming a conjecture of Bollobas and Leader in these cases. Moreover, we obtain similar results for two well-known extensions of the Erdos-Ko-Rado theorem, determining the minimum number of matchings of size q and the minimum number of t-disjoint pairs that appear in set systems larger than the corresponding extremal bounds. In the latter case, this provides a partial solution to a problem of Kleitman and West.
The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method, whose features are discussed in details, offers a reliable and robust approach to the direct and precise numerical evaluation of Feynman graph integrals.
The distribution of Ly$\alpha$ emission is an presently accessible method for studying the state of the intergalactic medium (IGM) into the reionization era. We carried out deep spectroscopic observations in order to search for Ly$\alpha$ emission from galaxies with photometric redshifts $z$ = 5.5 - 8.3 selected from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS). Utilizing data from the Keck/DEIMOS spectrograph, we explore a wavelength coverage of Ly$\alpha$ emission at $z$ ~ 5 - 7 with four nights of spectroscopic observations for 118 galaxies, detecting five emission lines with ~ 5$\sigma$ significance: three in the GOODS-N and two in the GOODS-S field. We constrain the equivalent width (EW) distribution of Ly$\alpha$ emission by comparing the number of detected objects with the expected number constructed from detailed simulations of mock emission lines that account for the observational conditions (e.g., exposure time, wavelength coverage, and sky emission) and galaxy photometric redshift probability distribution functions. The Ly$\alpha$ EW distribution is well described by an exponential form, $\text{dN/dEW}\propto \text{exp(-EW/}W_0)$, characterized by the $e$-folding scale ($W_0$) of ~ 60 - 100$\AA$ at 0.3 < $z$ < 6. By contrast, our measure of the Ly$\alpha$ EW distribution at 6.0 < $z$ < 7.0 rejects a Ly$\alpha$ EW distribution with $W_0$ > 36.4$\AA$ (125.3$\AA$) at 1$\sigma$ (2$\sigma$) significance. This provides additional evidence that the EW distribution of Ly$\alpha$ declines at $z$ > 6, suggesting an increasing fraction of neutral hydrogen in the IGM at that epoch.
Video based fall detection accuracy has been largely improved due to the recent progress on deep convolutional neural networks. However, there still exists some challenges, such as lighting variation, complex background, which degrade the accuracy and generalization ability of these approaches. Meanwhile, large computation cost limits the application of existing fall detection approaches. To alleviate these problems, a video based fall detection approach using human poses is proposed in this paper. First, a lightweight pose estimator extracts 2D poses from video sequences and then 2D poses are lifted to 3D poses. Second, we introduce a robust fall detection network to recognize fall events using estimated 3D poses, which increases respective filed and maintains low computation cost by dilated convolutions. The experimental results show that the proposed fall detection approach achieves a high accuracy of 99.83% on large benchmark action recognition dataset NTU RGB+D and real-time performance of 18 FPS on a non-GPU platform and 63 FPS on a GPU platform.
We present three necessary separability criteria for bipartite mixed states, the violation of each of these conditions is a sufficient condition for entanglement. Some ideas on the issue of finding a necessary and sufficient criterion of separability are also discussed.