ShantanuT01/DACTYL-Pretraining huggingface dataset:
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.
We derive the classical kappa-symmetric Type IIB string action on AdS(3) x S(3) by employing the SU(1,1|2)^2 algebra. We then gauge fix kappa-symmetry in the background adapted Killing spinor gauge and present the action in a very simple form.
The Feynman amplitude associated to a graph is a period of a certain motive. The sum of these motive classes over all connected graphs with no multiple edges or tadpoles and n vertices is defined in the Grothendieck ring of varieties. This sum is shown to lie in the subring generated by the affine line. It follows from work of Belkale and Brosnan that motives of individual graphs do not lie in this subring.
We suggest that a high proportion of brown dwarfs are formed by gravitational fragmentation of massive, extended discs around Sun-like stars. We argue that such discs should arise frequently, but should be observed infrequently, precisely because they fragment rapidly. By performing an ensemble of radiation-hydrodynamic simulations, we show that such discs typically fragment within a few thousand years to produce mainly brown dwarfs (including planetary-mass brown dwarfs) and low-mass hydrogen-burning stars. Subsequently most of the brown dwarfs are ejected by mutual interactions. We analyse the properties of these objects that form by disc fragmentation, and compare them with observations.
We introduce a two parameter ($\alpha, \beta>-1$) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\{ P^{(\alpha, \beta)}_k \}_{k \geq 0}$. The family includes previously discovered Plancherel measures for the infinite-dimensional orthogonal and symplectic groups. The construction uses certain BC-type orthogonal polynomials which generalize the characters of these groups.   The local asymptotics near the hard edge where one expects distinguishing behavior yields the multi-time $(\alpha, \beta)$-dependent discrete Jacobi kernel and the multi-time $\beta$-dependent hard-edge Pearcey kernel. For nonnegative integer values of $\beta$, the hard-edge Pearcey kernel had previously appeared in the asymptotics of non-intersecting squared Bessel paths at the hard edge.
Direct current in confined two-dimensional (2d) electron systems can become unstable with respect to the excitation of plasmons. Numerous experiments and simulations hint that structural asymmetry somehow promotes plasmon generation, but a constitutive relation between asymmetry and instability has been missing. We provide such relation in the present paper and show that bounded perfect 2d electron fluids in asymmetric structures are unstable under arbitrarily weak drive currents. To this end, we develop a perturbation theory for hydrodynamic plasmons and evaluate corrections to their eigenfrequency induced by carrier drift, scattering, and viscosity. We show that plasmon gain continuously increases with degree of plasmon mode asymmetry until it surrenders to viscous dissipation that also benefits from asymmetry. The developed formalism allows us to put a lower bound on the instability threshold current, which corresponds to the Reynolds number $R_{\min} = 2\sqrt{3}$ for one-dimensional plasmons in 2d channel under constant voltage bias.
There is a growing interest in the logical possibility that exceptional mathematical structures (exceptional Lie and superLie algebras, the exceptional Jordan algebra, etc.) could be linked to an ultimate "exceptional" formulation for a Theory Of Everything (TOE). The maximal division algebra of the octonions can be held as the mathematical responsible for the existence of the exceptional structures mentioned above. In this context it is quite motivating to systematically investigate the properties of octonionic spinors and the octonionic realizations of supersymmetry. In particular the $M$-algebra can be consistently defined for two structures only, a real structure, leading to the standard $M$-algebra, and an octonionic structure. The octonionic version of the $M$-algebra admits striking properties induced by octonionic $p$-forms identities.
In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian $(-\Delta)^s$ ($0<s<1$) on the interval $(-1,1)$. We prove the existence of a minimal (strictly positive) time $T_{\rm min}$ such that the fractional heat dynamics can be controlled from any initial datum in $L^2(-1,1)$ to a positive trajectory through the action of a positive control, when $s>1/2$. Moreover, we show that in this minimal time constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. We also give some numerical simulations that confirm our theoretical results.
The fabrication of memristors by drop-coating sol-gel Ti(OH)$_4$ solution onto either aluminium foil or sputter-coated aluminium on plastic is presented. The gel layer is thick, 37$\mu$m, but both devices exhibit good memristance I-V profiles. The drop coated aluminium foil memristors compare favourably with the sputter-coated ones, demonstrating an expansion in the accessibility of memristor fabrication. A comparison between aluminium and gold for use as the sputter-coated electrodes shows that aluminium is the better choice as using gold leads to device failure. The devices do not require a forming step.
We introduce a novel method for robust and accurate 3D object pose estimation from a single color image under large occlusions. Following recent approaches, we first predict the 2D projections of 3D points related to the target object and then compute the 3D pose from these correspondences using a geometric method. Unfortunately, as the results of our experiments show, predicting these 2D projections using a regular CNN or a Convolutional Pose Machine is highly sensitive to partial occlusions, even when these methods are trained with partially occluded examples. Our solution is to predict heatmaps from multiple small patches independently and to accumulate the results to obtain accurate and robust predictions. Training subsequently becomes challenging because patches with similar appearances but different positions on the object correspond to different heatmaps. However, we provide a simple yet effective solution to deal with such ambiguities. We show that our approach outperforms existing methods on two challenging datasets: The Occluded LineMOD dataset and the YCB-Video dataset, both exhibiting cluttered scenes with highly occluded objects. Project website: https://www.tugraz.at/institute/icg/research/team-lepetit/research-projects/robust-object-pose-estimation/
We investigate exchange current contributions to elastic electron-deuteron scattering using exactly Poincar\'e invariant quantum mechanics with a null-plane kinematic symmetry. Our model exchange current is motivated by one-pion-exchange physics. Exact current conservation and current covariance are satisfied by using this current to compute a linearly independent set of current matrix elements. The remaining current matrix elements are generated from the independent matrix elements using the covariance and current conservation constraints. The presence of the exchange current increases the sensitivity to the choice of independent current matrix elements. Two choices of independent matrix elements that have distinct motivations lead to a good description of all of the elastic scattering observables for momentum transfers below 8 (GeV)$^2$.
The bifurcation diagram of a model nonlinear Langevin equation with delayed feedback is obtained numerically. We observe both direct and oscillatory bifurcations in different ranges of model parameters. Below threshold, the stationary distribution function p(x) is a delta function at the trivial state x=0. Above threshold, p(x) ~ x^alpha at small x, with alpha = -1 at threshold, and monotonously increasing with the value of the control parameter above threshold. Unlike the case without delayed feedback, the bifurcation threshold is shifted by fluctuations by an amount that scales linearly with the noise intensity. With numerical information about time delayed correlations, we derive an analytic expression for p(x) which is in good agreement with the numerical results.
First principles FPLAPWcalculations were performed in the framework of Density Functional Theory (DFT), to study the electronic structures and magnetic properties for the new full-Heusler compounds: Sc2CoZ (Z=Si, Ge, Sn). The investigated materials are stable against decomposition, in ferromagnetic configuration and crystallize in the inverse Heusler structures. The half-metallic properties as function of the variation of unit cell volumes are analysed regarding the fourth main group constituent elements. The electronic structure calculations for Sc2CoSi and Sc2CoSn show half-metallic characters, with indirect band gaps of 0.544 eV and 0.408 eV at optimized lattice parameters of 6.28 A and 6.62 A, respectively. For Sc2CoGe compound, the Fermi energy is not pinned inside the energy band gap from minority density of states, neither for unit cell contraction or for enlargement. The calculated total magnetic moments are 1muB/f.u., for all compounds, in agreement with Slater-Pauling rule.
The Gelfond-Khovanskii residue formula computes the sum of the values of any Laurent polynomial over solutions of a system of Laurent polynomial equations whose Newton polytopes have sufficiently general relative position. We discuss two important consequences of this result: an explicit elimination algorithm for such systems and a new formula for the mixed volume. The integer coefficients that appear in the Gelfond-Khovanskii residue formula are geometric invariants that depend only on combinatorics of the polytopes. We explain how to compute them explicitly.
In the era of precision cosmology, even percentage level effects are significant on cosmological observables. The recent tension between the local and global values of $H_0$ is much more significant than this, and any possible solution might rely on us going beyond the standard $\Lambda$CDM cosmological model. For much smaller, yet potentially significant effects, spatial curvature from averaging and cosmological backreaction on observational predictions could play a role. This is especially true with the higher precision of new observational data and improved statistical techniques. In this paper, we discuss the observational viability of a class of physically motivated cosmologies which can be parametrized by a phenomenological two-scale backreaction model with decoupled spatial curvature parameters and two Hubble scales. Using the latest JLA Supernovae data together with some of the latest BAO data, we perform a Bayesian model selection analysis and find that the phenomenological models are not favoured over the standard $\Lambda$CDM cosmological model. Although there is still a preference for non-zero and unequal dynamic and geometric spatial curvatures, there is little evidence for differing Hubble scales within these phenomenological template models.
We show that the removal of angular momentum is possible in the presence of large scale magnetic stresses, arisen by fields much stronger than that required for magnetorotational instability, in geometrically thick, advective, sub-Keplerian accretion flows around black holes in steady-state, in the complete absence of alpha-viscosity. The efficiency of such angular momentum transfer via Maxwell stress, with the field well below its equipartition value, could be equivalent to that of alpha-viscosity, arisen via Reynolds stress, with $\alpha=0.01-0.08$. We find in our simpler vertically averaged advective disk model that stronger the magnetic field and/or larger the vertical-gradient of azimuthal component of magnetic field, stronger the rate of angular momentum transfer is, which in turn may lead to a faster rate of outflowing matter, which has important implications to describe the hard spectral states of black hole sources. When the generic origin of alpha-viscosity is still being explored, mechanism of efficient angular momentum transfer via magnetic stresses alone is very interesting.
The transfer reaction $^7{\rm Be(d,n)}^8{\rm B}$ is modelled for the recent low experimental energies using the DWBA. Tests of the validity of the ANC method for the extraction of the $S_{17}$ astrophysical factor are performed.   We show that a peripheral assumption is no longer accurate for center of mass energies greater than approximately 15 MeV. In all cases we found that core deformation and/or excitation effects to be small as long as the optical potential for the entrance channel is not strongly surface peaked. Multistep corrections to the DWBA were found to be small.   We also emphasize that the lack of knowledge of the optical potentials for the entrance and outgoing channels induces severe uncertainties in the extracted $S_{17}$ astrophysical factor.
We show a simple semidefinite program whose optimal value is equal to the maximum probability of perfectly distinguishing orthogonal maximally entangled states using any PPT measurement (a measurement whose operators are positive under partial transpose). When the states to be distinguished are given by the tensor product of Bell states, the semidefinite program simplifies to a linear program. In [Phys. Rev. Lett. 109, 020506 (2012) -- arXiv:1107.3224v1], Yu, Duan and Ying exhibit a set of 4 maximally entangled states in $C^4 \otimes C^4$, which is distinguishable by any PPT measurement only with probability strictly less than 1. Using semidefinite programming, we show a tight bound of 7/8 on this probability (3/4 for the case of unambiguous PPT measurements). We generalize this result by demonstrating a simple construction of a set of k states in $C^k \otimes C^k$ with the same property, for any k that is a power of 2. Finally, by running numerical experiments, we obtain some non-trivial results about the PPT-distinguishability of certain interesting sets of generalized Bell states in $C^5 \otimes C^5$ and $C^6 \otimes C^6$.
We study the distribution of line-of-sight velocities of galaxies in the vicinity of SDSS redMaPPer galaxy clusters. Based on their velocities, galaxies can be split into two categories: galaxies that are dynamically associated with the cluster, and random line-of-sight projections. Both the fraction of galaxies associated with the galaxy clusters, and the velocity dispersion of the same, exhibit a sharp feature as a function of radius. The feature occurs at a radial scale $R_{\rm edge} \approx 2.2R_{\rm{\lambda}}$, where $R_{\rm{\lambda}}$ is the cluster radius assigned by redMaPPer. We refer to $R_{\rm edge}$ as the "edge radius." These results are naturally explained by a model that further splits the galaxies dynamically associated with a galaxy cluster into a component of galaxies orbiting the halo and an infalling galaxy component. The edge radius $R_{\rm edge}$ constitutes a true "cluster edge", in the sense that no orbiting structures exist past this radius. A companion paper (Aung et al. 2020) tests whether the "halo edge" hypothesis holds when investigating the full three-dimensional phase space distribution of dark matter substructures in numerical simulations, and demonstrates that this radius coincides with a suitably defined splashback radius.
We report on the discovery of Cepheids in the field spiral galaxy NGC 3621, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope (HST). NGC 3621 is one of 18 galaxies observed as a part of The HST Key Project on the Extragalactic Distance Scale, which aims to measure the Hubble constant to 10% accuracy. Sixty-nine Cepheids with periods in the range 9--60 days were observed over 12 epochs using the F555W filter, and 4 epochs using the F814W filter. The HST F555W and F814W data were transformed to the Johnson V and Kron-Cousins I magnitude systems, respectively. Photometry was performed using two independent packages, DAOPHOT II/ALLFRAME and DoPHOT. Period-luminosity relations in the V and I bands were constructed using 36 fairly isolated Cepheids present in our set of 69 variables. Extinction-corrected distance moduli relative to the LMC of 10.63 +/- 0.07 mag and 10.56 +/- 0.10 mag were obtained using the ALLFRAME and DoPHOT data, respectively. True distance moduli of 29.13 +/- 0.18 mag and 29.06 +/- 0.18 mag, corresponding to distances of 6.3 Mpc and 6.1 Mpc, were obtained by assuming values of 18.50 +/- 0.10 mag for the distance modulus of the LMC and E(V-I) = 0.13 mag for the reddening of the LMC.
In a recent paper, Regev and Roichman introduced the <_L order and the L-descent number statistic, des_L, on the group of colored permutations, C_a \wr S_n. Here we define the L-reverse major index statistic, rmaj_L, on the same group and study the distribution of des_L and the bi-statistic (des_L, rmaj_L). We obtain new wreath-product analogues of the Eulerian and q-Euler-Mahonian polynomials, and a generalization of Carlitz's identity.
We present the analysis of the physical properties of the interstellar medium (ISM) in the nearby early-type galaxy NGC 3665, based on the far-infrared (FIR) photometric and spectroscopic data as observed by the Herschel Space Observatory. The fit to the spectral energy distribution reveals a high dust content in the galaxy, with the dust-to-stellar mass ratio of $M_{\rm dust}$/$M_\ast$ $\sim$ 1.1 $\times$ 10$^{-4}$ that is nearly three times larger than the mean value of local S0+S0a galaxies. For the ionized regions (H~\textsc{ii} regions), the electron density (n$_e$) is around 49.5 $\pm$ 11.9 cm$^{-3}$ based on the [N~\textsc{ii}]\,122\,\mum/[N~\textsc{ii}]\,205\,\mum\ ratio. For the photodissociation regions, the heating efficiency is in the range of 1.26 $\times$ 10$^{-3}$ and 1.37 $\times$ 10$^{-3}$ based on the ([C~\textsc{ii}$]+[$O~\textsc{i}]\,63\,\mum)/$L_{\rm TIR}$, which is slightly lower than other local galaxies; the hydrogen nucleus density and the strength of FUV radiation field are n $\sim$ 10$^{4}$ cm$^{-3}$ and G$_0$ $\sim$ 10$^{-0.25}$, respectively. The above results are consistent with the presence of weak AGN and a low level of star-forming activity in NGC 3665. Our results give strong support to the `morphological quenching' scenario, where a compact, massive bulge can stabilize amount of cool gas against star formation.
The open clusters in the Kepler and CoRoT fields potentially provide tight constraints for tests of stellar models and observational methods because they allow a combination of complementary methods. We are in the process of identi- fying and measuring parameters for detached eclipsing binaries (dEBs) in the open clusters in the Kepler and CoRoT fields. We make use of measurements of dEBs in the clusters to test the accuracy of asteroseismic scaling relations for mass. We are able to provide strong indications that the asteroseismic scaling relations over- estimate the stellar mass, but we are not yet able to distinguish between different proposed corrections from the literature. We argue how our ongoing measurements of more dEBs in more clusters, complemented by dEBs in the field, should be able to break the degeneracy. We also briefly describe how we can identify cluster stars that have evolved through non-standard evolution by making use of ensemble asteroseismology.
The composition dependence of the Yb valence and of the thermal expansion have been studied in the YbGa$_x$Ge$_{2-x}$ system. X-ray diffraction reveals that single-phased samples isostructural to YbGaGe are obtained in the range of 0.9 <= x <= 1.5. The magnetic susceptibility shows that the systems are almost nonmagnetic below room temperature, indicating a stable Yb2+ state for the x range 0.9 <= x <= 1.5. The lattice constants as well as the lattice volume of these systems are found to decrease monotonically with decreasing temperature, suggesting the absence of zero thermal-expansion previously reported for YbGaGe.
We investigate the origin of phenomenologically interesting small Yukawa couplings in Type I string theory. Utilising the framework of intersecting sets of D9 and orthogonal D5 branes we demonstrate the connection between extra dimensional volumes and Yukawa couplings. For example, we show that extra dimensions with inverse lengths of $10^8$ GeV can lead to $10^{-10}$ Yukawa couplings. String selection rules, arising from the D-Brane setup, impose non-trivial constraints on the set of allowed superpotentials. As a phenomenological application of these results we construct a type I string model of inflationary particle physics which involves small Yukawa couplings of order $10^{-10}$, and simultaneously solves the strong CP and $\mu$ problem of the MSSM, via the vacuum expectation value of the inflaton field.
The Bohm motion for a particle moving on the line in a quantum state that is a superposition of n+1 energy eigenstates is quasiperiodic with n frequencies.
We classify the canonical threefold singularities that allow an effective two-torus action. This extends classification results of Mori on terminal threefold singularities and of Ishida and Iwashita on toric canonical threefold singularities. Our classification relies on lattice point emptiness of certain polytopal complexes with rational vertices. Scaling the polytopes by the least common multiple $k$ of the respective denominators, we investigate $k$-emptiness of polytopes with integer vertices. We show that two dimensional $k$-empty polytopes either are sporadic or come in series given by Farey sequences. We finally present the Cox ring iteration tree of the classified singularities, where all roots, i.e. all spectra of factorial Cox rings, are generalized compound du Val singularities.
In this paper we strengthen to Morrey-Lorentz spaces the famous trace principle introduced by Adams. More precisely, we show that Riesz potential $I_{\alpha}$ is continuous   \begin{equation} \Vert I_{\alpha}f\Vert_{\mathcal{M}_{q, \infty}^{\lambda_{\ast}}(d\mu)}\lesssim \Arrowvert\mu\Arrowvert_{\beta}^{{1}/{q}}\,\Vert f\Vert_{\mathcal{M}_{p, \infty}^{\lambda}(d\nu)}\nonumber\\[0.02in] \end{equation} if and only if the Radon measure $d\mu$ supported in $\Omega\subset \mathbb{R}^n$ is controlled by $$\Arrowvert\mu\Arrowvert_{\beta}=\sup_{x\in\mathbb{R}^n,\,r>0}r^{-\beta}\mu(B(x,r))<\infty$$ provided that $1<p<q<\infty$ satisfies $n-\alpha p<\beta\leq n,\; \alpha=\frac{n}{\lambda}-\frac{\beta}{\lambda_\ast}\; \text{ and }\;\frac{\lambda_\ast}{q}\leq \frac{\lambda}{p}\nonumber\,$. Our result provide a new class of functions spaces which is larger than previous ones, since we have strict continuous inclusions $\dot{B}_{p,\infty}^{s}\hookrightarrow L^{\lambda, \infty}\hookrightarrow \mathcal{M}_{p}^{\lambda}\hookrightarrow\mathcal{M}_{p, \infty}^{\lambda} \nonumber $ as $1<p<\lambda<\infty$ and $s\in\mathbb{R}$ satisfies $\frac{1}{p}-\frac{s}{n}=\frac{1}{\lambda}$. If $d\mu$ is concentrated on $\partial\mathbb{R}^n_+$, as a byproduct we get Sobolev-Morrey trace inequality on half-spaces $\mathbb{R}^n_+$ which recovers the well-known Sobolev-trace inequality in $L^p(\mathbb{R}^n_+)$. Also, by a suitable analysis on non-doubling Cader\'on-Zygmund decomposition we show that \begin{equation} \Vert M_{\alpha}f\Vert_{\mathcal{M}_{p, \ell}^{\lambda}(d\mu)}\,\sim\, \Vert I_{\alpha}f\Vert_{\mathcal{M}_{p, \ell}^{\lambda}(d\mu)}\nonumber \end{equation} provided that $\mu(B_r(x))\sim r^{\beta}$ on support $\text{spt}(\mu)$ and $n-\alpha <\beta\leq n$ with $0<\alpha<n$. This result extends the previous ones.