ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using a chemical evolution model we investigate the intriguing suggestion that there are populations of stars in some globular clusters (e.g. NGC 2808, omega Centauri) with enhanced levels of helium (Y from about 0.28 to 0.40) compared to the majority of the population that presumably have a primordial helium abundance. We assume that a previous generation of massive low-metallicity Asymptotic Giant Branch (AGB) stars has polluted the cluster gas via a slow stellar wind. We use two independent sets of AGB yields computed from detailed models to follow the evolution of helium, carbon, nitrogen and oxygen in the cluster gas using a Salpeter initial mass function (IMF) and a number of top-heavy IMFs. In no case were we able to fit the observational constraints, Y > 0.30 and C+N+O approximately constant. Depending on the shape of the IMF and the yields, we either obtained Y approximately greater than 0.30 and large increases in C+N+O or Y < 0.30 and C+N+O approximately constant. These results suggest that either AGB stars alone are not responsible for the large helium enrichment or that any dredge-up from this generation of stars was less than predicted by standard models.
We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1.
Object detection in camera images, using deep learning has been proven successfully in recent years. Rising detection rates and computationally efficient network structures are pushing this technique towards application in production vehicles. Nevertheless, the sensor quality of the camera is limited in severe weather conditions and through increased sensor noise in sparsely lit areas and at night. Our approach enhances current 2D object detection networks by fusing camera data and projected sparse radar data in the network layers. The proposed CameraRadarFusionNet (CRF-Net) automatically learns at which level the fusion of the sensor data is most beneficial for the detection result. Additionally, we introduce BlackIn, a training strategy inspired by Dropout, which focuses the learning on a specific sensor type. We show that the fusion network is able to outperform a state-of-the-art image-only network for two different datasets. The code for this research will be made available to the public at: https://github.com/TUMFTM/CameraRadarFusionNet.
The combinatorial structure of a d-dimensional simple convex polytope can be reconstructed from its abstract graph [Blind & Mani 1987, Kalai 1988]. However, no polynomial/efficient algorithm is known for this task, although a polynomially checkable certificate for the correct reconstruction was found by [Joswig, Kaibel & Koerner 2000]. A much stronger certificate would be given by the following characterization of the facet subgraphs, conjectured by M. Perles:   ``The facet subgraphs of the graph of a simple d-polytope are exactly all the (d-1)-regular, connected, induced, non-separating subgraphs'' [Perles 1970].   We give examples for the validity of Perles conjecture: In particular, it holds for the duals of cyclic polytopes, and for the duals of stacked polytopes. On the other hand, we identify a topological obstruction that must be present in any counterexample to Perles' conjecture; thus, starting with a modification of ``Bing's house'', we construct explicit 4-dimensional counterexamples.
Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant probability on each query, but in general, requiring several iterations of the algorithm. We present a modified version to return the correct result with certainty without having user control over the quantum search oracle. Our deterministic, two-parameter "D2p" protocol utilizes generalized phase rotations replacing the phase inversions after a standard oracle query. The D2p protocol achieves a 100% success rate in no more than one additional iteration compared to the optimal number of steps in the original Grover's search enabling the same quadratic speed up. We also provide a visualization using the Bloch sphere for enhanced geometric intuition.
The possible existence of shape-coexisting nuclear configurations with tetrahedral symmetry is receiving an increasing attention due to unprecedented nuclear structure properties, in particular in terms of the exotic 4-fold nucleonic level degeneracies and the expected long lifetimes which may become a new decisive argument in the exotic nuclei research programs. The present article addresses the rotational structure properties of the tetrahedrally-symmetric even-even core configurations coupled with a single valence nucleon. We focus on the properties of the associated Coriolis-coupling Hamiltonian proposing the solutions based on the explicit construction of the bases of the irreducible representations of the tetrahedral point-group on the one-hand side and the microscopic angular-momentum and parity projection nuclear mean-field approach on the other. It is shown that for one-particle occupying an orbital belonging to the $E_{1/2}$ or $E_{5/2}$ irreducible representation, the rotational spectrum splits into two sequences, the structures analogous to those of the $K=1/2$ rotational bands in the axially symmetric nuclei. Although the spectrum is generally more complicated for one-particle occupying a 4-fold degenerate orbital belonging to the $G_{3/2}$ representation, an appearance of the correlated double-sequence structures persists. The spectra of the doubly-magic tetrahedral core plus one-particle systems can be well interpreted using the analytical solutions of the first order Coriolis-coupling Hamiltonian. We introduce the notion of the generalized decoupling parameters, which determine the size of the energy-splitting between the double-sequence structures.
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations (and numerical methods) applied to specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.
We study the effects of anisotropic thermal conduction on low-collisionality, astrophysical plasmas using two and three-dimensional magnetohydrodynamic simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable for either sign of the temperature gradient: the heat-flux-driven buoyancy instability (HBI) operates when the temperature increases with radius while the magnetothermal instability (MTI) operates in the opposite limit. In contrast to previous results, we show that, in the presence of a sustained temperature gradient, the MTI drives strong turbulence and operates as an efficient magnetic dynamo (akin to standard, adiabatic convection). Together, the turbulent and magnetic energies contribute up to ~10% of the pressure support in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5% of rho c_s^3. These findings are robust even in the presence of an external source of strong turbulence. Our results on the nonlinear saturation of the HBI are consistent with previous studies but we explain physically why the HBI saturates quiescently by re-orienting the magnetic field (suppressing the conductive heat flux through the plasma), while the MTI saturates by generating sustained turbulence. We also systematically study how an external source of turbulence affects the saturation of the HBI: such turbulence can disrupt the HBI only on scales where the shearing rate of the turbulence is faster than the growth rate of the HBI. In particular, our results provide a simple mapping between the level of turbulence in a plasma and the effective isotropic thermal conductivity. We discuss the astrophysical implications of these findings, with a particular focus on the intracluster medium of galaxy clusters.
Let $\mathcal Z_d$ be the zero cell of a $d$-dimensional, isotropic and stationary Poisson hyperplane tessellation. We study the asymptotic behavior of the expected number of $k$-dimensional faces of $\mathcal Z_d$, as $d\to\infty$. For example, we show that the expected number of hyperfaces of $\mathcal Z_d$ is asymptotically equivalent to $\sqrt{2\pi/3}\, d^{3/2}$, as $d\to\infty$. We also prove that the expected solid angle of a random cone spanned by $d$ random vectors that are independent and uniformly distributed on the unit upper half-sphere in $\mathbb R^{d}$ is asymptotic to $\sqrt 3 \pi^{-d}$, as $d\to\infty$.
In high-redshift ($z>5$) quasars, a large amount of dust ($\textstyle\sim 10^{8} \mathrm{M}_{\sun}$) has been observed. In order to explain the large dust content, we focus on a possibility that grain growth by the accretion of heavy elements is the dominant dust source. We adopt a chemical evolution model applicable to nearby galaxies but utilize parameters adequate to high-$z$ quasars. It is assumed that metals and dust are predominantly ejected by Type II supernovae (SNe). We have found that grain growth strongly depends on the grain size distribution. If we simply use the size distribution of grains ejected from SNe, grain growth is inefficient because of the lack of small grains (i.e.\ small surface-to-volume ratio of the dust grains). However, if we take small grain production by interstellar shattering into consideration, grain growth is efficient enough to account for the rich dust abundance in high-$z$ quasars. Our results not only confirm that grain growth is necessary to explain the large amount of dust in high-$z$ quasars, but also demonstrate that grain size distributions have a critical impact on grain growth.
We investigate the conformation-dependent electron transfer in a biphenyl molecule within a simple tight-binding framework. The overall junction current and circular currents in two benzene rings driven by applied bias voltage are calculated by using Green's function formalism. Our analysis may provide the possibilities of using organic molecules with loop substructures to design molecular spintronic devices, indicating the emergence of molecular spintronics.
An experimental success criterion for continuous-variable quantum teleportation and memories is to surpass a limit of the average fidelity achieved by the classical measure-and-prepare schemes with respect to a Gaussian distributed set of coherent states. We present a simple proof of the classical limit based on the familiar notions of the state-channel duality and the partial transposition. The present method enables us to produce a quantum-domain criterion associated with a given set of measured fidelities.
Photoexcitation is a powerful means in distinguishing different interactions and manipulating the states of matter, especially in complex quantum systems. As a well-known charge density wave (CDW) material, 1T-TaS2 has been widely studied experimentally thanks to its intriguing photoexcited responses. However, the microscopic atomic dynamics and underlying mechanism are still under debate. Here, we demonstrate photoexcitation induced ultrafast dynamics in 1T-TaS2 using time-dependent density functional theory molecular dynamics. We discover a novel collective mode induced by photodoping, which is significantly different from thermally-induced phonon mode in TaS2. In addition, our finding validates nonthermal melting of CDW induced at low light intensities, supporting that conventional hot electron model is inadequate to explain photoinduced dynamics. Our results provide a deep insight on coherent electron and lattice quantum dynamics during the formation and excitation of CDW in 1T-TaS2.
In this work, we present more detail of the calculation on the NLO QCD corrections to polarization of direct J/psi production via color singlet at Tevatron and LHC, as well as the results for Upsilon for the first time. Our results show that the J/psi polarization status drastically changes from transverse polarization dominant at LO into longitudinal polarization dominant in the whole range of the transverse momentum $p_t$ of J/psi when the NLO corrections are counted. For Upsilon production, the p_t distribution of the polarization status behaves almost the same as that for J/psi except that the NLO result is transverse polarization at small p_t range. Although the theoretical evaluation predicts a larger longitudinal polarization than the measured value at Tevatron, it may provide a solution towards the previous large discrepancy for J/psi and Upsilon polarization between theoretical predication and experimental measurement, and suggests that the next important step is to calculate the NLO corrections to hadronproduction of color octet state J/psi^(8) and Upsilon^(8). Our calculations are performed in two ways, namely we do and do not analytically sum over the polarizations, and then check them with each other.
We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $(\mathfrak{e}_n,\mathfrak{e}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4d SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4d theories from different origins via mirror symmetry.
We propose and analyse analogs of optical cavities for atoms using three-well Bose-Hubbard models with pumping and losses. We consider triangular configurations. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, preserving good coherence between the wells in the steady-state. We find quadrature squeezing and mode entanglement for some parameter regimes and demonstrate that the trimer with pumping and damping at the same well is the stronger option for producing non-classical states. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.
Pulsar wind nebulae are now well established as important probes both of neutron stars' relativistic winds and of the surrounding interstellar medium. Amongst this diverse group of objects, pulsar bow shocks have long been regarded as an oddity, only seen around a handful of rapidly moving neutron stars. However, recent efforts at optical, radio and X-ray wavelengths have identified many new pulsar bow shocks, and these results have consequently motivated renewed theoretical efforts to model these systems. Here I review the new results and ideas which have emerged on these spectacular systems, and explain how bow shocks and "Crab-like" nebulae now form a consistent picture within our understanding of pulsar winds.
We present the discovery of a 4 kpc molecular gas lane in the Cygnus A host galaxy, using ALMA CO 2-1 observations. The gas lane is oriented roughly perpendicular to the projected radio jet axis. The CO emission generally follows the clumpy dust lanes seen in HST I-band images. The total molecular gas mass is $30\times 10^8$ M$_\odot$ for Milky Way type clouds, and $3.6 \times 10^8$ M$_\odot$ for starburst conditions. There is a velocity change from the northern to southern CO peaks of about $\pm 175$~km~s$^{-1}$, and an apparently smooth velocity gradient between the peaks, although the emission in the central region is weak. In the inner $\sim 0.5"$ projected distance from the radio core, comparison of the CO velocities to those observed for H$_2$ 2.1218 $\mu$m emission shows higher velocities for the vibrationally excited warm molecular gas than the cooler CO 2-1 line emitting gas at similar projected radii. A possible explanation for these different projected velocities at a given radius is that the cooler CO gas is distributed in a clumpy ring at radius $\sim 1.5"$ to $2"$, while the warm H$_2$ 2.12$\mu$m emitting gas is interior to this ring. Of course, the current data cannot rule-out a clumpy, amorphous molecular gas distribution linearly distributed perpendicular to the radio jet axis. We consider surface brightness properties on scales down to $\sim 265$~pc, and discuss the Cygnus A results in the context of other radio galaxies with CO emission.
Jeong-O Lee et al. [Phy. Rev. B, 61, R16 362 (2000)] reported magnetoresistance and differential conductance measurements of multiwalled carbon nanotubes. The observed aperiodic conductance fluctuations and the negative magnetoresistance was interpreted to originate exclusively from changes in the density of states at the Fermi energy. We show that this interpretation is questionable and not supported by their measurements.
We study the elliptic genera of 6d strings based on their modular properties. They are weak Jacobi forms of weight 0, whose indices are determined from the 2d chiral anomalies. We propose the ansatz for the elliptic genera which reflects the analytic structure of instanton partition functions. Given a finite amount of initial BPS data, we completely determine the elliptic genera of 6d strings in various 6d SCFTs. We also apply our ansatz to study $\mathcal{N}=(2,0)$ and $(1,1)$ little strings as well as $\mathcal{N}=(1,0)$ heterotic little strings, for which T-duality of little string theories supplies a sufficient number of initial BPS data. The anomaly polynomials of 6d little strings are worked out, which is needed for the elliptic genera bootstrap. In some little string theories, the elliptic genera must have the extra contributions from the Coulomb branch, which correspond to the additional zero modes for the full strings. The modified ansatze for such elliptic genera are also discussed.
A well-known theorem in plane geometry states that any set of $n$ non-collinear points in the plane determines at least $n$ lines. Chen and Chv\'{a}tal asked whether an analogous statement holds within the framework of finite metric spaces, with lines defined using the notion of {\em betweenness}.   In this paper, we prove that in the plane with the $L_1$ (also called Manhattan) metric, a non-collinear set of $n$ points induces at least $\lceil n/2\rceil$ lines. This is an improvement of the previous lower bound of $n/37$, with substantially different proof. As a consequence, we also get the same lower bound for non-collinear point sets in the plane with the $L_{\infty}$ metric.
Let $f(z)=\sum_{n=1}^\infty \lambda_f(n)e^{2\pi i n z}\in S_{k}^{new}(\Gamma_0(N))$ be a normalized Hecke eigenform of even weight $k\geq2$ on $\Gamma_0(N)$ without complex multiplication. Let $\mathbb{P}$ denote the set of all primes. We prove that the sequence $\{\lambda_f(p)\}_{p\in\mathbb{P}}$ does not satisfy Benford's Law in any base $b\geq2$. However, given a base $b\geq2$ and a string of digits $S$ in base $b$, the set \[ A_{\lambda_f}(b,S):=\{\text{$p$ prime : the first digits of $\lambda_f(p)$ in base $b$ are given by $S$}\} \] has logarithmic density equal to $\log_b(1+S^{-1})$. Thus $\{\lambda_f(p)\}_{p\in\mathbb{P}}$ follows Benford's Law with respect to logarithmic density. Both results rely on the now-proven Sato-Tate Conjecture.
Given a sequence $\dot{L}^{\varepsilon}$ of L\'evy noises, we derive necessary and sufficient conditions in terms of their variances $\sigma^2(\varepsilon)$ such that the solution to the stochastic heat equation with noise $\sigma(\varepsilon)^{-1} \dot{L}^\varepsilon$ converges in law to the solution to the same equation with Gaussian noise. Our results apply to both equations with additive and multiplicative noise and hence lift the findings of S. Asmussen and J. Rosi\'nski [J. Appl. Probab. 38 (2001) 482-493] and S. Cohen and J. Rosi\'nski [Bernoulli 13 (2007) 195-210] for finite-dimensional L\'evy processes to the infinite-dimensional setting without making distributional assumptions on the solutions such as infinite divisibility. One important ingredient of our proof is to characterize the solution to the limit equation by a sequence of martingale problems. To this end, it is crucial to view the solution processes both as random fields and as c\`adl\`ag processes with values in a Sobolev space of negative real order.
We prove the existence of a potentially diagonalizable lift of a given automorphic mod $p$ Galois representation $\overline{\rho}:{\rm Gal}(\overline{F}/F)\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ for any totally real field $F$ and any rational prime $p>2$ under the adequacy condition by using automorphic lifting techniques developed by Barnet-Lamb, Gee, Geraghty, and Taylor. As an application, when $p$ is split completely in $F$, we prove a variant of Serre's weight conjecture for $\overline{\rho}$. The formulation of our Serre conjecture is done by following Toby Gee's philosophy. Applying these results to the case when $F=\mathbb{Q}$ with a detailed study of potentially diagonalizable, crystalline lifts with some prescribed properties, we also define classical (naive) Serre's weights. This weight would be the minimal weight among possible classical weights in some sense which occur in candidates of holomorphic Siegel Hecke eigen cusp forms of degree 2 with levels prime to $p$. The main task is to construct a potentially ordinary automorphic lift for $\overline{\rho}$ by assuming only the adequacy condition. The main theorems in this paper also extend many results obtained by Barnet-Lamb, Gee and Geraghty for potentially ordinary lifts and Gee and Geraghty for companion forms.