ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using the variational principle, we compute mass spectra and decay constants of ground state pseudoscalar and vector mesons in the light-front quark model (LFQM) with the QCD-motivated effective Hamiltonian including the hyperfine interaction. By smearing out the Dirac delta function in the hyperfine interaction, we avoid the issue of negative infinity in applying the variational principle to the computation of meson mass spectra and provide analytic expressions for the meson mass spectra. Our analysis with the smeared hyperfine interaction indicates that the interaction for the heavy meson sector including the bottom and charm quarks gets more point-like. We also consider the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of $(\omega,\phi)$ and $(\eta,\eta')$. Our variational analysis with the trial wave function including the two lowest order harmonic oscillator basis functions appears to improve the agreement with the data of meson decay constants and the heavy meson mass spectra over the previous computation handling the hyperfine interaction as perturbation.
Biominerals formed by animals provide skeletal support, and many other functions. They were previously shown to grow by aggregation of amorphous nanoparticles, but never to grow ion-by-ion from solution, which is a common growth mechanism for abiotic crystals. We analyze vaterite CaCO3 multi crystalline spicules from the solitary tunicate Herdmania momus, with Polarization dependent Imaging Contrast PIC mapping, scanning and aberration corrected transmission electron microscopies. The first fully quantitative PIC mapping data, presented here, measured 0{\deg} 30{\deg} angle spreads between immediately adjacent crystals. Such narrowly distributed crystal orientations demonstrate that crystallinity does not propagate from one crystal to another 0{\deg} angle spreads, nor that new crystals with random orientation 90{\deg} nucleate. There are no organic layers at the interface between crystals, hence a new, unknown growth mechanism must be invoked, with crystal nucleation constrained within 30{\deg}. Two observations are consistent with crystal growth from solution: vaterite microcrystals express crystal faces, and are smooth at the nanoscale after cryo fracture. The observation of 30{\deg} angle spreads, lack of interfacial organic layers, and smooth fracture figures broadens the range of known biomineralization mechanisms and may inspire novel synthetic crystal growth strategies. Spherulitic growth from solution is one possible mechanism consistent with all these observations.
We examine how the Seshadri constant of an ample line bundle at a very general point of an algebraic surface can carry important global geometric information about the surface. In particular, we obtain a numerical criterion for when a surface admits a dominant map to an algebraic curve.
We study convex cyclic polygons, that is, inscribed $n$-gons. Starting from P. Schreiber's idea, published in 1993, we prove that these polygons are not constructible from their side lengths with straightedge and compass, provided $n$ is at least five. They are non-constructible even in the particular case where they only have two different integer side lengths, provided that $n\neq 6$. To achieve this goal, we develop two tools of separate interest. First, we prove a limit theorem stating that, under reasonable conditions, geometric constructibility is preserved under taking limits. To do so, we tailor a particular case of Puiseux's classical theorem on some generalized power series, called Puiseux series, over algebraically closed fields to an analogous theorem on these series over real square root closed fields. Second, based on Hilbert's irreducibility theorem, we give a \emph{rational parameter theorem} that, under reasonable conditions again, turns a non-constructibility result with a transcendental parameter into a non-constructibility result with a rational parameter. For $n$ even and at least six, we give an elementary proof for the non-constructibility of the cyclic $n$-gon from its side lengths and, also, from the \emph{distances} of its sides from the center of the circumscribed circle. The fact that the cyclic $n$-gon is constructible from these distances for $n=4$ but non-constructible for $n=3$ exemplifies that some conditions of the limit theorem cannot be omitted.
Anomaly detection is a difficult problem in many areas and has recently been subject to a lot of attention. Classifying unseen data as anomalous is a challenging matter. Latest proposed methods rely on Generative Adversarial Networks (GANs) to estimate the normal data distribution, and produce an anomaly score prediction for any given data. In this article, we propose a simple yet new adversarial method to tackle this problem, denoted as History-based anomaly detector (HistoryAD). It consists of a self-supervised model, trained to recognize 'normal' samples by comparing them to samples based on the training history of a previously trained GAN. Quantitative and qualitative results are presented evaluating its performance. We also present a comparison to several state-of-the-art methods for anomaly detection showing that our proposal achieves top-tier results on several datasets.
Coincidence scattering of polarized electrons from nuclei with polarization transfer to outgoing nucleons is studied within the context of relativistic mean field theory. Effects introduced by the dynamical enhancement of the lower components of the bound and scattered nucleon wave functions are analyzed for the polarized response functions and transferred polarization asymmetries. Results obtained by projecting out the negative-energy components are compared with the fully-relativistic calculation. The crucial role played by the relativistic dynamics in some spin-dependent observables is clearly manifested even for low/medium values of the missing momentum. Kinematical relativistic effects are also analyzed. A discussion of the factorization approach and the mechanism for its breakdown is also briefly presented.
We consider direct diphoton production in hadron collisions, and we compute the next-to-next-to-leading order (NNLO) QCD radiative corrections at the fully-differential level. Our calculation uses the $q_T$ subtraction formalism and it is implemented in a parton level Monte Carlo program. The program allows the user to apply arbitrary kinematical cuts on the final-state photons and the associated jet activity, and to compute the corresponding distributions in the form of bin histograms. We present selected numerical results related to Higgs boson searches at the LHC and corresponding results at the Tevatron.
Rate coefficients have been measured for the reaction of CH radicals with formaldehyde, CH$_{2}$O, over the temperature range 31 - 133 K using a pulsed Laval nozzle apparatus combined with pulsed laser photolysis and laser induced fluorescence spectroscopy. The rate coefficients are very large and display a distinct decrease with decreasing temperature below 70 K, although classical collision rate theory fails to reproduce this temperature dependence. The measured rate coefficients have been parameterized and used as input for astrochemical models for both dark cloud and AGB stellar outflow scenarios. The models predict a distinct change (up to a factor of two) in the abundance of ketene, H$_{2}$CCO, which is the major expected molecular product of the CH + CH$_{2}$O reaction.
IceCube was completed in December 2010. It forms a lattice of 5160 photomultiplier tubes that monitor a volume of ~ 1 cubic km in the deep Antarctic ice for particle induced photons. The telescope was designed to detect neutrinos with energies greater than 100 GeV. Owing to subfreezing ice temperatures, the photomultiplier dark noise rates are particularly low. Hence IceCube can also detect large numbers of MeV neutrinos by observing a collective rise in all photomultiplier rates on top of the dark noise. With 2 ms timing resolution, IceCube can track subtle features in the temporal development of the supernova neutrino burst. For a supernova at the galactic center, its sensitivity matches that of a background-free megaton-scale supernova search experiment. The sensitivity decreases to 20 standard deviations at the galactic edge (30 kpc) and 6 standard deviations at the Large Magellanic Cloud (50 kpc). IceCube is sending triggers from potential supernovae to the Supernova Early Warning System. The sensitivity to neutrino properties such as the neutrino hierarchy is discussed and simulations of tantalizing signatures, such as the formation of a quark star or a black hole as well as the characteristics of shock waves are presented. All results are preliminary.
Co-segmentation is the automatic extraction of the common semantic regions given a set of images. Different from previous approaches mainly based on object visuals, in this paper, we propose a human centred object co-segmentation approach, which uses the human as another strong evidence. In order to discover the rich internal structure of the objects reflecting their human-object interactions and visual similarities, we propose an unsupervised fully connected CRF auto-encoder incorporating the rich object features and a novel human-object interaction representation. We propose an efficient learning and inference algorithm to allow the full connectivity of the CRF with the auto-encoder, that establishes pairwise relations on all pairs of the object proposals in the dataset. Moreover, the auto-encoder learns the parameters from the data itself rather than supervised learning or manually assigned parameters in the conventional CRF. In the extensive experiments on four datasets, we show that our approach is able to extract the common objects more accurately than the state-of-the-art co-segmentation algorithms.
Integrating different semiconductor materials into an epitaxial device structure offers additional degrees of freedom to select for optimal material properties in each layer. However, interface between materials with different valences (i.e. III-V, II-VI and IV semiconductors) can be difficult to form with high quality. Using ZnSe/GaAs as a model system, we explore the use of UV illumination during heterovalent interface growth by molecular beam epitaxy as a way to modify the interface properties. We find that UV illumination alters the mixture of chemical bonds at the interface, permitting the formation of Ga-Se bonds that help to passivate the underlying GaAs layer. Illumination also helps to reduce defects in the ZnSe epilayer. These results suggest that moderate UV illumination during growth may be used as a way to improve the optical properties of both the GaAs and ZnSe layers on either side of the interface.
We study two actions of the (degree 0) Picard group on the set of the spanning trees of a finite ribbon graph. It is known that these two actions, denoted $\beta_q$ and $\rho_q$ respectively, are independent of the base vertex $q$ if and only if the ribbon graph is planar. Baker and Wang conjectured that in a nonplanar ribbon graph without multiple edges there always exists a vertex $q$ for which $\rho_q\neq\beta_q$. We prove the conjecture and extend it to a class of ribbon graphs with multiple edges. We also give explicit examples exploring the relationship between the two torsor structures in the nonplanar case.
We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then present the minisuperspace Wheeler--DeWitt equation and elaborate on the problem of time, the imposition of boundary conditions, the semiclassical approximation, the origin of irreversibility, and singularity avoidance. Restriction is made to the framework of quantum geometrodynamics.
We propose a formulation of adaptive computation of free energy differences, in the ABF or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows to present a truly unifying framework for these methods, and to prove convergence results for certain classes of algorithms. From a numerical viewpoint, a parallel implementation of these methods is very natural, the replicas interacting through the reconstructed free energy. We show how to improve this parallel implementation by resorting to some selection mechanism on the replicas. This is illustrated by computations on a model system of conformational changes.
It has been proposed that the apparent discrepancies between the inferred primordial abundances of 6Li and 7Li and the predictions of big bang nucleosynthesis (BBN) can be resolved by the existence of a negatively-charged massive unstable supersymmetric particle (X-) during the BBN epoch. Here, we present new BBN calculations with an X- particle utilizing an improved nuclear reaction network including captures of nuclei by the particle, nuclear reactions and beta-decays of normal nuclei and nuclei bound to the X- particles (X-nuclei), and new reaction rates derived from recent rigorous quantum many-body dynamical calculations. We find that this is still a viable model to explain the observed 6Li and 7Li abundances. However, contrary to previous results, neutral X-nuclei cannot significantly affect the BBN light-element abundances. We also show that with the new rates the production of heavier nuclei is suppressed and there is no signature on abundances of nuclei heavier than Be in the X--particle catalyzed BBN model as has been previously proposed. We also consider the version of this model whereby the X- particle decays into the present cold dark matter. We analyze the this paradigm in light of the recent constraints on the dark-matter mass deduced from the possible detected events in the CDMS-II experiment. We conclude that based upon the inferred range for the dark-matter mass, only X- decay via the weak interaction can achieve the desired 7Li destruction while also reproducing the observed 6Li abundance.
We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the global minimality of universal constant configurations in a specific range of the physical parameters using a Poincar\'e-type inequality. Then, we prove that any energy minimizer takes its values into a fixed meridian of the sphere $\mathbb{S}^2$, and deduce uniqueness of minimizers up to the action of the appropriate symmetry group. We also prove a comparison principle for minimizers with different penalizations. Finally, we apply these results to a problem on a ball and show radial symmetry and monotonicity of minimizers. In dimension $N=2$ our results can be applied to the Oseen--Frank energy for nematic liquid crystals and micromagnetic energy in a thin-film regime.
Quark mass effects in ${\cal O}(\alpha_s^2)$ QCD corrections to the decay rates of intermediate Higgs bosons are studied. The total hadronic rate and the partial decay rate into bottom quarks are analyzed for the Standard (scalar) Higgs boson as well as for pseudoscalar Higgs bosons. The calculations of three different contributions are presented. First, the flavour singlet diagrams containing two closed fermion loops are calculated for a nonvanishing bottom mass in the heavy top limit. Their leading contribution, which is of the same order as the quasi-massless nonsinglet corrections, and the subleading terms are found. Large logarithms arise due to the separation of the pure gluon final state from the bottom final states. Second, quadratic bottom mass corrections originating from nonsinglet diagrams are presented.Third, nonsinglet corrections induced by virtual heavy top quarks are calculated in leading and subleading orders. It is demonstrated that, in order $\alpha_s^2$, the first contribution numerically dominates over the second and the third ones.
During most stages of stellar evolution the nuclear burning of lighter to heavier elements results in a radial composition profile which is stabilizing against buoyant acceleration, with light material residing above heavier material. However, under some circumstances, such as off-center ignition, the composition profile resulting from nuclear burning can be destabilizing, and characterized by an outwardly increasing mean molecular weight. The potential for instabilities under these circumstances, and the consequences that they may have on stellar structural evolution, remain largely unexplored. In this paper we study the development and evolution of instabilities associated with unstable composition gradients in regions which are initially stable according to linear Schwarzschild and Ledoux criteria. In particular, we explore the mixing taking place under various conditions with multi-dimensional hydrodynamic convection models based on stellar evolutionary calculations of the core helium flash in a 1.25 \Msun star, the core carbon flash in a 9.3\,\Msun star, and of oxygen shell burning in a star with a mass of 23\,\Msun. The results of our simulations reveal a mixing process associated with regions having outwardly increasing mean molecular weight that reside below convection zones. The mixing is not due to overshooting from the convection zone, nor is it due directly to thermohaline mixing which operates on a timescale several orders of magnitude larger than the simulated flows. Instead, the mixing appears to be due to the presence of a wave field induced in the stable layers residing beneath the convection zone which enhances the mixing rate by many orders of magnitude and allows a thermohaline type mixing process to operate on a dynamical, rather than thermal, timescale. We discuss our results in terms of related laboratory phenomena and associated theoretical developments.
We give a general $SU(2)_L\times SU(2)_R$ $\times U(1)_{EM}$ sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that $\sigma $ and $\pi ^0$ without electric charges have electromagnetic interaction effects coming from their internal structure. A general Lorentz transformation relative to external sources $J_{gauge}$ $=(J_{A_\mu},J_{A_\mu ^\kappa})$ is derived, using the general Lorentz transformation and the four-dimensional current of nuclear matter of the ground state with $J_{gauge}$ = 0, we give the four-dimensional general relations between the different currents of nuclear matter systems with $J_{gauge}\neq 0$ and those with $J_{gauge}=0$. The relation of the density's coupling with external magnetic field is derived, which conforms well to dense nuclear matter in a strong magnetic field. We show different condensed effects in strong interaction about fermions and antifermions, and give the concrete scalar and pseudoscalar condensed expressions of $\sigma_0$ and $\pi_0$ bosons. About different dynamical breaking and spontaneous vacuum symmetry breaking, the concrete expressions of different mass spectra are obtained in field theory. This paper acquires the running spontaneous vacuum breaking value $\sigma_0^{\prime},$ and obtains the spontaneous vacuum breaking in terms of the running $\sigma_0^{\prime}$, which make nucleon, $\sigma $ and $\pi $ particles gain effective masses. We achieve both the effect of external sources and nonvanishing value of the condensed scalar and pseudoscalar paticles. It is deduced that the masses of nucleons, $\sigma $ and $\pi $ generally depend on different external sources.
It is shown that the one-dimensional or two-dimensional radially symmetric isothermal compressible Navier-Stokes system has no non-trivial global smooth solutions if the initial density is compactly supported. This result is a generalization of Xin's work \cite{Xin98} to the isothermal case.
We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and divergent terms---in a way that makes manifest the exponentiation of infrared divergences at the integrand-level. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work's source files on the arXiv.
The Sy 2 galaxy NGC 1241 presents a 1.5 kpc large circumnuclear ring of star formation (CNR) embracing a small bar plus leading arms. Those structures are P alpha emitters, but barely seen in H alpha. It presents also stellar trailing arms inside the CNR. GEMINI and HST imagery allow the construction of high resolution (V-H) and (J-K_s) color maps as well as a (J-K_s) vs. K color-magnitude diagram (CMD) of this complex region. The CNR is heavily obscured in V, but a fairly transparent window appears in the direction of the nucleus. Nonetheless, the nucleus presents a (J-K_s) color that is redder than the CNR. The CNR is composed of extremely young HII regions still enshrouded in their dust cocoons. However, the nuclear (J-K_s) color can not be explained in this manner. Therefore, we propose the contribution of C-Stars as the most feasible mechanism for explaining the colors. If the nuclear stellar population is comparable to that of the LMC bar, 500 C-stars and 25000 AGB O-rich stars inside 50 pc may reproduce the observed colors. C-Stars release enriched material to the nuclear environment, probably fueling the central engine of this Sy 2 galaxy during the lifetime of stars with masses between 2 M_sun < M_C-star < 6 M_sun (C-star phase). The ejected material that remains trapped in the central potential might also explain the systematically observed increased strength of the optical CN-bands in Sy 2 galaxies and is consistent with the significant contribution of intermediate age stars to the optical continuum of low luminosity AGNs.
We study the polyharmonic Neumann and mixed boundary value problems on the Kor\'{a}nyi ball in the Heisenberg group $\H_n$. Necessary and sufficient solvability conditions are obtained for the nonhomogeneous polyharmonic Neumann problem and Neumann-Dirichlet boundary value problems.
Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation for product formulas of any given order, and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that the randomized approach has better empirical performance as well.