ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show the existence of a compact K\"ahler manifold which does not fit in a proper flat family over an irreducible base with one projective (possibly singular) fiber. We also give a topological version of this statement. This strengthens our earlier counterexamples to the Kodaira algebraic approximation problem.
Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F)]-modules. For these embedding problems we prove conditions on solvability, formulas for explicit construction, and results on automatic realizability.
In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment when a positive parameter $\epsilon$ goes to zero (a thin domain). Here we also allow that its boundary presents highly oscillatory behavior with different orders and variable profile. We take thin domains possessing the same order $\epsilon$ to the thickness and amplitude of the oscillations but assuming different order to the period of oscillations on the top and the bottom of the boundary. We combine methods from linear homogenization theory and the theory on nonlinear dynamics of dissipative systems to obtain the limit problem establishing convergence properties for the solutions. At the end we show the upper semicontinuity of the attractors and stationary states.
The distribution of the sunspot group size (area) and its dependence on the level of solar activity is studied. It is shown that the fraction of small groups is not constant but decreases with the level of solar activity so that high solar activity is largely defined by big groups. We study the possible influence of solar activity on the ability of a realistic observer to see and report the daily number of sunspot groups. It is shown that the relation between the number of sunspot groups as seen by different observers with different observational acuity thresholds is strongly non-linear and cannot be approximated by the traditionally used linear scaling ($k-$factors). The observational acuity threshold [$A_{\rm th}$] is considered to quantify the quality of each observer, instead of the traditional relative $k-$factor. A nonlinear $c-$factor based on $A_{\rm th}$ is proposed, which can be used to correct each observer to the reference conditions. The method is tested on a pair of principal solar observers, Wolf and Wolfer, and it is shown that the traditional linear correction, with the constant $k-$factor of 1.66 to scale Wolf to Wolfer, leads to an overestimate of solar activity around solar maxima.
MWC656 has been reported as classical Be star with a black hole companion. Revisited spectral variability properties render this unlikely, with a hot subdwarf more probable.
We investigate the evolution of the horizontal flow field around sunspots during their decay by analysing its extension and horizontal velocity around eight spots using SDO/HMI Doppler maps. By assuming a radially symmetrical flow field, the applied analysis method determines the radial dependence of the azimuthally averaged flow field. For comparison, we studied the flow in supergranules using the same technique. All investigated, fully fledged sunspots are surrounded by a flow field whose horizontal velocity profile decreases continuously from 881 m s$^{-1}$ at 1.1 Mm off the spot boundary, down to 199 m s$^{-1}$ at a mean distance of 11.9 Mm to that boundary. Once the penumbra is fully dissolved, however, the velocity profile of the flow changes: The horizontal velocity increases with increasing distance to the spot boundary until a maximum value of about 398 m s$^{-1}$ is reached. Then, the horizontal velocity decreases for farther distances to the spot boundary. In supergranules, the horizontal velocity increases with increasing distance to their centre up to a mean maximum velocity of 355 m s$^{-1}$. For larger distances, the horizontal velocity decreases. We thus find that the velocity profile of naked sunspots resembles that of supergranular flows. The evolution of the flow field around individual sunspots is influenced by the way the sunspot decays and by the interplay with the surrounding flow areas. Observations of the flow around eight decaying sunspots suggest that as long as penumbrae are present, sunspots with their moat cell are embedded in network cells. The disappearance of the penumbra (and consequently the moat flow) and the competing surrounding supergranular cells, both have a significant role in the evolution of the flow field: The moat cell transforms into a supergranule, which hosts the remaining naked spot.
A model for the p d --> p d eta reaction published earlier, including the final state interaction (FSI) of all particles, is revisited to investigate the low energy data on this reaction. The three body problem of p-d-eta scattering in the final state is approximated in terms of pairwise interactions between the three particles in the final state. Apart from a comparison with some preliminary data, two new findings relevant to the near threshold data analysis are reported. The first one points toward the limitations of an FSI factor used conventionally to extract the eta-deuteron scattering length and infer subsequently on the existence of eta-mesic states. The second result emphasizes the role of the $p-d$ FSI and the strong Coulomb repulsion near threshold. Finally, a comparison of the above model calculation with low energy data, excludes very large eta-nucleon scattering lengths.
Even with the recent advances in convolutional neural networks (CNN) in various visual recognition tasks, the state-of-the-art action recognition system still relies on hand crafted motion feature such as optical flow to achieve the best performance. We propose a multitask learning model ActionFlowNet to train a single stream network directly from raw pixels to jointly estimate optical flow while recognizing actions with convolutional neural networks, capturing both appearance and motion in a single model. We additionally provide insights to how the quality of the learned optical flow affects the action recognition. Our model significantly improves action recognition accuracy by a large margin 31% compared to state-of-the-art CNN-based action recognition models trained without external large scale data and additional optical flow input. Without pretraining on large external labeled datasets, our model, by well exploiting the motion information, achieves competitive recognition accuracy to the models trained with large labeled datasets such as ImageNet and Sport-1M.
We show that nanoparticles can have very rich ground state chemical order. This is illustrated by determining the chemical ordering of Ag-Au 309-atom Mackay icosahedral nanoparticles. The energy of the nanoparticles is described using a cluster expansion model, and a Mixed Integer Programming (MIP) approach is used to find the exact ground state configurations for all stoichiometries. The chemical ordering varies widely between the different stoichiometries, and display a rich zoo of structures with non-trivial ordering.
The Dresselhaus and Rashba effects are well-known phenomena in solid-state physics, in which spin-orbit coupling (SOC) splits spin-up and spin-down energy bands of nonmagnetic non-centrosymmetric crystals. Here, we discover a new phenomenon, dubbed as band splitting with vanishing spin polarizations (BSVSP), in which, as usual, SOC splits the energy bands in nonmagnetic non-centrosymmetric systems; surprisingly, however, both split bands show no net spin polarization along certain high-symmetry lines in the Brillouin zone. In order to rationalize this phenomenon, we propose a new classification of point groups into pseudo-polar and non-pseudo-polar groups. By means of first-principles simulations, we demonstrate that BSVSP can take place in both symmorphic (e.g., bulk GaAs) and non-symmorphic systems (e.g., two dimensional ferroelectric SnTe). Furthermore, we propose a novel linear magnetoelectric coupling in reciprocal space, which could be employed to tune the spin polarization with an external electric field. The BSVSP effect and its manipulation could therefore pave a new way to novel spintronic devices.
Neural architecture search (NAS) and network pruning are widely studied efficient AI techniques, but not yet perfect. NAS performs exhaustive candidate architecture search, incurring tremendous search cost. Though (structured) pruning can simply shrink model dimension, it remains unclear how to decide the per-layer sparsity automatically and optimally. In this work, we revisit the problem of layer-width optimization and propose Pruning-as-Search (PaS), an end-to-end channel pruning method to search out desired sub-network automatically and efficiently. Specifically, we add a depth-wise binary convolution to learn pruning policies directly through gradient descent. By combining the structural reparameterization and PaS, we successfully searched out a new family of VGG-like and lightweight networks, which enable the flexibility of arbitrary width with respect to each layer instead of each stage. Experimental results show that our proposed architecture outperforms prior arts by around $1.0\%$ top-1 accuracy under similar inference speed on ImageNet-1000 classification task. Furthermore, we demonstrate the effectiveness of our width search on complex tasks including instance segmentation and image translation. Code and models are released.
We report on measurements performed at low temperatures on a nanoelectromechanical system (NEMS) under (capacitive) parametric pumping. The excitations and detection schemes are purely electrical, and enable in the present experiment the straightforward measurement of forces down to about a femtonewton, for displacements of an Angstr\"om, using standard room temperature electronics. We demonstrate that a small (linear) force applied on the device can be amplified up to more than a 100 times, while the system is {\it truly moving}. We explore the dynamics up to about 50$~$nm deflections for cantilevers about 200$~$nm thick by 3$~$$\mu$m long oscillating at a frequency of 7$~$MHz. We present a generic modeling of nonlinear parametric amplification, and give analytic theoretical solutions enabling the fit of experimental results. We finally discuss the practical limits of the technique, with a particular application: the measurement of {\it anelastic damping} in the metallic coating of the device with an exceptional resolution of about 0.5$~$\%.
Non-resonant X-ray magnetic scattering has been used to study the magnetic structure of multiferroic TbMnO3 in its ferroelectric phase. Circularly polarized X-rays were combined with a full polarization analysis of the scattered beam to reveal important new information on the magnetic structure of this canonical multiferroic. An applied electric field is shown to create a magnetic nearly mono-domain state in which the cylcoidal order on the Mn sublattice rotates either clockwise or counter-clockwise depending on the sign of the field. It is demonstrated how this technique provides sensitivity to the absolute sense of rotation of the Mn moments, and to components of the ordering on the Tb sublattice and phase shifts that earlier neutron diffraction experiments could not resolve.
1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial relation between the ND, DD, NN and periodic boundary conditions.
We show that an earlier domain wall solution of type IIB supergravity provides a supersymmetric realization of the Randall-Sundrum brane-world, and give its ten-dimensional interpretation in terms of IIB 3-branes. We also explain how previous no-go theorems are circumvented. In particular, whereas D=5 supergravity scalars have AdS_5 energy E_0 <= 4 and are unable to support a D=5 positive tension brane, our scalar has E_0=8, and is the breathing mode of the S^5 compactification. Another essential element of the construction is the implementation of a Z_2 symmetry by patching together compactifications with opposite signs for their 5-form field strengths. This is thus a IIB analogue of a previous D=5 3-brane realization of the Horava-Witten orbifold. A mode-locking phenomenon avoids the appearance of negative energy zero-modes in spite of the necessity of a D=10 negative tension brane-source.
Calculations of microscopic optical potentials (OP's) (their real and imaginary parts) are performed to analyze the $^6$He+p elastic scattering data at a few tens of MeV/nucleon (MeV/N). The OP's and the cross sections are calculated using three model densities of $^6$He. Effects of the regularization of the NN forces and their dependence on nuclear density are investigated. Also, the role of the spin-orbit terms and of the non-linearity in the calculations of the OP's, as well as effects of their renormalization are studied. The sensitivity of the cross sections to the nuclear densities was tested and one of them that gives a better agreement with the data was chosen.
The halo factor is one of the experimental data which describes a distribution of neutrons in nuclear periphery. In the presented paper we use Skyrme-Hartree (SH) and the Relativistic Mean Field (RMF) models and we calculate the neutron excess factor $\Delta_B$ defined in the paper which differs slightly from halo factor $f_{\rm exp}$. The results of the calculations are compared to the measured data.
We numerically reproduce the density profiles for filaments that are in magnetohydrostatic and pressure equilibrium with their surroundings obtained in Tomisaka (2014) and show that these equilibria are dynamically stable. If the effect of ambipolar diffusion is considered, these filaments lose magnetic support initiating cloud collapse. The filaments do not lose magnetic flux. Rather the magnetic flux is redistributed within the filament from the centre towards the envelope.   The rate of the collapse is inversely proportional to the fractional ionisation and two gravitationally-driven ambipolar diffusion regimes for the collapse are observed as predicted in Mouschovias & Morton (1991). For high values of the ionisation coefficient, that is $X \geq 10^{-7}$, the gas is strongly coupled to the magnetic field and the Jeans length is larger than the ambipolar diffusion length scale. Then the collapse is governed by magnetically-regulated ambipolar diffusion. For $X \lesssim 10^{-8}$, the gas is weakly coupled to the magnetic field and the magnetic support is removed by gravitationally-dominated ambipolar diffusion. Here, neutrals and ions only collide sporadically, that is the ambipolar diffusion length scale is larger than the Jeans length.   When decaying turbulence is included, additional support is provided to the filament. This slows down the collapse of the filament even in the absence of a magnetic field. When a magnetic field is present, the collapse rate increases by a ratio smaller than for the non-magnetic case. This is because of a speed-up of the ambipolar diffusion due to larger magnetic field gradients generated by the turbulence and because the ambipolar diffusion aids the dissipation of turbulence below the ambipolar diffusion length scale. The highest increase in the rate is observed for the lowest ionisation coefficient and the highest turbulent intensity.
Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give results on integer partitions with parts from numbers in modular arithmetic progression. This includes recursive formulas for the number of partitions using these modular parts. The triple product identity can derive further recursive formulas. Additionally, there is a recursive formula for the related sum of divisors function. The specific triple product identity provides a framework to examine all the identities and can be used to define related theta functions.
Regarding three-dimensional (3D) topological insulators and semimetals as a stack of constituent 2D topological (or sometimes non-topological) layers is a useful viewpoint. Primarily, concrete theoretical models of the paradigmatic 3D topological phases such as Weyl semimetal (WSM), strong and weak topological insulators (STI/WTI), and Chern insulator (CI), are often constructed in that way. Secondarily, fabrication of the corresponding 3D topological material is also done in the same spirit; epitaxial growth technique is employed, making the resulting sample in the form of a thin film. Here, in this paper we calculate $\mathbb{Z}$- and $\mathbb{Z}_2$-indices and study evolution of the topological properties of such thin films of 3D topological systems, making also a comparative study of CI- vs. TI-type models belonging to different symmetry classes in this respect. Through this comparative study we suggest that WSM is to CI as STI is to WTI. Finally, to test the robustness of our scenario against disorder and relevance to experiments we have also studied numerically the two-terminal conductance of the system using transfer matrix method.
We consider invasion percolation on the randomly-weighted complete graph $K_n$, started from some number $k(n)$ of distinct source vertices. The outcome of the process is a forest consisting of $k(n)$ trees, each containing exactly one source. Let $M_n$ be the size of the largest tree in this forest. Logan, Molloy and Pralat (arXiv:1806.10975) proved that if $k(n)/n^{1/3} \to 0$ then $M_n/n \to 1$ in probability. In this paper we prove a complementary result: if $k(n)/n^{1/3} \to \infty$ then $M_n/n \to 0$ in probability. This establishes the existence of a phase transition in the structure of the invasion percolation forest around $k(n) \asymp n^{1/3}$.   Our arguments rely on the connection between invasion percolation and critical percolation, and on a coupling between multi-source invasion percolation with differently-sized source sets. A substantial part of the proof is devoted to showing that, with high probability, a certain fragmentation process on large random binary trees leaves no components of macroscopic size.
The aim of this paper is to establish some new results on the absolute continuity and the convergence in total variation for a sequence of d-dimensional vectors whose components belong to a finite sum of Wiener chaoses. First we show that the probability that the determinant of the Malliavin matrix of such vectors vanishes is zero or one, and this probability equals to one is equivalent to say that the vector takes values in the set of zeros of a polynomial. We provide a bound for the degree of this annihilating polynomial improving a result by Kusuoka. On the other hand, we show that the convergence in law implies the convergence in total variation, extending to the multivariate case a recent result by Nourdin and Poly. This follows from an inequality relating the total variation distance with the Fortet-Mourier distance. Finally, applications to some particular cases are discussed.
We investigate the appearance of di-neutron bound states in pure neutron matter within the Brueckner-Hartree-Fock approach at zero temperature. We consider Argonne $v_{18}$ and Paris bare interactions as well as chiral two- and three-nucleon forces. Self-consistent single-particle potentials are calculated controlling explicitly singularities in the $g$ matrix associated with bound states. Di-neutrons are loosely bound, with binding energies below $1$ MeV, but are unambiguously present for Fermi momenta below $1$ fm$^{-1}$ for all interactions. Within the same framework we are able to calculate and characterize di-neutron bound states, obtaining mean radii as high as $\sim 110$ fm. The resulting equations of state and mass-radius relations for pure neutron stars are analyzed including di-neutron contributions.
This is the first of a pair of papers which address the problem of measuring the unredshifted power spectrum in optimal fashion from a survey of galaxies, with arbitrary geometry, for Gaussian or non-Gaussian fluctuations, in real or redshift space. In this first paper, that pair weighting is derived which formally minimizes the expected variance of the unredshifted power spectrum windowed over some arbitrary kernel. The inverse of the covariance matrix of minimum variance estimators of windowed power spectra is the Fisher information matrix, which plays a central role in establishing optimal estimators. Actually computing the minimum variance pair window and the Fisher matrix in a real survey still presents a formidable numerical problem, so here a perturbation series solution is developed. The properties of the Fisher matrix evaluated according to the approximate method suggested here are investigated in more detail in the second paper.
Uniquely among the dwarf spheroidal (dSph) satellite galaxies of the Milky Way, Fornax hosts globular clusters. It remains a puzzle as to why dynamical friction has not yet dragged any of Fornax's five globular clusters to the centre, and also why there is no evidence that any similar star cluster has been in the past (for Fornax or any other dSph). We set up a suite of 2800 N-body simulations that sample the full range of globular-cluster orbits and mass models consistent with all existing observational constraints for Fornax. In agreement with previous work, we find that if Fornax has a large dark-matter core then its globular clusters remain close to their currently observed locations for long times. Furthermore, we find previously unreported behaviour for clusters that start inside the core region. These are pushed out of the core and gain orbital energy, a process we call 'dynamical buoyancy'. Thus a cored mass distribution in Fornax will naturally lead to a shell-like globular cluster distribution near the core radius, independent of the initial conditions. By contrast, CDM-type cusped mass distributions lead to the rapid infall of at least one cluster within \Delta t = 1-2Gyr, except when picking unlikely initial conditions for the cluster orbits (\sim 2% probability), and almost all clusters within \Delta t = 10Gyr. Alternatively, if Fornax has only a weakly cusped mass distribution, dynamical friction is much reduced. While over \Delta t = 10Gyr this still leads to the infall of 1-4 clusters from their present orbits, the infall of any cluster within \Delta t = 1-2Gyr is much less likely (with probability 0-70%, depending on \Delta t and the strength of the cusp). Such a solution to the timing problem requires that in the past the globular clusters were somewhat further from Fornax than today; they most likely did not form within Fornax, but were accreted.
We study the optical response of nanoribbons made from the $\alpha-T_3$ lattice under a weak magnetic field in the terahertz to far-infrared regime. It is found that the magnetic field can open a gap in the band structure and induce a new absorption peak with much reduced frequency in metallic armchair ribbons and a class of zigzag ribbons with particular boundaries. This tunable magneto-optical modulation effect is attributed to the interband transitions between the flat band and the propagating bands. By contrast, this magnetic modulation of gap opening and optical conductance is much weaker in metallic armchair graphene ribbons (the case of $\alpha=0$) in which the flat band is absent. The enhancement in the $\alpha-T_3$ model is analytically investigated and explained within the perturbation theory for metallic armchair ribbons. The magnetic field induced valley degeneracy lifting and valley splitting of the absorption peak are also discussed in the case of zigzag ribbons. These findings pave the way for magneto-optics devices based on the $\alpha-T_3$ model materials.