ShantanuT01/DACTYL-Pretraining huggingface dataset:
The aim of this work is to study global $3$-webs with vanishing curvature. We wish to investigate degree $3$ foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree $3$ foliations whose Legendre transform are webs with zero curvature.
The calculation of the hadronic light-by-light scattering contribution to the muon g-2 currently relies entirely on models. Measurements of the form factors which describe the interactions of hadrons with photons can help to constrain the models and reduce the uncertainty in a_{mu}(had. LbyL) = (116 \pm 40) x 10^{-11}. In the dominant pion-exchange contribution, the form factor F_{{pi^0}^*gamma^*gamma^*}((q_1 + q_2)^2, q_1^2, q_2^2) with an off-shell pion enters. In general, measurements of the transition form factor F(Q^2) = F_{{pi^0}^*gamma^*gamma^*}(m_{pi}^2, -Q^2, 0) are only sensitive to a subset of the model parameters. Thus, having a good description for F(Q^2) is only necessary, not sufficient, to determine a_{mu}(LbyL; pi^0). Simulations have shown that measurements at KLOE-2 should be able to determine the (pi^0 -> gamma gamma) decay width to 1% statistical precision and the transition form factor for small space-like momenta, 0.01 GeV^2 < Q^2 < 0.1 GeV^2, to 6% precision. In the two-loop integral for the pion-exchange contribution the relevant regions of momenta are in the range 0 - 1.5 GeV. With the (pi^0 -> gamma gamma) decay width from the PDG [PrimEx] and current data for the transition form factor, the error on a_{mu}(LbyL; pi^0) is (\pm 4 x 10^{-11}) [\pm 2 x 10^{-11}], not taking into account the uncertainty related to the off-shellness of the pion. Including the simulated KLOE-2 data reduces the error to (\pm (0.7 - 1.1) x 10^{-11}). For models like VMD, which have only few parameters that are completely determined by measurements of F(Q^2), this represents the total error. But maybe such models are too simplistic. In other models, e.g. those based on large-N_c QCD, parameters describing the off-shell pion dominate the uncertainty in a_{mu; large-N_c}(LbyL; pi^0) = (72 \pm 12) x 10^{-11}.
We study the impact of initial-state multiple parton radiation on transverse momentum $(q_T)$ distribution of Higgs boson produced via bottom quark fusion at hadron colliders. The shape of the resulting $q_T$ distribution is affected by the bottom-quark mass corrections and by the strong kinematical behavior of the bottom-quark parton density. We account for both features in the full range of $q_T$. To do this, we formulate the resummation calculation in a general-mass factorization (S-ACOT) scheme and introduce a correction in the resummed-term to account for the effect from large-$q_T$ kinematics of Higgs boson. The results of this resummation are compared to fixed-order and PYTHIA predictions.
The conventional weak-coupling expansion for the pressure of a hot plasma shows no sign of convergence unless the the coupling constant $g$ is tiny. In this talk, I discuss screened perturbation theory (SPT) which is a reorganization of the perturbative expansion by adding and subtracting a local mass term in the Lagrangian. We consider several different mass prescriptions, and compute the pressure to three-loop order. The SPT-improved approximations appear to converge for rather large values of the coupling constant.
Most existing Convolutional Neural Networks(CNNs) used for action recognition are either difficult to optimize or underuse crucial temporal information. Inspired by the fact that the recurrent model consistently makes breakthroughs in the task related to sequence, we propose a novel Multi-Level Recurrent Residual Networks(MRRN) which incorporates three recognition streams. Each stream consists of a Residual Networks(ResNets) and a recurrent model. The proposed model captures spatiotemporal information by employing both alternative ResNets to learn spatial representations from static frames and stacked Simple Recurrent Units(SRUs) to model temporal dynamics. Three distinct-level streams learned low-, mid-, high-level representations independently are fused by computing a weighted average of their softmax scores to obtain the complementary representations of the video. Unlike previous models which boost performance at the cost of time complexity and space complexity, our models have a lower complexity by employing shortcut connection and are trained end-to-end with greater efficiency. MRRN displays significant performance improvements compared to CNN-RNN framework baselines and obtains comparable performance with the state-of-the-art, achieving 51.3% on HMDB-51 dataset and 81.9% on UCF-101 dataset although no additional data.
Recent observations by Hinode/SOT show that MHD waves and mass flows are simultaneously present in the fine structure of solar prominences. We investigate standing kink magnetohydrodynamic (MHD) waves in flowing prominence threads from a theoretical point of view. We model a prominence fine structure as a cylindrical magnetic tube embedded in the solar corona with its ends line-tied in the photosphere. The magnetic cylinder is composed of a region with dense prominence plasma, which is flowing along the magnetic tube, whereas the rest of the flux tube is occupied by coronal plasma. We use the WKB approximation to obtain analytical expressions for the period and the amplitude of the fundamental mode as functions of the flow velocity. In addition, we solve the full problem numerically by means of time-dependent simulations. We find that both the period and the amplitude of the standing MHD waves vary in time as the prominence thread flows along the magnetic structure. The fundamental kink mode is a good description for the time-dependent evolution of the oscillations, and the analytical expressions in the WKB approximation are in agreement with the full numerical results. The presence of flow modifies the period of the oscillations with respect to the static case. However, for realistic flow velocities this effect might fall within the error bars of the observations. The variation of the amplitude due to the flow leads to apparent damping or amplification of the oscillations, which could modify the real rate of attenuation caused by an additional damping mechanism.
We propose a class of random scale-free spatial networks with nested community structures and analyze Reed-Frost epidemics with community related independent transmissions. We show that the epidemic threshold may be trivial or not depending on the relation among community sizes, distribution of the number of communities and transmission rates
Segmentation is a fundamental process in microscopic cell image analysis. With the advent of recent advances in deep learning, more accurate and high-throughput cell segmentation has become feasible. However, most existing deep learning-based cell segmentation algorithms require fully annotated ground-truth cell labels, which are time-consuming and labor-intensive to generate. In this paper, we introduce Scribble2Label, a novel weakly-supervised cell segmentation framework that exploits only a handful of scribble annotations without full segmentation labels. The core idea is to combine pseudo-labeling and label filtering to generate reliable labels from weak supervision. For this, we leverage the consistency of predictions by iteratively averaging the predictions to improve pseudo labels. We demonstrate the performance of Scribble2Label by comparing it to several state-of-the-art cell segmentation methods with various cell image modalities, including bright-field, fluorescence, and electron microscopy. We also show that our method performs robustly across different levels of scribble details, which confirms that only a few scribble annotations are required in real-use cases.
We consider the ordering dynamics of the Ising model on a square lattice where an additional fixed number of bonds connect any two sites chosen randomly. The total number of shortcuts added is controlled by two parameters $p$ and $\alpha$. The structural properties of the network are investigated which show that that the small world behaviour is obtained along the line $\alpha=\frac{\ln (N/2p)}{\ln N}$, which separates regions with ultra small world like behaviour and short ranged lattice like behaviour. We obtain a rich phase diagram in the $p-\alpha$ plane showing the existence of different types of active and absorbing states to which Ising model evolves and their boundaries.
We continue the investigation of Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A special choice of U(1) embedding in SU(3) allows more general metric ansatz with five metric functions. There are two possible singular orbits in the first order system of Spin(7) instanton equation. One is the flag manifold $SU(3)/T^2$ also known as the twister space of CP(2) and the other is CP(2) itself. Imposing a set of algebraic constraints, we find a two-parameter family of exact solutions which have SU(4) holonomy and are asymptotically conical. There are two types of asymptotically locally conical (ALC) metrics in our model, which are distingushed by the choice of $S^1$ circle whose radius stabilizes at infinity. We show that this choice of M theory circle selects one of possible singular orbits mentioned above. Numerical analyses of solutions near the singular orbit and in the asymptotic region support the existence of two families of ALC Spin(7) metrics: one family consists of deformations of the Calabi hyperKahler metric, the other is a new family of metrics on a line bundle over the twister space of CP(2).
The one-neutron nuclear breakup from the Carbon isotopes $^{19}$C and $^{17}$C, is calculated as an example of application of the theory of transfer to the continuum reactions in the formulation which includes spin coupling.   The effect of the energy sharing between the parallel and transverse neutron momentum distributions is taken into account thus resulting in a theory which is more general than sudden eikonal approaches. Both effects are necessary to understand properly the breakup from not too weakly bound $l_i>1$ orbitals. Breakup which leaves the core into an excited state below particle threshold is also considered. The core-target interaction is treated in the smooth cut-off approximation. By comparing to presently available experimental data we show how to make some hypothesis on the quantum numbers and occupancy of the neutron initial state. Possible ambiguities in the interpretation of inclusive cross sections are discussed.
We identify qualitative trends in the stacking sequence dependence of carrier-carrier interaction phenomena in multilayer graphene. Our theory is based on a new approach which explicitly exhibits the important role in interaction phenomena of the momentum-direction dependent intersite phases determined by the stacking sequence. Using this method, we calculate and compare the self-energies, density--density response functions, collective modes, and ground-state energies of several different few layer graphene systems. The influence of electron--electron interactions on important electronic properties can be understood in terms of competition between intraband exchange, interband exchange and correlation contributions that vary systematically with stacking arrangement.
The coherent state model (CSM) and the triaxial rotation-vibration model (TRVM) are alternatively used to describe the ground, gamma and beta bands of 228Th. CSM is also applied to the nuclei 126Xe and 130Ba, which were recently considered in TRVM. The two models are compared with respect to both their underlying assumptions and to their predicted results for energy levels and E2 branching ratios. Both models describe energies and quadrupole transitions of 228Th equally well and in good agreement with experiment, if the 0$_3^+$ level at 1120 keV is interpreted as the head of the beta band. The other two 0$^+$ levels at 832 and 939 keV are most likely not of a pure quadrupole vibration nature as has already been pointed out in the literature.
We analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate (non-globally hyperbolic) metric. Attention is drawn to the topological constraints on solutions describing monochromatic modes on both compact and non-compact manifolds. Energy and momentum currents are constructed and a new global sum rule discussed. The results offer a rigorous background for the formulation of a field theory of topologically induced particle production.
We study two-spin entanglement and order parameter fluctuations as a function of the system size in the XY model in a transverse field and in the isotropic XXX model. Both models are characterized by the occurrence of ground state degeneracy also when systems of finite size are considered. This is always true for the XXX model, but only at the factorizing field for the XY model. We study the size dependence of symmetric states, which, in the presence of degeneracy, can be expanded as a linear combination of broken symmetry states. We show that, while the XY model looses its quantum superposition content exponentially with the size $N$, a decrease of the order of 1/N is observed when the XXX model is considered. The emergence of two qualitatively different regimes is directly related to the difference in the symmetry of the models.
We observed the Seyfert 1 galaxy NGC 985 on multiple occasions to search for variability in its UV and X-ray absorption features in order to establish their location and physical properties. We use XMM-Newton to obtain X-ray spectra using the EPIC-pn camera, and the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST) to obtain UV spectra. Our observations are simultaneous and span timescales of days to years. We find that the soft X-ray obscuration that absorbed the low energy continuum of NGC 985 in August 2013 diminished greatly by January 2015. The total X-ray column density decreased from 2.1 x 10^22 cm^-2 to ~6 x 10^21 cm^-2. We also detect broad, fast UV absorption lines in COS spectra obtained during the 2013 obscuration event. Lines of C III*, Ly alpha, Si IV and C IV with outflow velocities of -5970 km/s and a full-width at half-maximum of 1420 km/s are prominent in the 2013 spectrum, but have disappeared in all but Ly alpha in the 2015 spectra. The ionization state and the column density of the UV absorbing gas is compatible with arising in the same gas as that causing the X-ray obscuration. The high velocity of the UV-absorbing gas suggests that the X-ray obscurer and the associated UV outflow are manifestations of an accretion disk wind.
The impact of relativistic pionic correlations and meson-exchange currents on the response functions for electromagnetic quasielastic electron scattering from nuclei is studied in detail. Results in first-order perturbation theory are obtained for one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Improving upon previous analyses where non-relativistic reductions of the currents were performed, here a fully relativistic analysis in which both forces and currents are treated consistently is presented. Lorentz covariance is shown to play a crucial role in enforcing the gauge invariance of the theory. Effects stemming uniquely from relativity in the pionic correlations are identified and, in particular, a comprehensive study of the self-energy contributions and of the currents associated with the pion is presented. First- and second-kind scaling for high momentum transfer is investigated.
We prove uniform versions of two classical results in analytic number theory.   The first is an asymptotic for the number of points of a complete lattice $\Lambda \subseteq \mathbb{R}^d$ inside the $d$-sphere of radius $R$. In contrast to previous works, we obtain error terms with implied constants depending only on $d$.   Secondly, let $\phi(s) = \sum_n a(n) n^{-s}$ be a `well behaved' zeta function. A classical method of Landau yields asymptotics for the partial sums $\sum_{n < X} a(n)$, with power saving error terms. Following an exposition due to Chandrasekharan and Narasimhan, we obtain a version where the implied constants in the error term will depend only on the `shape of the functional equation', implying uniform results for families of zeta functions with the same functional equation.
We report the transport measurements on the InAs self-assembled quantum dots (SAQDs) which have a unique structural zero-dimensionality, coupled to a superconducting quantum interference device (SQUID). Owing to the SQUID geometry, we directly observe a {\pi} phase shift in the current phase relation and the negative supercurrent indicating {\pi} junction behavior by not only tuning the energy level of SAQD by back-gate but also controlling the coupling between SAQD and electrodes by side-gate. Our results inspire new future quantum information devices which can link optical, spin, and superconducting state.
It has been shown, that a magnetopolaron discrete energy spectrum is realized in the optical experiments where exciting light is directed perpendicularly to a quantum well (QW) plane. The phonon dispersion as well as Coulomb attraction can only shift the magnetopolaron discrete energy levels and broad some of them.
Issuing from a geometry with nonmetricity and torsion we build up a classical theory of gravitation and electromagnetism. The theory is coordinate covariant as well Weyl-gauge covariant. Massless and massive photons, intrinsic electr. and magn. currents exist in this framework. The field EQ-s and EQ-s of motion are derived from a geometrically based action. It is shown that the magn.-magn. interaction is transmitted by massive photons. A magn. charge (monopole) cannot be located together with an electr. one. In absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.
We consider position measurements using the cross-correlated output of two tunnel junction position detectors. Using a fully quantum treatment, we calculate the equation of motion for the density matrix of the coupled detector-detector-mechanical oscillator system. After discussing the presence of a bound on the peak-to-background ratio in a position measurement using a single detector, we show how one can use detector cross correlations to overcome this bound. We analyze two different possible experimental realizations of the cross correlation measurement and show that in both cases the maximum cross-correlated output is obtained when using twin detectors and applying equal bias to each tunnel junction. Furthermore, we show how the double-detector setup can be exploited to drastically reduce the added displacement noise of the oscillator.
The number of non-isomorphic cubic fields L sharing a common discriminant d(L) = d is called the multiplicity m = m(d) of d. For an assigned value of d, these fields are collected in a multiplet M(d) = (L(1) ,..., L(m)). In this paper, the information in all existing tables of totally real cubic number fields L with positive discriminants d(L) < 10000000 is extended by computing the differential principal factorization types tau(L) in (alpha1, alpha2, alpha3, beta1, beta2, gamma, delta1, delta2, epsilon) of the members L of each multiplet M(d) of non-cyclic fields, a new kind of arithmetical invariants which provide succinct information about ambiguous principal ideals and capitulation in the normal closures N of non-Galois cubic fields L. The classification is arranged with respect to increasing 3-class rank of the quadratic subfields K of the S3-fields N, and to ascending number of prime divisors of the conductor f of N/K. The Scholz conjecture concerning the distinguished index of subfield units (U(N) : U(0)) = 1 for ramified extensions N/K with conductor f > 1 is refined and verified.
We present a new grid of stellar model calculations for stars on the Asymptotic Giant Branch between 1.0 and 6.0 M_sun. Our grid consists of 5 chemical mixtures between Z=0.0005 and Z=0.04, with both solar-like and $\alpha$-element enhanced metal ratios. We treat consistently the carbon-enhancement of the stellar envelopes by using opacity tables with varying C/O-ratio and by employing theoretical mass loss rates for carbon stars. The low temperature opacities have been calculated specifically for this project. For oxygen stars we use an empirical mass loss formalism. The third dredge-up is naturally obtained by including convective overshooting. Our models reach effective temperatures in agreement with earlier synthetic models, which included approximative carbon-enriched molecular opacities and show good agreement with empirically determined carbon-star lifetimes. A fraction of the models could be followed into the post-AGB phase, for which we provide models in a mass range supplementing previous post-AGB calculations. Our grid constitutes the most extensive set of AGB-models, calculated with the latest physical input data and treating carbon-enhancement due to the third dredge-up most consistently.
The precise determination of the Higgs boson CP properties is among the most important goals for existing and future colliders. In this work, we evaluate existing constraints on the CP nature of the Higgs interaction with top quarks taking into account all relevant inclusive and differential Higgs boson measurements. We study the model dependence of these constraints by allowing for deviations from the SM predictions also in the Higgs couplings to massive vector boson, photons, and gluons. Additionally, we evaluate the future prospects for constraining the CP nature of the top-Yukawa coupling by total rate measurements. In this context, we propose an analysis strategy for measuring tH production at the HL-LHC without relying on assumptions about the Higgs CP character.
In this note, motivated by our work on integral fully nonlinear equations, we provide a variation of the proof of Evans-Krylov theorem about the interior $C^{2,\alpha}$ a priori estimate for concave fully nonlinear elliptic equations. The proof we present is shorter compared to the original proofs, although the key tools used in the argument are the same.
We have used data taken as part of the Herschel infrared Galactic Plane survey (Hi-GAL) to study 3171 infrared-dark cloud (IRDC) candidates that were identified in the mid-infrared (8 {\mu}m) by Spitzer (we refer to these as 'Spitzer-dark' regions). They all lie in the range l=300 - 330 \circ and |b| 6 1 \circ. Of these, only 1205 were seen in emission in the far-infrared (250-500 {\mu}m) by Herschel (we call these 'Herschel-bright' clouds). It is predicted that a dense cloud will not only be seen in absorption in the mid-infrared, but will also be seen in emission in the far-infrared at the longest Herschel wavebands (250-500 {\mu}m). If a region is dark at all wavelengths throughout the mid-infrared and far-infrared, then it is most likely to be simply a region of lower background infrared emission (a 'hole in the sky'). Hence, it appears that previous surveys, based on Spitzer and other mid-infrared data alone, may have over-estimated the total IRDC population by a factor of 2. This has implications for estimates of the star formation rate in IRDCs in the Galaxy.We studied the 1205 Herschel-bright IRDCs at 250 {\mu}m, and found that 972 of them had at least one clearly defined 250-{\mu}m peak, indicating that they contained one or more dense cores. Of these, 653 (67 per cent) contained an 8-{\mu}m point source somewhere within the cloud, 149 (15 per cent) contained a 24-{\mu}m point source but no 8-{\mu}m source, and 170 (18 per cent) contained no 24-{\mu}m or 8-{\mu}m point sources. We use these statistics to make inferences about the lifetimes of the various evolutionary stages of IRDCs.