ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present Faraday Rotation Measure (RM) properties of seven active galactic nuclei (AGN), observed with the NRAO VLA at three epochs in 2012-2014. Data was taken at 1.4, 2.2, 5.0, 8.2, 15.4, 22.4, 33.5 and 43.1 GHz quasi simultaneously in full polarization mode. For the first time RMs were calculated in a range of wavelengths covering more than one order of magnitude: from 21 cm up to 6 mm. We measured RM for each source and showed a tendency to increase its value toward high frequencies according to the law |RM|~f^a with a=1.6+/-0.1. For 0710+439, we observed an increase over the frequency range of 4 orders of magnitude and measured one of the highest RM ever, (-89+/-1)*10^3 rad/m^2. Analysis of different epochs shows variations of the value and the sign of RM on short and long time-scales. This may be caused by changing physical conditions in the compact regions of the AGN jets, e.g. strength of magnetic field, particle density and so on.
In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given. We state a conjectured solution, which is an analog of the Brualdi- Hoffman conjecture for general graphs, and prove the conjecture in some special cases.
A new functional for the entropy that is asymptotically correct both in the high and low density limits is proposed. The new form is [ S=S^{(id)}+S^{(ln)}+S^{(r)}+S^{(c)} ] where the new term S^{(c)} depends on the p-bodies density fluctuations $\alpha_p$ and has the form [ S^{(c)}= <N> {ln 2-1+\sum_{p=2}^\infty \frac{(\ln 2) ^p}{p!}\alpha_p-[ \exp (\alpha_2-1)-\alpha_2]} +\hat S ], where $\hat S$ renormalizes the ring approximation S^{(r)}. This result is obtained by analyzing the functional dependence of the most general expression of the entropy: Two main results for S^{(c)} are proven: i) In the thermodynamic limit, only the functional dependence on the one body distribution function survives and ii) by summing to infinite order the leading contributions in the density a new numerical expression for the entropy is proposed with a new renormalized ring approximation included. The relationship of these results to the incompressible approximation to entropy is discussed.
We prove that there exist infinite families of regular bipartite Ramanujan graphs of every degree bigger than 2. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph.   We also establish the existence of infinite families of `irregular Ramanujan' graphs, whose eigenvalues are bounded by the spectral radius of their universal cover. Such families were conjectured to exist by Linial and others. In particular, we prove the existence of infinite families of (c,d)-biregular bipartite graphs with all non-trivial eigenvalues bounded by sqrt{c-1}+sqrt{d-1}, for all c, d \geq 3.   Our proof exploits a new technique for demonstrating the existence of useful combinatorial objects that we call the "method of interlacing polynomials'".
We report field- and current-induced domain wall (DW) depinning experiments in Ta/Co20Fe60B20/MgO nanowires through a Hall cross geometry. While purely field-induced depinning shows no angular dependence on in-plane fields, the effect of the current depends crucially on the internal DW structure, which we manipulate by an external magnetic in-plane field. We show for the first time depinning measurements for a current sent parallel to the DW and compare its depinning efficiency with the conventional case of current flowing perpendicularly to the DW. We find that the maximum efficiency is similar for both current directions within the error bars, which is in line with a dominating damping-like spin-orbit torque (SOT) and indicates that no large additional torques arise for currents parallel to the DW. Finally, we find a varying dependence of the maximum depinning efficiency angle for different DWs and pinning levels. This emphasizes the importance of our full angular scans compared to previously used measurements for just two field directions (parallel and perpendicular to the DW) and shows the sensitivity of the spin-orbit torque to the precise DW structure and pinning sites.
Measurements of specific heat between 80 mK to 4 K and electrical resistivity between 80 mK to 10 K were carried out for polycrystalline CePt3Si samples cut into small pieces (typically $\sim $10 mg). In the specific heat measurements, we observed an antiferromagnetic transition jump at TN = 2.2 K for all the samples, while the heights have large variations. As regards superconductivity, we observed two distinct transition jumps at Tcl $\sim$ 0.45 K and Tch $\sim$ 0.75 K, which were the same for all the samples. From the measurements of specific heat and resistivity, systematic relations were found between antiferromagnetic and superconducting transitions. We conclude that antiferromagnetism, whose transition temperature is 2.2 K, coexists with superconductivity, whose transition temperature is Tcl. In this sample, residual electronic specific heat coefficient in the superconducting state $\gamma_{\rm s}$ was quite small, and specific heat divided by temperature below Tcl decreased almost linearly with decreasing temperature. In order to reveal the characteristic properties of the magnetism and superconductivity of the CePt3Si system, it is important to study the two superconducting phases with Tcl and Tch, respectively.
In this article, we provide a short and elementary proof of the following result: For $n \geq 3$ the middle coefficient of $\Phi_n(x)$ is either zero (when $n$ is a power of $2$) or an odd integer.
We use the W_Ha versus [NII]/Ha (WHAN) diagram to provide a comprehensive emission-line classification of SDSS galaxies. This classification is able to cope with the large population of weak line galaxies that do not appear in traditional diagrams due to a lack of some of the diagnostic lines. A further advantage of the WHAN diagram is to allow the differentiation between two very distinct classes that overlap in the LINER region of traditional diagnostic diagrams. These are galaxies hosting a weakly active nucleus (wAGN) and "retired galaxies" (RGs), i.e. galaxies that have stopped forming stars and are ionized by their hot evolved low-mass stars. A useful criterion to distinguish true from fake AGN (i.e. the RGs) is the ratio (\xi) of the extinction-corrected L_Ha with respect to the Ha luminosity expected from photoionization by stellar populations older than 100 Myr. This ratio follows a markedly bimodal distribution, with a \xi >> 1 population composed by systems undergoing star-formation and/or nuclear activity, and a peak at \xi ~ 1 corresponding to the prediction of the RG model. We base our classification scheme on the equivalent width of Ha, an excellent observational proxy for \xi. Based on the bimodal distribution of W_Ha, we set the division between wAGN and RGs at W_Ha = 3 A. Five classes of galaxies are identified within the WHAN diagram: (a) Pure star forming galaxies: log [NII]/Ha < -0.4 and W_Ha > 3 A. (b) Strong AGN (i.e., Seyferts): log [NII]/Ha > -0.4 and W_Ha > 6 A. (c) Weak AGN: log [NII]/Ha > -0.4 and W_Ha between 3 and 6 A. (d) RGs: W_Ha < 3 A. (e) Passive galaxies (actually, line-less galaxies): W_Ha and W_[NII] < 0.5 A. A comparative analysis of star formation histories and of other properties in these different classes of galaxies corroborates our proposed differentiation between RGs and weak AGN in the LINER-like family. (Abridged)
We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures under simple assumptions. Hence, the convergence problem is not classical like in the convex case. By using the method in Benedetto et al. [J. Statist. Phys. 91 (1998) 1261-1271] about the monotonicity of the free-energy, and combining this with a complete description of the set of the stationary measures, we prove the global convergence of the self-stabilizing processes.
Rational double points are the simplest surface singularities. In this essay we will be mainly concerned with the geometry of the exceptional set corresponding to the resolution of a rational double point. We will derive the classification of rational double points in terms of Dynkin diagrams.
In these lectures several aspects of anyon in one and two dimensions are considered from the path integral formalism. This paper is based in a set of four lectures given by the author in the "V Latinoamerican Workshop of Particles and Fields, hel in Puebla, Mexico.
For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted by $\nu_{p}(x)$. For a polynomial $Q$ with integer coefficients, the sequence of valuations $\nu_{p}(Q(n))$ is shown to be either periodic or unbounded. The first case corresponds to the situation where $Q$ has no roots in the ring of $p$-adic integers. In the periodic situation, the period length is determined.
We analyse the out of equilibrium behavior of an Ising spin chain with an asymmetric kinetic constraint after a quench to a low temperature T. In the limit T\to 0, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a `glassy' divergence \teq=\exp(const/T^2) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature dependent exponent, \dbar ~ t^{T\ln 2}. We show that the equilibration time \teq also sets the timescale for the linear response of the system at low temperatures.
We give another bijective proof of a result of Corteel and Nadeau. We find a generating function related to unrestricted columns of permutation tableaux. As a consequence, we obtain a sign-imbalance formula for permutation tableaux. We extend the first bijection of Corteel and Nadeau between permutations and permutation tableaux to type $B$ objects. Using this type $B$ bijection, we generalize a result of Lam and Williams. We prove that the bijection of Corteel and Nadeau and our type $B$ bijection can be expressed as zigzag maps on the alternative representation.
The mechanism of $p^3$He backward elastic scattering is studied.   It is found that the triangle diagrams with the subprocesses $pd\to ^3$He$ \pi^0$,   $pd^*\to ^3$He$ \pi^0$ and $p(pp)\to^3$He$ \pi^+$, where $d^*$ and $pp$ denote the singlet deuteron and diproton pair in the $^1S_0$ state, respectively, dominate in the cross section at 0.3-0.8 GeV, and their contribution is comparable with that for a sequential transfer of a $np$ pair at 1-1.5 GeV.   The contribution of the $d^*+pp$, estimated on the basis of the spectator mechanism of the $p(NN)\to ^3$He$ \pi$ reaction, increases the $p^3$He$\to ^3$He$ p$ cross section by one order of magnitude as compared to the contribution of the deuteron alone.   Effects of the initial and final states interaction are taken into account.
Various lattice path models are reviewed. The enumeration is done using generating functions. A few bijective considerations are woven in as well. The kernel method is often used. Computer algebra was an essential tool. Some results are new, some have appeared before.   The lattice path models we treated, are: Hoppy's walks, the combinatorics of sequence A002212 in \cite{OEIS} (skew Dyck paths, Schr\"oder paths, Hex-trees, decorated ordered trees, multi-edge trees, etc.) Weighted unary-binary trees also occur, and we could improve on our old paper on Horton-Strahler numbers \cite{FlPr86}, by using a different substitution. Some material on ternary trees appears as well, as on Motzkin numbers and paths (a model due to Retakh), and a new concept called amplitude that was found in \cite{irene}. Some new results on Deutsch paths in a strip are included as well. During the Covid period, I spent much time with this beautiful concept that I dare to call Deutsch paths, since Emeric Deutsch stands at the beginning with a problem that he posted in the American Mathematical Monthly some 20 years ago. Peaks and valleys, studied by Rainer Kemp 40 years under the names \textsc{max}-turns and \textsc{min}-turns, are revisited with a more modern approach, streamlining the analysis, relying on the `subcritical case' (named so by Philippe Flajolet), the adding a new slice technique and once again the kernel method.
In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions.
We investigate a new problem of detecting hands and recognizing their physical contact state in unconstrained conditions. This is a challenging inference task given the need to reason beyond the local appearance of hands. The lack of training annotations indicating which object or parts of an object the hand is in contact with further complicates the task. We propose a novel convolutional network based on Mask-RCNN that can jointly learn to localize hands and predict their physical contact to address this problem. The network uses outputs from another object detector to obtain locations of objects present in the scene. It uses these outputs and hand locations to recognize the hand's contact state using two attention mechanisms. The first attention mechanism is based on the hand and a region's affinity, enclosing the hand and the object, and densely pools features from this region to the hand region. The second attention module adaptively selects salient features from this plausible region of contact. To develop and evaluate our method's performance, we introduce a large-scale dataset called ContactHands, containing unconstrained images annotated with hand locations and contact states. The proposed network, including the parameters of attention modules, is end-to-end trainable. This network achieves approximately 7\% relative improvement over a baseline network that was built on the vanilla Mask-RCNN architecture and trained for recognizing hand contact states.
The projected electrostatic potential of a thick crystal is reconstructed at atomic-resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast- readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin ($\lesssim 50$ {\AA}) samples. Instruments already coming on-line can overcome the remaining resolution-limiting effects in this method due to finite probe-forming aperture size, spatial incoherence and residual lens aberrations.
This article presents a semantic tracker which simultaneously tracks a single target and recognises its category. In general, it is hard to design a tracking model suitable for all object categories, e.g., a rigid tracker for a car is not suitable for a deformable gymnast. Category-based trackers usually achieve superior tracking performance for the objects of that specific category, but have difficulties being generalised. Therefore, we propose a novel unified robust tracking framework which explicitly encodes both generic features and category-based features. The tracker consists of a shared convolutional network (NetS), which feeds into two parallel networks, NetC for classification and NetT for tracking. NetS is pre-trained on ImageNet to serve as a generic feature extractor across the different object categories for NetC and NetT. NetC utilises those features within fully connected layers to classify the object category. NetT has multiple branches, corresponding to multiple categories, to distinguish the tracked object from the background. Since each branch in NetT is trained by the videos of a specific category or groups of similar categories, NetT encodes category-based features for tracking. During online tracking, NetC and NetT jointly determine the target regions with the right category and foreground labels for target estimation. To improve the robustness and precision, NetC and NetT inter-supervise each other and trigger network adaptation when their outputs are ambiguous for the same image regions (i.e., when the category label contradicts the foreground/background classification). We have compared the performance of our tracker to other state-of-the-art trackers on a large-scale tracking benchmark (100 sequences)---the obtained results demonstrate the effectiveness of our proposed tracker as it outperformed other 38 state-of-the-art tracking algorithms.
The thermal conductivities k of wurtzite InxGa1-xN are investigated using equilibrium molecular dynamics (MD) method. The k of InxGa1-xN rapidly declines from InN (k_InN = 141 W/mK) or GaN (k_GaN = 500 W/mK) to InxGa1-xN, and reaches a minimum (k_min = 19 W/mK) when x is around 0.5 at 300 K. The mean free path (MFP) of InxGa1-xN, ranging from 2 to 5 nm and following the same trend with the k, is extrapolated in our simulation and a parabolic relationship between x and MFP is established. We find that the k of InxGa1-xN decreases with increasing temperatures. The evolution of k of InxGa1-xN is also examined by projecting the momentum-energy relationship of phonons from MD trajectories. The phonon dispersion and phonon density of states for InxGa1-xN reflect a slightly more flattened dispersive phononic curve of the alloying system. Despite an overestimated k than experimental values, our calculated k at 300 K agrees well with the results obtained by solving Boltzmann transport equation and also has the same stoichiometric trend with the experimental data. Our study provides the coherent analysis of the effect of thickness, temperature and stoichiometric content on the thermal transport of InxGa1-xN which is helpful for the thermal management of InxGa1-xN based devices.
We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147,000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts $0.8 < z < 2.2$ and measure their spherically-averaged clustering in both configuration and Fourier space. Our observational dataset and the 1400 simulated realizations of the dataset allow us to detect a preference for BAO that is greater than 2.8$\sigma$. We determine the spherically averaged BAO distance to $z = 1.52$ to 3.8 per cent precision: $D_V(z=1.52)=3843\pm147 \left(r_{\rm d}/r_{\rm d, fid}\right)\ $Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flat $\Lambda$CDM best-fit cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find $\Omega_{\Lambda} > 0$ at 6.6$\sigma$ significance when testing a $\Lambda$CDM model with free curvature.
We perform first-principles calculations of the quasiparticle defect states, charge transition levels, and formation energies of oxygen vacancies in rutile titanium dioxide. The calculations are done within the recently developed combined DFT+GW formalism, including the necessary electrostatic corrections for the supercells with charged defects. We find the oxygen vacancy to be a negative U defect, where U is the defect electron addition energy. For the values of Fermi level below 2.8 eV (relative to the valence band maximum) we find the +2 charge state of the vacancy to be the most stable, while above 2.8 eV we find that the neutral charge state is the most stable.
We compute the expected neutrino fluence from SGRB 170817A, associated with the gravitational wave event GW 170817, directly based on Fermi observations in two scenarios: structured jet and off-axis (observed) top-hat jet. While the expected neutrino fluence for the structured jet case is very small, large off-axis angles imply high radiation densities in the jet, which can enhance the neutrino production efficiency. In the most optimistic allowed scenario, the neutrino fluence can reach only $10^{-4}$ of the sensitivity of the neutrino telescopes. We furthermore demonstrate that the fact that gamma-rays can escape limits the baryonic loading (energy in protons versus photons) and the off-axis angle for the internal shock scenario. In particular, for a baryonic loading of ten, the off-axis angle is more strongly constrained by the baryonic loading than by the time delay between the gravitational wave event and the onset of the gamma-ray emission.
We report Electron Spin Resonance (ESR) measurements on stage-I potassium intercalated graphite (KC$_8$). Angular dependent measurements show that the spin-lattice relaxation time is longer when the magnetic field is perpendicular to the graphene layer as compared to when the magnetic field is in the plane. This anisotropy is analyzed in the framework of the Elliott-Yafet theory of spin-relaxation in metals. The analysis considers an anisotropic spin-orbit Hamiltonian and the first order perturbative treatment of Elliott is reproduced for this model Hamiltonian. The result provides an experimental input for the first-principles theories of spin-orbit interaction in layered carbon and thus to a better understanding of spin-relaxation phenomena in graphene and in other layered materials as well.
Stimulated by recent experimental observation of $X_1(2900)$ just below the $\bar D_1K$ threshold, we extend our previous study of $\bar D_1D$ S-wave bound state by vector meson exchange to $\bar D_1K$ system as well as similar $\bar DK_1$, $D_1K$ and $DK_1$ systems to look for possible bound states. We find that the potential of $D K_1$ is attractive and strong enough to form bound states with mass around 3110 MeV for $DK_1(1270)$ and 3240 MeV for $DK_1(1400)$. $D_1 K$ is also attractive but weaker, hardly enough to form bound states. While $\bar DK_1$ becomes further less attractive, the potential between $\bar D_1 K$ is the weakest, definitely too weak to form any bound state, which excludes the recently observed $X_1(2900)$ to be a $\bar D_1 K$ bound state. We also give the decay properties of the predicted $D K_1$ bound states.
We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model. The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation. In this paper, we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation, extended from an earlier result on a special case.