ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate two Stieltjes continued fractions given by the paperfolding sequence and the Rudin-Shapiro sequence. By explicitly describing certain subsequences of the convergents $P_n(x)/Q_n(x)$ modulo $4$, we give the formal power series expansions (modulo $4$) of these two continued fractions and prove that they are congruent modulo $4$ to algebraic series in $\mathbb{Z}[[x]]$. Therefore, the coefficient sequences of the formal power series expansions are $2$-automatic. Write $Q_{n}(x)=\sum_{i\ge 0}a_{n,i}x^{i}$. Then $(Q_{n}(x))_{n\ge 0}$ defines a two-dimensional coefficient sequence $(a_{n,i})_{n,i\ge 0}$. We prove that the coefficient sequences $(a_{n,i}\mod 4)_{n\ge 0}$ introduced by both $(Q_{n}(x))_{n\ge 0}$ and $(P_{n}(x))_{n\ge 0}$ are $2$-automatic for all $i\ge 0$. Moreover, the pictures of these two dimensional coefficient sequences modulo $4$ present a kind of self-similar phenomenon.
In the conventional ghost imaging (GI), the image is retrieved by correlating the reference intensity fluctuation at a charge-coupled device (CCD) with the signal intensity fluctuation at a bucket detector. In this letter, we present the protocol of GI, it is called Second-order Cumulants ghost imaging (SCGI). The image is retrieved by the fluctuation information of correlating intensity fluctuation at two detectors, and the resolution limit can be enhanced than conventional GI. The experimental results of SCGI agreement with theoretical results.
Let $p$ be a prime number. Consider the injection \[   \iota:\mathbb{Z}/n\mathbb{Z}\to\mathbb{Z}/pn\mathbb{Z}:x\mapsto px,   \] and the elements $e^{u}.v:=(u,v)\in \mathbb{Z}/n\mathbb{Z}\rtimes \mathbb{Z}/n\mathbb{Z}^{\times}$ and $e^{w}.r:=(w,r)\in \mathbb{Z}_{p n}\rtimes \mathbb{Z}_{p n}^{\times}$. Suppose $e^{u}.v\in \mathbb{Z}/n\mathbb{Z}\rtimes \mathbb{Z}/n\mathbb{Z}^{\times}$ is seen as an automorphism of $\mathbb{Z}/n\mathbb{Z}$ by $e^{u}.v(x)=vx+u$; then $e^{u}.v$ is a quasipolarity if it is an involution without fixed points. In this brief note give an explicit formula for the number of quasipolarites of $\mathbb{Z}/n\mathbb{Z}$ in terms of the prime decomposition of $n$, and we prove sufficient conditions such that $(e^{w}.r)\circ \iota =\iota\circ (e^{u}.v)$, where $e^{w}.r$ and $e^{u}.v$ are quasipolarities.
Of all the activity observed on the Sun, two of the most energetic events are flares and Coronal Mass Ejections (CMEs). Usually, solar active regions that produce large flares will also produce a CME, but this is not always true (Yashiro et al., 2005). Despite advances in numerical modeling, it is still unclear which circumstances will produce a CME (Webb & Howard, 2012). Therefore, it is worthwhile to empirically determine which features distinguish flares associated with CMEs from flares that are not. At this time, no extensive study has used physically meaningful features of active regions to distinguish between these two populations. As such, we attempt to do so by using features derived from [1] photospheric vector magnetic field data taken by the Solar Dynamics Observatory's Helioseismic and Magnetic Imager instrument and [2] X-ray flux data from the Geostationary Operational Environmental Satellite's X-ray Flux instrument. We build a catalog of active regions that either produced both a flare and a CME (the positive class) or simply a flare (the negative class). We then use machine-learning algorithms to [1] determine which features distinguish these two populations, and [2] forecast whether an active region that produces an M- or X-class flare will also produce a CME. We compute the True Skill Statistic, a forecast verification metric, and find that it is a relatively high value of approximately 0.8 plus or minus 0.2. We conclude that a combination of six parameters, which are all intensive in nature, will capture most of the relevant information contained in the photospheric magnetic field.
In ESO period 65 (April-September 2000) the large programme 165.N-0276, led by Roger Cayrel, began making use of UVES at the Kueyen VLT telescope. Known within the Team and outside as ``First Stars'', it was aimed at obtaining high resolution, high signal-to-noise ratio spectra in the range 320 nm -- 1000 nm for a large sample of extremely metal-poor (EMP) stars identified from the HK objective prism survey.In this contribution we highlight the main results of the large programme.
A period-metallicity relation for oxygen-rich Miras derived from globular clusters is applied to similar variables in the galactic Bulge. The metallicity distribution in the Bulge thus obtained is in good agreement with that derived from K giants. This suggests that the periods of Miras are useful indicators of metallicity distributions, at least in old systems such as galactic bulges. For systems such as the LMC the situation is not yet clear.
The 2MASS, UKIDSS-LAS and VISTA VIKING surveys have all now observed the GAMA 9hr region in the $K_s$ band. Here we compare the detection rates, photometry, basic size measurements, and single-component GALFIT structural measurements for a sample of 37,591 galaxies. We explore the sensitivity limits where the data agree for a variety of issues including: detection, star-galaxy separation, photometric measurements, size and ellipticity measurements, and S\'{e}rsic measurements. We find that 2MASS fails to detect at least 20% of the galaxy population within all magnitude bins, however for those that are detected we find photometry is robust ($\pm$ 0.2 mag) to 14.7 AB mag and star-galaxy separation to 14.8 AB mag. For UKIDSS-LAS we find incompleteness starts to enter at a flux limit of 18.9 AB mag, star-galaxy separation is robust to 16.3 AB mag and structural measurements are robust to 17.7 AB mag. VISTA VIKING data is complete to approximately 20.0 AB mag and structural measurements appear robust to 18.8 AB mag.
We compare the variability properties of very high energy gamma-ray emitting BL Lac objects in the optical and radio bands. We use the variability information to distinguish multiple emission components in the jet, to be used as a guidance for spectral energy distribution modelling. Our sample includes 32 objects in the Northern sky that have data for at least 2 years in both bands. We use optical R-band data from the Tuorla blazar monitoring program and 15 GHz radio data from the Owens Valley Radio Observatory blazer monitoring program. We estimate the variability amplitudes using the intrinsic modulation index, and study the time-domain connection by cross-correlating the optical and radio light curves assuming power law power spectral density. Our sample objects are in general more variable in the optical than radio. We find correlated flares in about half of the objects, and correlated long-term trends in more than 40% of the objects. In these objects we estimate that at least 10%-50% of the optical emission originates in the same emission region as the radio, while the other half is due to faster variations not seen in the radio. This implies that simple single-zone spectral energy distribution models are not adequate for many of these objects.
We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main properties are presented, the associated Wigner function is calculated and its properties are discussed. It is shown that the angle probability density obtained from the Wigner function is a well-behaved function defined in the interval [-Pi,Pi), while the action probability only assumes integer values greater or equal than zero. It is emphasized the fact that the width of the angle probability density is governed by the free parameter q characterizing the polynomial.
The role of thermodynamics in the evolution of systems evolving under purely gravitational forces is not completely established. Both the infinite range and singularity in the Newtonian force law preclude the use of standard techniques. However, astronomical observations of globular clusters suggests that they may exist in distinct thermodynamic phases. Here, using dynamical simulation, we investigate a model gravitational system which exhibits a phase transition in the mean field limit. The system consists of rotating, concentric, mass shells of fixed angular momentum magnitude and shares identical equilibrium properties with a three dimensional point mass system satisfying the same condition. The mean field results show that a global entropy maximum exists for the model, and a first order phase transition takes place between "quasi-uniform" and ''core-halo'' states, in both the microcanonical and canonical ensembles. Here we investigate the evolution and, with time averaging, the equilibrium properties of the isolated system. Simulations were carried out in the transition region, at the critical point, and in each clearly defined thermodynamic phase, and striking differences were found in each case. We find full agreement with mean field theory when finite size scaling is accounted for. In addition, we find that (1) equilibration obeys power law behavior, (2) virialization, equilibration, and the decay of correlations in both position and time, are very slow in the transition region, suggesting the system is also spending time in the metastable phase, (3) there is strong evidence of long-lived, collective, oscillations in the supercritical region.
We construct a model for the formation of black holes within galactic bulges. The initial state is a slowly rotating isothermal sphere, characterized by effective transport speed $\aeff$ and rotation rate $\Omega$. The black hole mass is determined when the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole. This model reproduces the observed correlation between black hole masses and galactic velocity dispersions, $\mbh \approx 10^8 M_\odot (\sigma/200 \kms)^4$, where $\sigma = \sqrt{2} \aeff$. This model also predicts the ratio $\mrat$ of black hole mass to host mass: $\mrat$ $\approx$ 0.004 $(\sigma/200 \kms)$.
The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a unique determination of the probability distribution (called {\rm SRB} distribution on phase space providing the time averages of the observables. It also implies an expression for a few averages concrete enough to derive consequences of symmetry properties like the fluctuation theorem or to formulate a theory of coarse graining unifying the foundations of equilibrium and of nonequilibrium.
Hydrodynamic equations (HDEQs) are derived which describe spatio-temporal evolutions of the electron temperature and the chemical potential of two-dimensional systems in strong magnetic fields in states with large diagonal resistivity appearing at the breakdown of the quantum Hall effect. The derivation is based on microscopic electronic processes consisting of drift motions in a slowly-fluctuating potential and scattering processes due to electron-electron and electron-phonon interactions. In contrast with the usual HDEQs, one of the derived HDEQs has a term with an energy flux perpendicular to the electric field due to the drift motions in the magnetic field. As an illustration, the current distribution is calculated using the derived HDEQs.
An elementary recursive model accounting for the quark spin in the fragmentation of a quark into mesons is presented. The quark spin degree of freedom is represented by a two-components spinor. Spin one meson can be included. The model produces Collins effect and jet handedness. The influence of the initial quark polarisation decays exponentially with the rank of the meson, at dierent rates for longitudinal and transverse polarisations
Electronic control of blackbody emission from graphene plasmonic resonators on a silicon nitride substrate is demonstrated at temperatures up to 250 C. It is shown that the graphene resonators produce antenna-coupled blackbody radiation, manifest as narrow spectral emission peaks in the mid-IR. By continuously varying the nanoresonators carrier density, the frequency and intensity of these spectral features can be modulated via an electrostatic gate. We describe these phenomena as plasmonically enhanced radiative emission originating both from loss channels associated with plasmon decay in the graphene sheet and from vibrational modes in the SiNx.
The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large $k$ are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger $m$ and $k$, showing that for $k \geq 7 $, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.
We selected cepheids from the OGLE database for the Magellanic Clouds in the period range 10^{1.1} < P < 10^{1.4} days. There were 33 objects in the LMC and 35 in the SMC. We find that the median amplitude of cepheids in the LMC is 18% larger than in the SMC, a 4 sigma effect. This implies that the period - flux amplitude relation is not universal, and cannot be used to measure distances accurately.
The nonabelian Jacobian $\JA$ of a smooth projective surface $X$ is inspired by the classical theory of Jacobian of curves. It is built as a natural scheme interpolating between the Hilbert scheme $\XD$ of subschemes of length $d$ of $X$ and the stack ${\bf M}_X (2,L,d)$ of torsion free sheaves of rank 2 on $X$ having the determinant $\OO_X (L)$ and the second Chern class (= number) $d$. It relates to such influential ideas as variations of Hodge structures, period maps, nonabelian Hodge theory, Homological mirror symmetry, perverse sheave, geometric Langlands program.   These relations manifest themselves by the appearance of the following structures on $\JA$:   1) a sheaf of reductive Lie algebras,   2) (singular) Fano toric varieties whose hyperplane sections are (singular) Calabi-Yau varieties,   3) trivalent graphs.   This is an expository paper giving an account of most of the main properties of $\JA$ uncovered in [R1] and [R2].
We present improved post-Newtonian-inspired initial data for non-spinning black-hole binaries, suitable for numerical evolution with punctures. We revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining integral terms. These terms improve accuracy in the far zone and, for the first time, include realistic gravitational waves in the initial data. We investigate the behavior of these data both at the center of mass and in the far zone, demonstrating agreement of the transverse-traceless parts of the new metric with quadrupole-approximation waveforms. These data can be used for numerical evolutions, enabling a direct connection between the merger waveforms and the post-Newtonian inspiral waveforms.
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very small integration time step is required, which can severely impact the simulation run-time. Here, we introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation's run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e., distributions of the first waiting time). Here, we consider two ensembles: the equilibrium and a typical non-equilibrium ensembles. For both ensembles, it is shown that the time-averaged mean square displacement (TAMSD) exhibits a crossover from normal to anomalous diffusion due to the spacial confinement and this crossover does not vanish even in the long measurement time limit. Moreover, for the non-equilibrium ensemble, we show that the probability density function of the diffusion constant of TAMSD follows the transient Mittag-Leffler distribution, and that scatter in the TAMSD shows a clear transition from weak ergodicity breaking (an irreproducible regime) to ordinary ergodic behavior (a reproducible regime) as the measurement time increases. This convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution; in other words, the weak ergodicity breaking persists for a long time. In addition, it is shown that, besides the TAMSD, a class of observables also exhibits this slow convergence to ergodicity. We also point out that, even though the system with the equilibrium initial ensemble shows no aging, its behavior is quite similar to that for the non-equilibrium ensemble.
We examine the dynamical behavior of white light polar plume structures in the inner corona that are observed from the ground during total solar eclipses, based on their EUV hot and cool emission line counterparts observed from space. EUV observations from SDO/AIA of a sequence of rapidly varying coronal hole structures are analyzed. Evidence of events showing acceleration in the 1.25 Mk line of Fe XII at 193 A is given. The structures along the plume show an outward velocity of about 140 kms-1 that can be interpreted as an upwards propagating wave in the 304 A and 171 A lines; higher speeds are seen in 193 A (up to 1000 km/s). The ejection of the cold He II plasma is delayed by about 4 min in the lowest layer and more than 12 min in the highest level compared to the hot 193 A behavior. A study of the dynamics using time-slice diagrams reveals that a large amount of fast ejected material originates from below the plume, at the footpoints. The release of plasma material appears to come from a cylinder with quasi-parallel edge-enhanced walls. After the initial phase of a longitudinal acceleration, the speed substantially reduces and the ejecta disperse into the environment. Finally, the detailed temporal and spatial relationships between the cool and hot components were studied with simultaneous multi-wavelength observations, using more AIA data. The outward-propagating perturbation of the presumably magnetic walls of polar plumes supports the suggestion that Alfven waves propagate outwardly along these radially extended walls.
We report the MAXI observation of the gravitational-wave (GW) event GW170817 and the electromagnetic counterpart of GW170817. GW170817 is a binary neutron star coalescence candidate detected by the Advanced LIGO and Advanced Virgo detectors, and it is the first event for which the optical counterpart has been discovered. In the MAXI observation, the Gas Slit Camera (GSC) covered approximately 62% of the sky region of the GW event within 90% probability during the first 92 min of orbit after the trigger. No significant X-ray transient was detected in the error region, and the upper limit of the average flux with a significance of 3 $\sigma$ in the 2--10 keV band was 53/26 mCrab (one-orbit observation/one-day observation). In the optical counterpart of GW170817, the observational window of GSC at the position started at 20 s after the GW trigger, but the high voltage of GSC was unfortunately off at the time because the ISS was entering a high-particle-background region. The first observation of the position by GSC was eventually performed at 16797 sec (4.6 hours) since the GW trigger, yielding the 3 $\sigma$ upper limit of 8.60$\times$10$^{-9}$ erg cm$^{-2}$ s$^{-1}$ in the 2--10 keV band, though it was the earliest X-ray observation of the counterpart.
The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wave equation are related to those for a corresponding Schr\"odinger equation in the sense that all the potentials derived for the latter equation are also applicable for the wave equation under consideration. We show that in contrast to the Schr\"odinger equation the characteristic spatial length of the potential imposes a restriction on the energy spectrum that directly reflects the uncertainty principle. Studying the inverse-square-root bi-confluent Heun potential, it is shown that the uncertainty principle limits, from below, the principal quantum number for the bound states, i.e., physically feasible states have an infimum cut so that the ground state adopts a higher quantum number as compared to the Schr\"odinger case.
We consider quantum phase transitions out of topological Mott insulators in which the ground state of the fractionalized excitations (fermionic spinons) is topologically non-trivial. The spinons in topological Mott insulators are coupled to an emergent compact U(1) gauge field with a so-called "axion" term. We study the confinement transitions from the topological Mott insulator to broken symmetry phases, which may occur via the condensation of dyons. Dyons carry both "electric" and "magnetic" charges, and arise naturally in this system because the monopoles of the emergent U(1) gauge theory acquires gauge charge due to the axion term. It is shown that the dyon condensate, in general, induces simultaneous current and bond orders. To demonstrate this, we study the confined phase of the topological Mott insulator on the cubic lattice. When the magnetic transition is driven by dyon condensation, we identify the bond order as valence bond solid order and the current order as scalar spin chirality order. Hence, the confined phase of the topological Mott insulator is an exotic phase where the scalar spin chirality and the valence bond order coexist and appear via a single transition. We discuss implications of our results for generic models of topological Mott insulators.
We give a superfield formulation of the path integral on an arbitrary curved phase space, with or without first class constraints. Canonical tranformations and BRST transformations enter in a unified manner. The superpartners of the original phase space variables precisely conspire to produce the correct path integral measure, as Pfaffian ghosts. When extended to the case of second-class constraints, the correct path integral measure is again reproduced after integrating over the superpartners. These results suggest that the superfield formulation is of first-principle nature.