ShantanuT01/DACTYL-Pretraining huggingface dataset:
The relation of the solar surface magnetic field with mesogranular cells is studied using high spatial (~ 100 km) and temporal (~ 30 sec) resolution data obtained with the IMaX instrument aboard SUNRISE. First, mesogranular cells are identified using Lagrange tracers (corks) based on horizontal velocity fields obtained through Local Correlation Tracking. After ~ 20 min of integration, the tracers delineate a sharp mesogranular network with lanes of width below about 280 km. The preferential location of magnetic elements in mesogranular cells is tested quantitatively. Roughly 85% of pixels with magnetic field higher than 100 G are located in the near neighborhood of mesogranular lanes. Magnetic flux is therefore concentrated in mesogranular lanes rather than intergranular ones. Secondly, magnetic field extrapolations are performed to obtain field lines anchored in the observed flux elements. This analysis, therefore, is independent of the horizontal flows determined in the first part. A probability density function (PDF) is calculated for the distribution of distances between the footpoints of individual magnetic field lines. The PDF has an exponential shape at scales between 1 and 10 Mm, with a constant characteristic decay distance, indicating the absence of preferred convection scales in the mesogranular range. Our results support the view that mesogranulation is not an intrinsic convective scale (in the sense that it is not a primary energy-injection scale of solar convection), but also give quantitative confirmation that, nevertheless, the magnetic elements are preferentially found along mesogranular lanes.
We show that any normal irreducible affine $n$-dimensional $SL_n$-variety $X$ is determined by its automorphism group in the category of normal irreducible affine varieties: if $Y$ is an irreducible affine normal algebraic variety such that $Aut(X) \cong Aut(Y)$ as ind-groups, then $Y \cong X$ as varieties. If we drop the condition of normality on $Y$ , then $X$ is not uniquely determined and we classify all such varieties. In case $n \ge 3$, all the above results hold true if we replace $Aut(X)$ by $U(X)$, where $U(X)$ is the subgroup of $Aut(X)$ generated by all one-dimensional unipotent subgroups. In dimension $2$ we have some very interesting exceptions.
There has recently been a revival of interest in anti de-Sitter space (AdS) brought about by the conjectured duality beteeen physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, I begin with a historical review, including the ``Membrane at the end of the universe'' idea. Next I discuss two recent papers with Lu and Pope on on $AdS_{5} \times S^{5}$ and on $AdS_{3} \times S^{3}$, respectively. In each case we note that odd-dimensional spheres $S^{{2n+1}}$ may be regarded as U(1) bundles over $CP^{n}$ and that this permits an unconventional ``Hopf''duality along the U(1) fibre. This leads in particular to the phenomenon of BPS without BPS whereby states which appear to be non-BPS in one picture are seen to be BPS in the dual picture.
In this paper we develop an existence theory for small amplitude, steady, two-dimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity across the air--water interface, and a corresponding jump in the circulation of the fluids there. We consider both fluids to be inviscid, with the water region being irrotational and of finite depth. The air region is considered with constant vorticity in the case of infinite depth and with a general vorticity profile in the case of a finite, lidded atmosphere.
Let $M_k^!(\Gamma_0^+(3))$ be the space of weakly holomorphic modular forms of weight $k$ for the Fricke group of level $3$. We introduce a natural basis for $M_k^!(\Gamma_0^+(3))$ and prove that for almost all basis elements, all of their zeros in a fundamental domain lie on the circle centered at 0 with radius $\frac{1}{\sqrt{3}}$.
Variation of the volume- and surface-Schmidt laws (star-formation or SF law) with the galacto-centric distance R was investigated using 3D distributions of HII regions, HI, and molecular (H_2) gases in the Milky Way. Both the power-law index and SF coefficient were found to be variable with R. The index is flatter in the inner disc than in the outer Galaxy, and the coefficient is larger in the inner disc, decreasing steeply outward. There is also a mutual anti-correlation between the index and SF coefficient, and the SF law can be expressed by a single-parameter function of the SF coefficient. The variable SF law is discussed in relation to the self-regulation star formation.
It is well known that any entangled mixed state in $2\otimes 2$ systems can be purified via infinite copies of the mixed state. But can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system by local operation and classical communication? This is more meaningful in practical application. We give a necessary and sufficient condition of this distillability. This condition can be expressed as: there exists distillable-subspaces. According to this condition, one can judge whether a mixed state is distillable or not easily. We also analyze some properties of distillable-subspaces, and discuss the most efficient purification protocols. Finally, we discuss the distillable enanglement of two-quibt system for the case of finite copies.
The high spectral resolution and sensitivity of FUSE have enabled far-ultraviolet studies of AGN and QSOs that are a natural complement to observations using HST, Chandra, and XMM-Newton. Through synergistic use of the large sample of nearby AGN that serve as background probes of gas in the Galactic halo and the ISM, the FUSE PI team has observed a large number (approaching 100) of the nearest and brightest AGN. In addition to emission from O VI, we identify emission lines due to C III, N III, S IV, and He II in many of the Type-1 AGN. More than half of the Type 1 objects also show intrinsic absorption by the O VI doublet as well as C IV absorption and evidence of a soft X-ray warm absorber. Guest investigators have successfully coordinated FUSE observations of bright AGN with simultaneous HST and X-ray observations. These have contributed greatly to our understanding of the UV and X-ray absoring gas in AGN as either a wind from the accretion disk, or a thermally driven wind from the obscuring torus.
We calculate the one-loop effective potential for Horava-Lifshitz-like QED and Yukawa-like theory for arbitrary values of the critical exponent and the space-time dimension.
We study the low energy effective field theory of fermions with electric and magnetic dipole moments at finite temperature. We find that at one loop there is an interaction term of the Chern-Simon form ${\cal L_I}=m_\mu\>A_\nu {\tilde F}^{\mu\nu}$. The four vector $m_\mu \simeq d_i \mu_i m_i^2 ~{\partial_\mu}\>(ln T)$ is interpreted as a Chern- Simon type mass of photons, which is determined by the electric (magnetic) dipole moments $d_i$ ($\mu_i$) of the fermions in the vacuum polarisation loop diagram. The physical consequence of such a photon mass is that, photons of opposite circular polarisations, propagating through a hot medium, have different group velocities. We estimate that the time lag between the arrival times of the left and right circularly polarised light signals from pulsars. If the light propagates through a hot plasma (where the temperature in some regions is $T \sim 100 MeV$) then the time lag between the two circularly polarised signals of frequency $\omega$ will be $\Delta t(\omega) \simeq 10^{-6} /\omega$. It may be possible to observe this effect in pulsar signals which propagate through nebula at high temperatures.
The concept of time is discussed in the context of the canonical formulation of the gravitational field. Using a hypersurface orthogonal foliation, the arbitrariness of the lapse function is eliminated and the shift vector vanishes, allowing a consistent definition of time.
We present a mid-IR investigation of the scaling relations between supermassive black hole masses (MBH) and the structural parameters of the host spheroids in local galaxies. The work is based on two-dimensional bulge-disk decompositions of Spitzer/IRAC 3.6 um images of 57 galaxies with MBH estimates. Our estimates of effective radii (Re) and surface brightnesses, combined with velocity dispersions (sigma) from the literature, define a FP relation consistent with previous determinations but doubling the observed range in Re. None of our galaxies is an outlier of the FP, demonstrating the accuracy of our bulge-disk decomposition which also allows us to independently identify pseudobulges in our sample. We calibrate M/L at 3.6 um by using the tight Mdyn-Lbul relation (~0.1 dex of rms) and find that no color corrections are required to estimate the stellar mass. The 3.6 um luminosity is thus the best tracer of Mstar yet studied. We then explore the connection between MBH and bulge structural parameters (luminosity, mass, effective radius). We find tight correlations of MBH with both 3.6 um bulge luminosity and dynamical mass (MBH/Mdyn~1/1000), with rms of ~0.35 dex, similar to the MBH-sigma relation. Our results are consistent with previous determinations at shorter wavelengths. By using our calibrated M/L, we rescale MBH-Lbul to obtain the MBH-Mstar relation, which can be used as the local reference for high-z studies which probe the cosmic evolution of MBH-galaxy relations and where the stellar mass is inferred directly from luminosity measurements. The analysis of pseudobulges shows that 4 out of 9 lie on the scaling relations within the observed scatter, while those with small MBH are significantly displaced. We explore the different origins for such behavior, while considering the possibility of nuclear morphological components not reproduced by our two-dimensional decomposition.
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise to points by loosing a part of the entire structure is discussed. The counterpart of the traditional objects of differential geometry are studied.
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. Based on the coherence quantification method, we prove a simple factorization relation for the $l_1$ norm measure of coherence, and analyze under which condition this relation holds. We also obtain a more general relation which applies to arbitrary $N$-qubit state, and determine a condition for the transformation matrix of the quantum channel which can support permanently freezing of the $l_1$ norm of coherence. These results simplify determination of a general decoherence dynamics to that the investigation of evolution about the representative probe state.
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
We report experimental implementation of various types of qubit channels using an individual trapped ion. We analyzed experimental data and we performed tomographic reconstruction of quantum channels based on these data. Specifically, we studied phase damping channels, where the damping acts either in the xy-plane of the Bloch sphere or in an arbitrary plane that includes the origin of the Bloch sphere. We also experimentally realized and consequently analyzed quantum channels that in addition to phase damping affect also a polarization rotation. We used three reconstruction schemes for estimation of quantum channels from experimental data: (1) a linear inverse method, (2) a maximum likelihood estimation, and (3) a constrained maximum likelihood estimation. We took into account realistic experimental conditions where imperfect test-state preparations and biased measurements are incorporated into the estimation schemes. As a result we found that imperfections present in the process of preparation of test states and as well as in measurements of the considered ion trap system do not limit the control of the implementation of the desired channel. Even imperfect preparation of test state and subsequent measurements still provide sufficient resources for the complete quantum-channel tomography.
De Finetti's betting argument is used to justify finitely additive probabilities when only finitely many bets are considered. Under what circumstances can countably many bets be used to justify countable additivity? In this framework, one faces issues such as the convergence of the returns of the bet. Generalizations of de Finetti's argument depend on what type of conditions on convergence are required of the bets under consideration. Two new such conditions are compared with others presented in the literature.
In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.
We prove a reducibility result for a linear Klein-Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving, however we require it to be fast oscillating. In particular, provided that the external frequency is sufficiently large and chosen from a Cantor set of large measure, the original equation is conjugated to a time independent, diagonal one. We achieve this result in two steps. First, we perform a preliminary transformation, adapted to fast oscillating systems, which puts the original equation in a perturbative setting. Then we show that this new equation can be put to constant coefficients by applying a KAM reducibility scheme, whose convergence requires a new type of Melnikov conditions.
Large-scale magnetic fields at the surface of massive stars do not only influence the outer-most layers of the star, but also have consequences for the deep interior, only observationally accessible through asteroseismology. We performed a detailed characterization of the dipolar magnetic field at the surface of the B3.5V star HD 43317, a SPB/$\beta$ Cep hybrid pulsator, by studying the rotationally modulated magnetic field of archival and new Narval spectropolarimetry. Additionally, we employed a grid-based approach to compare the Zeeman signatures with model profiles. By studying the rotational modulation of the He lines in both the Narval and HARPS spectroscopy caused by co-rotating surface abundance inhomogeneities, we updated the rotation period to $0.897673\pm0.000004$d. The inclination angle between the rotation axis and the observer's line of sight remains ill-defined, because of the low level of variability in Stokes V and deformations in the intensity profiles by stellar pulsation modes. The obliquity angle between the rotation and magnetic axes is constrained to $\beta \in [67,90]^{\circ}$, and the strength of the dipolar magnetic field is of the order of 1kG to 1.5kG. This magnetic field at the stellar surface is sufficiently strong to warrant a uniformly rotating radiative envelope, causing less convective core overshooting, which should be visible in future forward seismic modeling.
It is well-known that there are two types of gamma-ray bursts (GRBs): short/hard and long/soft ones, respectively. The long GRBs are coupled to supernovae, but the short ones are associated with the so called macronovae (also known as kilonovae), which can serve as the sources of gravitational waves as well. The kilonovae can arise from the merging of two neutron-stars. The neutron stars can be substituded by more massive black holes as well. Hence, the topic of gamma-ray bursts (mainly the topic of short ones) and the topic of massive binaries, are strongly connected.   In this contribution, the redshifts of GRBs are studied. The surprising result - namely that the apparently fainter GRBs can be in average at smaller distances - is discussed again. In essence, the results of M\'esz\'aros et al. (2011) are studied again using newer samples of GRBs. The former result is confirmed by the newer data.
We investigate the anisotropy in cosmic microwave background Planck maps due to the coupling between its beam asymmetry and uneven scanning strategy. Introducing a pixel space estimator based on the temperature gradients, we find a highly significant (~20 \sigma) preference for these to point along ecliptic latitudes. We examine the scale dependence, morphology and foreground sensitivity of this anisotropy, as well as the capability of detailed Planck simulations to reproduce the effect, which is crucial for its removal, as we demonstrate in a search for the weak lensing signature of cosmic defects.
A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in \cite{ho:gnus, ardalan}, we regard that the boundary conditions are second class constraints in the sense of the Dirac's method. However, we show that this proposal is more useful if we consider an inverse of the Holographic map between a theory defined in the boundary to another with constraints but without boundary.
We have recently identified a previously unknown radial migration mechanism resulting from the overlap of spiral and bar resonances in galactic discs (Minchev & Famaey 2010, Minchev et al. 2010). This new mechanism is much more efficient than mixing by transient spirals and its presence is unavoidable in all barred galaxies, such as our own Milky Way. The consequences of this are a strong flattening in the metallicity gradient in the disc, an extended disc profile, and the formation of a thick disc component, all taking place in only a couple of Gyr. This timescale is drastically shorter than previously expected and thus can put strong constraints on the longevity, strength and pattern speeds of the Galactic bar and Spiral Structure.
The vacuum neutrino mixing is known to exhibit an approximate $\mu-\tau$ symmetry, which was shown to be preserved for neutrino propagating in matter. This symmetry reduces the neutrino transition probabilities to very simple forms when expressed in a rephasing invariant parametrization introduced earlier. Applications to long baseline experiments are discussed.
We discuss properties of baryon resonances belonging to the Nucleon, Delta, Sigma, Lambda, Xi and Omega families in a collective string-like model for the nucleon, in which the radial excitations are interpreted as rotations and vibrations of the string configuration. We find good overall agreement with the available data. The main discrepancies are found for low lying S-wave states, in particular N(1535), N(1650), Sigma(1750), Lambda*(1405), Lambda(1670) and Lambda(1800).
We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for properties of the Holstein polaron and bipolaron problems. Numerical solution of the Holstein model means that we determined the ground-state and low-lying excited states with arbitrary precision in the thermodynamic limit for any dimension. Moreover, we calculated the spectral properties (e.g. photoemission and phonon spectra), optical response and thermal transport, as well as the dynamics of polaron formation. Our approach takes into account the full quantum dynamics of the electrons and phonons and yields unbiased results for all electron-phonon interaction strengths and phonon frequencies, but is of particular value in the intermediate-coupling regime, where perturbation theories and other analytical techniques fail.
We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauss-Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure.
We study the influence of an open cluster environment on the formation and current structure of the Oort cloud. To do this, we have run 19 different simulations of the formation of the Oort Cloud for 4.5 Gyrs. In each simulation, the solar system spends its first 100 Myrs in a different open cluster environment before transitioning to its current field environment. We find that, compared to forming in the field environment, the inner Oort Cloud is preferentially loaded with comets while the Sun resides in the open cluster and that most of this material remains locked in the interior of the cloud for the next 4.4 Gyrs. In addition, the outer Oort Cloud trapping efficiencies we observe in our simulations are lower than previous formation models by about a factor of 2, possibly implying an even more massive early planetesimal disk. Furthermore, some of our simulations reproduce the orbits of observed extended scattered disk objects, which may serve as an observational constraint on the Sun's early environment. Depending on the particular open cluster environment, the properties of the inner Oort Cloud and extended scattered disk can vary widely. On the other hand, the outer portions of the Oort Cloud in each of our simulations are all similar.
A linked system of symmetric designs (LSSD) is a $w$-partite graph ($w\geq 2$) where the incidence between any two parts corresponds to a symmetric design and the designs arising from three parts are related. The original construction for LSSDs by Goethals used Kerdock sets, in which $v$ is a power of two. Some four decades later, new examples were given by Davis et.\ al.\ and Jedwab et.\ al.\ using difference sets, again with $v$ a power of two. In this paper we develop a connection between LSSDs and "linked simplices", full-dimensional regular simplices with two possible inner products between vertices of distinct simplices. We then use this geometric connection to construct sets of equiangular lines and to find an equivalence between regular unbiased Hadamard matrices and certain LSSDs with Menon parameters. We then construct examples of non-trivial LSSDs in which $w$ can be made arbitarily large for fixed even part of $v$. Finally we survey the known infinite families of symmetric designs and show, using basic number theoretic conditions, that $w=2$ in most cases.
In this paper, we study an important yet less explored aspect in video detection and tracking -- stability. Surprisingly, there is no prior work that tried to study it. As a result, we start our work by proposing a novel evaluation metric for video detection which considers both stability and accuracy. For accuracy, we extend the existing accuracy metric mean Average Precision (mAP). For stability, we decompose it into three terms: fragment error, center position error, scale and ratio error. Each error represents one aspect of stability. Furthermore, we demonstrate that the stability metric has low correlation with accuracy metric. Thus, it indeed captures a different perspective of quality. Lastly, based on this metric, we evaluate several existing methods for video detection and show how they affect accuracy and stability. We believe our work can provide guidance and solid baselines for future researches in the related areas.