ShantanuT01/DACTYL-Pretraining huggingface dataset:
Galaxy clustering data from current and upcoming large scale structure surveys can provide strong constraints on primordial non-Gaussianity through the scale-dependent halo bias. To fully exploit the information from galaxy surveys, optimal analysis methods need to be developed and applied to the data. Since the halo bias is sensitive to local non-Gaussianity predominately at large scales, the volume of a given survey is crucial. Consequently, for such analyses we do not want to split into redshift bins, which would lead to information loss due to edge effects, but instead analyse the full sample. We present an optimal technique to directly constrain local non-Gaussianity parametrised by $f_\mathrm{NL}^\mathrm{loc}$, from galaxy clustering by applying redshift weights to the galaxies. We derive a set of weights to optimally measure the amplitude of local non-Gaussianity, $f_\mathrm{NL}^\mathrm{loc}$, discuss the redshift weighted power spectrum estimators, outline the implementation procedure and test our weighting scheme against Lognormal catalogs for two different surveys: the quasar sample of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the emission line galaxy sample of the Dark Energy Spectroscopic Instrument (DESI) survey. We find an improvement of 30 percent for eBOSS and 6 percent for DESI compared to the standard Feldman, Kaiser $\&$ Peacock weights, although these predictions are sensitive to the bias model assumed.
Using a formalism of minitwistors, we derive infinitely many conserved charges for the $sl(\infty )$-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions.
The design of more complex and powerful neural network models has significantly advanced the state-of-the-art in visual object tracking. These advances can be attributed to deeper networks, or the introduction of new building blocks, such as transformers. However, in the pursuit of increased tracking performance, runtime is often hindered. Furthermore, efficient tracking architectures have received surprisingly little attention. In this paper, we introduce the Exemplar Transformer, a transformer module utilizing a single instance level attention layer for realtime visual object tracking. E.T.Track, our visual tracker that incorporates Exemplar Transformer modules, runs at 47 FPS on a CPU. This is up to 8x faster than other transformer-based models. When compared to lightweight trackers that can operate in realtime on standard CPUs, E.T.Track consistently outperforms all other methods on the LaSOT, OTB-100, NFS, TrackingNet, and VOT-ST2020 datasets. Code and models are available at https://github.com/pblatter/ettrack.
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists some form of absolute mathematical space or space-time, and that in a flat space approximation vectors can be imagined between defined points in this space-time, much as we can imagine an arrowed line drawn on a piece of paper. However, while classical vector quantities can be represented on paper, in the quantum domain physical quantities do not in general exist with precise values except in measurement; a change of apparatus, for example by rotating it, may affect the outcome of the measurement, so the condition for general covariance does not apply. The purpose of this paper is to re-examine covariance within the context of an orthodox, Dirac-Von Neumann interpretation of quantum mechanics, to replace it with a new condition, here called quantum covariance, and to show that quantum covariance is the required condition for the unification of general relativity with quantum mechanics for non-interacting particles.
We examine the ratios $r_h/r_J$ of projected half-mass and Jacobi radius as well as $r_t/r_J$ of tidal and Jacobi radius for open and globular clusters in the Milky Way using data of both observations and simulations. We applied an improved calculation of $r_J$ for eccentric orbits of globular clusters. A sample of 236 open clusters of Piskunov et al. within the nearest kiloparsec around the Sun has been used. For the Milky Way globular clusters, data are taken from the Harris catalogue. We particularly use the subsample of 38 Milky Way globular clusters for which orbits have been integrated by Dinescu et al. We aim to quantify the differences between open and globular clusters and to understand, why they form two intrinsically distinct populations. We find under certain assumptions, or, in other words, in certain approximations, (i) that globular clusters are presently Roche volume underfilling and (ii) with at least $3\sigma$ confidence that the ratio $r_h/r_J$ of half-mass and Jacobi radius is $3 - 5$ times larger at present for an average open cluster in our sample than for an average globular cluster in our sample and (iii) that a significant fraction of globular clusters may be Roche volume overfilling at pericentre with $r_t > r_J$. Another aim of this paper is to throw light on the underlying theoretical reason for the existence of the van den Bergh correlation between half-mass and galactocentric radius.
A theoretical approach for characterising the influence of asymmetry of noise distribution on the escape rate of a multi-stable system is presented. This was carried out via the estimation of an action, which is defined as an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with the results of numerical simulations. An approximation of the third order cumulant was shown to have limitations on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed so far is discussed for an adequate characterisation of the escape rate measured in experiments.
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly. Kitaev \cite{kitaev} showed how to approximate the Fourier transform for any order. Here we show how his construction can be made exact by using the technique known as ``amplitude amplification''. Although unlikely to be of any practical use, this construction e.g. allows to make Shor's discrete logarithm quantum algorithm exact. Thus we have the first example of an exact non black box fast quantum algorithm, thereby giving more evidence that ``quantum'' need not be probabilistic. We also show that in a certain sense the family of circuits for the exact QFFT is uniform. Namely the parameters of the gates can be calculated efficiently.
We calculate transverse momentum dependent quark splitting kernels $P_{gq}$ and $P_{qq}$ within $k_T$-factorization, completing earlier results which concentrated on gluon splitting functions $P_{gg}$ and $P_{qg}$. The complete set of splitting kernels is an essential requirement for the formulation of a complete set of evolution equations for transverse momentum dependent parton distribution functions and the development of corresponding parton shower algorithms.
We discuss the constraints of lepton mixing angles from lepton number violating processes such as neutrinoless double beta decay, (\mu^-)-(e^+) conversion and K decay, $K^- \to \pi^+\mu^-\mu^-$ which are allowed only if neutrinos are Majorana particles. The rates of these processes are proportional to the averaged neutrino mass defined by $<m_{\nu} >_{a b}\equiv |\sum_{j=1}^{3}U_{a j} U_{b j}m_j|$ in the absence of right-handed weak coupling. Here $a, b (j)$ are flavour(mass) eigen states and $U_{a j}$ is the left-handed lepton mixing matrix. We obtain the consistency conditions which are satisfied irrelevant to the concrete values of CP violation phases (three phases in Majorana neutrinos). These conditions constrain the lepton mixing angles, neutrino masses $m_i$ and (< m_{\nu} >_{a b}). By using these constraints we obtain the limits on the averaged neutrino masses for (\mu^-)-(e^+) conversion and K decay, $K^- \to \pi^+\mu^-\mu^-$.
In this paper, taking the large $R$ limit and using the complexity-volume duality, we investigate the holographic complexity growth rate of a field state defined on the universe located at an asymptotical AdS boundary in Gauss-Bonnet gravity and massive gravity, respectively. For the Gauss-Bonnet gravity case, its growth behavior of the state mainly presents three kinds of contributions: one, as a finite term viewed as an interaction term, comes from a conserved charge, the second one is from the spatial volume of the universe and the third one relates the curvature of the horizon in the AdS Gauss-Bonnet black hole, where the Gauss-Bonnet effect plays a vital role on such growth rate. For massive gravity case, except the first divergent term still obeying the growth rate of the spatial volume of the Universe, its results reveal the more interesting novel phenomenons: beside the conserved charge $E$, the graviton mass term also provides its effect to the finite term; and the third divergent term is determined by the spatial curvature of its horizon $k$ and graviton mass effect; furthermore, the graviton mass effect can be completely responsible for the second divergent term as a new additional term saturating an area law.
During an XMM-Newton observation, the eclipsing polar UZ For was found in a peculiar state with an extremely low X-ray luminosity and occasional X-ray and UV flaring. For most of the observation, UZ For was only barely detected in X-rays and about 800 times fainter than during a high state previously observed with ROSAT. A transient event, which lasted about 900 s, was detected simultaneously by the X-ray instruments and, in the UV, by the Optical Monitor. The transient was likely caused by the impact of 10^17-10^18 g of gas on the main accretion region of the white dwarf. The X-ray spectrum of the transient is consistent with 7 keV thermal bremsstrahlung from the shock-heated gas in the accretion column. A soft blackbody component due to reprocessing of X-rays in the white dwarf atmosphere is not seen. The likely origin of the UV emission during the transient is cyclotron radiation from the accretion column. We conclude from our analysis that the unusual flaring during the low state of UZ For was caused by intermittent increases of the mass transfer rate due to stellar activity on the secondary.
We present results of our 5-years-long program of ground-based spectroscopic and photometric observations of individual Kepler asteroseismic targets and the open clusters NGC6866 and NGC6811 from the Kepler field of view.We determined the effective temperature, surface gravity, metallicity, the projected rotational velocity and the radial velocity of 119 Kepler asteroseismic targets for which we acquired high-resolution spectra. For many of these stars the derived atmospheric parameters agree with Teff, log g, and [Fe/H] from the Kepler Input Catalog (KIC) to within their error bars. Only for stars hotter than 7000K we notice significant differences between the effective temperature derived from spectroscopy and Teff given in the KIC. For 19 stars which we observed photoelectrically, we measured the interstellar reddening and we found it to be negligible. Finally, our discovery of the delta Sct and gamma Dor pulsating stars in the open cluster NGC6866 allowed us to discuss the frequency of the occurrence of gamma Dor stars in the open clusters of different age and metallicity and show that there are no correlations between these parameters.
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change type according to Wright-Fisher resampling. At any time, each pair of individuals is linked by an edge with a probability that is given by a type-connection matrix, whose entries depend on the current empirical type distribution of the entire population via a fitness function. We show that, in the large-population-size limit and with an appropriate scaling of time, the evolution of the associated adjacency matrix converges to a random process in the space of graphons, driven by the type-connection matrix and the underlying Wright-Fisher diffusion on the multi-type simplex. In the limit as the number of types tends to infinity, the limiting process is driven by the type-connection kernel and the underlying Fleming-Viot diffusion.
Cosmic voids provide a powerful probe of the origin and evolution of structures in the Universe because their dynamics can remain near-linear to the present day. As a result they have the potential to connect large scale structure at late times to early-Universe physics. Existing "watershed"-based algorithms, however, define voids in terms of their morphological properties at low redshift. The degree to which the resulting regions exhibit linear dynamics is consequently uncertain, and there is no direct connection to their evolution from the initial density field. A recent void definition addresses these issues by considering "anti-halos". This approach consists of inverting the initial conditions of an $N$-body simulation to swap overdensities and underdensities. After evolving the pair of initial conditions, anti-halos are defined by the particles within the inverted simulation that are inside halos in the original (uninverted) simulation. In this work, we quantify the degree of non-linearity of both anti-halos and watershed voids using the Zel'dovich approximation. We find that non-linearities are introduced by voids with radii less than $5\,\mathrm{Mpc}\,h^{-1}$, and that both anti-halos and watershed voids can be made into highly linear sets by removing these voids.
Polarization observables of the three charge states of the pion for the $\gamma d\to\pi NN$ reaction with polarized photon beam and/or oriented deuteron target are evaluated over the whole $\Delta$(1232)-resonance region adopting a nonrelativistic model based on time-ordered perturbation theory. Results for the $\pi$-meson spectra, linear photon asymmetry, vector and tensor target asymmetries are presented. Particular attention is given, for the first time, to double polarization asymmetries for which we present results for $T_{20}^{\ell}$ and $T_{2\pm 2}^{\ell}$. We found that all other double polarization asymmetries of photon and deuteron target are vanished.
We present a teleparallel complex gravity as the foundation for the formulation of noncommutative gravity theory. The negative energy ghosts in the conventional formulation with U(1,3) local Lorentz connection no longer exists, since the local Lorentz invariance is broken down to U(1,3) global Lorentz symmetry. As desired, our teleparallel complex gravity theory also passes the key classical test of perihelion advance of Mercury. Based on this result, we present a lagrangian for the noncommutative teleparallel gravity theory.
The Einstein-Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43: 1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44: 1419, 2012) are recovered. We also obtain exact solutions for a neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the energy density, tangential pressure and anisotropy profiles are consistent with earlier treatments which suggest relevance in describing relativistic compact stars.
The paper deals with existence and multiplicity of solutions of the fractional Schr\"{o}dinger--Kirchhoff equation involving an external magnetic potential. As a consequence, the results can be applied to the special case \begin{equation*} (a+b[u]_{s,A}^{2\theta-2})(-\Delta)_A^su+V(x)u=f(x,|u|)u\,\, \quad \text{in $\mathbb{R}^N$}, \end{equation*} where $s\in (0,1)$, $N>2s$, $a\in \mathbb{R}^+_0$, $b\in \mathbb{R}^+_0$, $\theta\in[1,N/(N-2s))$, $A:\mathbb{R}^N\rightarrow\mathbb{R}^N$ is a magnetic potential, $V:\mathbb{R}^N\rightarrow \mathbb{R}^+$ is an electric potential, $(-\Delta )_A^s$ is the fractional magnetic operator. In the super- and sub-linear cases, the existence of least energy solutions for the above problem is obtained by the mountain pass theorem, combined with the Nehari method, and by the direct methods respectively. In the superlinear-sublinear case, the existence of infinitely many solutions is investigated by the symmetric mountain pass theorem.
We propose a definition of ``nonabelian mixed Hodge structure'' together with a construction associating to a smooth projective variety $X$ and to a nonabelian mixed Hodge structure $V$, the ``nonabelian cohomology of $X$ with coefficients in $V$'' which is a (pre-)nonabelian mixed Hodge structure denoted $H=Hom(X_M, V)$. We describe the basic definitions and then give some conjectures saying what is supposed to happen. At the end we compute an example: the case where $V$ has underlying homotopy type the complexified 2-sphere, and mixed Hodge structure coming from its identification with $\pp ^1$. For this example we show that $Hom (X_M,V)$ is a namhs for any smooth projective variety $X$.
Total irregularity of a simple undirected graph $G$ is defined to be $irr_t(G) = \frac{1}{2}\sum\limits_{u, v \in V(G)}|d(u) - d(v)|$. See Abdo and Dimitrov [2]. We allocate the \emph{Fibonacci weight,} $f_i$ to a vertex $v_j$ of a simple connected graph, if and only if $d(v_j) = i$ and define the \emph{total fibonaccian irregularity} or $f_t-irregularity$ denoted $firr_t(G)$ for brevity, as: $firr_t(G) = \sum\limits_{i=1}^{n-1}\sum\limits_{j=i+1}^{n}|f_i - f_j|.$ The concept of an \emph{edge-joint} is also introduced to be the simple undirected graph obtained from two simple undirected graphs $G$ and $H$ by linking the edge $vu_{v \in V(G), u \in V(H)}$. This paper presents results for the undirected underlying graphs of Jaco Graphs, $J_n(x)$. Finally we pose an open problem with regards to $firr_t^\pm(G).$
Video inpainting aims to fill the given spatiotemporal holes with realistic appearance but is still a challenging task even with prosperous deep learning approaches. Recent works introduce the promising Transformer architecture into deep video inpainting and achieve better performance. However, it still suffers from synthesizing blurry texture as well as huge computational cost. Towards this end, we propose a novel Decoupled Spatial-Temporal Transformer (DSTT) for improving video inpainting with exceptional efficiency. Our proposed DSTT disentangles the task of learning spatial-temporal attention into 2 sub-tasks: one is for attending temporal object movements on different frames at same spatial locations, which is achieved by temporally-decoupled Transformer block, and the other is for attending similar background textures on same frame of all spatial positions, which is achieved by spatially-decoupled Transformer block. The interweaving stack of such two blocks makes our proposed model attend background textures and moving objects more precisely, and thus the attended plausible and temporally-coherent appearance can be propagated to fill the holes. In addition, a hierarchical encoder is adopted before the stack of Transformer blocks, for learning robust and hierarchical features that maintain multi-level local spatial structure, resulting in the more representative token vectors. Seamless combination of these two novel designs forms a better spatial-temporal attention scheme and our proposed model achieves better performance than state-of-the-art video inpainting approaches with significant boosted efficiency.
In this chapter I give an overall description of the structure and evolution of stars of different masses, and review the main ingredients included in state-of-the-art calculations aiming at reproducing observational features. I give particular emphasis to processes where large uncertainties still exist as they have strong impact on stellar properties derived from large compilations of tracks and isochrones, and are therefore of fundamental importance in many fields of astrophysics.
We show that the BFT embedding method is problematic for mixed systems (systems possessing both first and second class constraints). The Chern-Simons theory as an example is worked out in detail. We give two methods to solve the problem leading to two different types of finite order BFT embedding for Chern-Simons theory.
In this work we analyse late-time (t > 100 d) optical spectra of low-redshift (z < 0.1) Type Ia supernovae (SNe Ia) which come mostly from the Berkeley Supernova Ia Program dataset. We also present spectra of SN 2011by for the first time. The BSNIP sample studied consists of 34 SNe Ia with 60 nebular spectra, to which we add nebular spectral feature measurements of 20 SNe Ia from previously published work (Maeda et al. 2011; Blondin et al. 2012), representing the largest set of late-time SN Ia spectra ever analysed. The full width at half-maximum intensity (FWHM) and velocities of the [Fe III] {\lambda}4701, [Fe II] {\lambda}7155, and [Ni II] {\lambda}7378 emission features are measured in most observations of spectroscopically normal objects where the data have signal-to-noise ratios >20 px^-1 and are older than 160 d past maximum brightness. The velocities of all three features are seen to be relatively constant with time, increasing only a few to ~20 km/s/d. The nebular velocity (v_neb, calculated by taking the average of the [Fe II] {\lambda}7155 and [Ni II] {\lambda}7378 velocities) is correlated with the near-maximum-brightness velocity gradient and early-time ejecta velocity. Nearly all high velocity gradient objects have redshifted nebular lines while most low velocity gradient objects have blueshifted nebular lines. No correlation is found between v_neb and {\Delta}m_15(B), and for a given light-curve shape there is a large range of observed nebular velocities. The data also indicate a correlation between observed (B-V)_max and v_neb.
This paper reports on a novel template-free monocular non-rigid surface reconstruction approach. Existing techniques using motion and deformation cues rely on multiple prior assumptions, are often computationally expensive and do not perform equally well across the variety of data sets. In contrast, the proposed Scalable Monocular Surface Reconstruction (SMSR) combines strengths of several algorithms, i.e., it is scalable with the number of points, can handle sparse and dense settings as well as different types of motions and deformations. We estimate camera pose by singular value thresholding and proximal gradient. Our formulation adopts alternating direction method of multipliers which converges in linear time for large point track matrices. In the proposed SMSR, trajectory space constraints are integrated by smoothing of the measurement matrix. In the extensive experiments, SMSR is demonstrated to consistently achieve state-of-the-art accuracy on a wide variety of data sets.