ShantanuT01/DACTYL-Pretraining huggingface dataset:
The X-Ray Telescope (XRT) onboard the Hinode satellite is an X-ray imager that observes the solar corona with unprecedentedly high angular resolution (consistent with its 1" pixel size). XRT has nine X-ray analysis filters with different temperature responses. One of the most significant scientific features of this telescope is its capability of diagnosing coronal temperatures from less than 1 MK to more than 10 MK, which has never been accomplished before. To make full use of this capability, accurate calibration of the coronal temperature response of XRT is indispensable and is presented in this article. The effect of on-orbit contamination is also taken into account in the calibration. On the basis of our calibration results, we review the coronal-temperature-diagnostic capability of XRT.
We obtain full information on the orbital parameters by combining radial velocity and astrometric measurements by means of Bayesian inference. We sample the parameter probability densities of orbital model parameters with a Markov chain Monte Carlo (McMC) method in simulated observational scenarios to test the detectability of planets with orbital periods longer than the observational timelines. We show that, when fitting model parameters simultaneously to measurements from both sources, it is possible to extract much more information from the measurements than when using either source alone. We demonstrate this by studying the orbit of recently found extra-solar planet HD 154345 b.
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a system of coupled ordinary differential equations. The process for decoupling them leads to a simple equation for $J$ - one of the Bondi-Sachs metric variables - known in the literature as the master equation. Then, this last equation is solved in terms of Bessel's functions of the first kind for the Minkowski's background, and in terms of the Heun's function in the Schwarzschild's case. In addition, when a matter source is considered, the boundary conditions across the time-like world tubes bounding the source are taken into account. These boundary conditions are computed for all multipole modes. Some examples as the point particle binaries in circular and eccentric orbits, in the Minkowski's background are shown as particular cases of this formalism.
Consider the following distribution dependent SDE: $$ {\mathrm d} X_t=\sigma_t(X_t,\mu_{X_t}){\mathrm d} W_t+b_t(X_t,\mu_{X_t}){\mathrm d} t, $$ where $\mu_{X_t}$ stands for the distribution of $X_t$. In this paper for non-degenerate $\sigma$, we show the strong well-posedness of the above SDE under some integrability assumptions in the spatial variable and Lipschitz continuity in $\mu$ about $b$ and $\sigma$. In particular, we extend the results of Krylov-R\"ockner \cite{Kr-Ro} to the distribution dependent case.
We classifiy Enriques surfaces covered by the supersingular K3 surface with the Artin invariant 1 in characteristic 2. There are exactly three types of such Enriques surfaces.
Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0's are ordinary voters and 1's are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that can have a nontrivial stationary distribution, space is represented by a tree. The dynamics are a variant of the biased voter: if $x$ has degree $d(x)$ then at rate $d(x)p_k$ the individual at $x$ consults $k\ge 1$ neighbors. If at least one neighbor is 1, they adopt state 1, otherwise they become 0. In addition at rate $p_0$ individuals with opinion 1 change to 0. As in the contact process on trees, we are interested in determining when the zealots survive and when they will survive locally.
Most ultraluminous X-ray sources (ULXs) are believed to be stellar mass black holes or neutron stars accreting beyond the Eddington limit. Determining the nature of the compact object and the accretion mode from broadband spectroscopy is currently a challenge, but the observed timing properties provide insight into the compact object and details of the geometry and accretion processes. Here we report a timing analysis for an 800 ks XMM-Newton campaign on the supersoft ultraluminous X-ray source, NGC 247 ULX-1. Deep and frequent dips occur in the X-ray light curve, with the amplitude increasing with increasing energy band. Power spectra and coherence analysis reveals the dipping preferentially occurs on $\sim 5$ ks and $\sim 10$ ks timescales. The dips can be caused by either the occultation of the central X-ray source by an optically thick structure, such as warping of the accretion disc, or from obscuration by a wind launched from the accretion disc, or both. This behaviour supports the idea that supersoft ULXs are viewed close to edge-on to the accretion disc.
Based on accurate X-ray structure analysis of GdB6 over the temperature range 85-300 K it has been shown that anomalously strong charge carrier scattering in the quantum diffusion regime of charge transport in this compound arises due to the formation of (i) dynamically coupled Gd3+ dimers of about 3.3 {\AA} in size with an energy of quasi-local oscillations ~ 7 - 8 meV and (ii) dynamic charge stripes along the [001] direction of the cubic lattice. It has been revealed that anharmonic approximation is useful when analyzing the static and dynamic components of the atomic displacement parameters of gadolinium. The barrier height of double-well potential of Gd3+ ions was determined both from low-temperature heat capacity measurements and from the electron density distribution reconstructed from X-ray data.
We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a LOCAL interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in $\hbar$, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example the method is applied to prove the Ward identities of the O(N) scalar field model.
A new method of writing down the path integral for spin-1 Heisenberg antiferromagnetic chain is introduced. In place of the conventional coherent state basis that leads to the non-linear sigma-model, we use a new basis called the fluctuating matrix product states (fMPS) which embodies inter-site entanglement from the outset. It forms an overcomplete set spanning the entire Hilbert space of the spin-1 chain. Saddle-point analysis performed for the bilinear-biquadratic spin model predicts Affeck-Kennedy-Lieb-Tasaki (AKLT) state as the ground state in the vicinity of the AKLT Hamiltonian. Quadratic effective action derived by gradient expansion around the saddle point is free from constraints that plagued the non-linear sigma model and exactly solvable. The obtained excitation modes agree precisely with the single-mode approximation result for the AKLT Hamiltonian. Excitation spectra for other BLBQ Hamiltonians are obtained as well by diagonalizing the quadratic action.
Newly born magnetars are good candidate sources of ultrahigh energy cosmic rays. These objects can in principle easily accelerate particles to the highest energies required to satisfy the ultrahigh energy cosmic ray scenario (E~10^{20-21} eV), thanks to their important rotational and magnetic energy reservoirs. Their acceleration mechanism, based on unipolar induction, predicts however a hard particle injection that does not fit the observed ultrahigh energy cosmic ray spectrum. Here we show that an adequate distribution of initial voltages among magnetar winds can be found to soften the spectrum. We discuss the effect of these distributions for the stochastic gravitational wave background signature produced by magnetars. The magnetar population characteristics needed to fit the ultrahigh energy cosmic ray spectrum could lead in most optimistic cases to gravitational wave background signals enhanced of up to four orders of magnitudes in the range of frequency 1-100 Hz, compared to the standard predictions. These signals could reach the sensitivities of future detectors such as DECIGO or BBO.
Nanoscale structuring holds promise to improve thermoelectric properties of materials for energy conversion and photodetection. We report a study of the spatial distribution of the photothermoelectric voltage in thin-film nanowire devices fabricated from single metal. A focused laser beam is used to locally heat the metal nanostructure via a combination of direct absorption and excitation of a plasmon resonance in Au devices. As seen previously, in nanowires shorter than the spot size of the laser, we observe a thermoelectric voltage distribution that is consistent with the local Seebeck coefficient being spatially dependent on the width of the nanostructure. In longer structures, we observe extreme variability of the net thermoelectric voltage as the laser spot is scanned along the length of the nanowire. The sign and magnitude of the thermoelectric voltage is sensitive to the structural defects, metal grain structure, and surface passivation of the nanowire. This finding opens the possibility of improved local control of the thermoelectric properties at the nanoscale.
In the coming decade, low-frequency radio arrays will begin to probe the epoch of reionization via the redshifted 21-cm hydrogen line. Successful interpretation of these observations will require effective statistical techniques for analyzing the data. Due to the difficulty of these measurements, it is important to develop techniques beyond the standard power spectrum analysis in order to offer independent confirmation of the reionization history, probe different aspects of the topology of reionization, and have different systematic errors. In order to assess the promise of probability distribution functions (PDFs) as statistical analysis tools in 21-cm cosmology, we first measure the 21-cm brightness temperature (one-point) PDFs in six different reionization simulations. We then parametrize their most distinct features by fitting them to a simple model. Using the same simulations, we also present the first measurements of difference PDFs in simulations of reionization. We find that while these statistics probe the properties of the ionizing sources, they are relatively independent of small-scale, sub-grid astrophysics. We discuss the additional information that the difference PDF can provide on top of the power spectrum and the one-point PDF.
Iwasawa algebras of compact $p$-adic Lie groups are completed group algebras with applications in number theory in studying class numbers of towers of number fields and representation theory of $p$-adic Lie groups. In our earlier work, we determined an explicit presentation of the Iwasawa algebra for the first principal congruence kernel of Chevalley groups over $\mathbb{Z}_p$. In this paper, for prime $p>n+1$, we extend our result to determine the explicit presentation, in the form of generators and relations, of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of $GL_n(\mathbb{Z}_p)$.
We propose a self-adapted Monte Carlo approach to automatically determine the critical temperature by simulating two systems with different sizes at the same temperature. The temperature is increased or decreased by checking the short-time average of the correlation ratios of the two system sizes. The critical temperature is achieved using the negative feedback mechanism, and the thermal average near the critical temperature can be calculated precisely. The proposed approach is a general method to treat second-order phase transition, first-order phase transition, and Berezinskii-Kosterlitz-Thouless transition on the equal footing.
The Bousso bound requires that one quarter the area of a closed codimension two spacelike surface exceeds the entropy flux across a certain lightsheet terminating on the surface. The bound can be violated by quantum effects such as Hawking radiation. It is proposed that at the quantum level the bound be modified by adding to the area the quantum entanglement entropy across the surface. The validity of this quantum Bousso bound is proven in a two-dimensional large N dilaton gravity theory.
To date the onset of large-scale star formation in galaxies and its link to gravitational stability of the galactic disk have not been fully understood. The nearby face-on spiral galaxy M51 is an ideal target for studying this subject. This paper combines CO, dust, HI, and stellar maps of M51 and its companion galaxy to study the H2/HI transition, the gas-to-dust ratios, and the stability of the disk against gravitational collapse. We combine maps of the molecular gas using 12CO 2--1 map HERA/IRAM-30m data and HI VLA data to study the total gas surface density and the phase transition of atomic to molecular gas. The total gas surface density is compared to the dust surface density from 850 micron SCUBA data. Taking into account the velocity dispersions of the molecular and atomic gas, and the stellar surface densities derived from the 2MASS K-band survey, we derive the total Toomre Q parameter of the disk. The gas surface density in the spiral arms is approximately 2-3 higher compared to that of the interarm regions. The ratio of molecular to atomic surface density shows a nearly power-law dependence on the hydrostatic pressure P_hydro. The gas surface density distribution in M51 shows an underlying exponential distribution with a scale length of h_gas=7.6 kpc representing 55% of the total gas mass, comparable to the properties of the exponential dust disk. In contrast to the velocity widths observed in HI, the CO velocity dispersion shows enhanced line widths in the spiral arms compared to the interarm regions. The contribution of the stellar component in the Toomre Q-parameter analysis is significant and lowers the combined Q-parameter Q_tot by up to 70% towards the threshold for gravitational instability. The value of Q_tot varies from 1.5-3 in radial averages. A map of Q_tot shows values around 1 on the spiral arms.
We have collected from the literature a list of early-type stars, situated at large distances from the galactic plane, for which evidence of youth seems convincing. We discuss two possible formation mechanisms for these stars: ejection from the plane by dynamical interactions within small clusters, and formation away from the plane, via induced shocks created by spiral density waves. We identify the stars that could be explained by each mechanism. We conclude that the ejection mechanism can account for about two thirds of the stars, while a combination of star formation at z = 500-800 pc from the plane and ejection, can account for 90 percent of these stars. Neither mechanism, nor both together, can explain the most extreme examples.
The inverse-Compton X-ray emission model for supernovae has been well established to explain the X-ray properties of many supernovae for over 30 years. However, no observational case has yet been found to connect the X-rays with the optical lights as they should be. Here, we report the discovery of a hard X-ray source that is associated with a Type II-b supernova. Simultaneous emission enhancements have been found in both the X-ray and optical light curves twenty days after the supernova explosion. While the enhanced X-rays are likely dominated by inverse-Compton scatterings of the supernova's lights from the Type II-b secondary peak, we propose a scenario of a high-speed supernova ejecta colliding with a low-density pre-supernova stellar wind that produces an optically thin and high-temperature electron gas for the Comptonization. The inferred stellar wind mass-loss rate is consistent with that of the supernova progenitor candidate as a yellow supergiant detected by the Hubble Space Telescope, providing an independent proof for the progenitor. This is also new evidence of the inverse-Compton emission during the early phase of a supernova.
A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point $p_{\mathrm {sd}}(q)=\sqrt{q}/(1+\sqrt{q})$, the Ising model with external field, and the colored random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events with no assumption of symmetry.
Let n be a nonzero integer and assume that a set S of positive integers has the property that xy+n is a perfect square whenever x and y are distinct elements of S. In this paper we find some upper bounds for the size of the set S. We prove that if |n| <= 400 then |S| <= 32, and if |n| > 400 then |S| < 267.81 log|n| (log log|n|)^2. The question whether there exists an absolute bound (independent on n) for |S| still remains open.
We present Hubble Space Telescope WFC3/UVIS (F275W, F336W) and ACS/WFC optical (F435W, F555W, and F814W) observations of the nearby grand-design spiral galaxy M101 as part of the Legacy Extragalactic UV Survey (LEGUS). Compact sources detected in at least four bands were classified by both human experts and the convolutional neural network StarcNet. Human experts classified the 2,351 brightest sources, retrieving $N_{c} = 965$ star clusters. StarcNet, trained on LEGUS data not including M101, classified all 4,725 sources detected in four bands, retrieving $N_{c} = 2,270$ star clusters. The combined catalog represents the most complete census to date of compact star clusters in M101. We find that for the 2,351 sources with both a visual- and ML-classification StarcNet is able to reproduce the human classifications at high levels of accuracy ($\sim 80-90\%$), which is equivalent to the level of agreement between human classifiers in LEGUS. The derived cluster age distribution implies a disruption rate of $dN/d\tau \propto \tau^{-0.45 \pm 0.14}$ over $10^{7} < \tau < 10^{8.5}$yr for cluster masses $\geq 10^{3.55} M_{\odot}$ for the central region of M101 and $dN/d\tau \propto \tau^{-0.02 \pm 0.15}$ for cluster masses $\geq 10^{3.38} M_{\odot}$ in the northwest region of the galaxy. The trends we recover are weaker than those of other nearby spirals (e.g. M51) and starbursts, consistent with the M101 environment having a lower-density interstellar medium, and providing evidence in favor of environmentally-dependent cluster disruption in the central, southeast, and northwest regions of M101.
The Stanley-Stembridge conjecture associates a symmetric function to each natural unit interval order $\mathcal P$. In this paper, we define relations \`a la Knuth on the symmetric group for each $\mathcal P$ and conjecture that the associated $\mathcal P$-Knuth equivalence classes are Schur-positive, refining theorems of Gasharov, Brosnan-Chow, and Guay-Paquet. The resulting equivalence graphs fit into the framework of D graphs studied by Assaf. Furthermore, we conjecture that the Schur expansion is given by column-readings of $\mathcal P$-tableaux that occur in the equivalence class. We prove these conjectures for $\mathcal P$ avoiding two specific suborders by introducing $\mathcal P$-analog of Robinson-Schensted insertion, giving an answer to a long standing question of Chow.
The possibility of revealing non-classical behaviours in the dynamics of a trapped ion via measurements of the mean value of suitable operators is reported. In particular we focus on the manifestation known as `` Parity Effect\rq\rq which may be observed \emph{directly measuring} the expectation value of an appropriate correlation operator. The experimental feasibility of our proposal is discussed.
Unification of gravity and electromagnetism based on a theory with an affine non-symmetric connection $\Gamma^\lambda_{\mu\nu} \neq \Gamma^\lambda_{\nu\mu}$ and $\Gamma_\mu = \Gamma^\lambda_{[\mu\lambda]}\neq 0$, proposed by S. N. Bose in 1953, is revisited in the context of modern developments in high energy physics. It is shown that electrogravity unification can be achieved at a {\em premetric} stage, and that this unification based on {\em projective invariance} is broken by matter fields, opening up the possibility of a unified theory of all forces in which gravity emerges as a classical field. The theory predicts $\alpha_{sym} = \frac{1}{9}$ in the projective invariant limit, where $\alpha$ is the fine structure constant
Let $M$ be an Anderson t-motive of dimension $n$ and rank $r$. Associated are two $\Bbb F_q[T]$-modules $H^1(M)$, $H_1(M)$ of dimensions $h^1(M)$, $h_1(M)\le r$ - analogs of $H^1(A,\Bbb Z)$, $H_1(A,\Bbb Z)$ for an abelian variety $A$. There is a theorem (Anderson): $h^1(M)=r \iff h_1(M)=r$; in this case $M$ is called uniformizable. It is natural to expect that always $h^1(M)=h_1(M)$. Nevertheless, we explicitly construct a counterexample. Further, we answer a question of D.Goss: is it possible that two Anderson t-motives that differ only by a nilpotent operator $N$ are of different uniformizability type, i.e. one of them is uniformizable and other not? We give an explicit example that this is possible.
The task of crowd counting is extremely challenging due to complicated difficulties, especially the huge variation in vision scale. Previous works tend to adopt a naive concatenation of multi-scale information to tackle it, while the scale shifts between the feature maps are ignored. In this paper, we propose a novel Hierarchical Scale Recalibration Network (HSRNet), which addresses the above issues by modeling rich contextual dependencies and recalibrating multiple scale-associated information. Specifically, a Scale Focus Module (SFM) first integrates global context into local features by modeling the semantic inter-dependencies along channel and spatial dimensions sequentially. In order to reallocate channel-wise feature responses, a Scale Recalibration Module (SRM) adopts a step-by-step fusion to generate final density maps. Furthermore, we propose a novel Scale Consistency loss to constrain that the scale-associated outputs are coherent with groundtruth of different scales. With the proposed modules, our approach can ignore various noises selectively and focus on appropriate crowd scales automatically. Extensive experiments on crowd counting datasets (ShanghaiTech, MALL, WorldEXPO'10, and UCSD) show that our HSRNet can deliver superior results over all state-of-the-art approaches. More remarkably, we extend experiments on an extra vehicle dataset, whose results indicate that the proposed model is generalized to other applications.
Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of particular interest in the light of recently discovered counterexamples to a conjecture of Mercat.
A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables, respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981).
We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the boundaries.