ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the nonlinear,inverse problem of computing the stored energy function of a hyperelastic material from the full knowledge of the displacement field. The displacement field is described as solution of the nonlinear, dynamic, elastic wave equation, where the first Piola-Kirchhoff stress tensor is given as the gradient of the stored energy function. We assume that we have a dictionary at hand such that the energy function is given as a conic combination of the dictionary's elements. In that sense the mathematical model of the direct problem is the nonlinear operator that maps the vector of expansion coefficients to the solution of the hyperelastic wave equation. In this article we summarize some continuity results for this operator and deduce its Fr\'{e}chet derivative as well as the adjoint of this derivative. Since the stored energy function encodes mechanical properties of the underlying, hyperelastic material, the considered inverse problem is of highest interest for structural health monitoring systems where defects are detected from boundary measurements of the displacement field. For solving the inverse problem iteratively by the Landweber method or Newton type methods, the knowledge of the Fr\'{e}chet derivative and its adjoint is of utmost importance.
We present N=2 supersymmetry transformations, both in N=1, D=4 Minkowski and anti-de Sitter superspaces, for higher superspin massless theories. It is noted that the existence of dual versions of massless supermultiplets with arbitrary superspin s may provide a basis for understanding duality in N=1, D=4 superstring theory. We further conjecture that the N=1, D=4 supergravity pre-potential together with all higher superspin s pre-potentials are components of an N=1, D=4 superstring pre-potential.
It has been argued that the long gamma-ray burst (GRB) of GRB 060614 without an associated supernova (SN) has challenged the current classification and fuel model for long GRBs, and thus a tidal disruption model has been proposed to account for such an event. Since it is difficult to detect SNe for long GRBs at high redshift, the absence of an SN association cannot be regarded as the solid criterion for a new classification of long GRBs similar to GRB 060614, called GRB 060614-type bursts. Fortunately, we now know that there is an obvious periodic substructure observed in the prompt light curve of GRB 060614. We thus use such periodic substructure as a potential criterion to categorize some long GRBs into a new class of bursts, which might have been fueled by an intermediate-mass black hole (IMBH) gulping a star, rather than a massive star collapsing to form a black hole. Therefore, the second criterion to recognize for this new class of bursts is whether they fit the tidal disruption model. From a total of 328 Swift GRBs with accurately measured durations and without SN association, we find 25 GRBs satisfying the criteria for GRB 060614-type bursts: seven of them are with known redshifts and 18 with unknown redshifts. These new bursts are ~6% of the total Swift GRBs, which are clustered into two subclasses: Type I and Type II with considerably different viscous parameters of accretion disks formed by tidally disrupting their different progenitor stars. We suggest that the two different kinds of progenitors are solar-type stars and white dwarfs: the progenitors for four Type I bursts with viscous parameter of around 0.1 are solar-type stars, and the progenitors for 21 Type II bursts with viscous parameter of around 0.3 are white dwarfs. The potential applications of this new class of GRBs as cosmic standard candles are discussed briefly
We consider a sequence $(\xi_n)_{n\ge1}$ of $i.i.d.$ random values living in the domain of attraction of an extreme value distribution. For such sequence, there exists $(a_n)$ and $(b_n)$, with $a_n>0$ and $b_n\in\ER$ for every $n\ge 1$, such that the sequence $(X_n)$ defined by $X_n=(\max(\xi_1,...,\xi_n)-b_n)/a_n$ converges in distribution to a non degenerated distribution. In this paper, we show that $(X_n)$ can be viewed as an Euler scheme with decreasing step of an ergodic Markov process solution to a SDE with jumps and we derive a functional limit theorem for the sequence $(X_n)$ from some methods used in the long time numerical approximation of ergodic SDE's.
We investigate the non-equilibrium insulator-metal transition driven in a SmNiO3 thin film by coherent optical excitation of the LaAlO3 substrate lattice. By probing the transient optical properties over a broad frequency range (100 - 800 cm^-1), we analyze both the time dependent metallic plasma and the infrared optical phonon line shapes. We show that the light-induced metallic phase in SmNiO3 has the same carrier density as the equilibrium metallic phase. We also report that the LaAlO3 substrate acts as a transducer only at the earlier time delays, as the vibrations are driven coherently. No long-lived structural rearrangement takes place in the substrate. Finally, we show that the transient insulator-metal transition occurs both below and above the N\'eel temperature. We conclude that the supersonic melting of magnetic order measured with ultrafast x-rays is not the driving force of the formation of the metallic phase. We posit that the insulator metal transition may origin from the rearrangement of ordered charges at the interface propagating into the film.
The detection of GW170817 in both gravitational waves and electromagnetic waves heralds the age of gravitational-wave multi-messenger astronomy. On 17 August 2017 the Advanced LIGO and Virgo detectors observed GW170817, a strong signal from the merger of a binary neutron-star system. Less than 2 seconds after the merger, a gamma-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO-Virgo-derived location of the gravitational-wave source. This sky region was subsequently observed by optical astronomy facilities, resulting in the identification of an optical transient signal within $\sim 10$ arcsec of the galaxy NGC 4993. These multi-messenger observations allow us to use GW170817 as a standard siren, the gravitational-wave analog of an astronomical standard candle, to measure the Hubble constant. This quantity, which represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Our measurement combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using electromagnetic data. This approach does not require any form of cosmic "distance ladder;" the gravitational wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be $70.0^{+12.0}_{-8.0} \, \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$ (maximum a posteriori and 68% credible interval). This is consistent with existing measurements, while being completely independent of them. Additional standard-siren measurements from future gravitational-wave sources will provide precision constraints of this important cosmological parameter.
We present the results of a numerical simulation of the history and future development of the Pleiades. This study builds on our previous one that established statistically the present-day structure of this system. Our simulation begins just after molecular cloud gas has been expelled by the embedded stars. We then follow, using an N body code, the stellar dynamical evolution of the cluster to the present and beyond. Our initial state is that which evolves, over the 125 Myr age of the cluster, to a configuration most closely matching the current one.   We find that the original cluster, newly stripped of gas, already had a virial radius of 4 pc. This configuration was larger than most observed, embedded clusters. Over time, the cluster expanded further and the central surface density fell by about a factor of two. We attribute both effects to the liberation of energy from tightening binaries of short period. Indeed, the original binary fraction was close to unity. The ancient Pleiades also had significant mass segregation, which persists in the cluster today.   In the future, the central density of the Pleiades will continue to fall. For the first few hundred Myr, the cluster as a whole will expand because of dynamical heating by binaries. The expansion process is aided by mass loss through stellar evolution, which weakens the system's gravitational binding. At later times, the Galactic tidal field begins to heavily deplete the cluster mass. It is believed that most open clusters are eventually destroyed by close passage of a giant molecular cloud. Barring that eventuality, the density falloff will continue for as long as 1 Gyr, by which time most of the cluster mass will have been tidally stripped away by the Galactic field.
In a previous paper we showed that for every polarization on an abelian variety there is a dual polarization on the dual abelian variety. In this note we extend this notion of duality to families of polarized abelian varieties. As a main consequence we obtain an involution on the set of moduli spaces of polarized abelian varieties of dimension $g$. In particular, the moduli spaces $\mathcal A_{(d_1,...,d_g)}$ and $\mathcal A_{(d_1,\frac{d_1d_g}{d_{g-1}},...,\frac{d_1d_g}{d_2},d_g)}$ are canonically isomorphic.
Suppose that G and H are finite, connected graphs, G regular, X is a lazy random walk on G and Z is a reversible ergodic Markov chain on H. The generalized lamplighter chain X* associated with X and Z is the random walk on the wreath product H\wr G, the graph whose vertices consist of pairs (f,x) where f=(f_v)_{v\in V(G)} is a labeling of the vertices of G by elements of H and x is a vertex in G. In each step, X* moves from a configuration (f,x) by updating x to y using the transition rule of X and then independently updating both f_x and f_y according to the transition probabilities on H; f_z for z different of x,y remains unchanged. We estimate the mixing time of X* in terms of the parameters of H and G. Further, we show that the relaxation time of X* is the same order as the maximal expected hitting time of G plus |G| times the relaxation time of the chain on H.
The Fornax cluster is the nearest, large cluster in the southern sky, and is currently experiencing active assembly of mass. It is thus the target of a number of ongoing observing campaigns at optical, near-infrared and radio wavelengths, using state-of-the-art facilities in the Southern hemisphere. Spectroscopic redshifts are essential not only for determining cluster membership, but also kinematics within the cluster and identifying substructures. We present a compilation of all available major spectroscopic campaigns undertaken within the Fornax region, including new and previously unpublished spectroscopy. This provides not only a comprehensive census of Fornax cluster membership as a resource for the many ongoing studies of this dynamic system, but also probes the large scale structure in the background volume.
The ${\it {spin \ \ light \ \ of \ \ neutrino}}$ ($SL\nu$) is a new possible mechanism of electromagnetic radiation by a massive neutrino (with a nonzero magnetic moment) moving in media. Since the prediction of this mechanism, the question has been debated in a number of publications as whether the effect can be of any significance for realistic astrophysical conditions. Although this effect is strongly suppressed due to smallness of neutrino magnetic moment, for ultra-high energy neutrinos (PeV neutrinos recently observed by the IceCube collaboration, for instance) the $SL\nu$ might be of interest in the case of neutrinos propagating in dense matter. An advanced view on the $SL\nu$ in matter is given, and several astrophysical settings (a neutron star, supernova, Gamma-Ray Burst (GRB), and relic neutrino background) for which the effect can be realized are considered. Taking into account the threshold condition and also several competing processes, we determine conditions for which the $SL\nu$ mechanism is possible. We conclude that the most favorable case of the effect manifestation is provided by ultra dense matter of neutron stars and ultrahigh energy of the radiating neutrino, and note that these conditions can be met within galaxy clusters. It is also shown that due to the $SL\nu$ specific polarization properties this electromagnetic mechanism is of interest in the connection with the observed polarization of GRB emission.
We investigate with relativistic MHD simulations the dissipation physics of BL Lac jets, by studying the synchrotron polarization signatures of particles accelerated by the kink instability in a magnetically-dominated plasma column. The nonlinear stage of the kink instability generates current sheets, where particles can be efficiently accelerated via magnetic reconnection. We identify current sheets as regions where s = J d/B is above some predefined threshold (where B is the field strength, J the current density and d the grid scale), and assume that the particle injection efficiency scales as proportional to the square of the current. X-ray emitting particles have short cooling times, so they only probe the field geometry of their injection sites. In contrast, particles emitting in the optical band, which we follow self-consistently as they propagate away from their injection sites while cooling, sample a larger volume, and so they may be expected to produce different polarimetric signatures. We find that the degree of polarization is roughly the same between X-ray and optical bands, because even the optical-emitting particles do not travel far from the current sheet where they were injected, due to lack of sufficient kink-generated turbulence. The polarization angle shows a different temporal evolution between the two bands, due to the different regions probed by X-ray and optical emitting particles. In view of the upcoming IXPE satellite, our results can help constrain whether kink-induced reconnection (as opposed to shocks) can be the source of multi-wavelength emission from BL Lacs.
In this paper, we combine the the latest observational data, including the WMAP five-year data (WMAP5), the baryon acoustic oscillations (BAO) and type Ia supernovae (SN) "union" compilation, and use the Markov Chain Monte Carlo method to determine the dark energy parameters. We pay particular attention to the Integrated Sache-Wolfe (ISW) data from the cross-correlations of cosmic microwave background (CMB) and large scale structure (LSS). In the \Lambda CDM model, we find that the ISW data, as a complement to the WMAP data, could significantly improve the constraint of curvature \Omega_k. We also check the improvement of constraints from the new prior on the Hubble constant and find this new prior could improve the constraint of \Omega_k by a factor of 2. Finally, we study the dynamical evolving EoS of dark energy from the current observational data. Based on the dynamical dark energy model, parameterizing as w(a)=w_0+w_a(1-a), we find that the \Lambda CDM model remains a good fit to the current data. When taking into account the ISW data, the error bars of w_0 and w_a could be shrunk slightly. Current constraints on the dynamical dark energy model are not conclusive. The future precision measurements are needed.
Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of (Q mod p) divides the order of (P mod p). Then there exist a K-endomorphism f of G and a non-zero integer c such that f(P)=cQ. Furthermore, we are able to prove the above result with weaker assumptions: instead of comparing the order of the points we only compare the radical of the order (radical support problem) or the l-adic valuation of the order for some fixed rational prime l (l-adic support problem).
Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it highlights results about the values of Dedekind sums, their density and uniform distribution. Further topics include mean values, large and small (absolute) values, and the behaviour of Dedekind sums near quadratic irrationals. The present paper can be considered as a supplement to the survey article [R. W. Bruggeman, On the distribution of Dedekind sums, Contemp. Math. 166 (1994), 197--210].
We present Karl G. Jansky Very Large Array (VLA) S- (2--4 GHz), C- (4--8 GHz), and X-band (8--12 GHz) continuum observations toward seven radio-loud quasars at $z>5$. This sample has previously been found to exhibit spectral peaks at observed-frame frequencies above $\sim$1 GHz. We also present upgraded Giant Metrewave Radio Telescope (uGMRT) band-2 (200 MHz), band-3 (400 MHz), and band-4 (650 MHz) radio continuum observations toward eight radio-loud quasars at $z>5$, selected from our previous GMRT survey, in order to sample their low-frequency synchrotron emission. Combined with archival radio continuum observations, all ten targets show evidence for spectral turnover. The turnover frequencies are $\sim$1--50 GHz in the rest frame, making these targets gigahertz-peaked-spectrum (GPS) or high-frequency-peaker (HFP) candidates. For the nine well-constrained targets with observations on both sides of the spectral turnover, we fit the entire radio spectrum with absorption models associated with synchrotron self-absorption and free-free absorption (FFA). Our results show that FFA in an external inhomogeneous medium can accurately describe the observed spectra for all nine targets, which may indicate an FFA origin for the radio spectral turnover in our sample. As for the complex spectrum of J114657.79+403708.6 at $z=5.00$ with two spectral peaks, it may be caused by multiple components (i.e., core-jet) and FFA by the high-density medium in the nuclear region. However, we cannot rule out the spectral turnover origin of variability. Based on our radio spectral modeling, we calculate the radio loudness $R_{2500\rm\, \AA}$ for our sample, which ranges from 12$^{+1}_{-1}$ to 674$^{+61}_{-51}$.
Crowd counting from unconstrained scene images is a crucial task in many real-world applications like urban surveillance and management, but it is greatly challenged by the camera's perspective that causes huge appearance variations in people's scales and rotations. Conventional methods address such challenges by resorting to fixed multi-scale architectures that are often unable to cover the largely varied scales while ignoring the rotation variations. In this paper, we propose a unified neural network framework, named Deep Recurrent Spatial-Aware Network, which adaptively addresses the two issues in a learnable spatial transform module with a region-wise refinement process. Specifically, our framework incorporates a Recurrent Spatial-Aware Refinement (RSAR) module iteratively conducting two components: i) a Spatial Transformer Network that dynamically locates an attentional region from the crowd density map and transforms it to the suitable scale and rotation for optimal crowd estimation; ii) a Local Refinement Network that refines the density map of the attended region with residual learning. Extensive experiments on four challenging benchmarks show the effectiveness of our approach. Specifically, comparing with the existing best-performing methods, we achieve an improvement of 12% on the largest dataset WorldExpo'10 and 22.8% on the most challenging dataset UCF_CC_50.
We study the circular orbits of charged particles around a weakly charged Schwarzschild black hole immersed in a weak, axisymmetric magnetic field. We start by reviewing the circular orbits of neutral particles and charged particles around only weakly charged and only weakly magnetized black holes. The case of a weakly magnetized and charged black hole is investigated then. In particular, we study the effect of the electromagnetic forces on the charged particles innermost stable circular orbits. We show that negative energy stable circular orbits are possible and that two bands of charged particles circular orbits, separated by a gap of no stable circular orbits can exist. The astrophysical aspects of our findings are discussed too.
Concatenation of the deep network representations extracted from different facial patches helps to improve face recognition performance. However, the concatenated facial template increases in size and contains redundant information. Previous solutions aim to reduce the dimensionality of the facial template without considering the occlusion pattern of the facial patches. In this paper, we propose an occlusion-guided compact template learning (OGCTL) approach that only uses the information from visible patches to construct the compact template. The compact face representation is not sensitive to the number of patches that are used to construct the facial template and is more suitable for incorporating the information from different view angles for image-set based face recognition. Instead of using occlusion masks in face matching (e.g., DPRFS [38]), the proposed method uses occlusion masks in template construction and achieves significantly better image-set based face verification performance on a challenging database with a template size that is an order-of-magnitude smaller than DPRFS.
We present a pilot-assisted coherent intradyne reception methodology for CV-QKD with true local oscillator. An optically phase-locked reference tone, prepared using carrier-suppressed optical single-sideband modulation, is multiplexed in polarisation and frequency to the 250 Mbaud quantum signal in order to provide optical frequency- and phase matching between quantum signal and local oscillator. Our concept allows for high symbol rates and can be operated at an extremely low excess-noise level, as validated by experimental measurements.
In this paper we estimate the number of gravitational arcs detectable in a wide-field survey such as that which will be operated by the Euclid space mission, assuming a {\Lambda}CDM cosmology. We use the publicly available code MOKA to obtain realistic deflection angle maps of mock gravitational lenses. The maps are processed by a ray-tracing code to estimate the strong lensing cross sections of each lens. Our procedure involves 1) the generation of a light-cone which is populated with lenses drawn from a theoretical mass-function; 2) the modeling of each single lens using a triaxial halo with a NFW (Navarro-Frenk-White) density profile and theoretical concentration-mass relation, including substructures, 3) the determination of the lensing cross section as a function of redshift for each lens in the light-cone, 4) the simulation of mock observations to characterize the redshift distribution of sources that will be detectable in the Euclid images. We focus on the so-called giant arcs, i.e. gravitational arcs characterized by large length-to-width ratios (l/w > 5, 7.5 and 10). We quantify the arc detectability at different significances above the level of the background. Performing 128 different realizations of a 15,000 sq. degree survey, we find that the number of arcs detectable at 1{\sigma} above the local background will be 8912,2914, and 1275 for l/w>5, 7.5 and 10, respectively. The expected arc numbers decrease to 2409, 790, and 346 for a detection limit at 3{\sigma} above the background level. From our analysis, we find that most of the lenses which contribute to the lensing optical depth are located at redshifts 0.4<zl<0.7 and that the 50% of the arcs are images of sources at zs > 3. This is the first step towards the full characterization of the population of strong lenses that will be observed by Euclid. [abridged]