ShantanuT01/DACTYL-Pretraining huggingface dataset:
Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.
The Kerr-Schild pencil of metrics $\tilde g_{ab}=g_{ab}+V l_al_b$, with $g_{ab}$ and $\tilde g_{ab}$ satisfying the vacuum Einstein equations, is investigated in the case when the null vector $l$ has vanishing twist. This class of Kerr-Schild metrics contains two solutions: the Kasner metric and a metric wich can be obtained from the Kasner metric by a complex coordinate transformation. Both are limiting cases of the K\'ota-Perj\'es metrics. The base space-time is a pp-wave.
We present the results of a computational X-ray cross correlation analysis (XCCA) study on two dimensional polygonal model structures. We show how to detect and identify the orientational order of such systems, demonstrate how to eliminate the influence of the "computational box" on the XCCA results and develop new correlation functions that reflect the sample's orientational order only. For this purpose, we study the dependence of the correlation functions on the number of polygonal clusters and wave vector transfer $q$ for various types of polygons including mixtures of polygons and randomly placed particles. We define an order parameter that describes the orientational order within the sample. Finally, we determine the influence of detector noise and non-planar wavefronts on the XCCA data which both appear to affect the results significantly and have thus to be considered in real experiments.
A detailed study of the influence of molecular beam epitaxial growth conditions on the structural and magnetic characteristics of CuMnSb films on lattice matched GaSb is presented. For a set of nine 40~nm thick layers, the Mn and Sb fluxes are varied to produce material with different elemental compositions. It is found that the layers grown under a relative Mn to Sb flux ratio of $\Phi_{\text{Mn}}$/$\Phi_{\text{Sb}}=1.24\pm0.02$ are closest to the stoichiometric composition, for which the N\'{e}el temperature ($T_\text{N}$) attains its maximum values. Mn-related structural defects are believed to be the driving contribution to changes in the vertical lattice parameter. Having established the optimum growth conditions, a second set of samples with CuMnSb layer thickness varied from 5 to 510 nm is fabricated. We show that for sufficiently large thicknesses, the magnetic characteristics ($T_\text{N}\simeq62$ K, Curie-Weiss temperature $\Theta_\text{CW} = -100$ K) of the stoichiometric layers do correspond to the parameters reported for bulk samples. On the other hand, we observe a reduction of $T_\text{N}$ as a function of the CuMnSb thickness for our thinnest layers. All findings reported here are of particular relevance for studies aiming at the demonstration of N\'{e}el vector switching and detection in this noncentrosymmetric antiferromagnet, which have been recently proposed.
We discuss the development of an angular-momentum-conserving variant of the Density Matrix Renormalization Group (DMRG) method for use in large-scale shell-model calculations of atomic nuclei and report a first application of the method to the ground state of $^{56}$Ni and improved results for $^{48}$Cr. In both cases, we see a high level of agreement with the exact results. A comparison of the two shows a dramatic reduction in the fraction of the space required to achieve accuracy as the size of the problem grows.
For the present analysis we simulate the reaction 129Xe 54+197Au79 at E=50 MeV/nucleon respectively[3]. This reaction is simulated at different impact parameters using hard equation of state. The stored phase space is then analyzed by using MST, MSTP and MSTB algorithms. MSTB and MSTP identifies the free nucleons as early as possible. In the two cases, a check in the form of binding energy and momentum cut helps to identify the fragments quite early. The normal MST takes quite a long time to identify the stable fragments which are residual of excited fragments.
We have surveyed Kepler's supernova remnant in search of the companion star of the explosion. We have gone as deep as 2.6 solar luminosities in the stars within 20% of the radius of the remnant. We use FLAMES at the VLT-UT2 telescope to obtain high resolution spectra of the stellar candidates selected from HST images. The resulting set of stellar parameters suggests that these stars come from a rather ordinary mixture of field stars (mostly giants). A few of the stars seem to have low [Fe/H] (< -1) and they are consistent with being metal-poor giants. The radial velocities and rotational velocities vrot sin i are very well determined. There are no fast rotating stars as vrot sin i < 20 km/s. The radial velocities from the spectra and the proper motions determined from HST images are compatible with those expected from the Besan\c{c}on model of the Galaxy. The strong limits placed on luminosity suggest that this supernova could have arisen either from the core-degenerate scenario or from the double-degenerate scenario.
Fine-grained object categorization aims for distinguishing objects of subordinate categories that belong to the same entry-level object category. The task is challenging due to the facts that (1) training images with ground-truth labels are difficult to obtain, and (2) variations among different subordinate categories are subtle. It is well established that characterizing features of different subordinate categories are located on local parts of object instances. In fact, careful part annotations are available in many fine-grained categorization datasets. However, manually annotating object parts requires expertise, which is also difficult to generalize to new fine-grained categorization tasks. In this work, we propose a Weakly Supervised Part Detection Network (PartNet) that is able to detect discriminative local parts for use of fine-grained categorization. A vanilla PartNet builds on top of a base subnetwork two parallel streams of upper network layers, which respectively compute scores of classification probabilities (over subordinate categories) and detection probabilities (over a specified number of discriminative part detectors) for local regions of interest (RoIs). The image-level prediction is obtained by aggregating element-wise products of these region-level probabilities. To generate a diverse set of RoIs as inputs of PartNet, we propose a simple Discretized Part Proposals module (DPP) that directly targets for proposing candidates of discriminative local parts, with no bridging via object-level proposals. Experiments on the benchmark CUB-200-2011 and Oxford Flower 102 datasets show the efficacy of our proposed method for both discriminative part detection and fine-grained categorization. In particular, we achieve the new state-of-the-art performance on CUB-200-2011 dataset when ground-truth part annotations are not available.
Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A result to compute the angle of the value function at the optimal thresholds of the stopping region is given. To illustrate the results, the optimal stopping problem of a compound Poisson process with two-sided exponential jumps and a two-sided payoff function is solved. In this example, the smooth-pasting condition does not hold.
The absolute proper motions of about 275 million stars from the Kharkov XPM catalog have been obtained by comparing their positions in the 2MASS and USNO--A2.0 catalogs with an epoch difference of about 45 yr for northern-hemisphere stars and about 17 yr for southern-hemisphere stars. The zero point of the system of absolute proper motions has been determined using 1.45 million galaxies. The equatorial components of the residual rotation vector of the ICRS/UCAC2 coordinate system relative to the system of extragalactic sources have been determined by comparing the XPM and UCAC2 stellar proper motions: \omega_{x,y,z}=(-0.06,0.17,-0.84)+/-(0.15,0.14,0.14) mas yr^{-1}. These parameters have been calculated using about 1 million faintest UCAC2 stars with magnitudes R_{UCAC2}>16^m and J>14^m.7,for which the color and magnitude equation effects are negligible.
We investigate the transport properties of narrow quantum wires realized in disordered two-dimensional electron gases in the presence of k-linear Rashba and Dresselhaus spin-orbit interaction (SOI), and an applied in-plane magnetic field. Building on previous work [Scheid, et al., PRL 101, 266401 (2008)], we find that in addition to the conductance, the universal conductance fluctuations also feature anisotropy with respect to the magnetic field direction. This anisotropy can be explained solely from the symmetries exhibited by the Hamiltonian as well as the relative strengths of the Rashba and Dresselhaus spin orbit interaction and thus can be utilized to detect this ratio from purely electrical measurements.
We study the effective physics of F-theory at order $\alpha'^3$ in derivative expansion. We show that the ten-dimensional type IIB eight-derivative couplings involving the graviton and the axio-dilaton naturally descend from pure gravity in twelve dimensions. Upon compactification on elliptically fibered Calabi-Yau fourfolds, the non-trivial vacuum profile for the axio-dilaton leads to a new, genuinely N=1, $\alpha'^3$ correction to the four-dimensional effective action.
We consider the task of pixel-wise semantic segmentation given a small set of labeled training images. Among two of the most popular techniques to address this task are Decision Forests (DF) and Neural Networks (NN). In this work, we explore the relationship between two special forms of these techniques: stacked DFs (namely Auto-context) and deep Convolutional Neural Networks (ConvNet). Our main contribution is to show that Auto-context can be mapped to a deep ConvNet with novel architecture, and thereby trained end-to-end. This mapping can be used as an initialization of a deep ConvNet, enabling training even in the face of very limited amounts of training data. We also demonstrate an approximate mapping back from the refined ConvNet to a second stacked DF, with improved performance over the original. We experimentally verify that these mappings outperform stacked DFs for two different applications in computer vision and biology: Kinect-based body part labeling from depth images, and somite segmentation in microscopy images of developing zebrafish. Finally, we revisit the core mapping from a Decision Tree (DT) to a NN, and show that it is also possible to map a fuzzy DT, with sigmoidal split decisions, to a NN. This addresses multiple limitations of the previous mapping, and yields new insights into the popular Rectified Linear Unit (ReLU), and more recently proposed concatenated ReLU (CReLU), activation functions.
High-pressure and high-field electron spin resonance (ESR) measurements have been performed on a single crystal of the orthogonal-dimer spin system SrCu$_{2}$(BO$_{3}$)$_{2}$. With frequencies below 1 THz, ESR signals associated with transitions from the singlet ground state to the one-triplet excited states and the two-triplet bound state were observed at pressures up to 2.1 GPa. We obtained directly the pressure dependence of the gap energies, finding a clear first-order phase transition at $P_{c}=1.85\pm0.05$ GPa. By comparing this pressure dependence with the calculated excitation energies obtained from an exact diagonalization, we determined the precise pressure dependence for inter- ($J'$) and intra-dimer ($J$) exchange interactions considering the Dzyaloshinski-Moriya interaction. Thus this system undergoes a first-order quantum phase transition from the dimer singlet phase to a plaquette singlet phase above the ratio $(J'/J)_{c}=0.660\pm0.003$.
We present the global group properties of two samples of galaxy groups containing 39 high quality X-ray selected systems and 38 optically (spectroscopically) selected systems in coincident spatial regions at 0.12<z<0.79. Only nine optical systems are associable with X-ray systems. We discuss the confusion inherent in the matching of both galaxies to extended X-ray emission and of X-ray emission to already identified optical systems. Extensive spectroscopy has been obtained and the resultant redshift catalog and group membership are provided here. X-ray, dynamical, and total stellar masses of the groups are also derived and presented. We explore the effects of applying three different kinds of radial cut to our systems: a constant cut of 1 Mpc and two r200 cuts, one based on the velocity dispersion of the system and the other on the X-ray emission. We find that an X-ray based r200 results in less scatter in scaling relations and less dynamical complexity as evidenced by results of the Anderson-Darling and Dressler-Schectman tests, indicating that this radius tends to isolate the virialized part of the system. The constant and velocity dispersion based cuts can overestimate membership and can work to inflate velocity dispersion and dynamical and stellar mass. We find Lx-sigma and Mstellar-Lx scaling relations for X-ray and optically selected systems are not dissimilar. The mean fraction of mass found in stars for our systems is approximately 0.014 with a logarithmic standard deviation of 0.398 dex. We also define and investigate a sample of groups which are X-ray underluminous given the total group stellar mass. For these systems the fraction of stellar mass contributed by the most massive galaxy is typically lower than that found for the total population of groups implying that there may be less IGM contributed from the most massive member in these systems. (Abridged)
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a generalized, subsystem version of color codes. In 3D they allow the transversal implementation of a universal set of gates by gauge fixing, while error-detecting measurements involve only 4 or 6 qubits.
Central to the application of many multi-view geometry algorithms is the extraction of matching points between multiple viewpoints, enabling classical tasks such as camera pose estimation and 3D reconstruction. Many approaches that characterize these points have been proposed based on hand-tuned appearance models or data-driven learning methods. We propose Soft Expectation and Deep Maximization (SEDM), an iterative unsupervised learning process that directly optimizes the repeatability of the features by posing the problem in a similar way to expectation maximization (EM). We found convergence to be reliable and the new model to be more lighting invariant and better at localize the underlying 3D points in a scene, improving SfM quality when compared to other state of the art deep learning detectors.
Optoelectronic measurements of carbon nanotube transistors have shown a wide variety of sensitivites to the incident light. Direct photocurrent processes compete with a number of extrinsic mechanisms. Here we show that visible light absorption in the silicon substrate generates a photovoltage that can electrically gate the nanotube device. The photocurrent induced by the changing gate voltage can be significantly larger than that due to direct electron-hole pair generation in the nanotube. The dominance of photogating in these devices is confirmed by the power and position dependence of the resulting photocurrent. The power dependence is strongly non-linear and photocurrents are measured through the device even when the laser illuminates up to 1~mm from the nanotube.
Studies of ${\cal N}=4$ super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain. These spin chains have fundamental ``magnon'' excitations which obey a dispersion relation that is periodic in the momentum of the magnons. This result for the dispersion relation was also shown to hold at arbitrary 't Hooft coupling. Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description. The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle. We use these results to compute the energy of a spinning string. We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory. We compute the overall S-matrix at large 't Hooft coupling using the string description and we find that it agrees with an earlier conjecture. We also find an infinite number of two magnon bound states at strong coupling, while at weak coupling this number is finite.
In this contribution we discuss the physics of strange hadrons in low energy ($\simeq 1-2 \rm AGeV$) heavy ion collision. In this energy range the relevant strange particle are the kaons and anti-kaons. The most interesting aspect concerning these particles are so called in-medium modifications. We will attempt to review the current status of understanding of these in medium modifications. In addition we will briefly discuss other issues related with kaon production, such as the nuclear equation of state and chemical equilibrium.
It is shown that self-similar blow-up for a fourth-order reaction-diffusion equation is incomplete in the sense that, in general, there exists a self-similar extension of solutions after blow-up. Other types of complete blow-up of non self-similar form are discussed.
The Wiener measure induces a measure of closed, convex, (d-1)-dimensional, Euclidean (hyper-)surfaces that are the convex hulls of closed d-dimensional Brownian bridges. I present arguments and numerical evidence that this measure, for odd d, is generated by a local classical action of length dimension two that depends on geometric invariants of the (d-1)-dimensional surface only.
In radiation damage cascade displacement spikes ions and electrons can reach very high temperatures and be out of thermal equilibrium. Correct modelling of cascades with molecular dynamics should allow for the non-adiabatic exchange of energy between ions and electrons using a consistent model for the electronic stopping, electronic temperature rise, and thermal conduction by the electrons. We present a scheme for correcting embedded atom potentials for these non-adiabatic properties at the level of the second-moment approximation, and parameterize for the bcc transition metals above the Debye temperature. We use here the Finnis-Sinclair and Derlet-Nguyen-Manh-Dudarev potentials as models for the bonding, but the corrections derived from them can be applied to any suitable empirical potential.
We present 4.5$\mu$m and 8$\mu$m photometric observations of 18 cool white dwarfs obtained with the Spitzer Space Telescope. Our observations demonstrate that four white dwarfs with T_eff< 6000 K show slightly depressed mid-infrared fluxes relative to white dwarf models. In addition, another white dwarf with a peculiar optical and near-infrared spectral energy distribution (LHS 1126) is found to display significant flux deficits in Spitzer observations. These mid-infrared flux deficits are not predicted by the current white dwarf models including collision induced absorption due to molecular hydrogen. We postulate that either the collision induced absorption calculations are incomplete or there are other unrecognized physical processes occuring in cool white dwarf atmospheres. The spectral energy distribution of LHS 1126 surprisingly fits a Rayleigh-Jeans spectrum in the infrared, mimicking a hot white dwarf with effective temperature well in excess of 10$^5$ K. This implies that the source of this flux deficit is probably not molecular absorption but some other process.
Oxygen was electrochemically intercalated into Sr$_2$IrO$_4$ sintered samples, single crystals and a thin film. We estimate the diffusion length to a few $\mu$m and the concentration of the intercalated oxygen to $\delta$ $\simeq$ 0.01. The latter is thus much smaller than for the cuprate and nickelate parent compounds, for which $\delta$ $>$ 0.1 is obtained, which could be a consequence of larger steric effects. The influence of the oxygen doping state on resistivity is small, indicating also a poor charge transfer to the conduction band. It is shown that electrochemical intercalation of oxygen may also contribute to doping, when gating thin films with ionic liquid in the presence of water.
Specific heat of the layered NaxCoO2 (x=0.65, 0.70 and 0.75) oxides has been measured in the temperature range of 3-360 K and magnetic field of 0 and 9 T. The analysis of data, assuming the combined effect of inter-layer superexchange and the phase separation into mesoscopic magnetic domains with localized spins embedded in a matrix with itinerant electronic character, suggests that the dominant contribution to the specific heat in the region of short-range ordering is mediated by quasi-2D antiferromagnetic clusters, perpendicular to the CoO2 layers.
We compute the p-adic Abel-Jacobi map of the product of a Hilbert modular surface and a modular curve at a null-homologous (modified) embedding of the modular curve in this product, evaluated on differentials associated to a Hilbert cuspidal form f of weight (2,2) and a cuspidal form of weight 2. We generalize this computation to suitable null-homological cycles in the fibre products of the universal families on the surface and the curve, evaluated at differentials associated to f and g of higher weights. We express the values of the p-adic Abel-Jacobi map at these weights in terms of a p-adic L- function associated to a Hida family of Hilbert modular forms and a Hida family of cuspidal forms. Our function is a Hilbert modular analogue of the p- adic L-function defined by Darmon and Rotger.
We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schr\"odinger equation in two space dimensions. We present a simple new proof that treats the case of radial initial data. The key ingredient is a localized virial/Morawetz estimate; the radial assumption aids in controlling the error terms resulting from the spatial localization.
Following Benjamin et al., a matrix with entries being sums of two neighbouring Catalan numbers is considered. Its LU-decomposition is given, by guessing the results and later prove it by computer algebra, with lots of human help. Specializing a parameter, the determinant turns out to be a Fibonacci number with odd index, confirming earlier results, obtained back then by combinatorial methods.