ShantanuT01/DACTYL-Pretraining huggingface dataset:
Starting in late 2013, the eROSITA telescope will survey the X-ray sky with unprecedented sensitivity. Assuming a detection limit of 50 photons in the (0.5-2.0) keV energy band with a typical exposure time of 1.6 ks, we predict that eROSITA will detect ~ 9.3 X 10^4 clusters of galaxies more massive than 5 X 10^13 Msun/h, with the currently planned all-sky survey. Their median redshift will be z ~ 0.35. We perform a Fisher-matrix analysis to forecast the constraining power of eROSITA on the LambdaCDM cosmology and, simultaneously, on the X-ray scaling relations for galaxy clusters. Special attention is devoted to the possibility of detecting primordial non-Gaussianity. We consider two experimental probes: the number counts and the angular clustering of a photon-count limited sample of clusters. We discuss how the cluster sample should be split to optimize the analysis and we show that redshift information of the individual clusters is vital to break the strong degeneracies among the model parameters. For example, performing a "tomographic" analysis based on photometric-redshift estimates and combining 1- and 2-point statistics will give marginal 1-sigma errors of Delta(sigma_8) ~ 0.036 and Delta(Omega_m) ~ 0.012 without priors, and improve the current estimates on the slope of the luminosity-mass relation by a factor of 3. Regarding primordial non-Gaussianity, eROSITA clusters alone will give Delta(f_NL) = 9, 36, 144 for the local, orthogonal and equilateral model, respectively. Measuring redshifts with spectroscopic accuracy would further tighten the constraints by nearly 40 per cent (barring f_NL which displays smaller improvements). Finally, combining eROSITA data with the analysis of temperature anisotropies in the cosmic microwave background by the Planck satellite should give sensational constraints on both the cosmology and the properties of the intracluster medium.
We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element. Essentially, this theory encompasses the study of a functor which maps certain geometries including graphs to Deitmar schemes with additional structure, as such introducing a new zeta function for graphs. The functor is then used to determine automorphism groups of the Deitmar schemes and base extensions to fields.
We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an approximation of the L2 projection operator onto piecewise constant functions on a coarse mesh, but which allows nudging to be done completely at the linear algebraic level, independent of the rest of the discretization, with a diagonal matrix that is simple to construct. We prove the new operator maintains stability and accuracy properties, and we apply it to algorithms for both fluid transport DA and incompressible Navier Stokes DA. For both applications we prove the DA solutions with arbitrary initial conditions converge to the true solution (up to optimal discretization error) exponentially fast in time, and are thus long-time accurate. Results of several numerical tests are given, which both illustrate the theory and demonstrate its usefulness on practical problems.
The analytic, nonlinear integral equation approach is used to calculate the finite-size corrections to the transfer matrix eigen-spectra of the critical dilute O(n) model on the square periodic lattice. The resulting bulk conformal weights extend previous exact results obtained in the honeycomb limit and include the negative spectral parameter regimes. The results give the operator content of the 19-vertex Izergin-Korepin model along with the conformal weights of the dilute $A_L$ face models in all four regimes.
We investigate the lattice dynamics and thermodynamics of nonmagnetic bcc vanadium as a function of temperature and pressure, using the first principles linear response linear-muffin-tin-orbital method. The calculated phonon density of states (DOS) show strong temperature dependence, different from inelastic neutron scattering measurements where the phonon DOS show little change from room temperature up to 1273 K. We obtain the Helmholtz free energy including both electronic and phonon contributions and calculate various equation of state properties such as the bulk modulus and the thermal expansion coefficient. A detailed comparison has been made with available experimental measurements.
Pests and diseases pose a key challenge to passion fruit farmers across Uganda and East Africa in general. They lead to loss of investment as yields reduce and losses increases. As the majority of the farmers, including passion fruit farmers, in the country are smallholder farmers from low-income households, they do not have the sufficient information and means to combat these challenges. While, passion fruits have the potential to improve the well-being of these farmers as they have a short maturity period and high market value , without the required knowledge about the health of their crops, farmers cannot intervene promptly to turn the situation around.   For this work, we have partnered with the Uganda National Crop Research Institute (NaCRRI) to develop a dataset of expertly labelled passion fruit plant leaves and fruits, both diseased and healthy. We have made use of their extension service to collect images from 5 districts in Uganda,   With the dataset in place, we are employing state-of-the-art techniques in machine learning, and specifically deep learning, techniques at scale for object detection and classification to correctly determine the health status of passion fruit plants and provide an accurate diagnosis for positive detections.This work focuses on two major diseases woodiness (viral) and brown spot (fungal) diseases.
The structure of $^{44}$Ti is studied in an oblique-basis that includes spherical and SU(3) shell-model basis states. The results show that the oblique-basis concept is applicable, even though the strong spin-orbit interaction, which breaks the SU(3) symmetry, generates significant splitting of the single-particle levels. Specifically, a model space that includes a few SU(3) irreducible representations (irreps), namely, the leading (12,0) and next to the leading (10,1) irreps -- including spin S=0 and 1 configurations of the latter, plus spherical shell-model configurations (SSMC) that have at least two valence nucleons confined to the $f_{7/2}$ orbit -- the SM(2) case, yield results that are comparable to SSMC with at least one valence nucleon confined to the $f_{7/2}$ orbit -- the SM(3) case.
Continuous-time quantum error correction (CTQEC) is an approach to protecting quantum information from noise in which both the noise and the error correcting operations are treated as processes that are continuous in time. This chapter investigates CTQEC based on continuous weak measurements and feedback from the point of view of the subsystem principle, which states that protected quantum information is contained in a subsystem of the Hilbert space. We study how to approach the problem of constructing CTQEC protocols by looking at the evolution of the state of the system in an encoded basis in which the subsystem containing the protected information is explicit. This point of view allows us to reduce the problem to that of protecting a known state, and to design CTQEC procedures from protocols for the protection of a single qubit. We show how previously studied CTQEC schemes with both direct and indirect feedback can be obtained from strategies for the protection of a single qubit via weak measurements and weak unitary operations. We also review results on the performance of CTQEC with direct feedback in cases of Markovian and non-Markovian decoherence, where we have shown that due to the existence of a Zeno regime in non-Markovian dynamics, the performance of CTQEC can exhibit a quadratic improvement if the time resolution of the weak error-correcting operations is high enough to reveal the non-Markovian character of the noise process.
Deviations from an idealized equilibrium phase transition picture in nuclear multifragmentation is studied in terms of the entropic index. We investigate different heat-capacity features in the canonical quantum statistical model of nuclear multifragmentation generalized in the framework of Tsallis nonextensive thermostatistics. We find that the negative branch of heat capacity observed in quasi-peripheral Au+Au collisions is caused primarily by the non-generic nonextensivity effects.
Recently Russell et al. [Phys. Rev. Lett. 120, 047401 (2018)] have reported a clear signal of many-particle contributions to cyclotron resonance in high-mobility hBN-encapsulated graphene, observing significant variations of resonance energies as a function of the filling factor $\nu$ for a series of interband channels. To elucidate their results, Coulombic contributions to the Landau-level spectra and cyclotron resonance in graphene are examined with a possible band gap taken into account and with emphasis on revealing electron-hole ($eh$) conjugation symmetry underlying such level and resonance spectra. Theory, based on the single-mode approximation, gives a practically good account of the experimental data; the data suggest a band gap of ~ 10 meV and show a profile that apparently reflects $eh$ conjugation symmetry.
We have performed three-dimensional, non-LTE radiative transfer calculations for 12CO and 13CO lines, applying them to our high-resolution hydrodynamic models of the `torus' around a SMBH in an active galactic nucleus. The hydrodynamic simulations reveal inhomogeneous and turbulent gas structure on a sub-pc scale in a circum-nuclear starburst region. Thick disks interlaced with filaments, clumps and holes are naturally formed due to the interplay among energy feedback from supernovae, self-gravity of the gas, galactic rotation, and radiative cooling. The intensity maps of the molecular lines for the circum-nuclear disks show a clumpy structure reflecting the intrinsic inhomogeneity and turbulent motion of the gas disk. The fine structure of the `torus' could be resolved in the nearby active galaxies using ALMA. We also found that the X-factor is not uniformly distributed in the central 100 pc region. The X-factor derived for 12CO(J=1-0) intensity depends strongly on the intensity, whereas the X for 12CO(3-2) is nearly constant over two orders of magnitude of the intensity. The suggested conversion factor for the molecular gas mass is X_CO (3-2) ~ 0.27 x 10^{20} cm^{-2} (K km s^{-1})^{-1}.
We ask whether a local Hamiltonian with a featureless (fully gapped and nondegenerate) ground state could exist in certain quantum spin systems. We address this question by mapping the vicinity of certain quantum critical point (or gapless phase) of the $d-$dimensional spin system under study to the boundary of a $(d+1)-$dimensional bulk state, and the lattice symmetry of the spin system acts as an on-site symmetry in the field theory that describes both the selected critical point of the spin system, and the corresponding boundary state of the $(d+1)-$dimensional bulk. If the symmetry action of the field theory is nonanomalous, i.e. the corresponding bulk state is a trivial state instead of a bosonic symmetry protected topological (SPT) state, then a featureless ground state of the spin system is allowed; if the corresponding bulk state is indeed a nontrivial SPT state, then it likely excludes the existence of a featureless ground state of the spin system. From this perspective we identify the spin systems with SU($N$) and SO($N$) symmetries on one, two and three dimensional lattices that permit a featureless ground state. We also verify our conclusions by other methods, including an explicit construction of these featureless spin states.
We prove some general recursions for the numbers of representations of positive integers as a sum x+y, x in X, y in Y, where X,Y are increasing sequences. In particular, we obtain recursions for the number of the Goldbach, Lemoine-Levy, Chen and other binary partitions.
In [18], Mozerov et al. propose to perform stereo matching as a two-step energy minimization problem. For the first step they solve a fully connected MRF model. And in the next step the marginal output is employed as the unary cost for a locally connected MRF model.   In this paper we intend to combine the two steps of energy minimization in order to improve stereo matching results. We observe that the fully connected MRF leads to smoother disparity maps, while the locally connected MRF achieves superior results in fine-structured regions. Thus we propose to jointly solve the fully connected and locally connected models, taking both their advantages into account. The joint model is solved by mean field approximations. While remaining efficient, our joint model outperforms the two-step energy minimization approach in both time and estimation error on the Middlebury stereo benchmark v3.
A model is developed with the aim of analyzing interacting superparamagnets. Model is built from magnetic dipolar interaction and demagnetizing mean field concepts. A useful expression for effective demagnetizing factors is achieved, which allows for the analysis of non uniform spatial distributions of nanoparticles. This expression is a function of demagnetizing factors associated with specimen and clusters shapes, and of the mean distances between near neighbor nanoparticles and between clusters, relative to the characteristic sizes of each of these two types of objects, respectively. It explains effects of magnetic dipolar interactions such as the observation of apparent nanoparticle magnetic-moments smaller than real ones. It is shown that by performing a minimum set of experimental determinations, model application allows retrieval of intrinsic properties, like magnetic moment and susceptibility in the absence of interactions. It also permits the estimation of mean interparticle and intercluster relative distances, and of demagnetizing factors associated with clusters shape. An expression for magnetic dipolar energy per nanoparticle is also derived. Model experimental test was performed by analysis of results reported in the literature and of original results. They correspond to magnetite particles dispersed in PEGDA-600 polymer, and in PVA ferrogels. Experimental results display different magnetic response when prism shaped specimens are measured along principal directions. Intrinsic properties and structural information were retrieved from the analysis, in excellent agreement with information obtained from FESEM images. In the studied samples nanoparticles were found to be in close contact to each other within almost randomly oriented clusters. Intercluster mean relative-distance was found to vary between 2.2 and 7.5, depending on particles volume fraction.
We apply stochastic quantization method to Kostov's matrix-vector models for the second quantization of orientable strings with Chan-Paton like factors, including both open and closed strings. The Fokker-Planck hamiltonian deduces an orientable open-closed string field theory at the double scaling limit. There appears an algebraic structure in the continuum F-P hamiltonian including a Virasoro algebra and a SU(r) current algebra.
We present a calculation of the width for $\chi_{cJ}\rightarrow e^{+}e^{-}$ decay. The amplitude of the process is computed within the NRQCD framework. The leading-order contribution is described by two terms associated with the two different integration domains in the electromagnetic loop describing two-photon annihilation of the heavy quark-antiquark pair. The corresponding operators are defined in the framework of NRQCD. The matrix element of one of these operators describes a configuration with an ultrasoft photon and can be associated with the higher Fock state of the heavy meson. In order to compute this contribution we use the heavy hadron chiral perturbation theory. We obtain that this contribution is numerically dominant. The obtained estimates for the decay widths of the $\chi_{c1}$ and $\chi_{c2}$ states are $0.09$ eV and $0.06$ eV, respectively.
We carry out high resolution calculations of the solar overshoot region with unprecedentedly realistic parameters, especially the small energy flux compared with $\rho c^3_\mathrm{s}$, where $\rho$ and $c_\mathrm{s}$ are density and speed of sound. Our main purpose is to investigate behavior of the overshoot and the small-scale dynamo with parameters as close as possible to those of the Sun. Our calculations show that the bottom part of the convection zone becomes subadiabatic, which efficiently suppresses downflows. As a result we see a steep transition from the CZ to the RZ whose width is estimated 0.4% of the local pressure scale height. This result is consistent with a semi-analytic convection/overshoot model. We also find that the small-scale dynamo becomes efficient with a smaller energy flux. The sudden suppression of the downflows around the base of the convection zone increases the efficiency of the small-scale dynamo.
Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity conserving relaxation theory. Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops.
Let Y be a random d-dimensional subcomplex of the (n-1)-dimensional simplex S obtained by starting with the full (d-1)-dimensional skeleton of S and then adding each d-simplex independently with probability p=c/n. We compute an explicit constant gamma_d=Theta(log d) so that for c < gamma_d such a random simplicial complex either collapses to a (d-1)-dimensional subcomplex or it contains the boundary of a (d+1)-simplex. We conjecture this bound to be sharp. In addition we show that there exists a constant gamma_d< c_d <d+1 such that for any c>c_d and a fixed field F, asymptotically almost surely H_d(Y;F) \neq 0.
IX Vel has been considered as one of the prototypical novalike cataclysmic variables with thermally stable accretion disks. Using All-Sky Automated Survey (ASAS-3) and All-Sky Automated Survey for Supernovae (ASAS-SN) observations, I found that IX Vel is a low-amplitude dwarf nova showing standstills. This object has been re-classified as a Z Cam-type dwarf nova. This conclusion is consistent with the mass-transfer rate using the Gaia parallax which places the object near the lower limit of the thermal stability. Using two-dimensional Least Absolute Shrinkage and Selection Operator (Lasso), I found that the cycle lengths of dwarf nova outbursts varied between 13 and 20 d. Analysis of the ASAS-3 data suggested that the cycle lengths are shorter and the amplitudes are smaller when the system is bright. Standstills occurred when the system was bright. These results support the idea that a subtle variation in the mass-transfer rate from the secondary causes transitions between outbursting state and standstills in Z Cam stars.
This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein-Uhlenbeck process. The time-change process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.
Time-resolved angle-resolved photoemission spectroscopy is one of the most powerful pump-probe measurements of materials driven far from equilibrium. Unlike the linear-response regime, where the frequency-dependent response function is independent of time, in a far-from-equilibrium experiment, the response function depends on two times in the time domain. In this work, we describe how one can use time-dependent frequency response functions and how they involve contributions from times that are near to each other. This implies that they should not be thought of as a frequency-dependent response at a single definite time. Instead, the Fourier uncertainty relations show that they involve contributions from ranges of times and must be interpreted in this light. We use this insight to help understand what time-resolved photoemission measurements actually measure.
New concept of intermediate- and short-range nuclear force proposed by the authors a few years ago is discussed briefly. The general concept is based on an assumption on generation of the dressed dibaryon in intermediate state in $NN$ interaction. This new mechanism has been shown to lead not only to numerous new predictions in hadronic physics but also should be responsible for a large portion of nuclear binding energy and properties of nuclear wavefunctions at high momenta.
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag, 1981 (English translation by G. Brauer and J. Goldman) and D. Marcus, Number Fields, Springer, 1977.
Recently, learning equivariant representations has attracted considerable research attention. Dieleman et al. introduce four operations which can be inserted into convolutional neural network to learn deep representations equivariant to rotation. However, feature maps should be copied and rotated four times in each layer in their approach, which causes much running time and memory overhead. In order to address this problem, we propose Deep Rotation Equivariant Network consisting of cycle layers, isotonic layers and decycle layers. Our proposed layers apply rotation transformation on filters rather than feature maps, achieving a speed up of more than 2 times with even less memory overhead. We evaluate DRENs on Rotated MNIST and CIFAR-10 datasets and demonstrate that it can improve the performance of state-of-the-art architectures.
Self-organization on crystal surface is studied as a two dimensional spinodal decomposition in presence of a surface stress. The elastic Green function is calculated for a $(001)$ cubic crystal surface taking into account the crystal anisotropy. Numerical calculations show that the phase separation is driven by the interplay between domain boundary energy and long range elastic interactions. At late stage of the phase separation process, a steady state appears with different nanometric patterns according to the surface coverage and the crystal elastic constants.