ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is known that the category of affine Lagrangian relations, AffLagRel_F, over a field, F, of integers modulo a prime p (with p > 2) is isomorphic to the category of stabilizer quantum circuits for p-dits. Furthermore, it is known that electrical circuits (generalized for the field F) occur as a natural subcategory of AffLagRel_F. The purpose of this paper is to provide a characterization of the relations in this subcategory -- and in important subcategories thereof -- in terms of parity-check and generator matrices as used in error detection.   In particular, we introduce the subcategory consisting of Kirchhoff relations to be (affinely) those Lagrangian relations that conserve total momentum or equivalently satisfy Kirchhoff's current law. Maps in this subcategory can be generated by electrical components (generalized for the field F): namely resistors, current dividers, and current and voltage sources. The "source" electrical components deliver the affine nature of the maps while current dividers add an interesting quasi-stochastic aspect.   We characterize these Kirchhoff relations in terms of parity-check matrices and in addition, characterizes two important subcategories: the deterministic Kirchhoff relations and the lossless relations. The category of deterministic Kirchhoff relations as electrical circuits are generated by resistors circuits. Lossless relations, which are deterministic Kirchhoff, provide exactly the basic hyper-categorical structure of these settings.
The Mott corrections to the higher moments of the heavy ion energy-loss distribution are calculated in a wide range of relative particle velocity on the basis of the Mott exact cross section. It is shown that the relative Mott corrections to the first-order Born central moments and normalized central moments reach a large value over the range under consideration.
In this paper, we propose a general dual convolutional neural network (DualCNN) for low-level vision problems, e.g., super-resolution, edge-preserving filtering, deraining and dehazing. These problems usually involve the estimation of two components of the target signals: structures and details. Motivated by this, our proposed DualCNN consists of two parallel branches, which respectively recovers the structures and details in an end-to-end manner. The recovered structures and details can generate the target signals according to the formation model for each particular application. The DualCNN is a flexible framework for low-level vision tasks and can be easily incorporated into existing CNNs. Experimental results show that the DualCNN can be effectively applied to numerous low-level vision tasks with favorable performance against the state-of-the-art methods.
We have defined a new type of clustering scheme preserving the connectivity of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving process. Our new clustering scheme performs much better for correlation length and dynamical critical exponents in high dimensions, where the conventional Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising Model to be z=2.13 and z=2.09, respectively at pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behaviour for randomly bond diluted lattices in d=2 and 3, in the light of this new transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law degree distributions, both in the pure and random cases.
We experimentally resolve several weakly coupled nuclear spins in diamond using a series of novelly designed dynamical decoupling controls. Some nuclear spin signals, hidden by decoherence under ordinary dynamical decoupling controls, are shifted forward in time domain to the coherence time range and thus rescued from the fate of being submerged by the noisy spin bath. In this way, more and remoter single nuclear spins are resolved. Additionally, the field of detection can be continuously tuned on sub-nanoscale. This method extends the capacity of nanoscale magnetometry and may be applicable in other systems for high-resolution noise spectroscopy.
The stellar Rotation $vs.$ Age relation is commonly considered as a useful tool to derive reliable ages for Sun-like stars. However, in the light of \kepler\ data, the presence of apparently old and fast rotators that do not obey the usual gyrochronology relations led to the hypothesis of weakened magnetic breaking in some stars. In this letter, we constrain the solar rotation evolutionary track using solar twins. Predicted rotational periods as a function of mass, age, [Fe/H] and given critical Rossby number ($Ro_{\rm crit}$) were estimated for the entire rotational sample. Our analysis favors the smooth rotational evolution scenario and suggests that, if the magnetic weakened breaking scenario takes place at all, it should arise after $Ro_{\rm crit}\gtrsim2.29$ or ages $\gtrsim$5.3 Gyr (at 95$\%$ confidence level).
We study the transport properties of quantum 1D systems under strong monitoring. The quantum Zeno effect inhibits transport and induces localization. Beyond the Zeno freezing and on long time scales, a new dynamics emerges in the form of a Markov process. Studying fermionic and bosonic chains under strong monitoring, we are able to identify the quantum origin of the classical exclusion process, inclusion process and a sub-class of the misanthrope process. Moreover, we show that passive monitoring cannot break time-reversal symmetry and that the transport generally loses its ballistic nature existing for weak measurements.
We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and also test it in a set of cosmological N-body simulations. We find that the relation is in excellent agreement with the simulations and is independent of number density and the nature of the distributions. We show that the relation between information entropy and mass variance can be used to determine the linear bias on large scales and detect the signatures of non-Gaussianity on small scales in galaxy distributions.
We study the prospects for measuring the dark matter distribution of voids with stacked weak lensing. We select voids from a large set of $N$-body simulations, and explore their lensing signals with the full ray-tracing simulations including the effect of the large-scale structure along the line-of-sight. The lensing signals are compared with simple void model predictions to infer the three-dimensional mass distribution of voids. We show that the stacked weak lensing signals are detected at significant level (S/N$\geq5$) for a 5000 degree$^2$ survey area, for a wide range of void radii up to $\sim50$ Mpc. The error from the galaxy shape noise little affects lensing signals at large scale. It is also found that dense ridges around voids have a great impact on the weak lensing signals, suggesting that proper modeling of the void density profile including surrounding ridges is essential for extracting the average total underdens mass of voids.
The spectral shape of the prompt emissions of gamma-ray bursts (GRBs) is typically expressed by the Band function: smooth joining of two power-law functions for high-energy and low-energy regions. To reveal the origin of the Band function, we revisit the stochastic acceleration model, in which electrons are accelerated via scattering with turbulent waves in the GRB outflow. The balance between the acceleration and synchrotron cooling yields a narrow energy-distribution similar to the Maxwellian distribution. The synchrotron spectrum becomes consistent with the observed hard photon index for the low-energy region. On the other hand, the narrow electron energy distribution contradicts the power-law spectrum for the high-energy region. We consider an evolution of the electron energy distribution to solve this problem. The turbulence and magnetic field induced by a certain hydrodynamical instability gradually decay. According to this evolution, the typical synchrotron photon energy also decreases with time. The time-integrated spectrum forms the power-law shape for the high-energy region. We discuss the required evolutions of the turbulence and magnetic field to produce a typical Band function. Although the decay of the turbulence is highly uncertain, recent numerical simulations for decaying turbulence seem comparatively positive for the stochastic acceleration model. Another condition required to reconcile observations is a much shorter duration of the stochastic acceleration than the dynamical timescale.
We discuss the statistical correlation properties of currents and energy flows generated by an adiabatic quantum pump. Our approach emphasizes the important role of quantized energy exchange between the sea of electrons and the oscillating scatterer. The pump-frequency introduces a natural energy scale. In the low temperature limit, thermal energy much smaller than a modulation quantum, the pump generates a shot-like noise which manifests itself in photon-assisted quantum mechanical exchange amplitudes. In the high temperature limit, thermal energy much larger than a modulation quantum, the pump producesa thermal-like noise due to ac-currents generated by the pump. We predict that with increasing temperature the frequency dependence of the noise changes. The current noise is linear in pump-frequency at low temperatures, is quadratic at intermediate temperatures, and is linear again at high temperatures. Similarly, in the same temperature regions, the heat flow noise is proportional to the third, second and first power of the pump-frequency.
We approximate a two--phase model by the compressible Navier-Stokes equations with a singular pressure term. Up to a subsequence, these solutions are shown to converge to a global weak solution of the compressible system with the congestion constraint studied for instance by P.L. Lions and N. Masmoudi [ Annales I.H.P., 1999]. The paper is an extension of the previous result obtained in one-dimensional setting by D. Bresch et al. [ C. R. Acad. Sciences Paris, 2014] to the multi-dimensional case with heterogeneous barrier for the density.
We propose a new model of Fast Radio Bursts (FRBs) based on stellar mass black hole-massive star binaries. We argue that the inhomogeneity of the circumstellar materials or/and the time varying wind activities of the stellar companion will cause the black hole to accrete at a transient super-Eddington rate. The collision among the clumpy ejecta in the resulted jet could trigger plasma instability. As a result, the plasma in the jet will emit coherent curvature radiation. When the jet cone aims toward the observer, the apparent luminosity can be $10^{41}-10^{42}$\,erg/s. The duration of the resulted flare is $\sim$ millisecond. The high event rate of the observed non-repeating FRBs can be explained. A similar scenario in the vicinity of a supermassive black hole can be used to explain the interval distribution of the repeating source FRB121102 qualitatively.
In this paper, we study the existence problem for cyclic $\ell$-cycle decompositions of the graph $K_m[n]$, the complete multipartite graph with $m$ parts of size $n$, and give necessary and sufficient conditions for their existence in the case that $2\ell \mid (m-1)n$.
The fraction of high-redshift sources which are multiply-imaged by intervening galaxies is strongly dependent on the cosmological constant, and so can be a useful probe of the cosmological model. However its power is limited by various systematic (and random) uncertainties in the calculation of lensing probabilities, one of the most important of which is the dynamical normalisation of elliptical galaxies. Assuming ellipticals' mass distributions can be modelled as isothermal spheres, the mass normalisation depends on: the velocity anisotropy; the luminosity density; the core radius; and the area over which the velocity dispersion is measured. The differences in the lensing probability and optical depth produced by using the correct normalisation can be comparable to the differences between even the most extreme cosmological models. The existing data is not sufficient to determine the correct normalisation with enough certainty to allow lensing statistics to be used to their full potential. However, as the correct lensing probability is almost certainly higher than is usually assumed, upper bounds on the cosmological constant are not weakened by these possibilities.
We use Hamilton equations to find optimal paths to big queues in Jackson networks. They are shown to be given by fluid trajectories of the dual network. The fluid equations are shown to be dual to the Hamilton equations. Thus, a version of the extended Onzager-Machlup principle is proved: a fluctuation trajectory is the time reversal of a relaxation trajectory of the dual dynamic. The case of a two-node network is given a geometric treatment.
In this work, the four-point Green functions relevant to the study of Friedel oscillations are calculated for a Luttinger liquid with a cluster of impurities around an origin using the powerful Non chiral bosonization technique (NCBT). The two-point functions obtained using the same method are used to calculate the dynamical density of states (DDOS), which exhibits a power law in energy and closed analytical expressions for the DDOS exponent is calculated. These results interpolates between the weak barrier and weak link cases which are typically studied in the literature. The dependence of the DDOS on the nature of interactions and the strength of the impurity clusters are highlighted. Finally the special case of the Luttinger parameter g=1/2 is studied and compared with existing results.
A relationship between the water maser detection rate and large nuclear column densities in AGN has often been cited in the literature. Indeed, detailed studies of luminous water masers, typically associated with the nuclear activity, allow us to investigate the innermost regions of AGN, with an impact on the still debated Unified Model for this class of objects.We have recently entertained a search for maser emission in a well-defined sample of Compton-thick AGN aimed at investigating, on firm statistical bases, the aforementioned relationship. While the survey is still ongoing, and is matter of a forthcoming publication, a new luminous water maser has been detected in the lenticular (field) S0 galaxy IRAS15480-0344, whose origin, associated with an accretion disc or a nuclear outflow/jet, needs to be assessed. Multi-epoch single-dish observations and VLBI measurements were performed to investigate the distribution, spatial extension, and variability of the maser emission in order to infer the main characteristics of the water megamaser. The new detection in IRAS15480-0344 is reported: a megamaser with a total single-dish isotropic luminosity of ~200 Lsun and a profile composed of two main features, a broad line with a full width to half maximum (FWHM) linewidth of ~90 km/s and a narrow (FWHM<1 km/s) one. We performed a follow-up to the detection with the Very Long Baseline Array (VLBA) and confidently detected only the narrow component, which is coincident with the nuclear radio continuum emission detected with the Very Large Array at 8.4 GHz. A weak narrow feature has also been detected in the velocity range of the broad feature and is located 15 pc to the north-west with respect to the stronger component. Neither maser spot is associated with the compact radio continuum sources derived from the same VLBA dataset. [Abridged]
We present the results of a galaxy-wide study of molecular gas and star formation in a sample of 76 HII regions in the nearby spiral galaxy NGC 300. We have measured the molecular gas at 250 pc scales using pointed CO(J=2-1) observations with the APEX telescope. We detect CO in 42 of our targets, deriving molecular gas masses ranging from our sensitivity limit of ~10^5 Msun to 7x10^5 Msun. We find a clear decline in the CO detection rate with galactocentric distance, which we attribute primarily to the decreasing radial metallicity gradient in NGC 300. We combine GALEX FUV, Spitzer 24 micron, and H-alpha narrowband imaging to measure the star formation activity in our sample. We have developed a new direct modeling approach for computing star formation rates that utilizes these data and population synthesis models to derive the masses and ages of the young stellar clusters associated with each of our HII region targets. We find a characteristic gas depletion time of 230 Myr at 250 pc scales in NGC 300, more similar to the results obtained for Milky Way Giant Molecular Clouds than the longer (>2 Gyr) global depletion times derived for entire galaxies and kpc-sized regions within them. This difference is partially due to the fact that our study accounts for only the gas and stars within the youngest star forming regions. We also note a large scatter in the NGC 300 SFR-molecular gas mass scaling relation that is furthermore consistent with the Milky Way cloud results. This scatter likely represents real differences in giant molecular cloud physical properties such as the dense gas fraction.
Flaring activity following gamma-ray bursts (GRBs), observed in both long and short GRBs, signals a long-term activity of the central engine. However, its production mechanism has remained elusive. Here we develop a quantitative model of the idea proposed by Perna et al. of a disc whose outer regions fragment due to the onset of gravitational instability. The self-gravitating clumps migrate through the disc and begin to evolve viscously when tidal and shearing torques break them apart. Our model consists of two ingredients: theoretical bolometric flare lightcurves whose shape (width, skewness) is largely insensitive to the model parameters, and a spectral correction to match the bandpass of the available observations, that is calibrated using the observed spectra of the flares. This simple model reproduces, with excellent agreement, the empirical statistical properties of the flares as measured by their width-to-arrival time ratio and skewness (ratio between decay and rise time). We present model fits to the observed lightcurves of two well-monitored flares, of GRB 060418 and of GRB 060904B. To the best of our knowledge, this is the first quantitative model able to reproduce the flare lightcurves and explain their global statistical properties.
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of overdensity modes. However, this assumption cannot hold on the largest scales where the number of modes is low. Whilst more accurate distributions have previously been developed in idealized cases, we derive a procedure suitable for analysing measured monopole power spectra with window effects, stochastic shot noise, and the dependence of the covariance matrix on the model being fitted all taken into account. A data transformation is proposed to give an approximately Gaussian likelihood, with a variance--correlation decomposition of the covariance matrix to account for its cosmological dependence. By comparing with the modified-$t$ likelihood derived under the usual normality assumption, we find in numerical tests that our new procedure gives more accurate constraints on the local non-Gaussianity parameter $f_\mathrm{NL}$, which is sensitive to the large-scale power. A simple data analysis pipeline is provided for straightforward application of this new approach in preparation for forthcoming large galaxy surveys such as DESI and Euclid.
Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin cascade domain. Asymptotic energetic and uniform pointwise estimates for the difference between the solution of the initial problem and the solution of the corresponding limiting problem are proved.
Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.
Adopting the Standard Halo Model (SHM) of an isotropic Maxwellian velocity distribution for dark matter (DM) particles in the Galaxy, the most stringent current constraints on their spin-dependent scattering cross-section with nucleons come from the IceCube neutrino observatory and the PICO-60 C$_3$F$_8$ superheated bubble chamber experiments. The former is sensitive to high energy neutrinos from the self-annihilation of DM particles captured in the Sun, while the latter looks for nuclear recoil events from DM scattering off nucleons. Although slower DM particles are more likely to be captured by the Sun, the faster ones are more likely to be detected by PICO. Recent N-body simulations suggest significant deviations from the SHM for the smooth halo component of the DM, while observations hint at a dominant fraction of the local DM being in substructures. We use the method of Ferrer et al. (2015) to exploit the complementarity between the two approaches and derive conservative constraints on DM-nucleon scattering. Our results constrain $\sigma_{\mathrm{SD}} \lesssim 3 \times 10^{-39} \mathrm{cm}^2$ (6 $ \times 10^{-38} \mathrm{cm}^2$) at $\gtrsim 90\%$ C.L. for a DM particle of mass 1~TeV annihilating into $\tau^+ \tau^-$ ($b\bar{b}$) with a local density of $\rho_{\mathrm{DM}} = 0.3~\mathrm{ GeV/cm}^3$. The constraints scale inversely with $\rho_{\mathrm{DM}}$ and are independent of the DM velocity distribution.
Observations of the thermal X-ray emission from radio pulsars implicate that the size of hot spots is much smaller then the size of the polar cap that follows from the purely dipolar geometry of pulsar magnetic field. Most plausible explanation of this phenomena is an assumption that the magnetic field at the stellar surface differs essentially from the purely dipolar field. We can determine magnetic field at the surface by the conservation of the magnetic flux through the area bounded by open magnetic field lines. Then the value of the surface magnetic field can be estimated as of the order of $10^{14}$ G. On the other hand observations show that the temperature of the hot spot is about a few million Kelvins. Based on these observations the Partially Screened Gap (PSG) model was proposed which assumes that the temperature of the actual polar cap (hot spot) equals to the so called critical temperature.   We discuss correlation between the temperature and corresponding area of the thermal X-ray emission for a number of pulsars. The results of our analysis show that the PSG model is suitable to explain both cases: when the hot spot is smaller and larger then conventional polar cap. We argue that in the second case structure and curvature of field lines allow pair creation in the closed field lines region thus the secondary particles can heat the stellar surface outside the actual polar cap.   We have found that the Curvature Radiation (CR) plays dominant role in avalanche pair production in the PSG. We studied dependence of the PSG parameters on the pulsar period, the magnetic field strength and the curvature of field lines.