ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar to compressed sensing approaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort correspondig to an informationally complete measurement.
This work is devoted to the Lipschitz contraction and the long time behavior of certain Markov processes. These processes diffuse and jump. They can represent some natural phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac semigroup, we prove a bound in Wasserstein metric. This bound is explicit and optimal in the sense of Wasserstein curvature. This notion of curvature is relatively close to the notion of (coarse) Ricci curvature or spectral gap. Several consequences and examples are developed, including an $L^2$ spectral for general Markov processes, explicit formulas for the integrals of compound Poisson processes with respect to a Brownian motion, quantitative bounds for Kolmogorov-Langevin processes and some total variation bounds for piecewise deterministic Markov processes.
The aim of this paper is to present an analysis of the new theorem by Pusey, Barrett and Rudolph (PBR) concerning ontic and epistemic hidden variables in quantum mechanics [Nature Phys. 8, 476 (2012)]. This is a kind of review and defense of my previous critical analysis done in the context of Bohmian mechanics. This is also the occasion for me to review some of the fundamental aspects of Bohmian theory rarely discussed in the literature. The paper is submitted for the issue PBR theorem and Beyond of IJQF (International Journal of Quantum Foundations).
We study numerically the one dimensional ferromagnetic Kondo lattice, a model widely used to describe nickel and manganese perovskites. By including a nearest neighbor Coulomb interaction (V) and a superexchange interaction between the localized moments (K), we obtain the phase diagram in parameter space for several dopings at T=0. Due to the competition between double and superexchange, we find a region where the formation of magnetic polarons induces a charge ordered (CO) state which survives also for V=0. This mechanism should be taken into account in theories of charge ordering involving spin degrees of freedom.
We investigate the standing kink modes of a cylindrical model of coronal loops. The density is stratified along the loop axis and changes discontinuously at the surface of the cylinder. The periods and mode profiles are studies with their deviation from those of the unstratified loops. The aim is to extract information on the density scale heights prevailing in the solar corona. The problem is reduced to solving a single second-order partial differential equation for $\delta B_z(r,z)$, the longitudinal component of the Eulerian perturbations of the magnetic field. This equation, in turn, is separated into two second-order ordinary, differential equations in $r$ and $z$ that are, however, connected through a dispersion relation between the frequencies and the longitudinal wave numbers. In the thin tube approximation, the eigensolutions are obtained by a perturbation technique, where the perturbation parameter is the density stratification parameter. Otherwise the problem is solved numerically.
Completing a corrupted image with correct structures and reasonable textures for a mixed scene remains an elusive challenge. Since the missing hole in a mixed scene of a corrupted image often contains various semantic information, conventional two-stage approaches utilizing structural information often lead to the problem of unreliable structural prediction and ambiguous image texture generation. In this paper, we propose a Semantic Guidance and Evaluation Network (SGE-Net) to iteratively update the structural priors and the inpainted image in an interplay framework of semantics extraction and image inpainting. It utilizes semantic segmentation map as guidance in each scale of inpainting, under which location-dependent inferences are re-evaluated, and, accordingly, poorly-inferred regions are refined in subsequent scales. Extensive experiments on real-world images of mixed scenes demonstrated the superiority of our proposed method over state-of-the-art approaches, in terms of clear boundaries and photo-realistic textures.
We perform a statistical analysis of experimental fully developed turbulence longitudinal velocity data in the Fourier space. We address the controversial issue of statistical intermittency of spatial Fourier modes by acting on the finite spectral resolution. We derive a link between velocity structure functions and the flatness of Fourier modes thanks to cascade models. Similar statistical behaviors are recovered in the analysis of spatial Fourier modes of vorticity obtained in an acoustic scattering experiment. We conclude that vorticity is long-range correlated and found more intermittent than longitudinal velocity.
A tight non-linear relation exists between the X-ray and UV emission in quasars (i.e. $L_{\rm X}\propto L_{\rm UV}^{\gamma}$), with a dispersion of $\sim$0.2~dex over $\sim$3~orders of magnitude in luminosity. Here we propose a modified version of this relation which involves the broad emission lines' full-width at half maximum, $L_{\rm X}\propto L_{\rm UV}^{\hat\gamma}\upsilon_{\rm fwhm}^{\hat\beta}$. We interpret this new relation through a simple, {\it ad-hoc} model of accretion disc corona, derived from previous works where it is assumed that reconnection and magnetic loops above the accretion disc can account for the production of the primary X-ray radiation. We find that the monochromatic optical-UV (2500 \AA) and X-ray (2 keV) luminosities depend on the black hole mass and accretion rate as $L_{\rm UV}\propto M_{\rm BH}^{4/3} (\dot{M}/\dot{M}_{\rm Edd})^{2/3}$ and $L_{\rm X}\propto M_{\rm BH}^{19/21} (\dot{M}/\dot{M}_{\rm Edd})^{5/21}$, respectively. Assuming a broad line region size function of the disc luminosity $R_{\rm blr}\propto L_{\rm disc}^{0.5}$ we finally have that $L_{\rm X}\propto L_{\rm UV}^{4/7} \upsilon_{\rm fwhm}^{4/7}$. Such relation is remarkably consistent with the slopes and the normalization obtained from a fit of a sample of 545 optically selected quasars from SDSS DR7 cross matched with the latest XMM-Newton catalogue 3XMM-DR6. The homogeneous sample used here has a dispersion of 0.21 dex, which is much lower than previous works in the literature and suggests a tight physical relation between the accretion disc and the X-ray emitting corona. The proposed new relation does not evolve with time, and thus it can be employed as a cosmological indicator to robustly estimate cosmological parameters.
The thermodynamic and spectroscopic behaviour of Schwarzschild black hole surrounded by quintessence are studied. We have derived the thermodynamic quantities and studied their behaviour for different values of quintessence parameter. We put the background space-time into the Kruskal-like coordinate to find the period with respect to Elucidean time. Also assuming that the adiabatic invariant obeys Bohr-Sommerfeld quantization rule, detailed study of area spectrum and entropy spectrum have been done for special cases of the quintessece state parameter. We find that the spectra are equally spaced.
In this article we prove optimal pointwise bounds for solutions to the semilinear wave equation with integer powers $p\geq 3$ on Kerr backgrounds with small angular momentum and small initial data.
For each $k = 0,\dots,n$ we construct a continuous phase $f_k$, with $f_k(0) = (n-2k)\frac{\pi}{2}$, and viscosity sub- and supersolutions $v_k$, $u_k$, of the elliptic PDE $\sum_{i=1}^n \arctan(\lambda_i(D^2 w)) = f_k(x)$ such that $v_k-u_k$ has an isolated maximum at the origin.   It has been an open question whether the comparison principle would hold in this second order equation for arbitrary continuous phases $f\colon\Omega\to (-n\pi/2,n\pi/2)$. Our examples show it does not.
Using the canonical Monte Carlo simulation technique, we study a Regge calculus model on triangulated spherical surfaces. The discrete model is statistical mechanically defined with the variables $X$, $g$ and $\rho$, which denote the surface position in ${\bf R}^3$, the metric on a two-dimensional surface $M$ and the surface density of $M$, respectively. The metric $g$ is defined only by using the deficit angle of the triangles in {$M$}. This is in sharp contrast to the conventional Regge calculus model, where {$g$} depends only on the edge length of the triangles. We find that the discrete model in this paper undergoes a phase transition between the smooth spherical phase at $b to infty$ and the crumpled phase at $b to 0$, where $b$ is the bending rigidity. The transition is of first-order and identified with the one observed in the conventional model without the variables $g$ and $\rho$. This implies that the shape transformation transition is not influenced by the metric degrees of freedom. It is also found that the model undergoes a continuous transition of in-plane deformation. This continuous transition is reflected in almost discontinuous changes of the surface area of $M$ and that of $X(M)$, where the surface area of $M$ is conjugate to the density variable $\rho$.
Recent measurements of the Cosmic Microwave Background (CMB) by the Planck Collaboration have produced arguably the most powerful observational evidence in support of the standard model of cosmology, i.e. the spatially flat $\Lambda$CDM paradigm. In this work, we perform model selection tests to examine whether the base CMB temperature and large scale polarization anisotropy data from Planck 2015 (P15) prefer any of eight commonly used one-parameter model extensions with respect to flat $\Lambda$CDM. We find a clear preference for models with free curvature, $\Omega_\mathrm{K}$, or free amplitude of the CMB lensing potential, $A_\mathrm{L}$. We also further develop statistical tools to measure tension between datasets. We use a Gaussianization scheme to compute tensions directly from the posterior samples using an entropy-based method, the surprise, as well as a calibrated evidence ratio presented here for the first time. We then proceed to investigate the consistency between the base P15~CMB data and six other CMB and distance datasets. In flat $\Lambda$CDM we find a $4.8\sigma$ tension between the base P15~CMB data and a distance ladder measurement, whereas the former are consistent with the other datasets. In the curved $\Lambda$CDM model we find significant tensions in most of the cases, arising from the well-known low power of the low-$\ell$ multipoles of the CMB data. In the flat $\Lambda$CDM $+A_\mathrm{L}$ model, however, all datasets are consistent with the base P15~CMB observations except for the CMB lensing measurement, which remains in significant tension. This tension is driven by the increased power of the CMB lensing potential derived from the base P15~CMB constraints in both models, pointing at either potentially unresolved systematic effects or the need for new physics beyond the standard flat $\Lambda$CDM model.
In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin-Ono equation. By solving a minimization problem on the line, we construct a family of even travelling waves $\psi_{c,\gamma}$. We also study the strong convergence of this family and we establish the uniqueness of $\psi_{c,\gamma}$ for $\gamma$ small enough. Note that this improves the results in [5] where the stability of the set of ground states is proven.
Magnetic field dependent universal conductance fluctuations (UCF's) are observed in weakly disordered indium tin oxide nanowires from 0.26 K up to $\sim 25$ K. The fluctuation magnitudes increase with decreasing temperature, reaching a fraction of $e^2/h$ at $T \lesssim 1$ K. The shape of the UCF patterns is found to be very sensitive to thermal cycling of the sample to room temperatures, which induces irreversible impurity reconfigurations. On the other hand, the UCF magnitudes are insensitive to thermal cycling. Our measured temperature dependence of the root-mean-square UCF magnitudes are compared with the existing theory [C. W. J. Beenakker and H. van Houten, Phys. Rev. B \textbf{37}, 6544 (1988)]. A notable discrepancy is found, which seems to imply that the experimental UCF's are not cut off by the thermal diffusion length $L_T$, as would be expected by the theoretical prediction when $L_T < L_\varphi$, where $L_\varphi$ is the electron dephasing length. The approximate electron dephasing length is inferred from the UCF magnitudes and compared with that extracted from the weak-localization magnetoresistance studies. A reasonable semiquantitative agreement is observed.
In the present study, we focus on the parity of the order parameters and clarify the order formation process in a system including two order parameters. Each order parameter shows each different parity under a gauge transformation, namely even and odd order parameters. For example, in a spin-glass model, the even order parameter corresponds to the spin-glass order parameter while the odd one corresponds to the magnetization. We introduce phenomenologically a set of Langevin equations to express the ordering process under a white Gaussian noise. Using two kinds of Fokker-Planck equations, we analyze the order formation process and the entropy production. Furthermore, we show the noise dependence of the onset time.
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds and the shortest, the longest and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.
The problem of detecting a novel class at run time is known as Open Set Detection & is important for various real-world applications like medical application, autonomous driving, etc. Open Set Detection within context of deep learning involves solving two problems: (i) Must map the input images into a latent representation that contains enough information to detect the outliers, and (ii) Must learn an anomaly scoring function that can extract this information from the latent representation to identify the anomalies. Research in deep anomaly detection methods has progressed slowly. One reason may be that most papers simultaneously introduce new representation learning techniques and new anomaly scoring approaches. The goal of this work is to improve this methodology by providing ways of separately measuring the effectiveness of the representation learning and anomaly scoring. This work makes two methodological contributions. The first is to introduce the notion of Oracle anomaly detection for quantifying the information available in a learned latent representation. The second is to introduce Oracle representation learning, which produces a representation that is guaranteed to be sufficient for accurate anomaly detection. These two techniques help researchers to separate the quality of the learned representation from the performance of the anomaly scoring mechanism so that they can debug and improve their systems. The methods also provide an upper limit on how much open category detection can be improved through better anomaly scoring mechanisms. The combination of the two oracles gives an upper limit on the performance that any open category detection method could achieve. This work introduces these two oracle techniques and demonstrates their utility by applying them to several leading open category detection methods.
We analyze the time-dependent formation of the spectral function of an Anderson impurity model in the Kondo regime within a numerically exact real-time quantum Monte Carlo framework. At steady state, splitting of the Kondo peak occurs with nontrivial dependence on voltage and temperature, and with little effect on the location or intensity of high-energy features. Examining the transient development of the Kondo peak after a quench from an initially uncorrelated state reveals a two-stage process where the initial formation of a single central Kondo peak is followed by splitting. We analyze the time dependence of splitting in detail and demonstrate a strong dependence of its characteristic timescale on the voltage. We expect both the steady state and the transient phenomenon to be experimentally observable.
Klein tunneling is a counterintuitive quantum-mechanical phenomenon, predicting perfect transmission of relativistic particles through higher energy barriers. This phenomenon was shown to be supported at normal incidence in graphene due to pseudospin conservation. Here I show that Klein tunneling analogue can occur in classical systems, and remarkably, not relying on mimicking graphene's spinor wavefunction structure. Instead, the mechanism requires a particular form of constitutive parameters of the penetrated medium, yielding transmission properties identical to the quantum tunneling in graphene. I demonstrate this result by simulating tunneling of sound in a two-dimensional acoustic metamaterial. More strikingly, I show that by introducing a certain form of anisotropy, the tunneling can be made unimpeded for any incidence angle, while keeping most of its original Klein dispersion properties. This phenomenon may be denoted by the omnidirectional Klein-like tunneling. The new tunneling mechanism and its omnidirectional variant may be useful for applications requiring lossless and direction-independent transmission of classical waves.
Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are included. Regularization has traditionally been used to constrain the solutions where the data failed to do so, e.g. in unlensed parts of the source. In this exploratory work, we go beyond the usual choices of regularization and adopt observationally motivated priors for the source brightness. We also perform a similar comparison when reconstructing lens potential perturbations, which are assumed to be stationary, i.e. permeate the entire field of view. We find that physically motivated priors lead to lower residuals, avoid overfitting, and are decisively preferred within a Bayesian quantitative framework in all the examples considered. For the perturbations, choosing the wrong regularization can have a detrimental effect that even high-quality data cannot correct for, while using a purely smooth lens model can absorb them to a very high degree and lead to biased solutions. Finally, our new implementation of the semi-linear inversion technique provides the first quantitative framework for measuring degeneracies between the source and the potential perturbations.
Based on the self-consistent equations of the order parameter $P_\infty$ and the mean cluster size $S$, we develop a novel self-consistent simulation (SCS) method for arbitrary percolation on the Bethe lattice (infinite homogeneous Cayley tree). By applying SCS to the well-known percolation models, random bond percolation and bootstrap percolation, we obtain prototype functions for continuous and discontinuous phase transitions. By comparing the key functions obtained from SCSs for the Achlioptas processes (APs) with a product rule and a sum rule to the prototype functions, we show that the percolation transition of AP models on the Bethe lattice is continuous regardless of details of growth rules.
We implement a spatially fixed mesh refinement under spherical symmetry for the characteristic formulation of General Relativity. The Courant-Friedrich-Levy (CFL) condition lets us deploy an adaptive resolution in (retarded-like) time, even for the nonlinear regime. As test cases, we replicate the main features of the gravitational critical behavior and the spacetime structure at null infinity using the Bondi mass and the News function. Additionally, we obtain the global energy conservation for an extreme situation, i.e. in the threshold of the black hole formation. In principle, the calibrated code can be used in conjunction with an ADM 3+1 code to confirm the critical behavior recently reported in the gravitational collapse of a massless scalar field in an asymptotic anti-de Sitter spacetime. For the scenarios studied, the fixed mesh refinement offers improved runtime and results comparable to code without mesh refinement.
We show that the number of unit distances determined by n points in R^3 is O(n^{3/2}), slightly improving the bound of Clarkson et al. established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [arXiv:1011.4105]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [arXiv:1104.4987].
Swift J1357.2-0933 underwent an episodic accretion in 2011 and provided very regular temporal and spectral evolution, making it an ideal source for exploring the nature of very faint X-ray transients (VFXTs). In this work, we present a detailed analysis on both X-ray and near-ultraviolet (NUV) light curves. The fluxes at all wavelengths display a near-exponential decays in the early phase and transits to a faster-decay at late times. The e-folding decay time-scales monotonically decrease with photon energies, and the derived viscous time-scale is $\tau_{\rm \dot{M}} \sim 60$ days. The time-scale in the late faster-decay stage is about a few days. The high ratio of NUV luminosity to X-ray luminosity indicates that the irradiation is unimportant in this outburst, while the near-exponential decay profile and the long decay time-scales conflict with the disc thermal-viscous instability model. We thus suggest that the disc is thermally stable during the observations. Adopting the truncated disc model, we obtain a lower limit of peak accretion rate of $0.03 \dot{M}_{\rm Edd}$ and the X-ray radiative efficiency $\eta < 5\times10^{-4}$, which decreases as the luminosity declines. The low X-ray radiative efficiency is caused by the combined action of advection and outflows, and naturally explains that the X-ray reprocessing is overwhelmed by the viscous radiation of the outer standard disc in the NUV regime. We also propose a possibility that the outer standard disc recedes from the central black hole, resulting in the faster-decay at late times.
The Hubble parameter is one of the central parameters in modern cosmology, which describes the present expansion rate of the universe. Their values inferred from the late-time observations are systematically higher than those from the early-time measurements by about $10\%$. To come to a robust conclusion, independent probes with accuracy at percent levels are crucial. Gravitational waves from compact binary coalescence events can be formulated into the standard siren approach to provide an independent Hubble parameter measurement. The future space-borne gravitational wave observatory network, such as the LISA-Taiji network, will be able to measure the gravitational wave signals in the Millihertz bands with unprecedented accuracy. By including several statistical and instrumental noises, we show that within 5 years operation time, the LISA-Taiji network is able to constrain the Hubble parameter within $1\%$ accuracy, and possibly beats the scatters down to $0.5\%$ or even better.