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Quantitative estimation of activity and quality for collections of functional genetic elements
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The next generation Virgo Cluster Survey. IX. Estimating the efficiency of galaxy formation on the lowest-mass scales
The Next Generation Virgo Cluster Survey has recently determined the luminosity function of galaxies in the core of the Virgo cluster down to unprecedented magnitude and surface brightness limits. Comparing simulations of cluster formation to the derived central stellar mass function, we attempt to estimate the stellar-to-halo-mass ratio (SHMR) for dwarf galaxies, as it would have been before they fell into the cluster. This approach ignores several details and complications, e.g., the contribution of ongoing star formation to the present-day stellar mass of cluster members, and the effects of adiabatic contraction and/or violent feedback on the subhalo and cluster potentials. The final results are startlingly simple, however; we find that the trends in the SHMR determined previously for bright galaxies appear to extend down in a scale-invariant way to the faintest objects detected in the survey. These results extend measurements of the formation efficiency of field galaxies by two decades in halo mass or five decades in stellar mass, down to some of the least massive dwarf galaxies known, with stellar masses of ∼10{sup 5} M{sub ⊙}.
Notes on a New Coherence Estimator
This document discusses some interesting features of the new coherence estimator in [1] . The estimator is d erived from a slightly different viewpoint. We discuss a few properties of the estimator, including presenting the probability density function of the denominator of the new estimator , which is a new feature of this estimator . Finally, we present an appr oximate equation for analysis of the sensitivity of the estimator to the knowledge of the noise value. ACKNOWLEDGEMENTS The preparation of this report is the result of an unfunded research and development activity. Sandia National Laboratories is a multi - program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE - AC04 - 94AL85000.
Accurate shear estimation with fourth-order moments
ABSTRACT As imaging surveys progress in exploring the large-scale structure of the Universe through the use of weak gravitational lensing, achieving sub-per cent accuracy in estimating shape distortions caused by lensing, or shear, is imperative for precision cosmology. In this paper, we extend the Fourier power function shapelets (FPFS) shear estimator using fourth-order shapelet moments and combine it with the original second-order shear estimator to reduce galaxy shape noise. We calibrate this novel shear estimator analytically to a sub-per cent level-accuracy using the AnaCal framework. This higher order shear estimator is tested with realistic image simulations, and after analytical correction for the detection/selection bias and noise bias, the multiplicative shear bias $|m|$ is below $3\times 10^{-3}$ (99.7 per cent confidence interval) for both isolated and blended galaxies. Once combined with the second-order FPFS shear estimator, the shape noise is reduced by $\sim 35~{{\ \rm per\ cent}}$ for isolated galaxies in simulations with Hyper Suprime-Cam and Vera C. Rubin Observatory Legacy Survey of Space and Time observational conditions. However, for blended galaxies, the effective number density does not significantly improve with the combination of the two estimators. Based on these results, we recommend exploration of how this framework can further reduce the systematic uncertainties in shear due to point spread function leakage and modelling error, and potentially provide improved precision in shear inference in high-resolution space-based images.
Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.
A complete non-perturbative renormalization prescription for quasi-PDFs
In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI' scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the $\overline{MS}$-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with $N_f = 2+1+1$ dynamical quarks, and a pion mass of around 375 MeV.
Contrast-to-noise ratio optimization for a prototype phase-contrast computed tomography scanner
In the field of biomedical X-ray imaging, novel techniques, such as phase-contrast and dark-field imaging, have the potential to enhance the contrast and provide complementary structural information about a specimen. In this paper, a first prototype of a preclinical X-ray phase-contrast CT scanner based on a Talbot-Lau interferometer is characterized. We present a study of the contrast-to-noise ratios for attenuation and phase-contrast images acquired with the prototype scanner. The shown results are based on a series of projection images and tomographic data sets of a plastic phantom in phase and attenuation-contrast recorded with varying acquisition settings. Subsequently, the signal and noise distribution of different regions in the phantom were determined. We present a novel method for estimation of contrast-to-noise ratios for projection images based on the cylindrical geometry of the phantom. Analytical functions, representing the expected signal in phase and attenuation-contrast for a circular object, are fitted to individual line profiles of the projection data. The free parameter of the fit function is used to estimate the contrast and the goodness of the fit is determined to assess the noise in the respective signal. The results depict the dependence of the contrast-to-noise ratios on the applied source voltages, the number of steps of the phase stepping routine, and the exposure times for an individual step. Moreover, the influence of the number of projection angles on the image quality of CT slices is investigated. Finally, the implications for future imaging purposes with the scanner are discussed.
Computing partition functions in the one-clean-qubit model
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( ε rel Z )] 2 , where M is the dimension of the quantum system, Z is the partition function, and ε rel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.
Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds
In this study, the computational burden of a large-eddy simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, will greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, it is shown how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. Lastly, it is also demonstrated how the improved statistical model adds critical insight to the performance of the model.
THE DEMOGRAPHICS OF BROAD-LINE QUASARS IN THE MASS-LUMINOSITY PLANE. II. BLACK HOLE MASS AND EDDINGTON RATIO FUNCTIONS
We employ a flexible Bayesian technique to estimate the black hole (BH) mass and Eddington ratio functions for Type 1 (i.e., broad line) quasars from a uniformly selected data set of {approx}58, 000 quasars from the Sloan Digital Sky Survey (SDSS) DR7. We find that the SDSS becomes significantly incomplete at M {sub BH} {approx}< 3 Multiplication-Sign 10{sup 8} M {sub Sun} or L/L {sub Edd} {approx}< 0.07, and that the number densities of Type 1 quasars continue to increase down to these limits. Both the mass and Eddington ratio functions show evidence of downsizing, with the most massive and highest Eddington ratio BHs experiencing Type 1 quasar phases first, although the Eddington ratio number densities are flat at z < 2. We estimate the maximum Eddington ratio of Type 1 quasars in the observable universe to be L/L {sub Edd} {approx} 3. Consistent with our results in Shen and Kelly, we do not find statistical evidence for a so-called sub-Eddington boundary in the mass-luminosity plane of broad-line quasars, and demonstrate that such an apparent boundary in the observed distribution can be caused by selection effect and errors in virial BH mass estimates. Based on the typical Eddington ratio in a given mass bin, we estimate growth times for the BHs in Type 1 quasars and find that they are comparable to or longer than the age of the universe, implying an earlier phase of accelerated (i.e., with higher Eddington ratios) and possibly obscured growth. The large masses probed by our sample imply that most of our BHs reside in what are locally early-type galaxies, and we interpret our results within the context of models of self-regulated BH growth.
Investigating the age distribution of fracture discharge using multiple environmental tracers, Bedrichov Tunnel, Czech Republic
We investigated the transit time distribution (TTD) of discharge collected from fractures in the Bedrichov Tunnel, Czech Republic, using lumped parameter models and multiple environmental tracers. We then utilize time series of δ 18 O, δ 2 H and 3 H along with CFC measurements from individual fractures in the Bedrichov Tunnel of the Czech Republic to investigate the TTD, and the uncertainty in estimated mean travel time in several fracture networks of varying length and discharge. We also compare several TTDs, including the dispersion distribution, the exponential distribution, and a developed TTD which includes the effects of matrix diffusion. The effect of seasonal recharge is explored by comparing several seasonal weighting functions to derive the historical recharge concentration. We identify best fit mean ages for each TTD by minimizing the error-weighted, multi-tracer χ2 residual for each seasonal weighting function. We use this methodology to test the ability of each TTD and seasonal input function to fit the observed tracer concentrations, and the effect of choosing different TTD and seasonal recharge functions on the mean age estimation. We find that the estimated mean transit time is a function of both the assumed TTD and seasonal weighting function. Best fits as measured by the χ2 value were achieved for the dispersion model using the seasonal input function developed here for two of the three modeled sites, while at the third site, equally good fits were achieved with the exponential model and the dispersion model and our seasonal input function. The average mean transit time for all TTDs and seasonal input functions converged to similar values at each location. The sensitivity of the estimated mean transit time to the seasonal weighting function was equal to that of the TTD. These results indicated that understanding seasonality of recharge is at least as important as the uncertainty in the flow path distribution in fracture networks and that unique identification of the TTD and mean transit time is difficult given the uncertainty in the recharge function. But, the mean transit time appears to be relatively robust to the structural model uncertainty. The results presented here should be applicable to other studies using environmental tracers to constrain flow and transport properties in fractured rock systems.
Derivative-free stochastic optimization via adaptive sampling strategies
In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.
Lyapunov-Based Iterative Learning of Regions of Attraction for Autonomous Systems
This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.
Lyapunov-Based Iterative Learning of the Region of Attraction for Autonomous Systems
This presentation introduces a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.
On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model
We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.
The Asymptotic Behavior of the Optimal Threshold Minimizing the Probability-of-Error Criterion
In this paper we consider the problem of estimation of a signal function from the noised observations via thresholding its wavelet coefficients. We find the asymptotic order of the optimal threshold that minimizes the probability of the maximum error between the estimates and the true wavelet coefficients exceeding a critical value.
Detecting False Data Injection Attacks Against Power System State Estimation With Fast Go-Decomposition Approach
State estimation is a fundamental function in modern energy management system, but its results may be vulnerable to false data injection attacks (FDIAs). FDIA is able to change the estimation results without being detected by the traditional bad data detection algorithms. In this paper, we propose an accurate and computational attractive approach for FDIA detection. In this work, we first rely on the low rank characteristic of the measurement matrix and the sparsity of the attack matrix to reformulate the FDIA detection as a matrix separation problem. Then, four algorithms that solve this problem are presented and compared, including the traditional augmented Lagrange multipliers (ALMs), double-noise-dual-problem (DNDP) ALM, the low rank matrix factorization, and the proposed new “Go Decomposition (GoDec).” Numerical simulation results show that our GoDec algorithm outperforms the other three alternatives and demonstrates a much higher computational efficiency. Furthermore, GoDec is shown to be able to handle measurement noise and applicable for large-scale attacks.