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Here the role and influence of aberrations in optical imaging systems employing partially coherent complex scalar fields is studied. Imaging systems require aberrations to yield contrast in the output image. For linear shift-invariant…
Consider a geometric range space $(X,\c{A})$ where each data point $x \in X$ has two or more values (say $r(x)$ and $b(x)$). Also consider a function $\Phi(A)$ defined on any subset $A \in (X,\c{A})$ on the sum of values in that range e.g.,…
We explore whether medium-resolution stellar spectra can be reconstructed from photometric observations, taking advantage of the highly compressible nature of the spectra. We formulate the spectral reconstruction as a least-squares problem…
Hadronic tau decay data is used to study the reliability of various finite energy sum rules (FESR's). For intermediate scales (of order 2-3 GeV^2), those FESR's with weights s^k are found to have significant errors, whereas those with…
A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that…
Motivated by problems in high-dimensional statistics such as mixture modeling for classification and clustering, we consider the behavior of radial densities as the dimension increases. We establish a form of concentration of measure, and…
Efficient computation of the angular bispectrum is an essential part of modelling large-scale structure observations, but it still remains an extremely challenging task. In this work, we compute the tree-level, unequal-time angular…
With the developments of large galaxy surveys or cosmic shear surveys it is now possible to map the dark matter distribution at truly cosmological scales. Detailed examinations of the statistical properties of the dark matter distribution…
We have developed a new Bayesian method to correct the flux densities of astronomical sources. The hybrid method combines a simulated likelihood to model survey selection together with an analytic source-count-based prior. The simulated…
We show that simple models of scalar-field dark energy leave a generic enhancement in the weak-lensing power spectrum when compared to the LCDM prediction. In particular, we calculate the linear-scale enhancement in the convergence (or…
Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on…
We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of…
Aims. We provide an easy-to-use full-spectrum fitting package and explore its applications to (i) the determination of the stellar atmospheric parameters and (ii) the study of the history of stellar populations. Methods. We developed ULySS,…
This paper investigates change-point of variance in panel data models with time series of $\alpha$-mixing. Based on the cumulative sum (CUSUM) method and the individual differences, we construct a CUSUM test for panel data models to detect…
Many data mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous…
Small-angle X-ray and neutron scattering (SAXS and SANS) are powerful techniques in material science and soft matter. In this study, it was addressed how multiple SAXS or SANS datasets are best weighted when doing simultaneous fitting.…
Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…
Image fusion aims to combine complementary information from multiple source images to generate more comprehensive scene representations. Existing methods primarily rely on the stacking and design of network architectures to enhance the…
The new particle accelerators and its experiments create a challenging data processing environment, characterized by large amount of data where only small portion of it carry the expected new scientific information. Modern detectors, such…
Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed…