Related papers: Non-linear Constrained Realizations of the Large S…
We use cosmological simulations to explore the large-scale effects of reionization. Since reionization is a process that involves a large dynamic range - from galaxies to rare bright quasars - we need to be able to cover a significant…
We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical…
We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
The parameter fit from a model grid is limited by our capability to reduce the number of models, taking into account the number of parameters and the non linear variation of the models with the parameters. The Local MultiLinear Regression…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
We model weak gravitational lensing of light by large-scale structure using ray tracing through N-body simulations. The method is described with particular attention paid to numerical convergence. We investigate some of the key…
We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and…
Data analysis and interpretation often relies on an approximation of an empirical dataset by some analytic functions or models. Actual implementations usually rely on a non-linear multi-dimensional optimization algorithm, typically…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. There have been recent efforts to generalize SRG analysis to Multiple-Input Multiple-Output (MIMO) systems. However,…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
Cosmological simulations of galaxy formation are limited by finite computational resources. We draw from the ongoing rapid advances in Artificial Intelligence (specifically Deep Learning) to address this problem. Neural networks have been…
A range of nonlinear image reconstruction procedures based on extremizing the generalized Shannon entropy, Kullback-Leibler cross-entropy and Renyi information measures and proposed by the author in early papers is presented. The…
Potential features in the primordial power spectrum have been searched for in galaxy surveys in recent years since these features can assist in understanding the nature of inflation. The null detection to date suggests that any such…
Percus showed that approximate theories for the structure of nonuniform hard sphere fluids can be generated by linear truncations of functional expansions of the nonuniform density rho (r) about that of an appropriately chosen uniform…
We propose a proper method to measure the size of the narrow line region (NLR) in distant quasars. The apparent angular size of the NLR is, in general, too small to resolve technically. However, it is possible to map the NLR if with…
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…