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We introduce a polynomial time algorithm for optimizing the class of star-convex functions, under no restrictions except boundedness on a region about the origin, and Lebesgue measurability. The algorithm's performance is polynomial in the…
The pair separations statistical methods devised to detect the topology of the universe rely on the accurate knowledge of the three-dimensional positions of the cosmic sources. The determination of these positions, however, involves…
Reliable celestial attitude determination is a critical requirement for autonomous spacecraft navigation, yet traditional "Lost-in-Space" (LIS) algorithms often suffer from high computational overhead and sensitivity to sensor-induced…
We investigate the construction of early stopping rules in the nonparametric regression problem where iterative learning algorithms are used and the optimal iteration number is unknown. More precisely, we study the discrepancy principle, as…
Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
The computation of the Log-determinant of large, sparse, symmetric positive definite (SPD) matrices is essential in many scientific computational fields such as numerical linear algebra and machine learning. In low dimensions, Cholesky is…
The luminosity distance can be used to determine the properties of large scale structure around the observer. To this purpose we develop a new inversion method to map luminosity distance to a LTB metric based on the use of the exact…
Large-scale low-Earth-orbit satellite constellations offer a promising platform for global low-latency networking, aided by faster propagation in free space than in fiber and copper. In such systems, end-to-end latency is largely determined…
Although convolution neural network based stereo matching architectures have made impressive achievements, there are still some limitations: 1) Convolutional Feature (CF) tends to capture appearance information, which is inadequate for…
Using the adaptive optics facilities at the 200-in Hale and 10-m Keck II, we observed in the near infrared a sample of 12 binary and multiple stars and one open cluster. We used the near diffraction limited images of these systems to…
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…
We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of…
A result of Spencer states that every collection of $n$ sets over a universe of size $n$ has a coloring of the ground set with $\{-1,+1\}$ of discrepancy $O(\sqrt{n})$. A geometric generalization of this result was given by Gluskin (see…
We study the optimal use of third order statistics in the analysis of weak lensing by large-scale structure. These higher order statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological…
We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which…
Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic…
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not…