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Quantifying uncertainty in large language models (LLMs) is important for safety-critical applications because it helps spot incorrect answers, known as hallucinations. One major trend of uncertainty quantification methods is based on…
We implement a machine learning algorithm to search for extra-terrestrial technosignatures in radio observations of several hundred nearby stars, obtained with the Parkes and Green Bank Telescopes by the Breakthrough Listen collaboration.…
The concept of the "statistical significance" of an observation, and how it is used in particle physics experiments is reviewed. More properly known as a "p-value," the statistical foundations for this concept are reviewed from a freqentist…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
In this paper we consider the problem of detecting statistically significant sequential patterns in multi-neuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays…
Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the…
We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability…
High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current…
The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was…
In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…
The search for faint emission or absorption lines in astronomical spectra has received considerable attention in recent years, especially in the X-ray wavelength range. These features usually appear as a deficit or excess of counts in a…
The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
We discuss the prospects for high-energy neutrino astronomy to study particle physics in the energy regime comparable to and beyond that obtainable at the current and planned colliders. We describe the various signatures of high-energy…
Higher order correlation measurements involve multiple event averages which must run over unequal events to avoid statistical bias. We derive correction formulas for small event samples, where the bias is largest, and utilize the results to…
The measurement of stellar properties such as chemical compositions, masses and ages, through stellar spectra, is a fundamental problem in astrophysics. Progress in the understanding, calculation and measurement of atomic properties and…
The production and manipulation of quantum correlation protocols will play a central role where the quantum nature of the correlation can be used as a resource to yield properties unachievable within a classical framework is a very active…
In quantum physics, measurements give random results and yield a corresponding random back action on the state of the system subject to measurement. If a quantum system is probed continuously over time, its state evolves along a stochastic…
Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent…
Exploring the expansion history of the universe, understanding its evolutionary stages, and predicting its future evolution are important goals in astrophysics. Today, machine learning tools are used to help achieving these goals by…