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Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty,…
One way of recovering information about the initial conditions of the Universe is by measuring features of the cosmological density field which are preserved during gravitational evolution and galaxy formation. In this paper we study the…
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…
Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…
In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited…
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by…
Cancer pathology is unique to a given individual, and developing personalized diagnostic and treatment protocols are a primary concern. Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the…
Geometry optimization is an important task in quantum chemical calculations to analyze the characteristics of molecules. A top concern on it is a long execution time because time-consuming energy and gradient calculations are repeated…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
We introduce a new framework for the low-energy nuclear structure calculations, which describes the single-particle wave function as a superposition of localized Gaussians. It is a hybrid of the Hartree-Fock and antisymmetrized molecular…
The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…
The quantum simulation of real molecules and materials is one of the most highly anticipated applications of quantum computing. Algorithms for simulating electronic structure using a first-quantized plane wave representation are especially…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
Identifying a small molecule from its mass spectrum is the primary open problem in computational metabolomics. This is typically cast as information retrieval: an unknown spectrum is matched against spectra predicted computationally from a…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
In physics, it is sometimes desirable to compute the so-called \emph{Density Of States} (DOS), also known as the \emph{spectral density}, of a real symmetric matrix $A$. The spectral density can be viewed as a probability density…
Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a…
A thesis providing a pedagogical introduction to the problem of achieving self-consistency in density functional theory. Contained is an introduction to the framework of Kohn-Sham density functional theory, leading then to the…
Exploring the free-energy landscape along reaction coordinates or system parameters $\lambda$ is central to many studies of high-dimensional model systems in physics, e.g. large molecules or spin glasses. In simulations this usually…
In this paper, we present a novel approach to geostatistical filtering which tackles two challenges encountered when applying this method to complex spatial datasets: modeling the non-stationarity of the data while still being able to work…