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Early detection and analysis of calcifications in mammogram images is crucial in a breast cancer diagnosis workflow. Management of calcifications that require immediate follow-up and further analyzing its benignancy or malignancy can result…
Hamiltonian parameter estimation is crucial in condensed matter physics, but time and cost consuming in terms of resources used. With advances in observation techniques, high-resolution images with more detailed information are obtained,…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
Simultaneous Localization and Mapping (SLAM) is considered an ever-evolving problem due to its usage in many applications. Evaluation of SLAM is done typically using publicly available datasets which are increasing in number and the level…
We review the most recent RANSAC-like hypothesize-and-verify robust estimators. The best performing ones are combined to create a state-of-the-art version of the Universal Sample Consensus (USAC) algorithm. A recent objective is to…
A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…
We present a method that can evaluate a RANSAC hypothesis in constant time, i.e. independent of the size of the data. A key observation here is that correct hypotheses are tightly clustered together in the latent parameter domain. In a…
We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
Load balancing is critical for successful large-scale high-performance computing (HPC) simulations. With modern supercomputers increasing in complexity and variability, dynamic load balancing is becoming more critical to use computational…
We propose a novel white-box approach to hyper-parameter optimization. Motivated by recent work establishing a relationship between flat minima and generalization, we first establish a relationship between the strong convexity of the loss…
In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC algorithms. Based on the theory, we give an explicit ratio of convergence rates for…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…
We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local…
Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking.…
Sharpness-Aware Minimization (SAM) optimizer enhances the generalization ability of the machine learning model by exploring the flat minima landscape through weight perturbations. Despite its empirical success, SAM introduces an additional…
We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples…
The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing algorithm which has been proposed to efficiently sample a multimodal probability measure. We show that this method can be seen as a variant of the well-known…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…