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Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Recently, we have developed a formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. This corresponds to an all-order resummation of certain terms (the so-called renormalon…
This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…
To accurately estimate locations and velocities of surrounding targets (cars) is crucial for advanced driver assistance systems based on radar sensors. In this paper we derive methods for fusing data from multiple radar sensors in order to…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Matching a target spectrum with known spectra in a spectral library is a common method for material identification in hyperspectral imaging research. Hyperspectral spectra exhibit precise absorption features across different wavelength…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We compute the Standard Model scalar coupling ($\lambda$) evolution in a particular QCD resummation scheme, where the QCD coupling becomes infrared finite due to the presence of a dynamically generated gluon mass, leading to the existence…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…
We propose a novel centrality definition-independent method for analyzing higher-order cumulants, specifically addressing the challenge of volume fluctuations that dominate in low-energy heavy-ion collisions. This method reconstructs…
In this thesis, we develop resummation algorithms suitable for perturbative QCD. In the first part, we propose a resummation technique applicable to the Regge limit. We develop a new systematic procedure for this limit in perturbative QCD…
Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
Cluster-randomized trials (CRTs) are widely used to evaluate group-level interventions and increasingly collect multiple outcomes capturing complementary dimensions of benefit and risk. Investigators often seek a single global summary of…
Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to…
We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when…
The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback…
Deep learning has demonstrated remarkable achievements in medical image segmentation. However, prevailing deep learning models struggle with poor generalization due to (i) intra-class variations, where the same class appears differently in…
The problem of precise evaluation of perturbative QCD predictions at moderate energies is addressed. In order to improve stability of the predictions with respect to change of the renormalization scheme it is proposed to replace the…