Manifolds (Mathematics) Geodesics (Mathematics) Space and time.
We investigate weak and strong refocusing of light rays in a space-time and related concepts. A strongly causal space-time ( X^ n +1 , g ) is emphstrongly refocusing at x ∈ X if there is a point y ≠ x such that all null-geodesics through y pass...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
The accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...
Shape modeling is an important area in computer vision and medical imaging. Shape models have proved valuable in the tasks of object representation, recognition, and classification. This thesis focuses on shape models of 3D surfaces extracted from...
In this thesis we review the methods for computation of cosmological correlations in the early universe known as the in-in formalism which are then applied to the problem of magnetogenesis from inflation. For this computation, a power-law single...
A yearly breast contrast-MR scan is recommended to high-risk women because of MR's high sensitivity to breast tumors. However, breast contrast-MR yields a high number of false positives that lead to expensive and sometimes unnecessary biopsy...
Continual improvements to clinical breast imaging technologies have led to ever earlier detections and increasingly accurate localizations of female breast cancers. While these advancements have certainly improved the prognoses of many patients,...
Casimir effect. Zero-point field. Electric conductivity. Quantum electrodynamics.
The Casimir force arises from an alteration of boundary condition in vacuum and is often regarded as a manifestation of quantum zero point energy. Considerable progress has been made in the last decade with an impressive achievement of experimental...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
While Cherenkov emission was discovered more than eighty years ago, the potential applications of imaging this during radiation therapy have just recently been explored. With approximately half of all cancer patients being treated by radiation at...
Microwave spectroscopy. Imaging systems -- Design and construction. Diagnostic imaging -- Digital techniques. Breast -- Cancer -- Diagnosis. Microwave imaging in medicine.
Microwave spectroscopy has been investigated as a possible modality for breast imaging because of the significant contrast in electrical properties between normal and malignant tissue over the microwave spectrum. A liquid-coupled, non-contacting...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
Robots -- Control systems. ; Robots -- Motion. ; Computer algorithms. ; Electronic data processing -- Distributed processing.
Self-reconfiguring robots are robots composed of many physically connected modules which can change their structural configuration to support multiple functionalities. We claim that self-reconfiguring robots are more versatile, extensible, and...
Microelectronics -- Design and construction. ; Micromachining. ; Strains and stresses. ; Silicon compounds.
This dissertation presents the use and extension of capabilities of surface machining technology, utilizing stress engineering between polysilicon and silicon nitride layers to build three-dimensional microstructures. A new theory and experimental...
Second harmonic generation. ; Second harmonic generation -- Mathematical models. ; Glass -- Effect of infrared radiation on. ; Glass -- Electric properties.
Colloidal nanoparticles are particles with sizes ranging from one nanometer to several hundred nanometers, which disperse evenly in a dispersion medium. In aqueous solutions, amphiphilic molecules organize themselves to form such colloidal systems...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
Cosmic acceleration could be an effect of a ""dark energy"" fluid pervading the Universe. It could also be an indication that general relativity is not the correct theory of gravity at cosmological length scales. Unfortunately, observations of the...
This thesis focuses on the emergence of universal dynamical scaling in quantum critical spin systems driven out of equilibrium, with emphasis on quench dynamics which involves isolated standard critical points, multi-critical points, and...
Microwave imaging (MI) is based on recovering dielectric properties (permittivity and conductivity) of materials. Over the last two decades, MI has attracted increasing interests in biomedical applications, in particular, for breast cancer...
Investigations into alternative breast cancer (BC) imaging techniques have become increasingly popular based on the limitations of traditional imaging modalities: X-ray mammography uses ionizing radiation, has limited intrinsic contrast and is...