Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of...
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Three-dimensional imaging in medicine -- Mathematical models. Intraoperative monitoring. Cerebral cortex -- Imaging. Computer vision. Space perception.
Brain deformation models have proven to be a powerful tool in compensating for soft tissue deformation during image-guided neurosurgery. The accuracy of these models can be improved by incorporating intraoperative measurements of brain motion. We...
Despite great progress in object recognition techniques, there is a mismatch between traditional approaches and the characteristics of real world vision tasks. We highlight in particular, three closely related areas of mismatch: i) recognition...
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,...
We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
The need for social connection is a pervasive and powerful human drive. When this fundamental need is not fulfilled, people place greater emphasis on forming social bonds and are motivated to behave in ways consistent with accomplishing these...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
Robustness to genetic perturbations is a fundamental property of all living things. The genetic code is degenerate, RNA secondary structure is robust to sequence changes, and protein structure is robust to amino acid substitutions. Complex systems...
Robots -- Control systems -- Design and construction. Mobile robots. Robots -- Dynamics.
This thesis examines the issues of vehicle and information dynamics in the control of a multi-robot system using a radial-basis potential function controller. Distributed control of multi-robot systems requires each robot to communicate state...
The experiments comprising this thesis aimed to characterize the neural and behavioral correlates of learning about and responding to the predictive information conveyed by social cues. Facial expressions are cues that convey critical information...
Optical tomography. ; Near infrared spectroscopy. ; Image analysis -- Mathematical models. ; Imaging systems -- Image quality -- Mathematical models. ; Image reconstruction -- Mathematical models. ; Least squares. Breast -- Tomography.
Diffuse optical tomography (DOT) has the potential to become a non-invasive and non-ionizing diagnostic imaging technique for breast cancer imaging. DOT uses near-infrared (NIR) light to illuminate the breast, generally through the use of fiber...
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...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
Boundary integral methods have long been used to solve boundary value problems for elliptic partial differential equations with piecewise constant coefficients, since they have several numerical advantages over conventional volume discretization....
Humans have a seemingly unique capacity to reflect upon information about the self to form evaluative attitudes that influence their quality of life and predict mental health outcomes. While psychologists have devoted decades of research to the...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
The new APM South Equatorial Strip Catalog $({-}17\sp\circ.5<\delta<2\sp\circ.5)$ is used to select a sample of early-type galaxies in three directions: (1) 15h10-16h10; (2) 20h30-21h50; (3) 00h10-01h30. The distances and peculiar motions of...
One of the most distinctive aspects of humans as a species is our propensity to form complex social networks made up of intense, non-reproductive bonds with non-kin. Navigating these networks presents a considerable cognitive challenge that is...
How the genome is shaped directly influences how it is expressed. In fact, the genome is organized at many different levels, each imparting specific regulation over transcription. Fundamental principles regulating genome organization are poorly...
Limbic system -- Psychophysiology. ; Neuropsychology. ; Cell interaction.
Previous research has identified neurons in a variety of limbic structures which discharge in relation to the animals ongoing head direction (HD) (Ranck 1984; Taube et al. 1990a) or location (O''Keefe & Dostrovsky 1971). Because these signals...
A fiber can transmit around 25 Tbit/s, but electronic signal processing today is performed at much slower speeds, usually 1-10 Gbit/s. To avoid this "bottleneck" in optical fiber communication systems, all signal processing will have to be done...
This thesis presents technologies for the design, fabrication, operation, and control of electrostatic MEMS micro-robots. It describes prototype micro-robots, with dimensions of 60 Î¼m by 250 Î¼m by 10 Î¼m, that are capable of controllable...
Breast -- Magnetic resonance imaging. Breast -- Tomography. Near infrared spectroscopy. Optical tomography. Imaging systems -- Design and construction. Diagnostic imaging -- Mathematical models.
We present new appearance editing algorithms that allow artists to perform complex editing operations on spatially-varying appearance datasets such as images and measured materials, in an intuitive and efficient manner. The goal is to develop...
In large and complex networks such as the Internet and road networks, traffic routing is typically decentralized. Users in the network choose their routes independently to minimize their own delay, leading to complicated and nonintuitive outcomes...
Brain -- Tomography. Magnetic resonance imaging -- Brain. Near infrared spectroscopy. Image processing -- Digital techniques.
Diffuse optical tomography (DOT) using near infrared (NIR) light has become a promising modality because it has the capability to non-invasively quantify oxygen saturation and hemoglobin content with potentially high temporal resolution and...
We present results from a modeling effort of simple shock phenomena in the Cygnus Loop and Cassiopeia A. Using multi-epoch MDM observations of a small, isolated cloud in the southwest region of the Cygnus Loop, we measure the velocity of the...