Three-dimensional imaging in medicine -- Mathematical models. ; Stereoencephalotomy.
In the past, clinicians skilled at image-guided neurosurgery have relied solely on pre-operative scans for their navigational information. Often in the course of surgery, tissue is purposely retracted/resected or inadvertently moved resulting in a...
Wireless communication systems. Computer networks. Routers (Computer networks).
A mesh network is a network of wireless routers that employ multi-hop routing and can be used to provide network access for mobile clients. Mobile mesh networks can be deployed rapidly to provide an alternate communication infrastructure for...
Coding theory. Characters of groups. Error-correcting codes (Information theory). Polynomials.
We introduce vector-valued character theory, a higher dimensional generalization of character theory. We then use vector-valued characters to extend the MacWilliams equivalence theorem for linear codes to a class of additive codes, called...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
We expect wireless body-area networks of pervasive wearable devices will enable in situ health monitoring, personal assistance, entertainment personalization, and home automation. As these devices become ubiquitous, we also expect them to...
Sensor networks are used in many realtime applications for collecting information from monitored environments and objects, such as moving vehicle tracking, battlefield reconnaissance, and habitat monitoring. Sensor networks are often deployed in...
Electronic data processing -- Distributed processing. ; Computer network architectures. ; Programming languages (Electronic computers) -- Semantics. ; Database management.
I tackle the problem of naming and sharing resources across administrative boundaries. Conventional systems manifest the hierarchy of typical administrative structure in the structure of their own mechanism. While natural for communication that...
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...
Graph algorithms. Nuclear magnetic resonance spectroscopy -- Data processing. Proteins -- Structure -- Mathematical models. Proteins -- Crosslinking -- Mathematical models. Protein folding -- Mathematical models.
The study of three-dimensional protein structures produces insights into protein function at the molecular level. Graphs provide a natural representation of protein structures and associated experimental data, and enable the development of graph...
This thesis considers the two special sensor networks for future sensor network design: mobile sensor networks and hybrid network of sensors and robots. To investigate two types of networks, we abstract two most important aspects that are ingrained...
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...
Diagnostic imaging -- Mathematics. Expectation-maximization algorithms. Imaging systems in medicine -- Mathematics.
We have developed a general-purpose registration algorithm for medical images and volumes. The transformation between images is modeled as locally affine but globally smooth, and explicitly accounts for local and global variations in image...
Proteins -- Structure -- Mathematical models. Recombinant proteins -- Mathematical models. Mathematical optimization -- Data processing. Dynamic programming. Protein engineering.
Site-directed protein recombination produces improved and novel protein variants by recombining sequence fragments from parent proteins. The resulting hybrids accumulate multiple mutations that have been evolutionarily accepted together. Subsequent...
All ecological theories regarding the distribution and relative abundance of species refer to organisms'' abilities to utilize an environment and (sometimes implicitly) their ability to colonize and re-colonize habitats that change in character or...
In order to most effectively investigate protein structure and improve protein function, it is necessary to carefully plan appropriate experiments. The combinatorial number of possible experiment plans demands effective criteria and efficient...
Two localized spectroscopic imaging methods were investigated to detect and discriminate microscopic pathologies at the surface of excised breast tissues in order to improve resection completeness during breast conserving surgery. A scanning in...
Problem Statement Patient safety in the modern hospital is supported by multiple human and technological systems, and this type of high-risk/high-complexity domain requires multiple layers of protection against harm. This fault-tolerant approach is...
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...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
For a local field K, we study the affine buildings Îž n and Î” n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Î” n in Îž 2 n ....
This research has established feasibility of surface temperature characterization using ruby fluorescence. Study was performed in pin-on-disk geometry, with balls made of different plastics sliding against the sapphire disk. Fluorescence signal was...
Modern distributed systems scatter sensors, storage, and computation throughout the environment. Ideally these devices communicate and share resources, but there is seldom motivation for a device''s owner to yield control to another user. We...
Pervasive computing leads to an increased integration between the real world and the computational world, and many applications in pervasive computing adapt to the user's context, such as the location of the user and relevant devices, the presence...
Earlier work has suggested that various neurological or neuropsychiatric disorders may result in characteristic spatial patterns in brain activation, potentially allowing their detection from maps of brain activity under different conditions....
I consider the problem of extending certain invariants of subsets of natural numbers to their equivalents for subsets of larger cardinals. The two specific questions I will address are the extension of the off-branch number [Special characters...
Human locomotion -- Computer-assisted instruction. ; Real-time data processing. ; Human-computer interaction.
Teaching physical motions such as riding, exercising, swimming, etc. to human beings is hard. Coaches face difficulties in communicating their feedback verbally and cannot correct the student mid-action; teaching videos are two dimensional and...