17042560
On The Geometry and Shape of Brain Sub-Manifolds
This paper develops mathematical representations for neuro-anatomically significant substructures of the brain and their variability in a population. The focus of the paper is on the neuro-anatomical variation of the geometry and the "shape" of two-dimensional surfaces in the brain. As examples, we focus on the cortical and hippocampal surfaces in an ensemble of Macaque monkeys and human MRI brains. The "shapes" of the substructures are quantified via the construction of templates; the variations are represented by defining probabilistic deformations of the template. Methods for empirically estimating probability measures on these deformations are developed by representing the deformations as Gaussian random vector fields on the embedded sub-manifolds. The Gaussian random vector fields are constructed as quadratic mean limits using complete orthonormal bases on the sub-manifolds. The complete orthonormal bases are generated using modes of vibrations of the geometries of the brain sub-manifolds. The covari...
7980241
Segmenting magnetic resonance images via hierarchical mixture modelling
We present a statistically innovative as well as scientifically and practically relevant method for automatically segmenting magnetic resonance images using hierarchical mixture models. Our method is a general tool for automated cortical analysis which promises to contribute substantially to the science of neuropsychiatry. We demonstrate that our method has advantages over competing approaches on a magnetic resonance brain imagery segmentation task.
15180139
Bayesian Segmentation via Asymptotic Partition Functions
Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic difference equations determined by finitely supported, stationary, linear difference operators, adjusted to be nonstationary at the boundaries. It is shown that as the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximum-likelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models are used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds.
13019795
Large deformation diffeomorphic metric mapping of fiber orientations
This paper proposes a method to match diffusion tensor magnetic resonance images (DT-MRI) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphisms on such vector fields, and provide an extension of the large deformation diffeomorphic metric-mapping framework to this type of dataset, resulting in optimizing for geodesies on the space of diffeomorphisms connecting two images. Two different distance function of vector fields are considered. Existence of the minimizers under smoothness assumptions on the compared vector fields is proved, and coarse to fine hierarchical strategies are detailed, to reduce both ambiguities and computation load. This is illustrated by numerical experiments on DT-MRI heart and brain images
5537969
Individualizing Anatomical Atlases of the Head
This paper presents diffeomorphic transformations of 3D anatomical image data in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional, large-deformation registration is accomplished by minimizing the mismatch between the template (atlas) and target image volumes constrained by solving the Navier Stokes fluid model on a vector field.
14414468
Information measures for object recognition accommodating signature variability
This paper presents measures characterizing the information content of remote observations of ground scenes imaged via optical and infrared sensors. Object recognition is posed in the context of deformable templates; the special Euclidean group is used to accommodate geometric variation of object pose. Principal component analysis of object signatures is used to represent and efficiently accommodate variation in object signature due to changes in the thermal state of the object surface. Mutual information measures, which are independent of the recognition system, are calculated quantifying both the information gain due to remote observations of the scene and the information loss due to signature variability. Signature model mismatch is quantitatively examined using the Kullback-Leibler divergence. Expressions are derived quadratically approximating the posterior conditional entropy on the orthogonal group for high signal-to-noise ratio. It is demonstrated that quadratic modules accurately characterize the posterior entropy for broad ranges of signal-to-mise ratio. Information gain in multiple-sensor scenarios is quantified, and it is demonstrated that the cost of signature uncertainty for the Comanche series of FLIR images collected by the US Army Night Vision Electronic Sensors Directorate is approximately 0.8 bits with an associated near doubling of mean-squared error uncertainty in pose.
28891049
Connected graphs which are not mod sum graphs
Abstract In this paper we prove that no wheel with the exception of W 4 can be a mod sum graph. We also give the unique (up to multiplication by positive integers) mod sum labelling of W 4 . We also prove that the symmetric complete bipartite graph K n . n is not a mod sum graph.
2078197
Collaborative Agents for C2 Teamwork Simulation
Existing team training software often requires that trainees be organized as physical teams and the members of the same team be trained at the same time. To demonstrate that team training software can be made more flexible, this paper presents an approach to incorporating software agents into the distributed command-and-control (C2) simulation software DDD, which supports only human players. Based on the multi-agent architecture CAST, the software agents are designed as a team to perform C2 tasks in the DDD. By associating the agents with the same basic capabilities as the DDD provides its human users, we illustrate how to specify the teamwork knowledge for the agent team, and how to make agents efficiently reason about the dynamic, partially observable environment. Different methods of communication and coordination among agents are also briefly described.
1871640
Exploring the Energy-Latency Trade-Off for Broadcasts in Energy-Saving Sensor Networks
Networking protocols for multi-hop wireless sensor networks (WSNs) are required to simultaneously minimize resource usage as well as optimize performance metrics such as latency and reliability. This paper explores the energy-latency-reliability trade-off for broadcast in multi-hop WSNs, by presenting a new protocol called PBBF (probability-based broadcast forwarding). PBBF works at the MAC layer and can be integrated into any sleep scheduling protocol. For a given application-defined level of reliability for broadcasts, the energy required and latency obtained are found to be inversely related to each other. Our analysis and simulation study quantify this relationship at the reliability boundary, as well as performance numbers to be expected from a deployment. PBBF essentially offers a WSN application designer considerable flexibility in choice of desired operation points
32344923
Two Minimum Dominating Sets with Minimum Intersection in Chordal Graphs
We prove that the problem of finding two minimum dominating sets (connected dominating sets or clique transversals) with minimum intersection is polynomially solvable on interval graphs. Furthermore, the problem of deciding whether or not there exist two disjoint minimum dominating sets (connected dominating sets or clique transversals) is shown to be NP-hard for chordal graphs.
46718511
Capability-Based Financial Instruments
Every novel cooperative arrangement of mutually suspicious parties interacting electronically -- every smart contract -- effectively requires a new cryptographic protocol. However, if every new contract requires new cryptographic protocol design, our dreams of cryptographically enabled electronic commerce would be unreachable. Cryptographic protocol design is too hard and expensive, given our unlimited need for new contracts.Just as the digital logic gate abstraction allows digital circuit designers to create large analog circuits without doing analog circuit design, we present cryptographic capabilities as an abstraction allowing a similar economy of engineering effort in creating smart contracts. We explain the E system, which embodies these principles, and show a covered-call-option as a smart contract written in a simple security formalism independent of cryptography, but automatically implemented as a cryptographic protocol coordinating five mutually suspicious parties.