Arthrodial joint markerless cross-parameterization and biomechanical visualization

Orthopedists invest significant amounts of effort and time trying to understand the biomechanics of arthrodial (gliding) joints. Although new image acquisition and processing methods currently generate richer-than-ever geometry and kinematic data sets that are individual specific, the computational and visualization tools needed to enable the comparative analysis and exploration of these data sets lag behind. In this paper, we present a framework that enables the cross-data-set visual exploration and analysis of arthrodial joint biomechanics. Central to our approach is a computer-vision-inspired markerless method for establishing pairwise correspondences between individual-specific geometry. Manifold models are subsequently defined and deformed from one individual-specific geometry to another such that the markerless correspondences are preserved while minimizing model distortion. The resulting mutually consistent parameterization and visualization allow the users to explore the similarities and differences between two data sets and to define meaningful quantitative measures. We present two applications of this framework to human-wrist data: articular cartilage transfer from cadaver data to in vivo data and cross-data-set kinematics analysis. The method allows our users to combine complementary geometries acquired through different modalities and thus overcome current imaging limitations. The results demonstrate that the technique is useful in the study of normal and injured anatomy and kinematics of arthrodial joints. In principle, the pairwise cross-parameterization method applies to all spherical topology data from the same class and should be particularly beneficial in instances where identifying salient object features is a nontrivial task.     

The Role of Arithmetic in Fast Parallel Matrix Inversion

In the last two decades several NC algorithms for solving basic linear algebraic problems have appeared in the literature. This interest was clearly motivated by the emergence of a parallel computing technology and by the wide applicability of matrix computations. The traditionally adopted computation model, however, ignores the arithmetic aspects of the applications, and no analysis is currently available demonstrating the concrete feasibility of many of the known fast methods. In this paper we give strong evidence to the contrary, on the sole basis of the issue of robustness, indicating that some theoretically brilliant solutions fail the severe test of the ``Engineering of Algorithms.' We perform a comparative analysis of several well-known numerical matrix inversion algorithms under both fixed- and variable-precision models of arithmetic. We show that, for most methods investigated, a typical input leads to poor numerical performance, and that in the exact-arithmetic setting no benefit derives from conditions usually deemed favorable in standard scientific computing. Under these circumstances, the only algorithm admitting sufficiently accurate NC implementations is Newton's iterative method, and the word size required to guarantee worst-case correctness appears to be the critical complexity measure. Our analysis also accounts for the observed instability of the considered superfast methods when implemented with the same floating-point arithmetic that is perfectly adequate for the fixed-precision approach. Received March 28, 1998; revised February 2, 1999, and April 21, 1999.     

Phonon physics and low temperature detectors of dark matter

We discuss a number of topics in phonon physics that are relevant to the design of low temperature phonon-based dark matter detectors. These topics include the generation of primæval phonons by the nuclear recoil, the processes by which these phonons decay into lower energy phonons, and the ballistic propagation of these excitations to the sensors on the crystal surface.     

The evaporation signal from α particles stopped in superfluid helium

Alpha particles stopped in a 3 liter volume of liquid helium at 30 mK are observed by the calorimetric detection of helium atoms evaporated from the free surface of the liquid. Quantum evaporation of the helium is produced by the rotons that are created by the particle. While the energy spectrum of the 5.5 MeV 's from the²⁴¹Am source has a width of less than 0.5%, the energy distribution of the observed evaporation signals extends from the low energy threshold of several keV up to a maximum of several 100 keV, depending on geometrical factors and the collection area of the calorimeter. The origin of the observed distribution may result in part from the presence of the substrate and a dependence on the direction of the track of the particle. A simple model of the generation of rotons by the particle will be discussed.     

Bayesian recognition of local 3-d shape by approximating image intensity functions with quadric polynomials

The recognition in image data of viewed patches of spheres, cylinders, and planes in the 3-D world is discussed as a first step to complex object recognition or complex object location and orientation estimation. Accordingly, an image is partitioned into small square windows, each of which is a view of a piece of a sphere, or of a cylinder, or of a plane. Windows are processed in parallel for recognition of content. New concepts and techniques include approximations of the image within a window by 2-D quadric polynomials where each approximation is constrained by one of the hypotheses that the 3-D surface shape seen is either planar, cylindrical, or spherical; a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere, or a piece of a cylinder, or a piece of a plane; lowpass filtering of the image by the approximation. The shape recognition is computationally simple, and for large windows is approximately Bayesian minimum-probability-of-error recognition. These classifications are useful for many purposes. One such purpose is to enable a following processor to use an appropriate estimator to estimate shape, and orientation and location parameters for the 3-D surface seen within a window.     

Density of dilute 3He-4He solutions

The number density of dilute ³He-⁴He solutions under saturated vapor pressure is calculated within the framework of quantum hydrodynamics. For temperatures T small compared to the ³He Fermi temperature T _F, results are given for ³He concentrations large enough to manifest ³He quasiparticle interactions. The nondegenerate regime (TT _F) is also considered in the limit of small ³He concentration. Relevance to experimental determination of quasiparticle energies and interactions is emphasized.Supported by the National Science Foundation under Grant No. GP-40831.     

Elastic wave emission from damage processes

The theory of elastic wave emission (i.e., acoustic emission; AE) from damage processes such as slip and microcracking is discussed. Analogous developments in the literature on earth-quake seismology and dynamic dislocation theory are noted and utilized. A general representation of the displacement field of an AE event is given in terms of the double-couple response to a distribution of moment density tensor in the source region. Results are specialized to a point source model and to a general far-field analysis of outgoing elastic waves, and conditions for validity of such representations and their low-frequency specializations are noted. Emitted wave fields are compared for tensile opening and slip events, and procedures which might enable the approximate determination of the size or area increase of tensile microcracks are discussed.     

Space-time tradeoffs for linear recursion

A linear recursive procedure is one each of whose executions activates at most one invocation of itself. When linear recursion cannot be replaced by iteration, it is usually implemented with a stack of size proportional to the depth of recursion. In this paper we analyze implementations of linear recursion which permit large reductions in storage space at the expense of a small increase in computation time. For example, if the depth of recursion isn, storage space can be reduced to \(\sqrt n \) at the cost of a constant factor increase in running time. The problem is treated by abstracting any implementation of linear recursion as the pebbling of a simple graph, and for this abstraction we exhibit the optimal space-time tradeoffs.     

Note: Rotational compliance and instantaneous center of rotation in segmented and V-shaped notch hinges

This note shows a technique for the calculation of rotational compliance (stiffness) and develops a generalized mathematical model for the virtual center of rotation position in concave, segmented, and V-shaped notch hinges using Chebyshev's polynomials. The calculational results are in a good agreement with experimental data and finite element model verified output with estimated differences of less than 10%. This agreement shows that our tractable model is a general one for rotational compliance and the evaluation of a virtual center of rotation position in any type of concave flexure notch hinges.     

Low-contention data structures

We consider the problem of minimizing contention in static (read-only) dictionary data structures, where contention is measured with respect to a fixed query distribution by the maximum expected number of probes to any given cell. The query distribution is known by the algorithm that constructs the data structure but not by the algorithm that queries it. Assume that the dictionary has n$n$ items. When all queries in the dictionary are equiprobable, and all queries not in the dictionary are equiprobable, we show how to construct a data structure in O(n)$O\left(n\right)$ space where queries require O(1)$O\left(1\right)$ probes and the contention is O(1/n)$O(1/n)$. Asymptotically, all of these quantities are optimal. For arbitrary   query distributions, we construct a data structure in O(n)$O\left(n\right)$ space where each query requires O(logn/loglogn)$O(logn/loglogn)$ probes and the contention is O(logn/(nloglogn))$O(logn/(nloglogn))$. The lack of knowledge of the query distribution by the query algorithm prevents perfect load leveling in this case: for a large class of algorithms, we present a lower bound, based on VC-dimension, that shows that for a wide range of data structure problems, achieving contention even within a polylogarithmic factor of optimal requires a cell-probe complexity of Ω(loglogn)$\Omega (loglogn)$.