## About

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Introduction

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January 2005 - present

## Publications

Publications (39)

The concept of the transverse tarsal joint is typically associated with accommodative twists of the foot, and with a midfoot flexion known as the midtarsal break. The specific joints associated for these motions are often assumed, but are rarely validated. The two most common candidates are "Chopart's Joint," which separates the cuboid and navicula...

Most textbooks describe the bifid spinous process as a shape associated with the typical cervical vertebra. Somewhere later they may acknowledge that cervical vertebrae are not always bifid, and that its appearance may be asymmetric. A high incidence of bifid cervical spinous processes may be a human characteristic, but because of known racial/geog...

Exploration of joint kinematics has a long history in anthropological literature. These data are often used to form inferences concerning early hominine functional patterns. Clinical kinematic data capture has become increasingly sophisticated and can now describe multiple joint rotations about obliquely oriented axes. This increased sophistication...

This study describes a unique assessment of primate intrinsic foot joint kinematics based upon bone pin rigid cluster tracking. It challenges the assumption that human evolution resulted in a reduction of midfoot flexibility, which has been identified in other primates as the “midtarsal break.” Rigid cluster pins were inserted into the foot bones o...

Terminologia Anatomica provides an incomplete list of terms used to describe movements (A03.0.00.055-A03.0.00.063). These terms are generally thought to be well understood. Yet, they have no standardized definitions. Descriptions of movement are based more on linguistic tradition than upon anatomical or kinematic convention. Although this may seem...

Kinematic analyses are often complicated by the casual creation of the reference planes used to describe the orientation of joint rotational axes. The human “anatomical position” is most often chosen as the standard referent. However, the identification of the anatomical position becomes complicated when it is based upon skeletal landmarks. Skeleta...

Functional Alignment is a new method to determine the orientation of a joint's primary rotational axis and the associated movement. It employs three unique concepts. First, data analyses are based upon assessment of spatial positions and not upon movement in a time sequence. Second, analyses are conducted on derived joint rotation matrices instead...

Secular-Trends ModelsAnalytical Methods
Temporal Stability of Secular-Trends ModelsModel ApplicationsConclusions
References Cited

Although three-dimensional data capture has become routine, statistical methods that take appropriate advantage of these multivariate data have not been widely developed. Researchers frequently rely on multiple isolated univariate statistical methods in the analysis of a joint's several axes of rotation and their associated motions. This approach r...

Each three-dimensional joint possesses at least one potentially oblique axis of rotation. Several systems are used to express joint axis alignment. One system, designated the plane projection (PP) method, describes angles based on orthogonal projections onto two, of the three, anatomical planes. Alternatively, a joint axis may be described in two d...

All areas of research have their own specialized terms. Typically jargon is used as a short cut among specialists to convey complex ideas with a few brief words or phrases. Several jargons traditionally have been used to describe movements of the foot and ankle. It has been long recognized that these terms have no uniform meanings, which leads to c...

The spinalis muscle is defined as the medial component of the erector spinae muscle group, and is typically subdivided into three regional components: m. spinalis thoracis, m. spinalis cervicis and m. spinalis capitis. Modern authorities, however, differ on the morphology of the cervicis and capitis portions and many claim that these regional disti...

The human gluteus maximus differs from that of the other hominoids because of its size and bony attachments. These differences raise questions concerning their sequence of appearance in human evolution. Given that humans practice a unique locomotor style, one wonders if the human gluteus maximus morphology is a prerequisite or a consequence of upri...

This report presents an analysis of data gathered in 1946, 1977, and 1988 anthropometric surveys of U.S. Army women to assess long-term changes in body dimensions. Fifteen dimensions are analyzed for two racial groups: Whites and Blacks. The results of these analyses describe trends that are slow, erratic, and yet statistically significant as linea...

Data from the recent U.S. Army Anthropometric Survey provide a unique opportunity to assess long-term changes in body dimensions within the Army population. This report considers secular trends for 22 body dimensions within four racial/cultural groups: Whites, Blacks, Hispanics, and Asian/Pacific Islanders. Individuals were grouped by year of birth...

This report presents the results of the analysis of data on the hand gathered during the 1987-1988 anthropometric survey of Army personnel. Data are presented in the form of summary statistics and percentile tables. In addition, correlations, regressions, analyses of variance and principal components for sex and racial groups, nonmetric trait frequ...

This report describes long-term changes in the body dimensions within the Army population for 22 body dimensions in four racial/cultural groups: Whites, Blacks, Hispanics and Asian/Pacific Islanders. Individuals were grouped by birth year into 12 five-year cohorts, which span the years 1911 to 1970. Rates of change were calculated by regressing age...

Typescript. Thesis (M.A.)--State University of New York at Binghamton, 1987. Bibliography: leaves [114]-122.

## Questions

Questions (2)

I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.

Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?

Do these methods produce a result that is mathematically correct? If not, what is the correct method?

The way I've been doing it is to use Singular Value Decomposition, so that M=U * S * V.transpose and then R=U * V.transpose. Essentially, removing the singular values, although I do not know exactly what that means.

However, if I follow the GramSchmidt process, I also get an orthonormal matrix, that sure looks like a rotation matrix but it is a different matrix than I would get following SVD.

The questions are Why? and more importantly What makes one method right and the other method wrong?

Example:

M=1 2 3

4 5 6
7 8 9

Use the SVD method to get:

R=-0.419386, -0.277519, 0.864349

-0.277519, 0.945739, 0.168998
0.864349, 0.168998, 0.473647

But use GramSchmidt and I get:

R=0.123091, 0.904534, 0.408248

0.492366, 0.301511, -0.816497
0.86164, -0.301511, 0.408248
Both R matrices are orthonormal and appear to be good rotation matrices. But, they are different matrices. One method has to be correct, but which one and why? I suppose both could be incorrect, but then what is the correct method for this conversion?