Rank Profile Research Articles

Iliac Artery Stent Placement with the Palmaz Stent: Follow-up Study

The long-term efficacy of iliac artery stent placement with the Palmaz stent was evaluated for treatment of limb ischemia. Iliac stent implantation for limb ischemia was performed on 108 limbs in 83 patients. Eighty patients (96.4%) were followed up clinically from 1 to 70 months (mean, 25.8 months), and 30 patients (37.5%) were followed up with angiography from 1 to 48 months (mean, 10.4 months). Patients were classified into six categories by using an ischemic ranking profile. Clinical success was defined as a minimum one-category improvement from preprocedure ranking. The clinical success rate was 98.9% immediately after the procedure and 86.2% at 48 months. Long-term success was statistically more common in patients with higher preprocedure and lower postprocedure ischemic ranking, and in patients without diabetes. Arteriography demonstrated a primary patency rate of 87.5% at latest follow-up, with five occlusions (12.5%) and only two (5.0%) restenoses. Average stenosis was 17.8% at 6 months and 24.7% at 2 years. Stent restenosis was statistically more common with a higher postprocedure pressure gradient. The complication rate was 9.7%, and 30-day mortality was 1.2%. Long-term clinical and angiographic follow-up demonstrates iliac artery stent placement with the Palmaz stent is safe and efficacious for treatment of limb ischemia.

Fast Triangular Factorization and Inversion of Hankel and Related Matrices with Arbitrary Rank Profile

The authors present a fast procedure for computing a “modified” triangular factorization of Hankel, quasi-Hankel (matrices congruent in a certain sense to Hankel matrices) and sign-modified quasi-Hankel (products of quasi-Hankel and signature matrices) matrices. A fast procedure for computing inverse of Hankel and quasi-Hankel matrices is also presented. A modified triangular factorization is an $LDL^ * $ factorization, where L is lower triangular with unit diagonal entries and D is a block diagonal matrix with possibly varying block sizes. Only matrices with all leading minors nonzero, often called strongly regular, will always have a purely diagonal and nonsingular D matrix. The matrices studied in this paper have diagonal blocks with a particular Hankel-(like) structure. The algorithms presented here are obtained by extending a generating function approach of Lev-Ari and Kailath for matrices with a generalized displacement structure. A particular application of the results is a fast method of computing the rank profile and inertia of the matrices involved.

Displacement structure approach to singular root distribution problems: the imaginary axis case

A general theory of tabular form root distribution procedures based on LDL* factorization of Bezoutians has been presented in this paper. In particular, we have concentrated on the singular cases arising in the Routh test. A one-to-one correspondence has been established between the rank profile of the underlying Bezoutians and the occurrence of the singular cases. Combining this interpretation with the newly developed factorization procedures of Pal and Kailath (1989), it has been possible to extend the new unified approach of Lev-Ari, Bistritz, and Kailath (1991) to the singular cases. By doing so not only did we obtain all the known procedures but we also obtained new results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Displacement structure approach to singular root distribution problems: the unit circle case

A general theory of tabular form root distribution procedures based on LDL* factorization of Bezoutians is presented. In particular, the authors concentrate on the singular cases arising in the Schur-Cohn test. A one-to-one correspondence is established between the rank profile of the underlying Bezoutians and the occurrence of the singular cases. Combining this interpretation with the newly developed factorization procedures of Pal and Kailath, it is possible to extend the new unified approach of Lev-Ari, Bistritz, and Kailath(1991) to the singular cases. By doing so, not only do the authors derive the well known Schur-Cohn procedure, but they also obtain new results. In fact, the authors are able to derive a new completely recursive procedure to deal with the first kind of singularity. >

Fast Triangular Factorization and Inversion of Hermitian, Toeplitz, and Related Matrices with Arbitrary Rank Profile

A fast procedure for computing a “modified” triangular factorization and inverse of Hermitian Toeplitz and quasi-Toeplitz (matrices congruent in a certain sense to Toeplitz matrices) matrices is presented. A modified triangular factorization is an $LDL^ * $ factorization where L is lower triangular with unit diagonal entries and D is a block diagonal matrix with possibly varying block sizes; only matrices with all leading minors nonzero, often called strongly regular, will always have a purely diagonal and nonsingular D matrix. For the matrices studied herein, the diagonal blocks also have a particular quasi-Toeplitz structure. The algorithms are obtained by extending a generating function approach of Lev-Ari and Kailath [Operator Theory: Adv. Appl.,18 (1986), pp. 301–324.] for matrices with a generalized displacement structure. A particular application of the result is a fast method of computing the rank profile and inertia of the matrices involved.

Relationship between Order of Variables and Determination of Policies When Using Judgment Analysis

The methodology for conducting a Judgment Analysis requires judges to rate or rank profiles comprised of a number of variables representing several stimulus dimensions. In this study we investigated the relationship between the order of variables (fixed or random) and 19 judges' rating policies. The results of the Judgment Analysis for the two methods of sequencing profile variables indicate that there is an association between the order of variables and the judges' ability to utilize them in their rankings. When variables were placed in the same order on all profiles, judges used more variables in creating their policies than when the order of the variables randomly changed from profile to profile.

An augmented smoothed rank profile algorithm for determination of source coherency structure

The problem is discussed of determining the source coherency structure and estimating the directions of arrival in the presence of coherent signals. The method is closely related to the smoothed rank profile (SRP) algorithm, which shows that for determining the source coherency structure, the number of elements required is greater than or equal to the total number of sources plus the highest degree of signal coherency present. In the modified approach suggested here, it is shown how the SRP method can be augmented by the incorporation of forward-backward averaged covariance to increase the likelihood of the successful determination of the source coherency structure with a limited number of sensors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On smoothed rank profile tests in eigenstructure methods for directions-of-arrival estimation

We propose a statistical procedure known as the smoothed rank profile (SRP) test that can be applied to an array covariance matrix to determine the source coherency structure and solvability of the directions-of-arrival estimation problem in the presence of coherent sources. The SRP is the rank profile of a telescoping series of matrices extracted from the observed array covariance matrix.

A generalization of the Levinson algorithm for Hermitian Toeplitz matrices with any rank profile

The paper describes a recursive algorithm for solving Hermitian Toeplitz systems of linear equations, without any restriction on the ranks of their nested Toeplitz subsystems. Such a general algorithm is needed, e.g., to obtain the eigenfilters for signal processing applications, or to compute the inverse of a nondefinite Toeplitz matrix. The regular portion of the algorithm is made of the classical Levinson recursion. The singular portion requires solving some well-defined systems of linear equations with gradient structure. The dimension of each of these sytems equals the amplitude of the corresponding singularity.

Monotonicity paradoxes in the theory of elections

An election procedure based on voter preference rankings is said to be monotonic if the alternative chosen by the procedure for any profile of voter preference rankings is also chosen after it is moved up in one or more of the profile's rankings. Several reasonable-sounding election procedures that are known to violate monotonicity are examined along with some new classes of non-monotonic procedures. Closely-related procedures that are monotonic are also identified. The procedural mechanisms and combinatorial structures that give rise to failures of monotonicity are analyzed in some detail.

Inverted orders for monotone scoring rules

When each of n judges ranks a set A of m objects from best to worst, and s=( s 1,…, s m ) is a decreasing sequence of real numbers, the collective ranking determined by s orders the objects in A according to their total scores. The total score of x equals s p times the number of judges who rank x in pth place, summed over p. For normalization purposes, let S m denote the set of all decreasing s=( s 1,…, s m ) for which s m − 1 =1 and s m =0. Given any m ⩾ 3, we show firstthat if s and s′ in S m are not identical, then some profile of judges' rankings yields a linear collective order for s′ that is the reverse or dual of the linear collective order for s. We then consider reversals in collective rankings when one object is removed from A. Suppose s is in S m and t is in S m − 1 , with m ≥ 3. A simple constructive proof shows that there is a profile of judges' rankings on A which yields a collective linear order for s such that, when any pre-specified object in A is removed, t yields the reverse ranking on the remaining m − 1 objects. More detailed results are derived for m=3, and shown to depend on the nature of s=( s 1, 1, 0). In particular, the sum-of-ranks procedure with s 1=2 permits fewer reversals than any other s 1>1.

MATURATION PATTERNS IN THE PERTH BASIN

Vitrinite reflectance data from wells drilled in the Perth Basin show that major variations exist in the pattern of rank distribution within the basin. Generally, rank gradients are low and near linear, but some wells show curvature of the rank profile in the Early Jurassic and Triassic parts of their sections. Curvature of the rank profile is generally associated with a shallow depth to basement, but the presence of very high ranks in parts of the Permian section on the Beagle Ridge suggests that a Permian to Jurassic thermal event associated with local igneous activity or the initiation of rifting, or both, may also be a controlling factor. Low, linear rank gradients from parts of the basin such as the Bunbury Trough and the thick Upper Jurassic sections of some of the deeper sub-basins are taken to indicate that low geothermal gradients have operated since the Permian,in the former instance and certainly since the Jurassic in the latter. Such conditions imply slow generation of hydrocarbons.Higher geothermal gradients and rank gradients in parts of the basin as in the north Dandaragan Trough and Vlaming Sub-basin imply enhanced hydrocarbon generation, particularly as calculated palaeotemperatures indicate that the advent of higher geothermal gradients is likely to have been relatively recent. Potential source rocks occur throughout the basin and provided that suitable structural and reservoir conditions can be delineated, the prospects of discovering more commercial hydrocarbon deposits are high.

Optical character of thermally metamorphosed coals of northern England

SUMMARYThe Carboniferous sediments of northern England have formed the context for an optical study of the effects of differing geothermal history on the included organic material. In the north of the area, the Northumbrian Trough contains 5000 m of cyclothemic Carboniferous sediments with frequent coals and is probably underlain by Old Red Sandstone rocks. To the south, the Alston Block comprises 1500 m of basically similar Carboniferous sediments underlain by highly metamorphosed Silurian slates and a Caledonoid granite. The contrasting nature of the basements has produced variable geothermal gradients and consequently varying coal rank throughout the Carboniferous succession.Alteration of the coals and dispersed organic matter in the sediments by the intrusion of a quartz dolerite sill, the Whin Sill, during Stephanian times has been closely examined. The optical changes induced by the thermal metamorphism depend on the initial rank of the sediments. It has been possible to deduce rank profiles through the succession at the time of intrusion; these can be closely related to the character of the basement. The area was subsequently subjected to hydrothermal (lead, zinc) mineralization.

COAL RANKS IN THE HARTON BOREHOLE: A REPLY

(Short communication) Unfortunately, it appears possible that Dr. Suggate has taken the term “higher-than-expected”, quoted in the last sentence of the section on coal rank in the paper by Ridd, Walker and Jones (1970, p. 91), rather out of context. The term was used relative to coal ranks in the nearby Northumbrian Trough where seams lower in the succession than the bottom of the Harton well are of very low rank. The authors in that paper wished to emphasize the difference that exists between the rank gradient at Harton and that in the Northumbrian Trough. While Dr. Suggate appears to agree with the authors in their interpretation of early, pre-Whin Sill, imposition of rank profile, he attributes this to thick Upper Carboniferous cover rather than high heat flow through the basement. This would necessitate a much greater thickness of Upper Carboniferous sediment in Durham than in Northumberland, which is unlikely in view of the pattern of earlier Carboniferous sedimentation. In addition, although the presence of a greater thickness of Upper Carboniferous strata at Harton would possibly increase the overall rank levels of the coals it would have the result of decreasing the rank gradient. The authors still feel that their interpretation, dependent on differences in the thermal properties of the basement, is the most probable explanation of the high rank gradient at Harton relative to that existing in the Northumbrian Trough.