Irwin S. Pressman

Statistical Analysis of Barefoot Impressions

Comparison of the shapes of barefoot impressions from an individual with footprints or shoes linked to a crime may be useful as a means of including or excluding that individual as possibly being at the scene of a crime. The question of the distinguishability of a persons barefoot print arises frequently. This study indicates that measurements taken from the outlines of inked footprint impressions show a great degree of variability between donors and a great degree of similarity for multiple impressions taken from the same donor. The normality of the set of measurements on footprint outlines that we have selected for this study is confirmed. A statistical justification for the use of the product rule on individual statistical precisions is developed.

Matrices with multiple symmetry properties: applications of centrohermitian and perhermitian matrices

Abstract Twelve known symmetry patterns of matrices are combined with three modest patterns to form a steiner triple system. We investigate matrices satisfying more than one symmetry pattern. We show how a group of operators on GL( n , C ) gives rise to distinct types of matrices which satisfy sets of patterns, and which give unique decompositions of matrices into components of each type. These give a new characterization of normal and unitary matrices. We extend symmetry patterns to vectors to study spectral properties of these matrices. When a (skew) symmetric basis of eigenvectors exist, we can infer symmetry properties of these matrices.

A large-scale statistical analysis of barefoot impressions.

In an earlier paper, outlines of footprints of persons walking normally were studied to determine whether different people make verifiably distinct footprints. Our basic null hypothesis is: given a footprint outline trace made by Subject A (Alice), then Subject B (Bob), a distinct person, cannot produce a footprint outline trace indistinguishable from that of Alice. We showed in the previous work that the probability of a chance match is less than 10(-8). In this paper we report two new advances in our research. First, we establish a rigorous mathematical framework for calculating worstcase and average chance-match probabilities. Second, we repeat the previous experiment to substantiate the earlier results, but with an expanded population sample size and a more representative and significantly bigger repeated sample. These improvements and a new automated tracing procedure for extracting all numerical measures lead to a sharpened accuracy with average chance match probabilities of 7.88 x 10-(10) for a general population. In other words, the odds of a chance match are one in 1.27 billion.

The optimal location of replicas in a network using a READ-ONE-WRITE-ALL policy

Abstract. We consider the problem of locating replicas in a network to minimize communications costs. Under the assumption that the read-one-write-all policy is used to ensure data consistency, an optimization problem is formulated in which the cost function estimates the total communications costs. The paper concentrates on the study of the optimal communications cost as a function of the ratio between the frequency of the read and write operations. The problem is reformulated as a zero-one linear programming problem, and its connection to the p-median problem is explained. The general problem is proved to be NP-complete. For path graphs a dynamic programming algorithm for the problem is presented.

Monte Carlo Algorithms for the Detection of Necessary Linear Matrix Inequality Constraints

We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMIs) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor. A necessary LMI is one whose removal changes the feasible region defined by all the LMI constraints. The general problem of checking whether or not a particular LMI is necessary is NP-complete. However, the methods we describe are polynomial in each iteration, and the number of iterations can be limited by stopping rules. This provides a practical method for reducing the size of some large Semidefinite Programming problems before one attempts to solve them. We demonstrate the applicability of this approach to solving instances of the Lowner ellipsoid problem. We also consider the problem of classification of all the constraints of a semidefinite programming problem as redundant or necessary.

Epidemiology and biomarker profile of pituitary adenohypophysial tumors

Recent studies have reported the prevalence of pituitary tumors to be ~1/1000 population. Many are prolactin-producing tumors that are managed medically, however, the epidemiology of surgically resected pituitary adenohypophysial neuroendocrine tumors has not been reported in a large series with detailed characterization. We reviewed 1055 adenohypophysial tumors from 1169 transsphenoidal resections from the pathology files of University Health Network, Toronto, 2001-2016. Tumors were characterized by immunohistochemical localization of transcription factors (Pit-1, ERα, SF-1, Tpit), hormones (adrenocorticotropin, growth hormone, prolactin, β-thyrotropin, β-folliculotropin, β-luteotropin, α-subunit), and other biomarkers (keratins, Ki67, p27, FGFR4). Electron microscopy was used only for unusual lesions. In this cohort, 51.3% of patients were female; the average age was 51 years. Gonadotroph tumors represented 42.5%. Pit-1-lineage-tumors represented 29.9%; these were subclassified as growth-hormone-predominant (somatotroph/mammosomatotroph/mixed; 53%), prolactin-predominant (lactotroph/acidophil-stem-cell; 28%), thyrotrophs (2%), plurihormonal (14%), and not-otherwise-specified (3%). Corticotroph tumors represented 17.1%. Only 4.5% were null cell tumors and 0.5% were unusual plurihormonal tumors. In 5.5% the tumor was not characterized for technical reasons (sample size, fixation, necrosis or other artifact). All corticotroph and plurihormonal tumors were positive for keratins; others tumors showed variable negativity with highest rates in gonadotroph (37.1%) and null cell tumors (28.2%). Tumors with a Ki67 ≥ 3% comprised 60% of this cohort. Global loss of p27 was most frequent in corticotroph neoplasms, specifically those associated with elevated glucocorticoid levels. Corticotroph and lactotroph tumors were more common among females; gonadotroph tumors were more common among males. Younger patients had mainly corticotroph and Pit-1-lineage neoplasms, whereas older patients harbored mainly gonadotroph tumors. This represents one of the largest surgical series of morphologically characterized pituitary tumors reported to date and the first to include the routine use of transcription factors for tumor classification. The data provide the basis for clinicopathologic correlations that are helpful for prognostic and predictive patient management.

The Shuffle Algorithm and Jordan Blocks

Abstract A shuffle is the horizontal interchange of a pair of blocks of the same size in a matrix. A general algorithm using row reduction and shuffles was first introduced by Luenberger, and then used by Anstreicher and Rothblum to give an algorithm to compute generalized nullspaces. We present a new, concise proof of this shuffle algorithm, and show how the shuffle algorithm can be used in deriving the Jordan blocks for a square matrix with known eigenvalues.

The Replica Location Problem and Chebyshev Polynomials of the Second Kind

Abstract. We study the optimal placement of replicas of data objects in a connected network with the topology of a straight-line segment. This special case of a NP-complete location problem has a remarkably attractive algebraic solution. The minimum cost problem gives rise to tridiagonal matrices that are both persymmetric and symmetric and these are used to prove the symmetry of the optimal solution. The eigenvalues and eigenvectors of these matrices are completely described by Chebyshev polynomials of the second kind to give a complete solution to the replica location problem. We denote the kth Chebyshev polynomials of the second kind by Uk. The Chebyshev identity arises naturally in examining the norms of the eigenvectors that occur.