On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

Wear of human teeth: a tribological perspective

The four main types of wear in teeth are attrition (enamel-on-enamel contact), abrasion (wear due to abrasive particles in food or toothpaste), abfraction (cracking in enamel and subsequent material loss), and erosion (chemical decomposition of the tooth). They occur as a result of a number of mechanisms including thegosis (sliding of teeth into their lateral position), bruxism (tooth grinding), mastication (chewing), toothbrushing, tooth flexure, and chemical effects. In this paper the current understanding of wear of enamel and dentine in teeth is reviewed in terms of these mechanisms and the major influencing factors are examined. In vitro tooth wear simulation and in vivo wear measurement and ranking are also discussed

Motile sperm organelle morphology examination (MSOME): intervariation study of normal sperm and sperm with large nuclear vacuoles

<p>Abstract</p> <p>Background</p> <p>Although the motile sperm organelle morphology examination (MSOME) was developed only as a selection criterion, its application as a method for classifying sperm morphology may represent an improvement in evaluation of semen quality, with potential clinical repercussions. The present study aimed to evaluate individual variations in the motile sperm organelle morphology examination (MSOME) analysis after a time interval.</p> <p>Methods</p> <p>Two semen samples were obtained from 240 men from an unselected group of couples undergoing infertility investigation and treatment. Mean time interval between the two semen evaluations was 119 +/- 102 days. No clinical or surgical treatment was realized between the two observations. Spermatozoa were analyzed at greater than or equal to 8400× magnification by inverted microscope equipped with DIC/Nomarski differential interference contrast optics. At least 200 motile spermatozoa per semen sample were evaluated and percentages of normal spermatozoa and spermatozoa with large nuclear vacuoles (LNV/one or more vacuoles occupying >50% of the sperm nuclear area) were determined. A spermatozoon was classified as morphologically normal when it exhibited a normal nucleus (smooth, symmetric and oval nucleus, width 3.28 +/- 0.20 μm, length 4.75 +/- 0.20 μm/absence of vacuoles occupying >4% of nuclear area) as well as acrosome, post-acrosomal lamina, neck and tail, besides not presenting cytoplasm around the head. One examiner, blinded to subject identity, performed the entire study.</p> <p>Results</p> <p>Mean percentages of morphologically normal and LNV spermatozoa were identical in the two MSOME analyses (1.6 +/- 2.2% vs. 1.6 +/- 2.1% <it>P </it>= 0.83 and 25.2 +/- 19.2% vs. 26.1 +/- 19.0% <it>P </it>= 0.31, respectively). Regression analysis between the two samples revealed significant positive correlation for morphologically normal and for LNV spermatozoa (r = 0.57 95% CI:0.47-0.65 <it>P </it>< 0.0001 and r = 0.50 95% CI:0.38-0.58 <it>P </it>< 0.0001, respectively).</p> <p>Conclusions</p> <p>The significant positive correlation and absence of differences between two sperm samples evaluated after a time interval with respect to normal morphology and LNV spermatozoa indicated that MSOME seems reliable (at least for these two specific sperm forms) for analyzing semen. The present result supports the future use of MSOME as a routine method for semen analysis.</p

Efficacy of hyaluronic acid binding assay in selecting motile spermatozoa with normal morphology at high magnification

<p>Abstract</p> <p>Background</p> <p>The present study aimed to evaluate the efficacy of the hyaluronic acid (HA) binding assay in the selection of motile spermatozoa with normal morphology at high magnification (8400x).</p> <p>Methods</p> <p>A total of 16592 prepared spermatozoa were selected and classified into two groups: Group I, spermatozoa which presented their head attached to an HA substance (HA-bound sperm), and Group II, those spermatozoa that did not attach to the HA substance (HA-unbound sperm). HA-bound and HA-unbound spermatozoa were evaluated according to the following sperm forms: 1-Normal morphology: normal nucleus (smooth, symmetric and oval configuration, length: 4.75+/-2.8 μm and width: 3.28+/-0.20 μm, no extrusion or invagination and no vacuoles occupied more than 4% of the nuclear area) as well as acrosome, post-acrosomal lamina, neck, tail, besides not presenting a cytoplasmic droplet or cytoplasm around the head; 2-Abnormalities of nuclear form (a-Large/small; b-Wide/narrow; c-Regional disorder); 3-Abnormalities of nuclear chromatin content (a-Vacuoles: occupy >4% to 50% of the nuclear area and b-Large vacuoles: occupy >50% of the nuclear area) using a high magnification (8400x) microscopy system.</p> <p>Results</p> <p>No significant differences were obtained with respect to sperm morphological forms and the groups HA-bound and HA-unbound. 1-Normal morphology: HA-bound 2.7% and HA-unbound 2.5% (P = 0.56). 2-Abnormalities of nuclear form: a-Large/small: HA-bound 1.6% vs. HA-unbound 1.6% (P = 0.63); b-Wide/narrow: HA-bound 3.1% vs. HA-unbound 2.7% (P = 0.13); c-Regional disorders: HA-bound 4.7% vs. HA-unbound 4.4% (P = 0.34). 3. Abnormalities of nuclear chromatin content: a-Vacuoles >4% to 50%: HA-bound 72.2% vs. HA-unbound 72.5% (P = 0.74); b-Large vacuoles: HA-bound 15.7% vs. HA-unbound 16.3% (P = 0.36).</p> <p>Conclusions</p> <p>The findings suggest that HA binding assay has limited efficacy in selecting motile spermatozoa with normal morphology at high magnification.</p

Observations on morphologic changes in the aging and degenerating human disc: Secondary collagen alterations

BACKGROUND: In the annulus, collagen fibers that make up the lamellae have a wavy, planar crimped pattern. This crimping plays a role in disc biomechanical function by allowing collagen fibers to stretch during compression. The relationship between morphologic changes in the aging/degenerating disc and collagen crimping have not been explored. METHODS: Ultrastructural studies were performed on annulus tissue from 29 control (normal) donors (aged newborn to 79 years) and surgical specimens from 49 patients (aged 16 to 77 years). Light microscopy and specialized image analysis to visualize crimping was performed on additional control and surgical specimens. Human intervertebral disc tissue from the annulus was obtained in a prospective morphologic study of the annulus. Studies were approved by the authors' Human Subjects Institutional Review Board. RESULTS: Three types of morphologic changes were found to alter the crimping morphology of collagen: 1) encircling layers of unusual matrix disrupted the lamellar collagen architecture; 2) collagen fibers were reduced in amount, and 3) collagen was absent in regions with focal matrix loss. CONCLUSIONS: Although proteoglycan loss is well recognized as playing a role in the decreased shock absorber function of the aging/degenerating disc, collagen changes have received little attention. This study suggests that important stretch responses of collagen made possible by collagen crimping may be markedly altered by morphologic changes during aging/degeneration and may contribute to the early tissue changes involved in annular tears

Tooth development and replacement in the Atlantic Cutlassfish, Trichiurus lepturus, with comparisons to other Scombroidei

Atlantic Cutlassfish, Trichiurus lepturus, have large, barbed, premaxillary and dentary fangs, and sharp dagger-shaped teeth in their oral jaws. Functional teeth firmly ankylose to the dentigerous bones. We used dry skeletons, histology, SEM, and micro-CT scanning to study 92 specimens of T. lepturus from the western North Atlantic to describe its dentition and tooth replacement. We identified three modes of intraosseous tooth replacement in T. lepturus depending on the location of the tooth in the jaw. Mode 1 relates to replacement of premaxillary fangs, in which new tooth germs enter the lingual surface of the premaxilla, develop horizontally, and rotate into position. We suggest that growth of large fangs in the premaxilla is accommodated by this horizontal development. Mode 2 occurs for dentary fangs: new tooth germs enter the labial surface of the dentary, develop vertically, and erupt into position. Mode 3 describes replacement of lateral teeth, in which new tooth germs enter a trench along the crest of the dentigerous bone, develop vertically, and erupt into position. Such distinct modes of tooth replacement in a teleostean species are unknown. We compared modes of replacement in T. lepturus to 20 species of scombroids to explore the phylogenetic distribution of these three replacement modes. Alternate tooth replacement (in which new teeth erupt between two functional teeth), ankylosis, and intraosseous tooth development are plesiomorphic to Bluefish + other Scombroidei. Our study highlights the complexity and variability of intraosseous tooth replacement. Within tooth replacement systems, key variables include sites of formation of tooth germs, points of entry of tooth germs into dentigerous bones, coupling of tooth germ migration and bone erosion, whether teeth develop horizontally or immediately beneath the tooth to be replaced, and how tooth eruption and ankylosis occur. Developmentally different tooth replacement processes can yield remarkably similar dentitions

Nondegenerate Super-Anti-de Sitter Algebra and a Superstring Action

We construct an Anti-de Sitter(AdS) algebra in a nondegenerate superspace. Based on this algebra we construct a covariant kappa-symmetric superstring action, and we examine its dynamics: Although this action reduces to the usual Green-Schwarz superstring action in flat limit, the auxiliary fermionic coordinates of the nondegenerate superspace becomes dynamical in the AdS background.Comment: Latex, 12 pages, explanations added, version to be published in Phys. Rev.

Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit

This paper considers a spacecraft pursuit-evasion problem taking place in low earth orbit. The problem is formulated as a zero-sum differential game in which there are two players, a pursuing spacecraft that attempts to minimize a payoff, and an evading spacecraft that attempts to maximize the same payoff. We introduce two associated optimal control problems and show that a saddle point for the differential game exists if and only if the two optimal control problems have the same optimal value. Then, on the basis of this result, we propose two computational methods for determining a saddle point solution: a semi-direct control parameterization method (SDCP method), which is based on a piecewise-constant control approximation scheme, and a hybrid method, which combines the new SDCP method with the multiple shooting method. Simulation results show that the proposed SDCP and hybrid methodsare superior to the semi-direct collocation nonlinear programming method (SDCNLP method), which is widely used to solve pursuit-evasion problems in the aerospace field