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

SPHERES as Formation Flight Algorithm Development and Validation Testbed: Current Progress and Beyond

The MIT-SSL SPHERES testbed provides a facility for the development of algorithms necessary for the success of Distributed Satellite Systems (DSS). The initial development contemplated formation flight and docking control algorithms; SPHERES now supports the study of metrology, control, autonomy, artificial intelligence, and communications algorithms and their effects on DSS projects. To support this wide range of topics, the SPHERES design contemplated the need to support multiple researchers, as echoed from both the hardware and software designs. The SPHERES operational plan further facilitates the development of algorithms by multiple researchers, while the operational locations incrementally increase the ability of the tests to operate in a representative environment. In this paper, an overview of the SPHERES testbed is first presented. The SPHERES testbed serves as a model of the design philosophies that allow for the various researches being carried out on such a facility. The implementation of these philosophies are further highlighted in the three different programs that are currently scheduled for testing onboard the International Space Station (ISS) and three that are proposed for a re-flight mission: Mass Property Identification, Autonomous Rendezvous and Docking, TPF Multiple Spacecraft Formation Flight in the first flight and Precision Optical Pointing, Tethered Formation Flight and Mars Orbit Sample Retrieval for the re-flight mission

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

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

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

Towards standard setting for patient-reported outcomes in the NHS homeopathic hospitals

We report findings from a pilot data collection study within a programme of quality assurance, improvement and development across all five homeopathic hospitals in the UK National Health Service (NHS).&lt;p&gt;&lt;/p&gt; &lt;b&gt;Aims&lt;/b&gt; (1) To pilot the collection of clinical data in the homeopathic hospital outpatient setting, recording patient-reported outcome since first appointment; (2) to sample the range of medical complaints that secondary-care doctors treat using homeopathy, and thus identify the nature and complexity of complaints most frequently treated nationally; (3) to present a cross section of outcome scores by appointment number, including that for the most frequently treated medical complaints; (4) to explore approaches to standard setting for homeopathic practice outcome in patients treated at the homeopathic hospitals.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Methods&lt;/b&gt; A total of 51 medical practitioners took part in data collection over a 4-week period. Consecutive patient appointments were recorded under the headings: (1) date of first appointment in the current series; (2) appointment number; (3) age of patient; (4) sex of patient; (5) main medical complaint being treated; (6) whether other main medical complaint(s); (7) patient-reported change in health, using Outcome Related to Impact on Daily Living (ORIDL) and its derivative, the ORIDL Profile Score (ORIDL-PS; range, –4 to +4, where a score &#8804;−2 or &#8805;+2 indicates an effect on the quality of a patient's daily life); (8) receipt of other complementary medicine for their main medical complaint.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Results&lt;/b&gt; The distribution of patient age was bimodal: main peak, 49 years; secondary peak, 6 years. Male:female ratio was 1:3.5. Data were recorded on a total of 1797 individual patients: 195 first appointments, 1602 follow-ups (FUs). Size of clinical service and proportion of patients who attended more than six visits varied between hospitals. A total of 235 different medical complaints were reported. The 30 most commonly treated complaints were (in decreasing order of frequency): eczema; chronic fatigue syndrome (CFS); menopausal disorder; osteoarthritis; depression; breast cancer; rheumatoid arthritis; asthma; anxiety; irritable bowel syndrome; multiple sclerosis; psoriasis; allergy (unspecified); fibromyalgia; migraine; premenstrual syndrome; chronic rhinitis; headache; vitiligo; seasonal allergic rhinitis; chronic intractable pain; insomnia; ulcerative colitis; acne; psoriatic arthropathy; urticaria; ovarian cancer; attention-deficit hyperactivity disorder (ADHD); epilepsy; sinusitis. The proportion of patients with important co-morbidity was higher in those seen after visit 6 (56.9%) compared with those seen up to and including that point (40.7%; P &lt; 0.001). The proportion of FU patients reporting ORIDL-PS &#8805; +2 (improvement affecting daily living) increased overall with appointment number: 34.5% of patients at visit 2 and 59.3% of patients at visit 6, for example. Amongst the four most frequently treated complaints, the proportion of patients that reported ORIDL-PS &#8805; +2 at visit numbers greater than 6 varied between 59.3% (CFS) and 73.3% (menopausal disorder).&lt;p&gt;&lt;/p&gt; &lt;b&gt;Conclusions&lt;/b&gt; We have successfully piloted a process of national clinical data collection using patient-reported outcome in homeopathic hospital outpatients, identifying a wide range and complexity of medical complaints treated in that setting. After a series of homeopathy appointments, a high proportion of patients, often representing “effectiveness gaps” for conventional medical treatment, reported improvement in health affecting their daily living. These pilot findings are informing our developing programme of standard setting for homeopathic care in the hospital outpatient context

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.