Enumerative Problems of Doubly Stochastic Matrices and the Relation to Spectra

This work concerns the spectra of doubly stochastic matrices whose entries are rational numbers with a bounded denominator. When the bound is fixed, we consider the enumeration of these matrices and also the enumeration of the orbits under the action of the symmetric group. In the case where the bound is two, we investigate the symmetric case. Such matrices are in fact doubly stochastic, and have a nice characterization when we are in the special case where the diagonal is zero. As a central tool to this investigation, we utilize Birkhoff\u27s theorem that asserts that the doubly stochastic matrices are exactly the polytope defined by the convex hull of permutation matrices. In particular, we consider the spectra along segments in the Birkhoff polytope

Review of nutrient actions on age-related macular degeneration

The actions of nutrients and related compounds on age-related macular degeneration (AMD) are explained in this review. The findings from 80 studies published since 2003 on the association between diet and supplements in AMD were reviewed. Antioxidants and other nutrients with an effect on AMD susceptibility include carotenoids (lutein and zeaxanthin, β-carotene), vitamins (vitamin A, E, C, D, B), mineral supplements (zinc, copper, selenium), dietary fatty acids [monounsaturated fatty acids, polyunsaturated fatty acids (PUFA both omega-3 PUFA and omega-6 PUFA), saturated fatty acids and cholesterol], and dietary carbohydrates. The literature revealed that many of these antioxidants and nutrients exert a protective role by functioning synergistically. Specifically, the use of dietary supplements with targeted actions can provide minimal benefits on the onset or progression of AMD; however, this does not appear to be particularly beneficial in healthy people. Furthermore, some supplements or nutrients have demonstrated discordant effects on AMD in some studies. Since intake of dietary supplements, as well as exposure to damaging environmental factors, is largely dependent on population habits (including dietary practices) and geographical localization, an overall healthy diet appears to be the best strategy in reducing the risk of developing AMD. As of now, the precise mechanism of action of certain nutrients in AMD prevention remains unclear. Thus, future studies are required to examine the effects that nutrients have on AMD and to determine which factors are most strongly correlated with reducing the risk of AMD or preventing its progression

The Role of Phytonutrients in Skin Health

Photodamage is known to occur in skin with exposure to sunlight, specifically ultraviolet (UV) radiation. Such damage includes inflammation, oxidative stress, breakdown of the extracellular matrix, and development of cancer in the skin. Sun exposure is considered to be one of the most important risk factors for both nonmelanoma and melanoma skin cancers. Many phytonutrients have shown promise as photoprotectants in clinical, animal and cell culture studies. In part, the actions of these phytonutrients are thought to be through their actions as antioxidants. In regard to skin health, phytonutrients of interest include vitamin E, certain flavonoids, and the carotenoids, β-carotene, lycopene and lutein

A Review of the Evidence Germane to the Putative Protective Role of the Macular Carotenoids for Age-Related Macular Degeneration

There is a consensus that age-related macular degeneration (AMD) is the result of (photo)- oxidative-induced retinal injury and its inflammatory sequelae, the latter being influenced by genetic background. The dietary carotenoids, lutein (L), zeaxanthin (Z), and meso-zeaxanthin (meso-Z), accumulate at the macula, where they are collectively known as macular pigment (MP). The anatomic (central retinal), biochemical (anti-oxidant) and optical (short-wavelength- filtering) properties of this pigment have generated interest in the biologically plausible rationale that MP may confer protection against AMD. Level 1 evidence has shown that dietary supplementation with broad-spectrum anti-oxidants results in risk reduction for AMD progression. Studies have demonstrated that MP rises in response to supplementation with the macular carotenoids, although level 1 evidence that such supplementation results in risk reduction of AMD and/or its progression is still lacking. Although appropriately weighted attention should be accorded to higher levels of evidence, the totality of available data should be appraised in an attempt to inform professional practice. In this context, the literature demonstrates that supplementation with the macular carotenoids is probably the best means of fortifying the anti-oxidant defenses of the macula, thus putatively reducing the risk of AMD and/or its progression

Prevention of age-related macular degeneration

Age-related macular degeneration (AMD) is one of the leading causes of blindness in the developed world. Although effective treatment modalities such as anti-VEGF treatment have been developed for neovascular AMD, there is still no effective treatment for geographical atrophy, and therefore the most cost-effective management of AMD is to start with prevention. This review looks at current evidence on preventive measures targeted at AMD. Modalities reviewed include (1) nutritional supplements such as the Age-Related Eye Disease Study (AREDS) formula, lutein and zeaxanthin, omega-3 fatty acid, and berry extracts, (2) lifestyle modifications, including smoking and body-mass-index, and (3) filtering sunlight, i.e. sunglasses and blue-blocking intraocular lenses. In summary, the only proven effective preventive measures are stopping smoking and the AREDS formula

The role of the carotenoids, lutein and zeaxanthin, in protecting against age-related macular degeneration: A review based on controversial evidence

PURPOSE: A review of the role of the carotenoids, lutein and zeaxanthin, and their function in altering the pathogenesis of age-related macular degeneration (AMD). METHODS: Medline and Embase search. RESULTS: Recent evidence introduces the possibility that lutein and zeaxanthin, carotenoids found in a variety of fruits and vegetables may protect against the common eye disease of macular degeneration. This potential and the lack to slow the progression of macular degeneration, has fueled high public interest in the health benefits of these carotenoids and prompted their inclusion in various supplements. The body of evidence supporting a role in this disease ranges from basic studies in experimental animals to various other clinical and epidemiological studies. Whilst some epidemiological studies suggest a beneficial role for carotenoids in the prevention of AMD, others are found to be unrelated to it. Results of some clinical studies indicate that the risk for AMD is reduced when levels of the carotenoids are elevated in the serum or diet, but this correlation is not observed in other studies. Published data concerning the toxicity of the carotenoids or the optimum dosage of these supplements is lacking. CONCLUSION: An intake of dietary supplied nutrients rich in the carotenoids, lutein and zeaxanthin, appears to be beneficial in protecting retinal tissues, but this is not proven. Until scientifically sound knowledge is available we recommend for patients judged to be at risk for AMD to: alter their diet to more dark green leafy vegetables, wear UV protective lenses and a hat when outdoors. Future investigations on the role of nutrition, light exposure, genetics, and combinations of photodynamic therapy with intravitreal steroid (triamcinolone-acetonide) injections hold potential for future treatment possibilities

Discourse in the Secondary Math and Science Classroom

Next Generation Science Standards (NGSS) and Common Core State Math Standards (CCSMS) are the newest guidelines that Michigan science and math teachers must follow in their classrooms. These new standards have a focus on classroom discussion, and helping students to understand why math and science concepts work. These new standards create equity between male and female students, and give students the opportunity to conduct discussions among themselves. I created a survey in order to explore how teachers in math and science classrooms in Michigan\u27s central Upper Peninsula perceive NGSS and CCSMS, and how they view equity in their classrooms. In an attempt to see the classrooms from an objective point of view, the teachers who participated in the survey were asked if they would allow a researcher into their classroom to observe concepts of equity. Teachers taking the survey agreed or disagreed about various statements about NGSS and/or CCSMS and about classroom participation. Sixty seven percent of teachers said they somewhat agree they have a complete understanding of NGSS and/or CCSMS, while 23% strongly agreed. When responding to statements about male and female participation, 13% of teachers surveyed said males participate more, while 20% said females participate more in classroom discussion. This research is just the beginning of the research focused on NGSS and CCSMS. Initial research reveals classroom discussions may improve equity in the classroom

Antioxidant vitamin and mineral supplements for age-related macular degeneration.

BACKGROUND: It has been proposed that antioxidants may prevent cellular damage in the retina by reacting with free radicals produced in the process of light absorption. OBJECTIVES: The objective of this review is to assess the effects of antioxidant vitamin and/or mineral supplementation on the progression of age-related macular degeneration. SEARCH STRATEGY: The Cochrane Controlled Trials Register - CENTRAL/CCTR, which contains the Cochrane Eyes and Vision Group specialised register (Cochrane Library Issue 3 2001), MEDLINE (1966 to August 2001), EMBASE (1980 to September 2001), the Science Citation Index, and the reference lists of relevant articles were searched. Investigators of included studies were contacted for further information. SELECTION CRITERIA: Randomised trials comparing an antioxidant vitamin and/or mineral supplement (alone or in combination) to control in people with age-related macular degeneration are included in this review. DATA COLLECTION AND ANALYSIS: The reviewer extracted data and assessed trial quality. Due to the variable methods of collecting and presenting outcome data, no statistical summary measure was calculated. MAIN RESULTS: Seven trials, which randomised 4119 people with signs of age-related macular degeneration, are included in this review. One unpublished trial of zinc supplementation (170 participants) is awaiting assessment. The majority of people (88%) were randomised in one trial that found a modest beneficial effect of antioxidant and zinc supplementation on progression to advanced age-related macular degeneration (odds ratio 0.72, 99% confidence interval 0.52 to 0.98). People supplemented with antioxidants and zinc were less likely to lose 15 or more letters of visual acuity (equivalent to a doubling of the visual angle) (odds ratio 0.79, 99% confidence interval 0.60 to 1.04). This effect was seen more strongly in people with moderate to severe disease. There were few events in people with early signs of the disease. The trial evaluated many safety outcomes, of which hospitalisation for genitourinary problems was more common in people taking zinc and yellowing of skin was more common in people taking antioxidant micronutrients. The other six trials in this review were small and the results were inconsistent. REVIEWER'S CONCLUSIONS: The evidence as to the effectiveness of antioxidant vitamin and mineral supplementation in halting the progression of age-related macular degeneration is dominated by one large trial that showed modest benefit in people with moderate to severe signs of the disease. There is no evidence at present that people with early signs of the disease should take supplementation, however, current studies are underpowered to answer that question. Long term harm from supplementation cannot be ruled out, particularly in smokers. The generalisability of these findings to other populations with different nutritional statuses is not known. Further large well-conducted randomised controlled trials in other populations are required

Estrogenic Activity in the Environment: Municipal Wastewater Effluent, River, Ponds, and Wetlands

Estrogenic activity of regional water samples was evaluated. Samples obtained from wetlands and ponds involved in various agricultural land uses, from three river sites over four seasons, and from municipal wastewater effluent held in storage lagoons were evaluated. The estrogen- responsive cell line MCF-7 BOS was used in the E-screen assay to determine 17β-estradiol equivalents (E2 Eq) of water samples extracted by solid-phase extraction. Estrogenic activity in surrounding wetlands and ponds from different land uses was not different, with 10-12 M E2 Eq (0.3 ppt). Estrogenic activity of Red River samples was within the same range as wetland–pond samples. The highest activity was found downstream from municipal wastewater treatment effluent discharge sites, in winter when river flow was lowest (approximately 6 x 10-13 ME2 Eq). Results showed that 7 of 20 wetland–pond samples and 5 of 12 river samples were below the limits of quantitation (approximately 3 x 10-14 M E2 Eq). Toxicity was found in fall and summer river samples upstream from municipal wastewater release sites. The timing of toxicity did not coincide to the presence of elevated fecal coliforms. Estrogenic activity in wastewater effluent from lagoons decreased over time (approximately 25 to 5 x 10-13 M E2 Eq) with an apparent half-life of 8 d for one lagoon. The median concentration of detectable estrogenic activity in regional water samples was approximately 50-fold less than the median 17β-estradiol concentration of estradiol detected in some U.S. streams in previous studies