Structured Random Matrices

Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact or approximate symmetries, such as matrices with i.i.d. entries, for which precise analytic results and limit theorems are available. Much less well understood are matrices that are endowed with an arbitrary structure, such as sparse Wigner matrices or matrices whose entries possess a given variance pattern. The challenge in investigating such structured random matrices is to understand how the given structure of the matrix is reflected in its spectral properties. This chapter reviews a number of recent results, methods, and open problems in this direction, with a particular emphasis on sharp spectral norm inequalities for Gaussian random matrices.Comment: 46 pages; to appear in IMA Volume "Discrete Structures: Analysis and Applications" (Springer

Cooling Strategies for Greenhouses in Summer: Control of Fogging by Pulse Width Modulation

The possibilities for improving the control of greenhouse fogging systems, were studied by comparing several combinations of ventilation cooling techniques, shade screening and low-pressure fogging. The study was divided into three parts: experiments, modelling and simulations. In the first part of the paper, ten combinations of five cooling techniques were tested during the summers of 2002 and 2003 in a 132m2 greenhouse with a steel structure and a single-layer methacrylate cover located in Madrid, Spain. An analysis of variance of the climatic parameters was carried out to determine which combinations produced significant differences in inside temperature or relative humidity. Comparing the values for the inside to outside temperature difference, the combination of a shade screen and above-screen fogging achieved a difference in temperature almost the same as that for under-screen fogging, but the relative humidity was significantly lower. In the second part of the study a dynamic model was developed (2002) and validated (2003). The mean absolute error obtained for inside temperature was similar in the fit and the validation and it was less than 1.5 1C in both cases. The model was used to simulate the inside air temperature for a fog system working without shading, and above and under a shade screen. Control algorithms were developed for reducing system water consumption. In the three cases a simple on/off control with a fixed fogging cycle was compared with a pulse width modulation (PWM) strategy, in which the duration of the fogging pulse was increased as a function of inside temperature. The strategies with PWM applied to the fog system were able to reduce water consumption by 8–15% with respect to the strategies with a fixed fogging cycle

Iso-osmotic regulation of nitrate accumulation in lettuce (Lactuca sativa L.)

Concerns about possible health hazards arising from human consumption of lettuce and other edible vegetable crops with high concentrations of nitrate have generated demands for a greater understanding of processes involved in its uptake and accumulation in order to devise more sustainable strategies for its control. This paper evaluates a proposed iso-osmotic mechanism for the regulation of nitrate accumulation in lettuce (Lactuca sativa L.) heads. This mechanism assumes that changes in the concentrations of nitrate and all other endogenous osmotica (including anions, cations and neutral solutes) are continually adjusted in tandem to minimise differences in osmotic potential of the shoot sap during growth, with these changes occurring independently of any variations in external water potential. The hypothesis was tested using data from six new experiments, each with a single unique treatment comprising a separate combination of light intensity, N source (nitrate with or without ammonium) and nitrate concentration carried out hydroponically in a glasshouse using a butterhead lettuce variety. Repeat measurements of plant weights and estimates of all of the main soluble constituents (nitrate, potassium, calcium, magnesium, organic anions, chloride, phosphate, sulphate and soluble carbohydrates) in the shoot sap were made at intervals from about 2 weeks after transplanting until commercial maturity, and the data used to calculate changes in average osmotic potential in the shoot. Results showed that nitrate concentrations in the sap increased when average light levels were reduced by between 30 and 49 % and (to a lesser extent) when nitrate was supplied at a supra-optimal concentration, and declined with partial replacement of nitrate by ammonium in the external nutrient supply. The associated changes in the proportions of other endogenous osmotica, in combination with the adjustment of shoot water content, maintained the total solute concentrations in shoot sap approximately constant and minimised differences in osmotic potential between treatments at each sampling date. There was, however, a gradual increase in osmotic potential (ie a decline in total solute concentration) over time largely caused by increases in shoot water content associated with the physiological and morphological development of the plants. Regression analysis using normalised data (to correct for these time trends) showed that the results were consistent with a 1:1 exchange between the concentrations of nitrate and the sum of all other endogenous osmotica throughout growth, providing evidence that an iso-osmotic mechanism (incorporating both concentration and volume regulation) was involved in controlling nitrate concentrations in the shoot

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

The association between family and community social capital and health risk behaviours in young people: an integrative review

Background: Health risk behaviours known to result in poorer outcomes in adulthood are generally established in late childhood and adolescence. These ‘risky’ behaviours include smoking, alcohol and illicit drug use and sexual risk taking. While the role of social capital in the establishment of health risk behaviours in young people has been explored, to date, no attempt has been made to consolidate the evidence in the form of a review. Thus, this integrative review was undertaken to identify and synthesise research findings on the role and impact of family and community social capital on health risk behaviours in young people and provide a consolidated evidence base to inform multi-sectorial policy and practice.<p></p> Methods: Key electronic databases were searched (i.e. ASSIA, CINAHL, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, Embase, Medline, PsycINFO, Sociological Abstracts) for relevant studies and this was complemented by hand searching. Inclusion/exclusion criteria were applied and data was extracted from the included studies. Heterogeneity in study design and the outcomes assessed precluded meta-analysis/meta-synthesis; the results are therefore presented in narrative form.<p></p> Results: Thirty-four papers satisfied the review inclusion criteria; most were cross-sectional surveys. The majority of the studies were conducted in North America (n=25), with three being conducted in the UK. Sample sizes ranged from 61 to 98,340. The synthesised evidence demonstrates that social capital is an important construct for understanding the establishment of health risk behaviours in young people. The different elements of family and community social capital varied in terms of their saliency within each behavioural domain, with positive parent–child relations, parental monitoring, religiosity and school quality being particularly important in reducing risk.<p></p> Conclusions: This review is the first to systematically synthesise research findings about the association between social capital and health risk behaviours in young people. While providing evidence that may inform the development of interventions framed around social capital, the review also highlights key areas where further research is required to provide a fuller account of the nature and role of social capital in influencing the uptake of health risk behaviours.<p></p&gt

Bidirectional Associations Between Sibling Relationships and Parental Support During Adolescence

Sibling relationships and parental support are important for adolescents’ development and well-being, yet both are likely to change during adolescence. Since adolescents participate in both the sibling relationship and the parent–child relationship, we can expect sibling relationships and parental support to be associated with each other. Theoretically, it can be expected that there is either a spillover from one relationship to another (congruence hypothesis) or that one relationship can compensate for the other (compensation hypothesis). However, research examining these associations in adolescence is limited. The present study longitudinally investigated the bidirectional associations between sibling relationships and parental support during adolescence. For five consecutive years, data were collected using self-reports of 428 families, consisting of a father, a mother, and two adolescent siblings. The mean ages of the first-born (52.8% males) and second-born (47.7% males) were 15 and 13 years at T1, respectively. For the second-born siblings, prospective associations were found between sibling relationships and adolescent-reported parental support in early adolescence, with no differences between same-sex and mixed-sex dyads. These associations were not found for first-born siblings or for parents’ reports of support. The findings suggest a spillover from the sibling relationship to adolescent-reported parental support only in early adolescence. Findings and implications are discussed in terms of the congruence/spillover and the compensation hypothesis

Advice about Life Plans from Mothers, Fathers, and Siblings in Always-Married and Divorced Families during Late Adolescence

The frequency of advice about life plans that older adolescents in always-married and divorced families received from mothers, fathers, and siblings was examined. Also, a pattern-analytic approach that grouped adolescents according to the amount of advice about life plans received from each parent and a sibling was employed to explore the connections between patterns of advice and adolescents' future occupational, educational, and family plans. The sample included 544 and 95 older adolescents in always-married and divorced families, respectively. Findings suggested that while adolescents relied on mothers for advice in both always-married and divorced families, adolescents in divorced families depended on fathers and siblings for advice less often than did adolescents in always-married families. Although there was some evidence of family context differences in the connections between patterns of advice and life plans, overall, adolescents in both family contexts who received more advice from a parent and, in some cases, a sibling compared to other adolescents were the most positive about their future life plans.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45291/1/10964_2004_Article_345952.pd