Bounds for coefficients of cusp forms and extremal lattices

A cusp form $f(z)$ of weight $k$ for \SL_{2}(\Z) is determined uniquely by its first $\ell := \dim S_{k}$ Fourier coefficients. We derive an explicit bound on the $n$th coefficient of $f$ in terms of its first $\ell$ coefficients. We use this result to study the non-negativity of the coefficients of the unique modular form of weight $k$ with Fourier expansion $$F_{k,0}(z) = 1 + O(q^{\ell + 1}).$$ In particular, we show that $k = 81632$ is the largest weight for which all the coefficients of $F_{0,k}(z)$ are non-negative. This result has applications to the theory of extremal lattices.Comment: To appear in Bulletin of the London Mathematical Societ

Binding specificity of Bacillus thuringiensis Cry1Aa for purified, native Bombyx mori aminopeptidase N and cadherin-like receptors

BACKGROUND: To better understand the molecular interactions of Bt toxins with non-target insects, we have examined the real-time binding specificity and affinity of Cry1 toxins to native silkworm (Bombyx mori) midgut receptors. Previous studies on B. mori receptors utilized brush border membrane vesicles or purifed receptors in blot-type assays. RESULTS: The Bombyx mori (silkworm) aminopeptidase N (APN) and cadherin-like receptors for Bacillus thuringiensis insecticidal Cry1Aa toxin were purified and their real-time binding affinities for Cry toxins were examined by surface plasmon resonance. Cry1Ab and Cry1Ac toxins did not bind to the immobilized native receptors, correlating with their low toxicities. Cry1Aa displayed moderate affinity for B. mori APN (75 nM), and unusually tight binding to the cadherin-like receptor (2.6 nM), which results from slow dissociation rates. The binding of a hybrid toxin (Aa/Aa/Ac) was identical to Cry1Aa. CONCLUSIONS: These results indicate domain II of Cry1Aa is essential for binding to native B. mori receptors and for toxicity. Moreover, the high-affinity binding of Cry1Aa to native cadherin-like receptor emphasizes the importance of this receptor class for Bt toxin research

Distinct Profile Differences in Subjective Cognitive Decline in the General Public Are Associated with Metacognition, Negative Affective Symptoms, Neuroticism, Stress, and Poor Quality of Life

BACKGROUND: Subjective cognitive decline (SCD) is increasingly recognized in both the clinical and research arenas as a risk factor for mild cognitive impairment (MCI) and dementia. Although SCD is etiologically heterogeneous and potentially treatable, in comparison to MCI and Alzheimer’s disease, SCD remains poorly characterized with its clinical relevance often questioned. OBJECTIVE: This study’s aim was to improve the characterization of SCD within the general public. METHODS: Individuals with SCD were compared to those without via a battery of measures. RESULTS: Both the SCD and the non-SCD group correlational analysis identified significant relationships between worse SCD, worse metacognitive dysfunction, negative affective symptoms, and greater levels of stress. The SCD group displayed additional correlational relationships between Cognitive Change Index (Self report) (CCI-S) scores, higher neuroticism scores, and poorer quality of life (QoL). Partial correlation analysis in the SCD group suggests CCI-S scores, anxiety, depression, and metacognition are intercorrelated. Ad hoc analyses using metacognition as the grouping variable found that those experiencing worse metacognitive dysfunction were significantly more likely to experience poorer SCD, psychological and social QoL, greater levels of anxiety, depression, stress, and neuroticism. CONCLUSION: The emerging pattern from the analysis indicates that SCD appears associated with sub-clinical negative affective difficulties, metacognitive, and other psycho-social issues, and poorer QoL. Dysfunctional cognitive control at a meta-level may impact someone’s ability to rationally identify cognitive changes, increase worry about cognitive changes, and allow such changes to impact their lives more than those with superior metacognitive control. Findings could impact SCD assessment, monitoring, early intervention, and ultimately reducing risk of further decline

Liability: How to Stay out of Court

Liability can be defined as being held legally responsible for an incident that may occur. As student affairs professionals, one must be very cautious as to stay out of court. Every word or action a student affairs professional does may be scrutinized and twisted to make them or their given university legally responsible for any adverse incidents that they may have had some involvement with. Incidents which student affairs professionals may be held responsible for can range anywhere from student deaths to expulsion/removal from school and much more. This handbook is designed to better educate you about liability and how to help keep you out of court

Macadamia industry benchmark report: 2009 to 2016 seasons, Project MC15005

The benchmarking project is supporting improved productivity and profitability within the Australian macadamia industry. The current project builds on previous benchmarking and best practice work conducted since 2001. Yield, quality and planting information has been collected annually from macadamia farms throughout Australia since 2009. This information is provided either directly by growers or by processors on their behalf. Cost of production data has also been collected annually since 2013. Each season all benchmarking participants receive a confidential, personalised report that compares their individual farm performance with the average performance of similar farms based on a range of criteria including region, locality, farm size, management structure, irrigation status and tree age. These reports highlight individual and average farm performance trends over multiple seasons. This industry report has been produced to provide growers, processors, consultants, investors and other industry stakeholders with a summary of yield, quality and cost of production trends within the Australian macadamia industry

The Special Needs of Women on College Campuses

The authors embarked on a journey to understand the special needs of women college students. They discovered two major themes that were explored in greater depth in an attempt to explain why these themes were more specific to college women than other populations. Although these needs may be extrapolated to other populations of college students they were of particular concern to the female college student population. The authors began by selecting a non-scientific restricted pool of female college students than spanned first-year, second-year and junior or third-year students. This student sample was interviewed to discover their concerns or perceptions about violence and sexual discrimination against women on college campuses. The interview questions and responses were abbreviated and included, followed by a discussion of each theme. The interview subjects stated that violence was not a major concern however; they did offer suggestions to improve safety. This led the authors to conclude that although they did not explicitly state violence as a concern it remains an implicit concern. The second theme explored was discrimination based on gender. The interviewed sample had a varied response to having been the victim of gender discrimination. Of greater concern was the perception of what constituted gender harassment, what procedures and processes were in place and available to respond to these occurrences and how to report an incident

Sparse panicle1 is required for inflorescence development in Setaria viridis and maize.

Setaria viridis is a rapid-life-cycle model panicoid grass. To identify genes that may contribute to inflorescence architecture and thus have the potential to influence grain yield in related crops such as maize, we conducted an N-nitroso-N-methylurea (NMU) mutagenesis of S. viridis and screened for visible inflorescence mutant phenotypes. Of the approximately 2,700 M2 families screened, we identified four recessive sparse panicle mutants (spp1-spp4) characterized by reduced and uneven branching of the inflorescence. To identify the gene underlying the sparse panicle1 (spp1) phenotype, we performed bulked segregant analysis and deep sequencing to fine map it to an approximately 1 Mb interval. Within this interval, we identified disruptive mutations in two genes. Complementation tests between spp1 and spp3 revealed they were allelic, and deep sequencing of spp3 identified an independent disruptive mutation in SvAUX1 (AUXIN1), one of the two genes in the ∼1 Mb interval and the only gene disruption shared between spp1 and spp3. SvAUX1 was found to affect both inflorescence development and root gravitropism in S. viridis. A search for orthologous mutant alleles in maize confirmed a very similar role of ZmAUX1 in maize, which highlights the utility of S. viridis in accelerating functional genomic studies in maize