Calculus on the Sierpinski Gasket I: Polynomials, Exponentials and Power Series

We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which have previously been studied in connection with Taylor approximations and splines. Here the main technical result is an estimate of the size of the monomials analogous to x^n/n!. We propose a definition of entire analytic functions as functions represented by power series whose coefficients satisfy exponential growth conditions that are stronger than what is required to guarantee uniform convergence. We present a characterization of these functions in terms of exponential growth conditions on powers of the Laplacian of the function. These entire analytic functions enjoy properties, such as rearrangement and unique determination by infinite jets, that one would expect. However, not all exponential functions (eigenfunctions of the Laplacian) are entire analytic, and also many other natural candidates, such as the heat kernel, do not belong to this class. Nevertheless, we are able to use spectral decimation to study exponentials, and in particular to create exponentially decaying functions for negative eigenvalues

Using Positive Youth Development Constructs to Design a Drug Education Curriculum for Junior Secondary Students in Hong Kong

This paper outlines the design of a new curriculum for positive youth development (P.A.T.H.S. II) in Hong Kong. The paper discusses the conceptual base for designing a drug-education curriculum for junior-secondary students using four positive youth development constructs—cognitive competence, emotional competence, beliefs in the future, and self-efficacy. The program design is premised on the belief that adolescents do have developmental assets; therefore, the curriculum is designed to develop their psychosocial competencies. The goal of the curriculum is to develop the selfhood of these youths and ultimately achieve the goal of successful adolescent development

Using Positive Youth Development Constructs to Design a Money Management Curriculum for Junior Secondary School Students in Hong Kong

This paper aims to discuss the relationships between the selected positive youth development constructs and the enhancement of Hong Kong junior secondary school students' money management skills, values, and attitudes. Various issues of money management of adolescents are reviewed. These issues include the need for money management programs for adolescents, the content and coverage of an appropriate money management program, and its relationships with the selected positive youth development constructs. The curriculum units for secondary 3 students are taken as examples to illustrate the design of the program. It is believed that promoting cognitive competence, self-efficacy, and spirituality could be an effective way to enhance students' money management skills, values, and attitudes, thus preparing them better for facing the finance-related issues in life

Sex Differences in 6-Year Progression of White Matter Hyperintensities in Non-Demented Older Adults: Sydney Memory and Ageing Study

Objectives: To examine sex differences in the associations between vascular risk factors and 6-year changes in the volume of white matter hyperintensities (WMH), and between changes in WMH volumes and changes in cognitive performance, in a cohort of non-demented older adults. Methods: WMH volumes at 3 time-points (baseline, and 2- and 6-year follow-up) were automatically quantified in participants of Sydney Memory and Ageing Study (N = 605; age range = 70-92 years; 54.78% female). Linear mixed models were applied to examine the effects of vascular risk factors and cognitive consequences of the progression of WMH, as well as the sex moderation effects in the associations. Results: Total (TWMH), periventricular (PVWMH), and deep (DWMH) WMH volumes increased by 9.47%, 7.70%, and 11.78% per year, respectively. No sex differences were found in WMH progression rates. After Bonferroni correction, increases in PVWMH volumes over time were associated with decline in global cognition, especially in visuospatial and memory domains. Men with more increases in PVWMH volumes over time had greater declines in visuospatial abilities. Moreover, higher average TWMH volumes across time-points were associated with poorer average performance in processing speed and executive function domains across time. Higher average PVWMH volumes across time-points were also associated with worse average performance in the executive function domain over time, among women but not men. Conclusion: The findings highlighted sex differences in the associations between WMH progression and cognition decline over time, suggesting sex-specific strategies in managing WMH accumulations in ageing. Keywords: Cerebral small vessel disease, white matter hyperintensities, sex differences, brain ageing, cognitive decline

Construction of regio- and stereoregular poly(enaminone)s by multicomponent tandem polymerizations of diynes, diaroyl chloride and primary amines

Polyhydroaminations for the synthesis of stable nitrogen-substituted conjugated polymers with welldefined structures remain a great challenge and the control of the regio- and stereochemistry of the enamine product of the hydroamination is non-trivial. Herein we report an efficient tandem polymerization of alkynes, carbonyl chlorides and primary amines to afford regio- and stereoregular conjugated poly(enaminone)s. The atom-economical one-pot sequential polycoupling–hydroamination polymerization catalyzed by Pd(PPh3)2Cl2/CuI proceeded smoothly under mild conditions, furnishing nitrogensubstituted conjugated polymers with high molecular weights (up to 46 100) and high regio-/stereoregularities (100%) in nearly quantitative yields (up to 99%). The single crystal structure of the model compound, together with the NMR spectra comparison of the model compound and polymers provided direct insight into the stereo selectivity of the polymerization, verifying the sole Z-vinyleneisomer of the polymers. Through the exquisite structural design strategy of the intramolecular hydrogen bond of the resulting hydroamination product, the tautomerization between enamine and imine as well as E/Z isomerization was successfully avoided, providing products with high chemical stability and sole Z-vinylene isomers. The conjugated polymers display excellent solubility in common organic solvents, good film forming ability, and high thermal stability. The hydrogen bond formation of the polymer helps to block the potential photo-induced electron transfer process and the polymer shows a unique aggregation enhanced emission phenomenon: their solutions are weakly emissive, while their nanoaggregates or thin films are brightly emissive. Furthermore, thin films of the polymers enjoy high refractive indices (1.9103–1.6582) in a wide wavelength region of 400–1000 nm, which can be further modulated by UV irradiation. Meanwhile, well-resolved fluorescent photopatterns of the polymers can be fabricated through the UV irradiation of thin films via a copper photomask

Difference in distribution functions:A new diffusion weighted imaging metric for estimating white matter integrity

Diffusion weighted imaging (DWI) is a widely recognized neuroimaging technique to evaluate the microstructure of brain white matter. The objective of this study is to establish an improved automated DWI marker for estimating white matter integrity and investigating ageing related cognitive decline. The concept of Wasserstein distance was introduced to help establish a new measure: difference in distribution functions (DDF), which captures the difference of reshaping one's mean diffusivity (MD) distribution to a reference MD distribution. This new DWI measure was developed using a population-based cohort (n=19,369) from the UK Biobank. Validation was conducted using the data drawn from two independent cohorts: the Sydney Memory and Ageing Study, a community-dwelling sample (n=402), and the Renji Cerebral Small Vessel Disease Cohort Study (RCCS), which consisted of cerebral small vessel disease (CSVD) patients (n=171) and cognitively normal controls (NC) (n=43). DDF was associated with age across all three samples and better explained the variance of changes than other established DWI measures, such as fractional anisotropy, mean diffusivity and peak width of skeletonized mean diffusivity (PSMD). Significant correlations between DDF and cognition were found in the UK Biobank cohort and the MAS cohort. Binary logistic analysis and receiver operator characteristic curve analysis of RCCS demonstrated that DDF had higher sensitivity in distinguishing CSVD patients from NC than the other DWI measures. To demonstrate the flexibility of DDF, we calculated regional DDF which also showed significant correlation with age and cognition. DDF can be used as a marker for monitoring the white matter microstructural changes and ageing related cognitive decline in the elderly

Multiple social groups support adjustment to retirement across cultures

Research has demonstrated the positive effects that social identification with multiple groups has on people's health and well-being, in part during the transition from work to retirement. However, these effects have not been examined outside Western retirement contexts. This study addresses this gap.This investigation aims to examine the contribution that group membership and identification with multiple social groups makes to supporting retirees' physical health and well-being across cultures.Responses from a representative sample of 10,513 retired individuals from 51 countries drawn from the World Values Survey were used in this analysis. This research focused on the number of group memberships, identification with multiple groups, subjective health, and well-being that respondents reported.Analysis showed that belonging to multiple groups positively predicted retirees' health and well-being in both Western and non-Western cultural contexts. In line with cross-cultural research, there was evidence that country-level collectivism moderated the strength of this association, with the effect being weaker in collectivistic (vs. individualistic) countries.Findings confirm the utility of using the social identity approach to understand people's adjustment to retirement across cultures

Glucose in the hypothalamic paraventricular nucleus regulates GLP-1 release.

Glucokinase (GK) is highly expressed in the hypothalamic paraventricular nucleus (PVN); however, its role is currently unknown. We found that GK in the PVN acts as part of a glucose-sensing mechanism within the PVN that regulates glucose homeostasis by controlling glucagon-like peptide 1 (GLP-1) release. GLP-1 is released from enteroendocrine L cells in response to oral glucose. Here we identify a brain mechanism critical to the release of GLP-1 in response to oral glucose. We show that increasing expression of GK or injection of glucose into the PVN increases GLP-1 release in response to oral glucose. On the contrary, decreasing expression of GK or injection of nonmetabolizable glucose into the PVN prevents GLP-1 release. Our results demonstrate that gluco-sensitive GK neurons in the PVN are critical to the response to oral glucose and subsequent release of GLP-1

Efficacy of probucol on cognitive function in Alzheimer's disease: study protocol for a double-blind, placebo-controlled, randomised phase II trial (PIA study).

INTRODUCTION: Preclinical, clinical and epidemiological studies support the hypothesis that aberrant systemic metabolism of amyloid beta (Aβ) in the peripheral circulation is causally related to the development of Alzheimer's disease (AD). Specifically, recent studies suggest that increased plasma concentrations of lipoprotein-Aβ compromise the brain microvasculature, resulting in extravasation and retention of the lipoprotein-Aβ moiety. The latter results in an inflammatory response and neurodegeneration ensues. Probucol, a historic cholesterol-lowering drug, has been shown in murine models to suppress lipoprotein-Aβ secretion, concomitant with maintaining blood-brain-barrier function, suppressing neurovascular inflammation and supporting cognitive function. This protocol details the probucol in Alzheimer's study, a drug intervention trial investigating if probucol has potential to attenuate cognitive decline, delay brain atrophy and reduce cerebral amyloid burden in patients with mild-to-moderate AD. METHODS AND ANALYSIS: The study is a phase II, randomised, placebo-controlled, double-blind single-site clinical trial held in Perth, Australia. The target sample is 314 participants with mild-to-moderate AD. Participants will be recruited and randomised (1:1) to a 104-week intervention consisting of placebo induction for 2 weeks followed by 102 weeks of probucol (Lorelco) or placebo. The primary outcome is changed in cognitive performance determined via the Alzheimer's Disease Assessment Scales-Cognitive Subscale test between baseline and 104 weeks. Secondary outcomes measures will be the change in brain structure and function, cerebral amyloid load, quality of life, and the safety and tolerability of Lorelco, after a 104week intervention. ETHICS AND DISSEMINATION: The study has been approved by the Bellberry Limited Human Research Ethics Committee (approval number: HREC2019-11-1063; Version 4, 6 October 2021). Informed consent will be obtained from participants prior to any study procedures being performed. The investigator group will disseminate study findings through peer-reviewed publications, key conferences and local stakeholder events. TRIAL REGISTRATION NUMBER: Australian New Zealand Clinical Trials Registry (ACTRN12621000726853)