A Survey on the Ternary Purely Exponential Diophantine Equation ax+by=cza^x + b^y = c^z

Let $a$, $b$, $c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions $(x,y,z)$ of the ternary purely exponential diophantine equation $a^x + b^y = c^z$

Role of diet and genetics on aging brain and cognition

Cognitive decline in old age is normative, but decline can be exacerbated in individuals with Alzheimer’s disease (AD) risk factors. Recent studies suggest that certain dietary regimens may slow or exacerbate this decline. However, it is uncertain how changes in whole food consumption affects fluid intelligence (FI) performance, an index of reasoning ability, in adults with or without AD genetic risk over time. Genetic risk for Alzheimer’s disease (AD) is mostly found on Chromosome 19 in the APOE-TOMM40-APOC1 region. Specifically, the Apolipoprotein E ε4 (APOE4) haplotype confers the greatest genetic risk for late-onset Alzheimer’s disease (AD). Food Frequency Questionnaire and Fluid Intelligence Test scores, assessed three times across 6 years, were obtained from UK Biobank to cross-sectionally and longitudinally examine which whole foods were most related to FI. Results indicated that both non-carriers (APOE4-) and especially carriers (APOE4+) showed increased FI with daily cheese and alcohol consumption at baseline. Conversely, decreased FI was seen among APOE4- with daily vegetable consumption over time. Among APOE4+, regular salt use showed worse FI scores over time. Our findings broadly suggest that reducing FI-related cognitive decline may be related to limiting meat, salt, and vegetable consumption, while increasing intake of wheat products, cheese, as well as the consumption of alcohol in moderation. Food recommendations, with AD genetic and family history factors in consideration, may minimize cognitive decline. Translocase of Outer Mitochondrial Membrane-40 (TOMM40) is the only nuclear-encoded gene that controls mitochondrial protein transport, which is critical for maintaining cellular bioenergetics and is progressively disrupted in AD. TOMM40 rs2075650 (‘650) is one of the most consistent loci to show associations with several neural and cognitive outcomes relevant to AD. For example, TOMM40 ‘650 genotypes might affect neural network strength, an early brain marker that is disrupted along the AD continuum. Therefore, 21 orthogonally derived neural networks were examined among 8,222 participants in the UK Biobank cohort. Results indicated that TOMM40 ‘650 G allele may be related to functional connectivity in auditory and language comprehension areas. This relationship may be modified by sex interactions. Differences were observed between G carriers and non-carriers among males, but not females. Not surprisingly, APOE4 was associated with several neural networks that share brain topology generally affected by AD pathology

The ecology, biogeography, history and future of two globally important weeds : Cardiospermum halicacabum Linn. and C. grandiflorum Sw.

Members of the balloon vine genus, Cardiospermum, have been extensively moved around the globe as medicinal and horticultural species, two of which are now widespread invasive species; C. grandiflorum and C. halicacabum. A third species, C. corindum, may also have significant invasion potential. However, in some regions the native status of these species is not clear, hampering management. For example, in South Africa it is unknown whether C. halicacabum and C. corindum are native, and this is a major constraint to on-going biological control programmes against invasive C. grandiflorum. We review the geography, biology and ecology of selected members of the genus with an emphasis on the two most widespread invaders, C. halicacabum and C. grandiflorum. Specifically, we use molecular data to reconstruct a phylogeny of the group in order to shed light on the native ranges of C. halicacabum and C. corindum in southern Africa. Phylogenetic analyses indicate that southern African accessions of these species are closely related to South American taxa indicating human-mediated introduction and/or natural long distance dispersal. Then, on a global scale we use species distribution modelling to predict potential suitable climate regions where these species are currently absent. Native range data were used to test the accuracy with which bioclimatic modelling can identify the known invasive ranges of these species. Results show that Cardiospermum species have potential to spread further in already invaded or introduced regions in Australia, Africa and Asia, underlining the importance of resolving taxonomic uncertainties for future management efforts. Bioclimatic modelling predicts Australia to have highly favourable environmental conditions for C. corindum and therefore vigilance against this species should be high. Species distribution modelling showed that native range data over fit predicted suitable ranges, and that factors other than climate influence establishment potential. This review opens the door to better understand the global biogeography of the genus Cardiospermum, with direct implications for management, while also highlighting gaps in current research

AFRICAN AMERICAN HIGH SCHOOL STUDENTS’ ATTITUDES TOWARD MATHEMATICS AND PERCEPTIONS OF EXTANT CULTURALLY RELEVANT PEDAGOGY AND ETHNOMATHEMATICS

African American students\u27 severe underachievement in mathematics in comparison to their peers has been framed as an achievement gap that continues to widen despite the efforts of many education scholars and leaders. Throughout history in the United States, mathematics education has been designed, developed, and delivered within a Eurocentric philosophy. Consequently, African American students have been at a systemic disadvantage in terms of perceiving the cultural relevance of mathematics; which has served as a detriment to their academic success. By merging ethnomathematics and culturally relevant pedagogy (CRP) into a theoretical framework, this study investigates these issues and proposes a shift in mathematics education toward a more culturally aware approach. In this study, it is argued that implementing a multicultural education approach such as ethnomathematics into the mathematics curriculum coupled with employing culturally relevant pedagogical practices will increase relevance in the mathematics education for African American students. The purpose of this study was to gain African American high school students’ perception of mathematics, as well as their cultural awareness and its relation to mathematics education. To gain students’ perceptions about mathematics education from a cultural respect, 375 students in grades 9-12 completed three online surveys which were (1) a four-item demographic questionnaire (age, gender, grade, ethnicity), (2) the 40-item Attitude Towards Mathematics Inventory (ATMI), and (3) the 12-item Students Perception about Cultural Awareness (SPCA) survey. This study incorporated a quantitative, correlational research design. To address research questions one and two, Pearson correlations were conducted to examine the associations between the variables of interest which were (1) Value, (2) Enjoyment, (3) Sense of Security, (4) Motivation, and (5) Cultural Awareness. Variables (1), (2), (3), (4) were derived from the ATMI survey through factor analysis while variable (5) was constructed from the SPCA survey. To address research question three, a MANOVA was conducted to assess for differences in attitudes toward mathematics and perceptions of cultural awareness by ethnicity. For research questions one and two, it was found that there was a statistically significant correlation between the variables of interest. For research question three, it was found that there was not a statistically significant difference in the variables of interest by ethnicity. In further analysis of the data, it was found that many African American students have a substandard attitude of value, enjoyment, sense of security, and motivation toward mathematics. Nonetheless, these students had a high sense of cultural awareness and cultural pride. Generally, the students felt that the incorporation of culture into mathematics would assist in raising their achievement to some degree. This study highlights recommendations to educational leaders to learn about the culture of their students, allow that data to inform policy decisions, and lead a shift to the approach of mathematics education toward the theories of ethnomathematics and CRP

Beyond probabilities: A possibilistic framework to interpret ensemble predictions and fuse imperfect sources of information

AbstractEnsemble forecasting is widely used in medium‐range weather predictions to account for the uncertainty that is inherent in the numerical prediction of high‐dimensional, nonlinear systems with high sensitivity to initial conditions. Ensemble forecasting allows one to sample possible future scenarios in a Monte‐Carlo‐like approximation through small strategical perturbations of the initial conditions, and in some cases stochastic parametrization schemes of the atmosphere–ocean dynamical equations. Results are generally interpreted in a probabilistic manner by turning the ensemble into a predictive probability distribution. Yet, due to model bias and dispersion errors, this interpretation is often not reliable and statistical postprocessing is needed to reach probabilistic calibration. This is all the more true for extreme events which, for dynamical reasons, cannot generally be associated with a significant density of ensemble members. In this work we propose a novel approach: a possibilistic interpretation of ensemble predictions, taking inspiration from possibility theory. This framework allows us to integrate in a consistent manner other imperfect sources of information, such as the insight about the system dynamics provided by the analogue method. We thereby show that probability distributions may not be the best way to extract the valuable information contained in ensemble prediction systems, especially for large lead times. Indeed, shifting to possibility theory provides more meaningful results without the need to resort to additional calibration, while maintaining or improving skills. Our approach is tested on an imperfect version of the Lorenz '96 model, and results for extreme event prediction are compared against those given by a standard probabilistic ensemble dressing

A British Bureaucratic Revolution? Autonomy Without Control, or “Freer Markets, More Rules”

This paper addresses a puzzle : how to account for changes in the routine behavior of groups, organizations and individuals in Britain ? Following a detailed analysis of state/market interdependence and the role of the state in creating the market, an analysis drawn from the thinking of Weber and Polanyi, we suggest adapting Weber’s notion of bureaucratic revolution : in what we call the British bureaucratic revolution, the state has played an essential role in social change by creating institutions and rules that are lastingly reorienting actors’ behavior. The example of the healthcare field is examined in order to identify the specific mechanisms that have been impacting on behavior within an approximately ten-year period ; namely, the introduction of 1) competitive practices (sanction/reward) and 2) of auditing and inspection. If this interpretation is valid, then it is reasonable to assume that the effects of this bureaucratic revolution extend beyond Britain

Une révolution bureaucratique britannique ?:Autonomie sans contrôle ou « freer markets, more rules »

L'article a pour point de départ un puzzle: comment rendre compte des transformations des comportements routiniers de groupes, d'organisations et d'individus en Grande-Bretagne? À partir d'une analyse précise des interdépendances entre État et marché et du rôle de l'État dans la création du marché tirée de Weber et de Polanyi, nous proposons de reprendre et d'adapter la notion de révolution bureaucratique avancée par Weber. Nous défendons la thèse selon laquelle la révolution bureaucratique britannique se traduit par le fait que l'État joue un rôle essentiel dans le changement social en créant des règles, des institutions qui orientent dans la durée le comportement des acteurs. L'exemple de la santé est ensuite mobilisé pour identifier des mécanismes précis qui exercent leur influence sur une durée d'une dizaine d'années, à savoir l'introduction de dispositifs de concurrence (sanction récompense) d'une part, d'audit et d'inspection d'autre part. Si notre interprétation est pertinente, on peut envisager que les effets de cette révolution bureaucratique s'exercent dans d'autres contextes que celui de la Grande-Bretagne.This article originated with a puzzle: how best to account for changes in the behavior of groups, organizations and individuals in Great Britain? A detailed analysis of what Weber and Polanyi identified as interdependencies between state and market, and of the state's role in creating the market, led to the decision to adapt the notion of bureaucratic revolution put forward by Weber. We argue that the British bureaucratic revolution is reflected in the fact that the state plays an essential role in social change by creating rules and institutions that lastingly orient actors' behavior. The examples of health and local authorities are then used to identify mechanisms that were influential throughout a ten-year period; specifically the introduction of competition features (rewards and punishments) and of auditing and inspection. If our interpretation is accurate, the effects of this bureaucratic revolution may well come to be felt in contexts other than Great Britain