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Dicuil (9th century) on triangular and square numbers

Dicuil was a ninth-century Irish monk who taught at the Carolingian school of Louis the Pious. He wrote a Computus or astronomical treatise in Latin in about 814–16, which contains a chapter on triangular and square numbers. Dicuil describes two methods for calculating triangular numbers: the simple method of summing the natural numbers, and the more complex method of multiplication, equivalent to the formula n(n + 1)/2. He also states that a square number is equal to twice a triangular number minus the generating number, equivalent to n2 = 2[n(n + 1)/2] – n. The multiplication formula for triangular numbers was first explicitly described in about the third century AD by the Greek authors Diophantus and Iamblichus. It was also known as a solution to other mathematical problems as early as 300 BC. It reappeared in the West in the sixteenth century. Dicuil thus fills a gap in our medieval knowledge

Neural signatures of cognitive flexibility and reward sensitivity following nicotinic receptor stimulation in dependent smokers : a randomized trial

IMPORTANCE Withdrawal from nicotine is an important contributor to smoking relapse. Understanding how reward-based decision making is affected by abstinence and by pharmacotherapies such as nicotine replacement therapy and varenicline tartrate may aid cessation treatment. OBJECTIVE To independently assess the effects of nicotine dependence and stimulation of the nicotinic acetylcholine receptor on the ability to interpret valence information (reward sensitivity) and subsequently alter behavior as reward contingencies change (cognitive flexibility) in a probabilistic reversal learning task. DESIGN, SETTING, AND PARTICIPANTS Nicotine-dependent smokers and nonsmokers completed a probabilistic reversal learning task during acquisition of functional magnetic resonance imaging (fMRI) in a 2-drug, double-blind placebo-controlled crossover design conducted from January 21, 2009, to September 29, 2011. Smokers were abstinent from cigarette smoking for 12 hours for all sessions. In a fully Latin square fashion, participants in both groups underwent MRI twice while receiving varenicline and twice while receiving a placebo pill, wearing either a nicotine or a placebo patch. Imaging analysis was performed from June 15, 2015, to August 10, 2016. MAIN OUTCOME AND MEASURES A well-established computational model captured effects of smoking status and administration of nicotine and varenicline on probabilistic reversal learning choice behavior. Neural effects of smoking status, nicotine, and varenicline were tested for on MRI contrasts that captured reward sensitivity and cognitive flexibility. RESULTS The study included 24 nicotine-dependent smokers (12 women and 12 men; mean [SD] age, 35.8 [9.9] years) and 20 nonsmokers (10 women and 10 men; mean [SD] age, 30.4 [7.2] years). Computational modeling indicated that abstinent smokers were biased toward response shifting and that their decisions were less sensitive to the available evidence, suggesting increased impulsivity during withdrawal. These behavioral impairments were mitigated with nicotine and varenicline. Similarly, decreased mesocorticolimbic activity associated with cognitive flexibility in abstinent smokers was restored to the level of nonsmokers following stimulation of nicotinic acetylcholine receptors (familywise error-corrected P<.05). Conversely, neural signatures of decreased reward sensitivity in smokers (vs nonsmokers; familywise error-corrected P<.05) in the dorsal striatum and anterior cingulate cortex were not mitigated by nicotine or varenicline. CONCLUSIONS AND RELEVANCE There was a double dissociation between the effects of chronic nicotine dependence on neural representations of reward sensitivity and acute effects of stimulation of nicotinic acetylcholine receptors on behavioral and neural signatures of cognitive flexibility in smokers. These chronic and acute pharmacologic effects were observed in overlapping mesocorticolimbic regions, suggesting that available pharmacotherapies may alleviate deficits in the same circuitry for certain mental computations but not for others

International Giving by U.S. Community Foundations: Local Communities with Global Reach

This report, a joint effort by the Council on Foundations and Foundation Center, examines the current state and recent trends in international giving and engagement by large U.S. community foundations. The first-ever analysis of this type suggests that many community foundations are beginning to adopt a broader, more nuanced definition of "community" than they have in the past.The report documents how funds channeled from U.S. community foundations support international programs and recipients and highlights five U.S. community foundations and their approaches to global engagement and international grantmaking. For this report, we analyzed all the international grants made by U.S. community foundations included in Foundation Center's set of 1,000 of the largest U.S. Foundations from 2011 to 2014, which included 10,533 grants worth $697 million

Recognising the development of expert practice in undergraduate research: a TREASURE project update

The difference between novice and expert researchers lies in much more than possession of explicit, discipline-based knowledge and technical expertise. The transition to expert practice involves the contextualised internalisation of this knowledge and understanding, often through a process of deliberate and extensive practice. Acquisition of such tacit knowledge is coupled with the development of attitudes such as self-confidence, pragmatism, criticality and comfort with uncertainty, leading to a capacity to make (often unconscious) expert judgments. While most teaching and assessment during an undergraduate science degree focuses firmly on declarative (and declared) knowledge, undergraduate research projects can provide the first steps in the transition to expert practice. However, we believe that more could be done to make these experiences as effective as possible in developing the knowledge and attributes described above. The TREASURE project aims to help students recognise their transition to expert-like behaviour by asking them to reflect on their research project throughout the semester. This emphasis on process and practice may also help reduce the student’s focus on results or research products as the sole indicator of success and provide useful input to supervisors about student thinking. Results from TREASURE’s first year will be presented

Do undergraduate research experiences influence student understanding of the uncertainties inherent in scientific knowledge?

Uncertainty is an inescapable facet of life and as our world becomes more complex, the levels of uncertainty also rise. This is the so-called supercomplex world as described by Barnett (2007), a world in which science based disciplines are well placed to deal with these complexities. However, it is hard to argue that current science education pedagogies are preparing our future graduates to become effective advocates for science in this most certainly, uncertain world. Previous studies of graduate students by Perry in the 1960s and Schommer in the 1990s provided evidence that as students progress they start to see knowledge as less deterministic, more uncertain and complex as well as crossing thresholds of understanding (Ross et al., 2010). Recently an OLT project grant was awarded to the Australian National University, University of Western Sydney and Canberra University with the title Teaching Research Evaluation and Assessment Strategies for Undergraduate Research Experiences” (TREASURE). This project evaluated student thinking around research experiences in both a final semester capstone unit as well as independent research units. Over 60 students kept a reflective blog of their learning in these research experiences. It was encouraging to observe that the entire cohort demonstrated appropriate usage of standard scientific research processes. However, few of the students in the capstone unit were able to extend their understanding to encompass the concept that science knowledge and processes can be uncertain, complex and indeterminate. This is of concern in the context of the newly articulated Threshold Learning Outcomes in Science (TLOs) “Demonstrate a coherent understanding of biomedical science by articulating the methods of science and explaining why current scientific knowledge is both contestable and testable by further inquiry.” This observation suggests that we may be overestimating our expectations of the level of learning engendered by the current undergraduate research experiences. This in turn raises the question of whether we are satisfied that many of our graduates do not attain this threshold standard? Perhaps the time has come to develop a formal pedagogy of uncertainty

Estimating Residential Solar Potential Using Aerial Data

Project Sunroof estimates the solar potential of residential buildings using high quality aerial data. That is, it estimates the potential solar energy (and associated financial savings) that can be captured by buildings if solar panels were to be installed on their roofs. Unfortunately its coverage is limited by the lack of high resolution digital surface map (DSM) data. We present a deep learning approach that bridges this gap by enhancing widely available low-resolution data, thereby dramatically increasing the coverage of Sunroof. We also present some ongoing efforts to potentially improve accuracy even further by replacing certain algorithmic components of the Sunroof processing pipeline with deep learning

Effects of Prenatal Drug Exposure on Adolescent Brain Activation During a Visuospatial Working Memory Task

Background: Previous research examining effects of prenatal drug exposure (PDE) has yielded mixed results regarding cognitive performance during school age years. Associations between PDE and tests of global functioning (IQ and academic achievement) tend to be minimal and are typically attenuated by environmental variables (e.g., caregiving environment). On the other hand, significant negative associations have been reported in tests of executive functioning (sustained attention, inhibitory control, and behavioral regulation), even with covariate control. These findings are consistent with animal models of PDE that report developmental abnormalities in brain regions associated with strong dopaminergic innervation including the striatum, anterior cingulate cortex, and prefrontal cortex. In humans, these regions are putatively involved in executive functions that coordinate the basic cognitive processes required for goal-directed action (e.g., attention inhibitory control, planning, working memory). The objective of the present study was to assess the effects of PDE on brain functioning during adolescence. Methods: fMRI was used to examine visuospatial working memory (VSWM) in 35 adolescents (mean: 14.3 years); 20 with intrauterine exposure to cocaine, heroin, or both and 15 unexposed children from the same community. All participants performed a 2-back VSWM paradigm that required dynamic storage and manipulation of spatial information. Whole-brain functional EPI scans were acquired using a 3T Siemens Scanner with standard parameters. Participants completed one 6-minute block-design run that alternated between a 30 second control condition (which required observation of visual stimuli, sustained attention, and a motor response) and 30 seconds of the VSWM condition. Brain responses were analyzed using the AFNI software package with appropriate contrasts and p < 0.05 corrected for multiple comparisons. Results: Across all participants, the VSWM task activated the frontal-parietal attention network including bilateral superior parietal lobules, precuneus, middle frontal gyri, superior frontal gyri, and insular cortex. Significant deactivations were observed in regions of the “default network,” including the left anterior cingulate gyrus, medial frontal gyrus, posterior cingulate, and bilateral parahippocampal cortices. Whole-brain between group comparisons with both age and gender entered as covariates revealed 3 regions that were differentially activated in the drug-exposed compared to the non-exposed group. These regions included right inferior parietal lobe, right precentral gryus, and left cuneus. The drug-exposed group showed deactivation of the right inferior parietal lobule compared to no change in the non-exposed group. The non-exposed group showed activations in both the right precentral gyrus and left cuneus compared to no change in the drug-exposed group. These differences in activations were detected despite equivalent behavioral performance on the task (i.e., accuracy and response time) and after statistically controlling environmental variables that differed between the groups, including placement in nonmaternal care, maternal age at time of birth and prenatal exposure to cigarettes. Discussion: Despite similar task performance, adolescents with a history of PDE showed different neural activations than the comparison group. Regions that were differentially activated are implicated in sequencing task information (i.e., right parietal lobe), working memory performance in healthy control children (i.e., right precentral gyrus), and visual attention (i.e., left cuneus). These results suggest regions and components of working memory processing that may be differentially affected by PDE in adolescence.This study was supported by the National Institute on Drug Abuse (NIDA) – Intramural Research Program and NIDA grants R01-DA07432 and R01-DA021059