Differential characters of Drinfeld modules and de Rham cohomology

We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra, both of which have had notable Diophantine applications. We determine the structure of the group of differential characters. This shows the existence of a family of interesting differential modular functions on the moduli of Drinfeld modules. It also leads to a canonical $F$-crystal equipped with a map to the de Rham cohomology of the Drinfeld module. This $F$-crystal is of a differential-algebraic nature, and the relation to the classical cohomological realizations is presently not clear

Assessing non-market benefits of seagrass restoration in the Gulf of Gdańsk

Seagrass meadows (Zostera marina) are an important ecosystem in the coastal environment of the Baltic Sea. This study employs a discrete choice experiment to value a set of non-market benefits provided by seagrass meadows in the Gulf of Gdańsk, Poland. The benefits valued in this study are a reduction of filamentous algae in the water and on the beach; access to seagrass meadows for boaters and divers; and improved water clarity. Results show significant willingness to pay for each attribute and differences of value estimates across different groups of survey respondents. It is discussed how to link choice attributes and estimated values with established ecosystem benefit categories in order to facilitate value transfer

An Analysis of Graduate Teaching Assistants’ Noticing Skills During Calculus and Physics Tutoring Scenarios

Professional noticing of mathematical thinking, as defined by Jacobs, Lamb, and Philipp (2010) can be broken down into three components: attending to relevant cues, interpreting the mathematical understanding, and deciding the next best instructional steps. Most research on this topic has been conducted with elementary children. However, there is a gap in the research on professional noticing at more advanced levels, particularly college students. The purpose of this study was to take the concept of professional noticing and apply it to mathematics education at the post-secondary level. Specifically, the question we sought to answer in this study was: To what extent do mathematics and physics Teaching Assistants (TAs) attend and interpret student thinking when making decisions in their classroom? Mathematics and Physics TAs (n = 20) participated in this study focusing on their professional noticing skills when analyzing a college student struggling with two calculus-based problems. Results show that the TAs struggle most with interpreting student understanding and that those with more experience are better at deciding the next steps. Additionally, there is some data to support that knowledge of the content can impact their decision-making skills

Blink rate and blink timing in children with ADHD and the influence of stimulant medication

Spontaneous eye blink rate is modulated by task demands and internal state, and is demonstrated to reflect central dopamine activity. Also, spontaneous eye blinks are strategically timed around salient stimuli. This study investigates whether children with attention deficit hyperactivity disorder (ADHD) show reduced blink rates, blink modulation and blink timing, and whether this is influenced by stimulant medication. The electrooculogram was measured in 18 typically developing children, 16 children with ADHD off methylphenidate (Mph), and 16 children with ADHD on Mph during a rest period and during performance of a 60-min visual selective attention task. Blink rate and timing was extracted from the electrooculogram. No evidence was found for aberrant blink rate or blink modulation in children with ADHD off Mph. All groups increased blink rates from rest to task, and no group differences were found in blink rate during rest and task, or in the modulation of blink rate from rest to task. Time-on task resulted in a similar increase in blink rates in all three groups. Stimulant medication appeared not to influence blink rate and blink modulation, except that in the ADHD off Mph group the blink rate was enhanced only under conditions with performance feedback. All groups inhibited blinks before stimulus presentation and strategically timed their blinks after the stimulus. Children with ADHD off Mph showed reduced blink inhibition before the stimulus; however, given the low incidence (\1 % of the trials) and long latency this is not likely to impair their visual intake