Calculation of the scaled complex error function \(w(z)\) by recurrence is discussed, and a new method for determining the number of steps required to achieve a given accuracy is introduced. This method is found to work throughout the complex plane, except for a short section of the real line, centred at the origin. An algorithm based on this analysis is implemented; Taylor series with stored coefficients are used to compute \(w(z)\) in a small region where recurrence is not efficient. The new algorithm is tested extensively and found to outperform earlier recurrence-based codes. It also performs favourably against recent codes based on other methods.

This paper describes S.P.O.T., a game-based application for promoting children's practical understanding of ML concepts and applications. Current tools for teaching ML in K-12 engage students in playful exploration of ML mechanisms and teach ML from a cognitive perspective. However, in S.P.O.T, learners interact with ML within real-life sociopolitical contexts and examine how ML predictions impact their daily lives and communities. Through the immersion of stories that mirror children's lived experiences, S.P.O.T. provides elementary school aged children with opportunities to learn how machine learning applications function and develop children's abilities to critically examine, question, and reimagine the consequences of ML decisions in the real world.

We formalize and attack the problem of generating new images from old ones that are as diverse as possible, only allowing them to change without restrictions in certain parts of the image while remaining globally consistent. This encompasses the typical situation found in generative modelling, where we are happy with parts of the generated data, but would like to resample others (``I like this generated castle overall, but this tower looks unrealistic, I would like a new one''). In order to attack this problem we build from the best conditional and unconditional generative models to introduce a new network architecture, training procedure, and a new algorithm for resampling parts of the image as desired.

For a fixed integer $n\geq 2,$ we show that a permutation of the least residues mod $p$ of the form $f(x)=Ax^k$ mod $p$ cannot map a residue class mod $n$ to just one residue class mod $n$ once $p$ is sufficiently large, other than the maps $f(x)=\pm x$ mod $p$ when $n$ is even and $f(x)=\pm x$ or $\pm x^{(p+1)/2}$ mod $p$ when $n$ is odd.

An algorithm for accurately computing the lower incomplete gamma function γ ( a , t ) in the case where a = n + 1/2, n ∈ Z and t < 0 is described. Series expansions and analytic continuation are employed to compute the function for certain critical values of n , and these results are used to initiate stable recurrence. The algorithm has been implemented in Fortran 2003, with precompuations carried out in Maple.