Space-Time Isogeometric Analysis of Parabolic Evolution Equations

We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces

Sher 25: pulsating but apparently alone

The blue supergiant Sher25 is surrounded by an asymmetric, hourglass-shaped circumstellar nebula, which shows similarities to the triple-ring structure seen around SN1987A. From optical spectroscopy over six consecutive nights, we detect periodic radial velocity variations in the stellar spectrum of Sher25 with a peak-to-peak amplitude of ~12 km/s on a timescale of about 6 days, confirming the tentative detec-tion of similar variations by Hendry et al. From consideration of the amplitude and timescale of the signal, coupled with observed line profile variations, we propose that the physical origin of these variations is related to pulsations in the stellar atmosphere, rejecting the previous hypothesis of a massive, short-period binary companion. The radial velocities of two other blue supergiants with similar bipolar nebulae, SBW1 and HD 168625, were also monitored over the course of six nights, but these did not display any significant radial velocity variations.Comment: 9 pages, 7 figures. Accepted for publication in MNRA

Explanatory machine learning for sequential human teaching

The topic of comprehensibility of machine-learned theories has recently drawn increasing attention. Inductive Logic Programming (ILP) uses logic programming to derive logic theories from small data based on abduction and induction techniques. Learned theories are represented in the form of rules as declarative descriptions of obtained knowledge. In earlier work, the authors provided the first evidence of a measurable increase in human comprehension based on machine-learned logic rules for simple classification tasks. In a later study, it was found that the presentation of machine-learned explanations to humans can produce both beneficial and harmful effects in the context of game learning. We continue our investigation of comprehensibility by examining the effects of the ordering of concept presentations on human comprehension. In this work, we examine the explanatory effects of curriculum order and the presence of machine-learned explanations for sequential problem-solving. We show that 1) there exist tasks A and B such that learning A before B has a better human comprehension with respect to learning B before A and 2) there exist tasks A and B such that the presence of explanations when learning A contributes to improved human comprehension when subsequently learning B. We propose a framework for the effects of sequential teaching on comprehension based on an existing definition of comprehensibility and provide evidence for support from data collected in human trials. Empirical results show that sequential teaching of concepts with increasing complexity a) has a beneficial effect on human comprehension and b) leads to human re-discovery of divide-and-conquer problem-solving strategies, and c) studying machine-learned explanations allows adaptations of human problem-solving strategy with better performance.Comment: Submitted to the International Joint Conference on Learning & Reasoning (IJCLR) 202

A randomized library approach to identifying functional lox site domains for the Cre recombinase

The bacteriophage P1 Cre/loxP site-specific recombination system is a useful tool in a number of genetic engineering processes. The Cre recombinase has been shown to act on DNA sequences that vary considerably from that of its bacteriophage recognition sequence, loxP. However, little is known about the sequence requirements for functional lox-like sequences. In this study, we have implemented a randomized library approach to identify the sequence characteristics of functional lox site domains. We created a randomized spacer library and a randomized arm library, and then tested them for recombination in vivo and in vitro. Results from the spacer library show that, while there is great plasticity, identity between spacer pairs is the most important factor influencing function, especially in in vitro reactions. The presence of one completely randomized arm in a functional loxP recombination reaction revealed that only three wild-type loxP arms are necessary for successful recombination in Cre-expressing bacteria, and that there are nucleotide preferences at the first three and last three positions of the randomized arm for the most efficiently recombined sequences. Finally, we found that in vitro Cre recombination reactions are much more stringent for evaluating which sequences can support efficient recombination compared to the 294-CRE system