Smoothness of stabilisers in generic characteristic

Let $R$ be a commutative unital ring. Given a finitely-presented affine $R$-group $G$ acting on a finitely-presented $R$-scheme $X$ of finite type, we show that there is a prime $p_0$ so that for any $R$-algebra $k$ which is a field of characteristic $p > p_0$, the centralisers in $G_k$ of all subsets $U \subseteq X(k)$ are smooth. We prove this using the Lefschetz principle together with careful application of Gr\"{o}bner basis techniques.Comment: 15 page

Monitoring Frequency of Intra‐Fraction Patient Motion Using the ExacTrac System for LINAC‐based SRS Treatments

Purpose: The aim of this study was to investigate the intra‐fractional patient motion using the ExacTrac system in LINAC‐based stereotactic radiosurgery (SRS). Method: A retrospective analysis of 104 SRS patients with kilovoltage image‐guided setup (Brainlab ExacTrac) data was performed. Each patient was imaged pre‐treatment, and at two time points during treatment (1st and 2nd mid‐treatment), and bony anatomy of the skull was used to establish setup error at each time point. The datasets included the translational and rotational setup error, as well as the time period between image acquisitions. After each image acquisition, the patient was repositioned using the calculated shift to correct the setup error. Only translational errors were corrected due to the absence of a 6D treatment table. Setup time and directional shift values were analyzed to determine correlation between shift magnitudes as well as time between acquisitions. Results: The average magnitude translation was 0.64 ± 0.59 mm, 0.79 ± 0.45 mm, and 0.65 ± 0.35 mm for the pre‐treatment, 1st mid‐treatment, and 2nd mid‐treatment imaging time points. The average time from pre‐treatment image acquisition to 1st mid‐treatment image acquisition was 7.98 ± 0.45 min, from 1st to 2nd mid‐treatment image was 4.87 ± 1.96 min. The greatest translation was 3.64 mm, occurring in the pre‐treatment image. No patient had a 1st or 2nd mid‐treatment image with greater than 2 mm magnitude shifts. Conclusion: There was no correlation between patient motion over time, in direction or magnitude, and duration of treatment. The imaging frequency could be reduced to decrease imaging dose and treatment time without significant changes in patient position

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre-existing concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization

Behavioural and neural modulation of win-stay but not lose-shift strategies as a function of outcome value in Rock, Paper, Scissors

Competitive environments in which individuals compete for mutually-exclusive outcomes require rational decision making in order to maximize gains but often result in poor quality heuristics. Reasons for the greater reliance on lose-shift relative to win-stay behaviour shown in previous studies were explored using the game of Rock, Paper, Scissors and by manipulating the value of winning and losing. Decision-making following a loss was characterized as relatively fast and relatively inflexible both in terms of the failure to modulate the magnitude of lose-shift strategy and the lack of significant neural modulation. In contrast, decision-making following a win was characterized as relatively slow and relatively flexible both in terms of a behavioural increase in the magnitude of win-stay strategy and a neural modulation of feedback-related negativity (FRN) and stimulus-preceding negativity (SPN) following outcome value modulation. The win-stay / lose-shift heuristic appears not to be a unified mechanism, with the former relying on System 2 processes and the latter relying on System 1 processes. Our ability to play rationally appears more likely when the outcome is positive and when the value of wins are low, highlighting how vulnerable we can be when trying to succeed during competition

Smoothed particle magnetohydrodynamic simulations of protostellar outflows with misaligned magnetic field and rotation axes

We have developed a modified form of the equations of smoothed particle magnetohydrodynamics which are stable in the presence of very steep density gradients. Using this formalism, we have performed simulations of the collapse of magnetised molecular cloud cores to form protostars and drive outflows. Our stable formalism allows for smaller sink particles (< 5 AU) than used previously and the investigation of the effect of varying the angle, {\theta}, between the initial field axis and the rotation axis. The nature of the outflows depends strongly on this angle: jet-like outflows are not produced at all when {\theta} > 30{\deg}, and a collimated outflow is not sustained when {\theta} > 10{\deg}. No substantial outflows of any kind are produced when {\theta} > 60{\deg}. This may place constraints on the geometry of the magnetic field in molecular clouds where bipolar outflows are seen.Comment: Accepted for publication in MNRAS, 13 pages, 14 figures. Animations can be found at http://www.astro.ex.ac.uk/people/blewis/research/outflows_misaligned_fields.htm

Gut microbiota influences female choice and fecundity in the nuptial gift-giving species, Drosophila subobscura (Diptera: Drosophilidae)

Recently, there has been rapidly growing interest in the effects of the microbiota on host physiology and behaviour. Due to the nutritional value of bacteria, gut microfl ora may be particularly important in species that present nuptial gifts during courtship. Here, we explore whether the presence or absence of gut microbiota in males and females of the nuptial gift-giving species Drosophila subobscura (Collin, 1936) alters mating behaviour in terms of female preference, male investment, and female fecundity. We found that females that had been fed antibiotics, compared to females with intact gut bacteria, were more willing to mate with a male that had been fed normally. However female fecundity was higher when both males and females lacked gut bacteria compared to both individuals having a full complement of gut bacteria. This implies that the presence of the microbiota acts to reduce female fecundity in this species, and that male gut bacterial content infl uences female fecundity. Our results provide further evidence to the growing consensus that the microbiota of an individual may have important effects on both reproductive behaviour and physiology, and suggest that it may also contribute to the nutritional value of the nuptial gift in this system