On Newton's Method for Entire Functions

The Newton map N_f of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of N_f. We study the behavior of N_f in a component V of C\U. If V can be surrounded by an invariant curve within U and satisfies the condition that each point in the extended plane has at most finitely many preimages in V, we show that V contains another immediate basin of N_f or a virtual immediate basin. A virtual immediate basin is an unbounded invariant Fatou component in which the dynamics converges to infty through an absorbing set.Comment: 19 pages, 4 figures. Changes in Version 2: Sharpened the result in Section

Virtual Immediate Basins of Newton Maps and Asymptotic Values

Newton's root finding method applied to a (transcendental) entire function f:C->C is the iteration of a meromorphic function N. It is well known that if for some starting value z, Newton's method converges to a point x in C, then f has a root at x. We show that in many cases, if an orbit converges to infinity for Newton's method, then f has a `virtual root' at infinity. More precisely, we show that if N has an invariant Baker domain that satisfies some mild assumptions, then 0 is an asymptotic value for f. Conversely, we show that if f has an asymptotic value of logarithmic type at 0, then the singularity over 0 is contained in an invariant Baker domain of N, which we call a virtual immediate basin. We show by way of counterexamples that this is not true for more general types of singularities.Comment: 15 pages, 1 figur

Intrinsic Motivation and Mental Replay enable Efficient Online Adaptation in Stochastic Recurrent Networks

Autonomous robots need to interact with unknown, unstructured and changing environments, constantly facing novel challenges. Therefore, continuous online adaptation for lifelong-learning and the need of sample-efficient mechanisms to adapt to changes in the environment, the constraints, the tasks, or the robot itself are crucial. In this work, we propose a novel framework for probabilistic online motion planning with online adaptation based on a bio-inspired stochastic recurrent neural network. By using learning signals which mimic the intrinsic motivation signalcognitive dissonance in addition with a mental replay strategy to intensify experiences, the stochastic recurrent network can learn from few physical interactions and adapts to novel environments in seconds. We evaluate our online planning and adaptation framework on an anthropomorphic KUKA LWR arm. The rapid online adaptation is shown by learning unknown workspace constraints sample-efficiently from few physical interactions while following given way points.Comment: accepted in Neural Network

Survival of thermophilic spore-forming bacteria in a 90+ year old milk powder from Ernest Shackelton's Cape Royds Hut in Antarctica

Milk powder taken to Antarctica on Shackelton's British Antarctic Expedition in 1907 was produced in New Zealand by a roller drying process in the first factory in the world dedicated to this process. Thermophilic bacilli are the dominant contaminants of modern spray-dried milk powders and the 1907 milk powder allows a comparison to be made of contaminating strains in roller-dried and spray-dried powders. Samples of milk powder obtained from Shackelton's Hut at Cape Royds had low levels of thermophilic contamination (<500 cfu ml−1) but the two dominant strains (Bacillus licheniformis strain F and Bacillus subtilis) were typical of those found in spray-dried powders. Soil samples from the floor of the hut also contained these strains, whereas soils distant from the hut did not. Differences in the RAPD profiles of isolates from the milk powder and the soils suggest that contamination of the milk from the soil was unlikely. It is significant that the most commonly encountered contaminant strain in modern spray-dried milk (Anoxybacillus flavithermus strain C) was not detected in the 1907 sample

Development and field assessment of a quantitative PCR for the detection and enumeration of the noxious bloom-former Anabaena planktonica

Anabaena planktonica is a harmful, bloom-forming freshwater cyanobacterium, which has arrived recently in New Zealand. In the short time since its incursion (<10 yr), A. planktonica has spread rapidly throughout lakes in the North Island. To date, the identification and enumeration of A. planktonica has been undertaken using light microscopy. There is an urgent demand for a highly sensitive and specific quantitative detection method that can be combined with a high sample processing capability in order to increase sampling frequency. In this study, we sequenced 36 cyanobacterial 16S rRNA genes (partial), complete intergenic transcribed spacers (ITS), and 23S rRNA genes (partial) of fresh-water cyanobacteria found in New Zealand. The sequences were used to develop an A. Planktonica specific TaqMan QPCR assay targeting the long ITS1-L and the 5´ terminus of the 23S rRNA gene. The QPCR method was linear (R2 = 0.999) over seven orders of magnitude with a lower end sensitivity of approximately five A. planktonica cells in the presence of exogenous DNA. The quantitative PCR (QPCR) method was used to assess the spatial distribution and seasonal population dynamics of A. planktonica from the Lower Karori Reservoir (Wellington, New Zealand) over a five-month period. The QPCR results were compared directly to microscopic cell counts and found to correlate significantly (95% confidence level) under both bloom and non-bloom conditions. The current QPCR assay will be an invaluable tool for routine monitoring programs and in research investigating environmental factors that regulate the population dynamics and the blooming of A. planktonica

Tools for the Assessment of Undergraduate Research Outcomes

The recent focus on the importance of assessment has resulted in the development of a number of tools to assess student learning outcomes (e.g. Angelo & Cross, 1993). However, most of these tools have focused on what students learn in the classroom. The outcomes of student involvement in research tend to be less well defined, and therefore more difficult to measure, than the outcomes of traditional classroom learning. Nevertheless, some of the existing assessment tools may be appropriate for the assessment of learning through research, and others have recently been developed explicitly for that purpose (e.g. Lopatto, 2004; Tariq, Stefani, Butcher, & Heylings, 1998). Of the many outcomes listed for psychology majors by the American Psychological Association (APA, 2002), those that seem to be particularly likely to be enhanced by conducting research include understanding research methods, critical thinking, and oral and written communication (assuming that the student writes a paper or gives an oral presentation of the research)