Algorithmic Randomness for Infinite Time Register Machines

A concept of randomness for infinite time register machines (ITRMs), resembling Martin-L\"of-randomness, is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of van Lambalgen's theorem holds

Strategies to control Cirsium arvense under organic farming conditions

Three strategies for controlling Cirsium arvense including (1) repeated stubble tillage with subsequent forage crop cultivation, (2) repeated mowing of a grass-clover ley, and (3) forage crop cultivation following a grass-clover ley ploughed in May/June (3) were investigated in field experiments over 3 years. The development of C. arvense shoot density was regularly assessed on sub-plots with defined thistle densities. In the medium-term (9 months), treatment 1 decreased shoot density and regrowth capacity of C. arvense more effectively than a mowed grass-clover ley (2). However, after 22 months, treatments 1 and 2 resulted in a similar strong reduction of C. arvense shoot density of 95 % and 97 %, respectively. At this time, the efficacy of treatment 3 was lower (89 %), however, not significantly different to that of treatments 1 and 2. After 26 months, the effect of all treatments was still apparent; however, the efficacy of treatment 3 was significantly lower than that of treatment 2. Generally, the different strategies showed only minor differences, thus delivering options for optimal strategies of thistle control under given specific conditions of site and cropping systems

Combination of different methods for direct control of Vicia hirsuta in winter wheat

Combinations of three different direct methods for controlling Vicia hirsuta (kainite application, flame weeding and harrowing) were investigated in field experiments. They were based on different strategies at early growth stages of V. hirsuta and standardised harrowing at late growth stages. The highest efficacy of kainite application and flame weeding was achieved at the one leaf stage of V. hirsuta. Winter wheat regeneration from damage caused by both kainite and thermal control was satisfactory when treatments were applied at early growth stages (GS 23). Vicia hirsuta plants that survived kainite application or flame weeding were successfully controlled by repeated harrowing at later crop growth stages; crop growth was not affected. Seed production of V. hirsuta declined with increasing harrowing in all treatments; however the strongest and most reliable reduction was achieved when flame weeding had been previously applied. All combinations of direct measures reduced winter wheat grain-yield losses and enhanced thousand-grain weight more efficiently than the use of a single method only. The highest wheat-grain yield was gained after repeated harrowing (3 times) both with and without kainite application

Efficient Identification of Equivalences in Dynamic Graphs and Pedigree Structures

We propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations we are interested in include equality testing, set operations, isolating unique states, duplication counting, or finding equivalence classes under identifiability constraints. A motivating application is locating equivalence classes in identity-by-descent (IBD) graphs, graph structures in pedigree analysis that change over genetic marker location. The nodes of these graphs are unlabeled and identified only by their connecting edges, a constraint easily handled by our approach. The general framework introduced is powerful enough to build a range of testing functions for IBD graphs, dynamic populations, and other structures using a minimal set of operations. The theoretical and algorithmic properties of our approach are analyzed and proved. Computational results on several simulations demonstrate the effectiveness of our approach.Comment: Code for paper available at http://www.stat.washington.edu/~hoytak/code/hashreduc

An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report)

By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected. In models without choice we employ a "surjective" version of the exponential function. We then prove a choiceless Easton's theorem: one can force the surjective exponential function on all infinite cardinals to take arbitrary cardinal values, provided monotonicity and Cantor's theorem are satisfied, irrespective of cofinalities