Parameterizing by the Number of Numbers

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for ILPF to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable

A simple linear-time algorithm for finding path-decompositions of small width

We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This provides a simple proof of the result by Bodlaender that many families of graphs of bounded pathwidth can be recognized in linear time.Comment: 9 page

Obstructions to within a few vertices or edges of acyclic

Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for finding obstructions by using a bounded treewidth (or pathwidth) search. We illustrate this approach by characterizing certain families of cycle-cover graphs based on the two well-known problems: $k$-{\sc Feedback Vertex Set} and $k$-{\sc Feedback Edge Set}. Our search is based on a number of algorithmic strategies by which large constants can be mitigated, including a randomized strategy for obtaining proofs of minimality.Comment: 16 page

Climate change : a response surface study of the effects of CO2 and temperature on the growth of French beans

The possible impact of global rises in atmospheric CO2 concentration and temperature on the growth and development of French beans (Phaseolus vulgaris) was examined using growth cabinets. Five CO2 concentrations of 350, 450, 550, 650 and 750 vpm and five temperatures of 14·5, 15·5, 16·5, 17·5 and 18·5°C were tested using a fractional factorial design comprising nine treatment combinations of the two factors. Plants were grown under constant irradiance, common atmospheric humidities (vpd 0·5 kPa) and non-limiting supplies of water and mineral nutrients. The plant growth response was modelled by fitting polynomial response function curves to the times to first flower opening, first bean set, 50% maturity and the number and yield of beans. The effects of temperature were large and positive for most of the measured variables, whereas the effects of CO2 were small and negative or non-existent. Increased temperature substantially reduced the time to flowering and the time from bean set to 50% maturity and increased the number and yield of mature beans whereas increased CO2 concentration had little effect on plant growth except that bean yield was very slightly reduced. There was no significant evidence of interaction between the CO2 concentration effects and the temperature effects. The time to maturity and yield of mature beans was simulated for the 2020s (2010 to 2039) and the 2050s (2040 to 2069) using the fitted polynomial models and four climate change scenarios suggested by the UK Climate Impacts Programme. These simulations showed that, depending upon the assumed scenario, the 2020s yields could rise by 39–84% and time to maturity reduce by between 6 and 15 days whereas the 2050s yields could rise by 51–118% and time to maturity reduce by between 9 and 25 days

Vulnerability of horticultural crop production to extreme weather events

The potential impact of future extreme weather events on horticultural crops was evaluated. A review was carried out of the sensitivities of a representative set of crops to environmental challenges. It confirmed that a range of environmental factors are capable of causing a significant impact on production, either as yield or quality loss. The most important of these were un-seasonal temperature, water shortage or excess,and storms. Future scenarios were produced by the LARS-WG1, a stochastic weather generator linked with UKCIP02 projections of future climate. For the analyses, 150 years of synthetic weather data were generated for baseline, 2020HI and 2050HI scenarios at defined locations. The output from the weather generator was used in case studies, either to estimate the frequency of a defined set of circumstances known to have impact on cropping, or as inputs to models of crop scheduling or pest phenology or survival. The analyses indicated that episodes of summer drought severe enough to interrupt the continuity of supply of salads and other vegetables will increase while the frequency of autumns with sufficient rainfall to restrict potato lifting will decrease. They also indicated that the scheduling of winter cauliflowers for continuity of supply will require the deployment of varieties with different temperature sensitivities from those in use currently. In the pest insect studies, the number of batches of Agrotis segetum (cutworm) larvae surviving to third instar increased with time, as did the potential number of generations of Plutella xylostella (diamond-back moth) in the growing season, across a range of locations. The study demonstrated the utility of high resolution scenarios in predicting the likelihood of specific weather patterns and their potential effect on horticultural production. Several limitations of the current scenarios and biological models were also identified

The effect of cultural and environmental factors on potato seed tuber morphology and subsequent sprout and stem development

Seed crops of the variety Estima were grown in each of 2 years using two planting dates, two harvest dates, two plant densities and two irrigation regimes to produce seed tubers which had experienced different cultural and environmental conditions. The effects of these treatments on tuber characteristics, sprout production and stem development in the ware crop were then determined in subsequent experiments using storage regimes of 3 and 10 °C. Time of planting the seed crop affected numbers of eyes, sprouts and above ground stems in the subsequent ware crop because environmental conditions around the time of tuber initiation appeared to alter tuber shape. Cooler, wetter conditions in the 7 days after tuber initiation were associated with tubers which were longer, heavier and had more eyes, sprouts and above ground stems. In contrast, the time of harvesting the seed crop did not affect tuber shape or numbers of above ground stems and there was no interaction with tuber size. The density of the seed crop had no effect on any character measured and irrigation well after tuber initiation did not affect tuber shape, numbers of sprouts or numbers of stems. Seed production treatments, which resulted in earlier dormancy break, were associated with tubers that produced more sprouts and above ground stems, in contrast to the conventional understanding of apical dominance. Storage at 3 °C gave fewer sprouts, a lower proportion of eyes with sprouts and fewer stems than storage at 10 °C. The major effects on stem production appear to result from environmental conditions at the time of tuber initiation of the seed crop and sprouting temperature

Team morale and leadership styles of project managers in China construction projects

W112 Culture in Construction: Paper ID: 779The relationships of project team morale and the supervisory styles of project leaders are examined in this paper based on P-M theories which assume dichotomous styles of performance-oriented and maintenance-oriented leadership. In P-M theories, leadership affects motivational arousal directly through a combination of pressure and support where the work structuring aspects of leadership, which affect motivation by clarifying paths to goals, are less central. Generally, previous research supported both P- and M-oriented leadership styles being consistently and positively related to organisational performance measures, although the M-oriented style of leadership was found to be more effective in functional organisations and P-oriented leadership was more effective in the engineering project field of temporary organisations. Situational contingencies in this study are assumed to affect subordinates’ interpretations of leadership primarily, i.e. the leadership styles reported by subordinates are assumed not to reflect the objective level of leadership behaviour. Instead, those measures reflect the amount of a leadership function that subordinates experience given their own personalities, cultural background and the situational contingencies that they face. The subjects in an exploratory study of joint venture projects in China reported in this paper reflect the influence of leadership styles on the level of team morale and project time performance in given sets of situational contingencies.postprintThe 2010 World Congress of CIB on Building a Better World, University of Salford, Salford, U.K., 10-14 May 2010. In Proceedings: TG59 and W112 - Special Track 18th CIB World Building Congress, 2010, p. 180-19

Expanding the expressive power of Monadic Second-Order logic on restricted graph classes

We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known Monadic Second-Order logic by the addition of cardinality constraints, can be solved in FPT time parameterized by vertex cover. The second meta-theorem shows that the MSO partitioning problems introduced by Rao can also be solved in FPT time with the same parameter. The significance of our contribution stems from the fact that these formalisms can describe problems which are W[1]-hard and even NP-hard on graphs of bounded tree-width. Additionally, our algorithms have only an elementary dependence on the parameter and formula. We also show that both results are easily extended from vertex cover to neighborhood diversity.Comment: Accepted for IWOCA 201

Fluctuation spectroscopy as a probe of granular superconducting diamond films

We present resistance versus temperature data for a series of boron-doped nanocrystalline diamond films whose grain size is varied by changing the film thickness. Upon extracting the fluctuation conductivity near to the critical temperature we observe three distinct scaling regions -- 3D intragrain, quasi-0D, and 3D intergrain -- in confirmation of the prediction of Lerner, Varlamov and Vinokur. The location of the dimensional crossovers between these scaling regions allows us to determine the tunnelling energy and the Thouless energy for each film. This is a demonstration of the use of \emph{fluctuation spectroscopy} to determine the properties of a superconducting granular system