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

Unbinding of giant vortices in states of competing order

Funding: EPSRC (UK) via Grants No. EP/I031014/1 and No. EP/H049584/1.We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/root Delta and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/1n(1/Delta), where Delta denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.Publisher PDFPeer reviewe

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

Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

Analysis of clusterin expression changes as a biomarker of osteoarthritis

Purpose: The discovery and validation of arthritis-related biomarkers and establishment of methodology for proteomic studies in osteoarthritis (OA) are needed. Proteomics strategies have identified many proteins that may relate to pathological mechanisms of OA, however targeted approaches are required to validate the roles of these proteins. This study aimed to use mass spectrometry and western blotting to identify peptides from several proteins in the secretome of chondrocytes, cartilage explants and osteochondral biopsies treated with inflammatory cytokines over a 2-week period, to evaluate their potential as biomarkers of OA progression. Methods: Healthy cartilage was obtained from fetlock joints of skeletally mature horses, euthanized for unrelated veterinary reasons. Cartilage explants were isolated using a 6 mm biopsy, with discs placed into wells (3 discs per 1 ml DMEM + 1% Pen/Strep) before incubation for 24 hours (37 °C, 5% CO2). After this equilibration period, the media was removed and replaced with either fresh DMEM + 1% Pen/Strep or DMEM supplemented with 1% Pen/Strep containing TNFα and IL-1β both at 10ng/ml. Explants were culture for 7–14 days with the cytokines replaced every 4th day. For cell based assays chondrocytes were isolated from tissue using 70U pronase for 1hr at 37 °C and overnight digestion at 37°C using a 0.2% collagenase II solution. The cell suspension was filtered and washed before being seeded into culture flasks and cultured until confluence was reached (37°C, 5% CO2). Once cultures were established cells were split into two groups: healthy control (DMEM supplemented with 1% Pen/Strep and 10% foetal calf serum) or stimulated cells (DMEM as above plus TNFα and IL-1β both at 10ng/ml). Chondroyctes were cytokine-stimulated for up to one week. Cells were used in experiments up to the 2nd passage. Results: Mass spectrometry data showed that peptides representative of clusterin were found to decrease following 7 days of inflammatory stimulation. Western blotting of secreted proteins in media of cartilage explants or chondrocyte showed that clusterin expression was reduced following 7 days of cytokine treatment. Catabolic matrix metalloproteinase enzymes MMP1, MMP3 and MMP13, as well the matrix component cartilage oligomeric protein (COMP) were all found to have an increased abundance in the media of the cytokine treated samples. This data was supported by qPCR for clusterin gene expression which showed initially mRNA levels increased 3 day after inflammatory stimulation but expression was lost after 7 days. Western blotting of media from the osteochondral biopsies showed an increase in clusterin expression after 7 days of inflammatory stimulation however clusterin protein expression could not be detected after 14 days of treatment, indicating a delayed response compared to cartilage tissue alone. Conclusions: The equine chondrocytes, cartilage explant and osteochondral biopsy models exhibited highest clusterin secretion in untreated cultures. IL-1β and TNFα treatment caused a reduction in clusterin secretion. Clusterin acts as a chaperone to aid protein refolding in situations of stress and is constitutively secreted by mammalian cells. IL-1β and TNFα appear to interrupt clusterin secretion and therefore the protection it may offer healthy functioning cells. Previous studies have reported variable data, with some studies indicating a decrease in clusterin in OA, while others indicate an increase in clusterin expression. Our results suggest the clusterin increases immediately after inflammatory stimulation but is lost after prolonged exposure. Therefore, levels of secreted clusterin may be a candidate biomarker for OA progression

The Challenge of Integrating Renewable Generation in the Alberta Electricity Market

Renewable electric generation is forecast to enjoy an increasing share of total capacity and supply regimes in the future. Alberta is no exception to this trend, having initiated policy incentives in response to calls for increasing the fraction of wind and solar energy available to the province over the next decade.1 This call is coming from various sectors including advocacy groups, the provincial government and some utilities. The University of Calgary’s School of Public Policy convened a roundtable discussion on Sept. 15, 2015. Given the wide-ranging aspects of increased renewables integration (for example the policy options, economic forces and engineering/technical issues) the topic demands attention from a wide range of experts and stakeholders. To that end, we endeavoured to group expert panellists and representatives of utilities, public agencies, academe and consumer groups to consider the planning necessary to integrate new renewable capacity into the existing and future grid system in the province and its potential impact. The purpose of the roundtable was to facilitate and foster a knowledge exchange between interested and knowledgeable parties while also aggregating this knowledge into a more complete picture of the challenges and potential strategies associated with increased renewables integration in the Alberta electricity grid

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

Parameterized lower bound and NP-completeness of some HH-free Edge Deletion problems

For a graph $H$, the $H$-free Edge Deletion problem asks whether there exist at most $k$ edges whose deletion from the input graph $G$ results in a graph without any induced copy of $H$. We prove that $H$-free Edge Deletion is NP-complete if $H$ is a graph with at least two edges and $H$ has a component with maximum number of vertices which is a tree or a regular graph. Furthermore, we obtain that these NP-complete problems cannot be solved in parameterized subexponential time, i.e., in time $2^{o(k)}\cdot |G|^{O(1)}$, unless Exponential Time Hypothesis fails.Comment: 15 pages, COCOA 15 accepted pape