4,411 research outputs found

    Determinantal Sieving

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    We introduce determinantal sieving, a new, remarkably powerful tool in the toolbox of algebraic FPT algorithms. Given a polynomial P(X)P(X) on a set of variables X={x1,,xn}X=\{x_1,\ldots,x_n\} and a linear matroid M=(X,I)M=(X,\mathcal{I}) of rank kk, both over a field F\mathbb{F} of characteristic 2, in 2k2^k evaluations we can sieve for those terms in the monomial expansion of PP which are multilinear and whose support is a basis for MM. Alternatively, using 2k2^k evaluations of PP we can sieve for those monomials whose odd support spans MM. Applying this framework, we improve on a range of algebraic FPT algorithms, such as: 1. Solving qq-Matroid Intersection in time O(2(q2)k)O^*(2^{(q-2)k}) and qq-Matroid Parity in time O(2qk)O^*(2^{qk}), improving on O(4qk)O^*(4^{qk}) (Brand and Pratt, ICALP 2021) 2. TT-Cycle, Colourful (s,t)(s,t)-Path, Colourful (S,T)(S,T)-Linkage in undirected graphs, and the more general Rank kk (S,T)(S,T)-Linkage problem, all in O(2k)O^*(2^k) time, improving on O(2k+S)O^*(2^{k+|S|}) respectively O(2S+O(k2log(k+F)))O^*(2^{|S|+O(k^2 \log(k+|\mathbb{F}|))}) (Fomin et al., SODA 2023) 3. Many instances of the Diverse X paradigm, finding a collection of rr solutions to a problem with a minimum mutual distance of dd in time O(2r(r1)d/2)O^*(2^{r(r-1)d/2}), improving solutions for kk-Distinct Branchings from time 2O(klogk)2^{O(k \log k)} to O(2k)O^*(2^k) (Bang-Jensen et al., ESA 2021), and for Diverse Perfect Matchings from O(22O(rd))O^*(2^{2^{O(rd)}}) to O(2r2d/2)O^*(2^{r^2d/2}) (Fomin et al., STACS 2021) All matroids are assumed to be represented over a field of characteristic 2. Over general fields, we achieve similar results at the cost of using exponential space by working over the exterior algebra. For a class of arithmetic circuits we call strongly monotone, this is even achieved without any loss of running time. However, the odd support sieving result appears to be specific to working over characteristic 2

    Stake-governed tug-of-war and the biased infinity Laplacian

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    In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The game ends when the counter reaches the boundary, a fixed subset of the vertices, at which point one player pays the other an amount determined by the boundary vertex. Economists and mathematicians have independently studied tug-of-war for many years, focussing respectively on resource-allocation forms of the game, in which players iteratively spend precious budgets in an effort to influence the bias of the coins that determine the turn victors; and on PDE arising in fine mesh limits of the constant-bias game in a Euclidean setting. In this article, we offer a mathematical treatment of a class of tug-of-war games with allocated budgets: each player is initially given a fixed budget which she draws on throughout the game to offer a stake at the start of each turn, and her probability of winning the turn is the ratio of her stake and the sum of the two stakes. We consider the game played on a tree, with boundary being the set of leaves, and the payment function being the indicator of a single distinguished leaf. We find the game value and the essentially unique Nash equilibrium of a leisurely version of the game, in which the move at any given turn is cancelled with constant probability after stakes have been placed. We show that the ratio of the players' remaining budgets is maintained at its initial value λ\lambda; game value is a biased infinity harmonic function; and the proportion of remaining budget that players stake at a given turn is given in terms of the spatial gradient and the λ\lambda-derivative of game value. We also indicate examples in which the solution takes a different form in the non-leisurely game.Comment: 69 pages with four figures. Updated to include discussion of the economics literature of tug-of-wa

    Mars delivery service - development of the electro-mechanical systems of the Sample Fetch Rover for the Mars Sample Return Campaign

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    This thesis describes the development of the Sample Fetch Rover (SFR), studied for Mars Sample Return (MSR), an international campaign carried out in cooperation between the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The focus of this document is the design of the electro-mechanical systems of the rover. After placing this work into the general context of robotic planetary exploration and summarising the state of the art for what concerns Mars rovers, the architecture of the Mars Sample Return Campaign is presented. A complete overview of the current SFR architecture is provided, touching upon all the main subsystems of the spacecraft. For each area, it is discussed what are the design drivers, the chosen solutions and whether they use heritage technology (in particular from the ExoMars Rover) or new developments. This research focuses on two topics of particular interest, due to their relevance for the mission and the novelty of their design: locomotion and sample acquisition, which are discussed in depth. The early SFR locomotion concepts are summarised, covering the initial trade-offs and discarded designs for higher traverse performance. Once a consolidated architecture was reached, the locomotion subsystem was developed further, defining the details of the suspension, actuators, deployment mechanisms and wheels. This technology is presented here in detail, including some key analysis and test results that support the design and demonstrate how it responds to the mission requirements. Another major electro-mechanical system developed as part of this work is the one dedicated to sample tube acquisition. The concept of operations of this machinery was defined to be robust against the unknown conditions that characterise the mission. The design process led to a highly automated robotic system which is described here in its main components: vision system, robotic arm and tube storage

    Identification of Micro- and Submicron (Nano) Plastics in Water Sources and the Impact of COVID-19 on Plastic Pollution

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    One of the most significant environmental issues that our society may deal with this century could be plastics. The world's water bodies, as well as land and air, are becoming more and more contaminated by plastic due to the ongoing and expanding manufacturing of these synthetic materials, as well as the lack of an effective strategy for managing plastic waste. The fact that plastics break down into smaller particles (micro and nanoplastics) by action of environmental physical and chemical reactions, and do not degrade biologically in a reasonable time, is a cause of concern as plastics are believed to cause harm in animals, plants and humans.To identify the types of plastics prevalent in aquatic habitats, a number of procedures have been developed, from sampling to identification. After a water body has been sampled using nets, pumps, or other tools, depending on the type of sample taken, it is usually necessary to treat the samples for separation and purification. The next stage is to employ analytical techniques to identify the synthetic contaminants. The most common approaches are microscopy, spectroscopy, and thermal analysis. This thesis gives an overview of where in the environment microplastics (MPs) and nanoplastics (NPs) can be found and summarizes the most important technologies applied to analyse the importance of plastics as a contaminant in water bodies. The development of standardised analytical procedures is still necessary as most of them are not suitable for the identification of particles below 50 μm due to resolution limitations. The preparation and analysis of samples are usually time-consuming factors that shall be considered. Particularly for MP and NP analysis in aqueous samples, thermal analysis methods based on sample degradation are generally not considered to be the most effective approach. Nevertheless, Pyrolysis - Gas Chromatography Time-of-Flight Mass Spectrometry (Py-GCToFMS) is used in this thesis to propose a novel approach as due to its unique detection abilities, and with a novel filtration methodology for collection, it enables the identification of tiny particle sizes (>0.1 μm) in water samples.PTFE membranes were selected to filter the liquid samples using a glass filtration system. This way, the synthetic particles will be deposited on the membranes and will allow the study and analysis of the precipitated material. PTFE is a readily available, reasonably priced, and adaptable product that makes sample preparation quick and simple.The three plastics under study—polypropylene (PP), polystyrene (PS), and polyvinyl chloride (PVC)—can be identified from complex samples at trace levels thanks to the employment of these widely used membranes and the identification of various and specific (marker) ions. The technique was examined against a range of standards samples that contained predetermined concentrations of MPs and NPs. Detection levels were then determined for PVC and PS and were found to be below <50 μg/ L, with repeatable data showing good precision (RSD <20 %). The examination of a complex matrix sample taken from a nearby river contributed to further validate this innovative methodology; the results indicated the existence of PS with a semi-quantifiable result of 250.23 g/L. Because of this, PY-GCToFMS appears to be a method that is appropriate for the task of identifying MPs and NPs from complex mixtures.This thesis also focuses on the environmental challenge that disposable plastic face masks (DPFMs) pose, which has been made significantly worse due to the COVID-19 pandemic. By the time this thesis was written, the production of disposable plastic facemasks had reached to approximately 200 million a day, in a global effort to tackle the spread of the new SARS-CoV-2 virus. This thesis investigates the emissions of pollutants from several different DPFM brands (medical and non-medical) that were submerged in water to replicate the conditions in the environment after these DPFMs have been discarded. The DPFM leachates were filtered using inorganic membranes type and characterized using Fourier transform infrared spectroscopy (FTIR), Scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDS), Light/Optical Microscopy (LM/OM), Inductively coupled plasma mass spectrometry (ICP-MS) and Liquid chromatography–mass spectrometry (LC-MS). Micro and nano scale polymeric fibres, particles, siliceous fragments and leachable inorganic and organic chemicals were observed from all of the tested DPFMs. For non-medical DPFMs, traces of concerning heavy metals were detected in association with silicon containing fragments (i.e. lead up to 6.79 μg/L). ICP-MS also confirmed the presence of other leachable metals like cadmium (up to 1.92 μg/L), antimony (up to 3.93 μg/L) and copper (up to 4.17 μg/L). LC-MS analysis identified organic species related to plastic additives; polyamide-66 monomer and oligomers (nylon-66 synthesis), surfactant molecules, and dye-like molecules were all tentatively identified in the leachate. The question of whether DPFMs are safe to use daily and what implications may be anticipated after their disposal into the environment is brought up by the toxicity of some of the chemicals discovered.The previous approach is expanded to medical DPFMs with the utilisation of Field Emission Gun Scanning Electron Microscope (FEG-SEM) in order to get high resolution images of the micro and nanoparticles deposited on the membranes. It is also incorporated the use of 0.02 μm pore size inorganic membranes to better identify the nanoparticles released.Separated aqueous samples were also obtained by submerging medical DPFMs for 24 hours to be analysed using ICP-MS and LC-MS.Both particles and fibres in the micro and nano scale were found in all 6 DPFMs brands of this study. EDS analysis revealed the presence of particles containing different heavy metals like lead, mercury, and arsenic among others. ICP-MS analysis results confirmed traces of heavy metals (antimony up to 2.41 μg/L and copper up to 4.68 μg/L). LC-MS analysis results identified organic species related to plastic additives and contaminants; polyamide-66 monomer and oligomers (nylon-66 synthesis), surfactant molecules, and polyethylene glycol were all tentatively identified in the leachate. The toxicity of some of the chemicals found raises the question of whether DPFMs are safe to be used on a daily basis and what consequences are to be expected after their disposal into the environment

    Modelling the folding pathway of DNA nanostructures

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    DNA origami is a robust technique for bottom-up nano-fabrication. It encodes a target shape into uniquely addressable interactions between a set of short 'staple' strands and a long 'scaffold' strand. The mechanisms of self-assembly, particularly regarding kinetics, need to be better understood. Origami design usually relies on optimising the thermodynamic stability of the target structure, and thermal annealing remains the most fool-proof assembly protocol. This work focuses on studying the folding pathway of three types of origami through simulations: a reconfigurable T-junction origami, several traditional origami, and origami with coated scaffolds. The T-junction origami is intended as an economically feasible method of changing the uniqueness of interactions. My contribution to this work is to characterise the basic structural motif through oxDNA, a nucleotide-resolution model of DNA. The thesis then focuses on extending a domain-level model of DNA origami to study several experimental origami designs. We reveal design-dependent free energy barriers using biased simulations and relate this to the observed hysteresis in experiments. We also highlight the role of specific design elements in determining the folding pathway. A novel method of lowering the temperature of error-free assembly using coated scaffolds is then presented, with simulations indicating the existence of an activation barrier. By exposing particular regions of the scaffold, we can lower assembly time and temperature

    A systematic review and meta-analysis of interventions based on metacognition and self-regulation in school-aged mathematics

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    Mathematics is an important gatekeeper for educational and professional opportunities and a useful tool for discovery and expression. Given previous research and theory demonstrating potential for metacognitive and self-regulated learning (MC/SRL) interventions to support mathematics achievement with diverse learners, a systematic review was conducted to evaluate their effectiveness within the years of general education, with pupils of ages three to 18. Appropriately-designed studies that were reported in English between 2005 and 2019 were included. Following a systematic search, with double-reviewing and expert consultation for consistency, 1,761 bibliographic items were screened, resulting in 60 included studies. Qualitative aspects of the designs, contexts, participants, and intervention activities were synthesised narratively. Posttest-only and adjusted, random effects meta-analyses were performed using a single mathematics achievement measure from each study. The results indicate a generally positive effect from the included interventions (combined Cohen’s d=0.46, SE=0.08, 95% CI=0.30 to 0.60). This represents a somewhat more modest effect compared with previous reviews in this area, possibly due to a greater range of included reports. No risk of publication bias was identified, reflecting the breadth and diversity of included studies, but efforts to mitigate heterogeneity were only partially successful. Interventions using structured problem-solving with metacognitive prompts were more effective than those not using it, while dissertations reported lower effects than journal articles. No differences were found based on participant age or intervention dose. Primary studies used a variety of assessments and differed on reporting of interventions and quality-related factors, and there remained substantial heterogeneity in the meta-analysis. Implications of this review for educational theory, research, and practice are discussed, with emphasis on reporting studies fully, using broad-scope, comparable assessments, and investing in comprehensive metacognitive and self-regulated learning interventions that can support lasting change in teaching and learning

    The role of the periplasmic Cu metallochaperone AccA in metalating the Cu-dependent nitrite reductase AniA in Neisseria gonorrhoea

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    Neisseria gonorrhoeae (the gonococcus) respires nitrite (NO2-). This process requires the nitrite reductase, AniA, which contains T1- and T2Cu in its active sites. We have characterised AccA, a PCuAC homologue with an extended His- and Met-rich C-terminal domain, as a likely periplasmic Cu- binding metallochaperone that metalates AniA. In this study, biochemical examination of purified AccA and site-directed variants confirms that it binds one Cu(I) atom with femtomolar affinity in the conserved 2 His, 2 Met binding site. The C-terminal domain binds Cu(II) with picomolar affinity, although precise ligands remain unknown. Gonococcal strains lacking AccA or any conserved His and Met residue in AccA fail to grow and reduce NO2-. This phenotype is reversed when Cu(II) salts are supplemented in the growth medium. These results suggest that, in the absence of AccA, AniA is expressed as an apo-enzyme, but is re-metalated if the periplasmic buffered Cu pool increases. Interestingly, gonococcal strains lacking the C-terminal domain of AccA show reduced growth and NO2- consumption only in the presence of the Cu(I) chelator BCS, suggesting a role during Cu starvation. Cu-transfer experiments using purified proteins confirmed AccA metalates both Cu sites in AniA with metal coordinated by both the Cu primary and C-terminal Cu binding sites. However, the C-terminal tail was required for metalation of the T2-site. AniA is expressed as a monomer and Cu binding induces protein trimerisation. This may offer an alternative role of why AccA is required to metalate AniA in vitro. This work raises questions regarding the thermodynamics and kinetics of how metalloproteins acquire Cu from the buffered cellular pool via metallochaperones

    Runtime Analysis of Success-Based Parameter Control Mechanisms for Evolutionary Algorithms on Multimodal Problems

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    Evolutionary algorithms are simple general-purpose optimisers often used to solve complex engineering and design problems. They mimic the process of natural evolution: they use a population of possible solutions to a problem that evolves by mutating and recombining solutions, identifying increasingly better solutions over time. Evolutionary algorithms have been applied to a broad range of problems in various disciplines with remarkable success. However, the reasons behind their success are often elusive: their performance often depends crucially, and unpredictably, on their parameter settings. It is, furthermore, well known that there are no globally good parameters, that is, the correct parameters for one problem may differ substantially to the parameters needed for another, making it harder to translate previous successfully implemented parameters to new problems. Therefore, understanding how to properly select the parameters is an important but challenging task. This is commonly known as the parameter selection problem. A promising solution to this problem is the use of automated dynamic parameter selection schemes (parameter control) that allow evolutionary algorithms to identify and continuously track optimal parameters throughout the course of evolution without human intervention. In recent years the study of parameter control mechanisms in evolutionary algorithms has emerged as a very fruitful research area. However, most existing runtime analyses focus on simple problems with benign characteristics, for which fixed parameter settings already run efficiently and only moderate performance gains were shown. The aim of this thesis is to understand how parameter control mechanisms can be used on more complex and challenging problems with many local optima (multimodal problems) to speed up optimisation. We use advanced methods from the analysis of algorithms and probability theory to evaluate the performance of evolutionary algorithms, estimating the expected time until an algorithm finds satisfactory solutions for illustrative and relevant optimisation problems as a vital stepping stone towards designing more efficient evolutionary algorithms. We first analyse current parameter control mechanisms on multimodal problems to understand their strengths and weaknesses. Subsequently we use this knowledge to design parameter control mechanisms that mitigate the weaknesses of current mechanisms while maintaining their strengths. Finally, we show with theoretical and empirical analyses that these enhanced parameter control mechanisms are able to outperform the best fixed parameter settings on multimodal optimisation
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