Selection and sorting with limited storage

AbstractWhen selecting from, or sorting, a file stored on a read-only tape and the internal storage is rather limited, several passes of the input tape may be required. We study the relation between the amount of internal storage available and the number of passes required to select the Kth highest of N inputs. We show, for example, that to find the median in two passes requires at least ω(N12) and at most O(N12log N) internal storage. For probabilistic methods, θ(N12) internal storage is necessary and sufficient for a single pass method which finds the median with arbitrarily high probability

Circuit size is nonlinear in depth

AbstractTwo fundamental complexity measures for a Boolean function f are its circuit depth d(f) and its circuit size c(f). It is shown that c≳ 14d·log2d for all f

Excited electronic states of MnO4−:Challenges for wavefunction and density functional response theories

AbstractThe lowest excited electronic states of the permanganate ion MnO4− are calculated using a hierarchy of coupled cluster response approaches, as well as time-dependent density functional theory. It is shown that while full linear response coupled cluster with singles and doubles (or higher) performs well, that permanganate represents a stern test for approximate coupled cluster response models, and that problems can be traced to very large orbital relaxation effects. TD-DFT is reasonably robust although errors around 0.6eV are still observed. In order to further investigate the strong correlations prevalent in the electronic ground state large-scale RASSCF calculations were also performed. Again very large orbital relaxation in the correlated wavefunction is observed. Although the system can qualitatively be described by a single configuration, multi-reference diagnostic values show that care must be taken in this and similar metal complexes

On the tree-transformation power of XSLT

XSLT is a standard rule-based programming language for expressing transformations of XML data. The language is currently in transition from version 1.0 to 2.0. In order to understand the computational consequences of this transition, we restrict XSLT to its pure tree-transformation capabilities. Under this focus, we observe that XSLT~1.0 was not yet a computationally complete tree-transformation language: every 1.0 program can be implemented in exponential time. A crucial new feature of version~2.0, however, which allows nodesets over temporary trees, yields completeness. We provide a formal operational semantics for XSLT programs, and establish confluence for this semantics

Rapid detection of Ganoderma-infected oil palms by microwave ergosterol extraction with HPLC and TLC

Detection of basal stem rot (BSR) by Ganoderma of oil palms was based on foliar symptoms and production of basidiomata. Enzyme-Linked Immunosorbent Assays-Polyclonal Antibody (ELISA-PAB) and PCR have been proposed as early detection methods for the disease. These techniques are complex, time consuming and have accuracy limitations. An ergosterol method was developed which correlated well with the degree of infection in oil palms, including samples growing in plantations. However, the method was capable of being optimised. This current study was designed to develop a simpler, more rapid and efficient ergosterol method with utility in the field that involved the use of microwave extraction. The optimised procedure involved extracting a small amount of Ganoderma, or Ganoderma-infected oil palm suspended in low volumes of solvent followed by irradiation in a conventional microwave oven at 70 °C and medium high power for 30 s, resulting in simultaneous extraction and saponification. Ergosterol was detected by thin layer chromatography (TLC) and quantified using high performance liquid chromatography with diode array detection. The TLC method was novel and provided a simple, inexpensive method with utility in the field. The new method was particularly effective at extracting high yields of ergosterol from infected oil palm and enables rapid analysis of field samples on site, allowing infected oil palms to be treated or culled very rapidly. Some limitations of the method are discussed herein. The procedures lend themselves to controlling the disease more effectively and allowing more effective use of land currently employed to grow oil palms, thereby reducing pressure to develop new plantations.This project was supported by the Fundamental Research Grant Scheme (FRGS), administered through the Ministry of Higher Education, Malaysia (Grant No: 5524175)

Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.Comment: 18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 pape

City-wide wastewater genomic surveillance through the successive emergence of SARS-CoV-2 Alpha and Delta variants

Genomic surveillance of SARS-CoV-2 has provided a critical evidence base for public health decisions throughout the pandemic. Sequencing data from clinical cases has helped to understand disease transmission and the spread of novel variants. Genomic wastewater surveillance can offer important, complementary information by providing frequency estimates of all variants circulating in a population without sampling biases. Here we show that genomic SARS-CoV-2 wastewater surveillance can detect fine-scale differences within urban centres, specifically within the city of Liverpool, UK, during the emergence of Alpha and Delta variants between November 2020 and June 2021. Furthermore, wastewater and clinical sequencing match well in the estimated timing of new variant rises and the first detection of a new variant in a given area may occur in either clinical or wastewater samples. The study's main limitation was sample quality when infection prevalence was low in spring 2021, resulting in a lower resolution of the rise of the Delta variant compared to the rise of the Alpha variant in the previous winter. The correspondence between wastewater and clinical variant frequencies demonstrates the reliability of wastewater surveillance. However, discrepancies in the first detection of the Alpha variant between the two approaches highlight that wastewater monitoring can also capture missing information, possibly resulting from asymptomatic cases or communities less engaged with testing programmes, as found by a simultaneous surge testing effort across the city

A broadscale analysis of host-symbiont cophylogeny reveals the drivers of phylogenetic congruence

This is the final version. Available on open access from Wiley via the DOI in this recordData availability statement: A copy of the source data and R code used in this study have been deposited at figshare.com: https://doi.org/10.6084/m9.figshare.14393309 This article has earned Open Data and Open Materials badges. Data and materials are available at: https://figshare.com/articles/dataset/Dataset_for_ELE_EV_ELE13757/14393309?file=27503576 and https://figshare.com/articles/dataset/Dataset_for_ELE_EV_ELE13757/14393309?file=27503579Symbioses exert substantial biological influence, with great evolutionary and ecological relevance for disease, major evolutionary transitions, and the structure and function of ecological communities. Yet, much remains unknown about the patterns and processes that characterise symbioses. A major unanswered question is the extent to which symbiont phylogenies mirror those of their hosts and if patterns differ for parasites and mutualists. Addressing this question offers fundamental insights into evolutionary processes, such as whether symbionts typically codiverge with their hosts or if diversity is generated via host switches. Here, we perform a meta-analysis of host-symbiont phylogenetic congruence, encompassing 212 host-symbiont cophylogenetic studies that include ~10,000 species. Our analysis supersedes previous qualitative assessments by utilising a quantitative framework. We show that symbiont phylogeny broadly reflects host phylogeny across biodiversity and life-history, demonstrating a general pattern of phylogenetic congruence in host-symbiont interactions. We reveal two key aspects of symbiont life-history that promote closer ties between hosts and symbionts: vertical transmission and mutualism. Mode of symbiosis and mode of transmission are intimately interlinked, but vertical transmission is the dominant factor. Given the pervasiveness of symbioses, these findings provide important insights into the processes responsible for generating and maintaining the Earth's rich biodiversity.Kungliga Fysiografiska Sällskapet i LundAustralian Research Council (ARC