The Euclid-Mullin graph

We introduce the Euclid-Mullin graph, which encodes all instances of Euclid's proof of the infinitude of primes. We investigate structural properties of the graph both theoretically and numerically; in particular, we prove that it is not a tree.Comment: 24 pages, 2 figures, to appear in Journal of Number Theor

A 42-Letter Pangrammatic Window

A pangrammatic window is a block of text containing each letter of the alphabet exactly once

Disjoint Word Chains

The purpose of this note is to investigate the longest disjoint word chains for various other sets of words and to explain the computer-assisted solution of such problems

Jumble Java Byte Code to Measure the Effectiveness of Unit Tests

Jumble is a byte code level mutation testing tool for Java which inter-operates with JUnit. It has been designed to operate in an industrial setting with large projects. Heuristics have been included to speed the checking of mutations, for example, noting which test fails for each mutation and running this first in subsequent mutation checks. Significant effort has been put into ensuring that it can test code which uses custom class loading and reflection. This requires careful attention to class path handling and coexistence with foreign class-loaders. Jumble is currently used on a continuous basis within an agile programming environment with approximately 370,000 lines of Java code under source control. This checks out project code every fifteen minutes and runs an incremental set of unit tests and mutation tests for modified classes. Jumble is being made available as open source

cis-2,6-Dibenzyl­cyclo­hexa­none

In the title compound, C20H22O, the mol­ecule is a meso isomer with the two benzyl groups cis to each other. The central cyclo­hexa­none ring adopts a chair conformation. The mol­ecule lies on a noncrystallographic mirror plane and the dihedral angles of the benzyl groups with respect to the ketone moiety are 88.06 (6) and 89.07 (6)°

Clinically relevant enhancement of human sperm motility using compounds with reported phosphodiesterase inhibitor activity

STUDY QUESTION: Can we identify compound(s) with reported phosphodiesterase inhibitor (PDEI) activity that could be added to human spermatozoa in vitro to enhance their motility without compromising other sperm functions? SUMMARY ANSWER: We have identified several compounds that produce robust and effective stimulation of sperm motility and, importantly, have a positive response on patient samples. WHAT IS KNOWN ALREADY: For >20 years, the use of non-selective PDEIs, such as pentoxifylline, has been known to influence the motility of human spermatozoa; however, conflicting results have been obtained. It is now clear that human sperm express several different phosphodiesterases and these are compartmentalized at different regions of the cells. By using type-specific PDEIs, differential modulation of sperm motility may be achieved without adversely affecting other functions such as the acrosome reaction (AR). STUDY DESIGN, SIZE, DURATION: This was a basic medical research study examining sperm samples from normozoospermic donors and subfertile patients attending the Assisted Conception Unit (ACU), Ninewells Hospital Dundee for diagnostic semen analysis, IVF and ICSI. Phase 1 screened 43 commercially available compounds with reported PDEI activity to identify lead compounds that stimulate sperm motility. Samples were exposed (20 min) to three concentrations (1, 10 and 100 µM) of compound, and selected candidates (n = 6) progressed to Phase 2, which provided a more comprehensive assessment using a battery of in vitro sperm function tests.  PARTICIPANTS/MATERIALS, SETTING, METHODS: All healthy donors and subfertile patients were recruited at the Medical Research Institute, University of Dundee and ACU, Ninewells Hospital Dundee (ethical approval 08/S1402/6). In Phase 1, poor motility cells recovered from the 40% interface of the discontinuous density gradient were used as surrogates for patient samples. Pooled samples from three to four different donors were utilized in order to reduce variability and increase the number of cells available for simultaneous examination of multiple compounds. During Phase 2 testing, semen samples from 23 patients attending for either routine diagnostic andrology assessment or IVF/ICSI were prepared and exposed to selected compounds. Additionally, 48 aliquots of prepared samples, surplus to clinical use, were examined from IVF (n = 32) and ICSI (n = 16) patients to further determine the effects of selected compounds under clinical conditions of treatment. Effects of compounds on sperm motility were assessed by computer-assisted sperm analysis. A modified Kremer test using methyl cellulose was used to assess sperm functional ability to penetrate into viscous media. Sperm acrosome integrity and induction of apoptosis were assessed using the acrosomal content marker PSA-FITC and annexin V kit, respectively. MAIN RESULTS AND THE ROLE OF CHANCE: In Phase 1, six compounds were found to have a strong effect on poor motility samples with a magnitude of response of ≥60% increase in percentage total motility. Under capacitating and non-capacitating conditions, these compounds significantly (P ≤ 0.05) increased the percentage of total and progressive motility. Furthermore, these compounds enhanced penetration into a cervical mucus substitute (P ≤ 0.05). Finally, the AR was not significantly induced and these compounds did not significantly increase the externalization of phosphatidylserine (P = 0.6, respectively). In general, the six compounds maintained the stimulation of motility over long periods of time (180 min) and their effects were still observed after their removal. In examinations of clinical samples, there was a general observation of a more significant stimulation of sperm motility in samples with lower baseline motility. In ICSI samples, compounds #26, #37 and #38 were the most effective at significantly increasing total motility (88, 81 and 79% of samples, respectively) and progressive motility (94, 93 and 81% of samples, respectively). In conclusion, using a two-phased drug discovery screening approach including the examination of clinical samples, 3/43 compounds were identified as promising candidates for further study. LIMITATIONS, REASONS FOR CAUTION: This is an in vitro study and caution must be taken when extrapolating the results. Data for patients were from one assessment and thus the robustness of responses needs to be established. The n values for ICSI samples were relatively small. WIDER IMPLICATIONS OF THE FINDINGS: We have systematically screened and identified several compounds that have robust and effective stimulation (i.e. functional significance with longevity and no toxicity) of total and progressive motility under clinical conditions of treatment. These compounds could be clinical candidates with possibilities in terms of assisted reproductive technology options for current or future patients affected by asthenozoospermia or oligoasthenozoospermia

Use of genome sequencing to investigate the molecular basis of bacteriaphage interaction of the Escherichia coli O157 typing phages and the elucidation of the biological and public health significance of phage type

Background Shiga toxin producing Escherichia coli (STEC) O157 causes severe gastrointestinal disease and haemolytic uremic syndrome, and has a major impact on public health worldwide with regular outbreaks and sporadic infection. Phage typing, i.e. the susceptibility of STEC O157 strains to a bank of 16 bacteriophages, has been used in the UK to differentiate STEC O157 for the past 25 years and the phage type (PT) can be an epidemiological marker of strains associated with severe disease or associated with cases that occur from foreign travel. However, little is known about the molecular interactions between the typing phages (TP) and STEC O157. The aims of this thesis were to use whole genome sequencing to elucidate the genetic basis for phage typing of STEC O157 and through this understand genetic differences between strains relevant to disease severity and epidemiology. Results Sequencing the STEC O157 TPs revealed that they were clustered into 4 groups based on sequence similarity that corresponded with their infectivity. Long read sequencing revealed microevolutionary events occuring in STEC O157 genomes over a short time period (approximately 1 year), evidenced by the loss and gain of prophage regions and plasmids. An IncHI2 plasmid was found responsible for a change in Phage Type (PT) from PT8 to PT54 during two related outbreaks at the same restaurant. These changes resulted in a strain (PT54) that was fitter under certain growth conditions and associated with a much larger outbreak (140 as opposed to 4 cases). TraDIS (Transposon directed Insertion site sequencing) was used to identify 114 genes associated with phage sensitivity and 44 genes involved in phage resistance, emphasising the complex nature of identifying specific genetic markers of phage susceptibility or resistance. Further work is required to prove their phage-related functions but several are likely to encode novel phage receptors. Deletion of a Stx2a prophage from a PT21/28 strain led to a strain that typed as PT32, supporting the concept that the highly pathogenic PT21/28 lineage I strains emerged from Stx2c+ PT32 strains in the last two decades by acquisition of Stx2a-encoding prophages. Conclusions This body of work has highlighted the complexity of bacteriophage interaction and investigated the genetic basis for susceptibility and resistance in E. coli. The grouping of the TPs showed that resistance or susceptibility to all members of a typing group was likely to be caused by one mechanism. IncHI2 was identified as one of the markers for the PT54 phenotype. The Stx2a prophage region was associated with the switch from PT32 to PT21/28, although PT32 strains containing both Stx2a and Stx2c-encoding prophages have been isolated and can provide insights into phage variation underpinning the susceptibility to the relevant typing phages. The TraDIS results indicated that susceptibility or resistance was governed by multiple genetic factors and not controlled by a single gene. The significance of LPS for initial protection from phage adsorption was evident and a number of novel genes controlling phage susceptibility and resistance identified including the Sap operon and stringent starvation protein A respectively. While SNP-based typing provides an excellent indication of the evolution and relatedness of strains, phage typing can provide real insights into short term evolution of the bacteria as PTs can be altered by mobile elements such as prophages and plasmids. This study has shown that, although complex, genetic determinants for PT can be mined from the genome and allow us to understand the evolution of this zoonotic pathogen between host species and during outbreaks

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy