The jumping champion conjecture

An integer $d$ is called a jumping champion for a given $x$ if $d$ is the most common gap between consecutive primes up to $x$. Occasionally several gaps are equally common. Hence, there can be more than one jumping champion for the same $x$. For the $n$th prime $p_{n}$, the $n$th primorial $p_{n}^{\sharp}$ is defined as the product of the first $n$ primes. In 1999, Odlyzko, Rubinstein and Wolf provided convincing heuristics and empirical evidence for the truth of the hypothesis that the jumping champions greater than 1 are 4 and the primorials $p_{1}^{\sharp}, p_{2}^{\sharp}, p_{3}^{\sharp}, p_{4}^{\sharp}, p_{5}^{\sharp}, ...$, that is, $2, 6, 30, 210, 2310, ....$ In this paper, we prove that an appropriate form of the Hardy-Littlewood prime $k$-tuple conjecture for prime pairs and prime triples implies that all sufficiently large jumping champions are primorials and that all sufficiently large primorials are jumping champions over a long range of $x$.Comment: 19 pages, 1 tabl

Comparing the dynamic flow properties and compaction properties of pharmaceutical powder mixtures

The dynamic flow properties and compaction characteristics of mannitol and mannitol-sodium carbonate mixtures (80/20, 70/30 and 60/40 by mass) were measured using a Freeman FT4 powder rheometer. The results showed that the mixtures containing up to 30% sodium carbonate had better flow properties and improved compaction characteristics when compared with mannitol alone. The study demonstrated the feasibility of combining a more expensive pharmaceutical excipient with a cheaper ingredient, without compromising desired powder characteristics. It may also provide a useful method for assessing the suitability of new formulations for use as direct compression bases, as part of a wider range of powder flow tests

Spray dried combinations of lactoferrin with antibiotics appear superior to monotherapy for reducing biofilm formation by pseudomonas aeruginosa

SD Apo Lactoferrin-Tobramycin/Gentamicin Combinations are superior to monotherapy in the eradication of Pseudomonas aeruginosa Biofilm in the lungs Wilson Oguejiofor1, Lindsay J. Marshall1, Andrew J. Ingham1, Robert Price2, Jag. Shur2 1School of Life and Health Sciences, Aston University, Birmingham, UK. 2School of Pharmacy and Pharmacology, University of Bath, Bath, UK. KEYWORDS: lactoferrin, apo lactoferrin, spray drying, biofilm, cystic fibrosis Introduction Chronic lung infections from the opportunistic pathogeen Pseudomonas aeruginosa has been recognised as a major contributor to the incidences of high morbidity and mortality amongst cystic fibrosis (CF) patients (1,2). Currently, strategies for managing lung infections in CF patients involves the aggressive use of aerosolised antibiotics (3), however, increasing evidence suggests that the biofilm component of P. aeruginosa in the lower airway remains unperturbed and is associated with the development of antibiotic resistance. If this is so then, there is an urgent need to suitably adjust the current treatment strategy so that it includes compounds that prevent biofilm formation or disrupt established biofilms. It is well understood that biofilm formation is strongly dependent on iron (Fe3+) availability (4), therefore aerosolised anti-infective formulations which has the ability to chelate iron may essentially be a well suited therapy for eliminating P. aeruginosa biofilms on CF airway epithelial cells (5). In this study, we report the use of combination therapy; an aminoglycosides (tobramycin and gentamicin) and an antimicrobial peptide (lactoferrin) to significantly deplete P. aeruginosa biofilms. We demonstrate that lactoferrin-tobramycin and lactoferrin-gentamicin combinations are superior to the single antibiotic regime currently being employed to combat P. aeruginosa biofilms. MATERIALS AND METHOD Antibiotics: The antibiotics used in this study included gentamicin and tobramycin supplied by Fagron, UK. Bacterial strain and growth conditions: Pseudomonas aeruginosa strain PAO1 was provided by Prof. Peter Lambert of Aston University, Birmingham UK. The Strains were routinely grown from storage in a medium supplemented with magnesium chloride, glucose and casamino acids. Dialysis of lactoferrin: Apo lactoferrin was prepared by dialyzing a suspension of lactoferrin for 24 hrs at 4 °C against 20 mmol/L sodium dihydrogen phosphate, 20 mmol/L sodium acetate and 40 mmol/L EDTA (pH 3.5). Ferric ion (Fe3+) removal was verified by atomic absorption spectroscopy measurements. Spray drying of combinations of lactoferrin and apo lactoferrin with the different aminoglycosides: Combinations of tobramycin and gentamicin with the different preparations of lactoferrin were spray dried (SD) as a 2% (w/v) aqueous suspension. The spray drying parameters utilized for the production of suitable micron-sized particles includes: Inlet temperature, 180°C, spray flow rate, 606 L/hr; pump setting, 10%; aspirator setting, 85% (34m3/hr) to produce various outlet temperatures ranging from 99 - 106°C. Viability assay: To test the bactericidal activity of the various combinations, a viability assay was performed as previously described by Xu, Xiong et al. (6) with some modifications. Briefly, 10µL of ~ c. 6.6 x 107 CFU mL-1 P. aeruginosa strain PAO1 suspension were incubated (37°C, 60 mins) with 90 µL of a 2 µg/mL concentration of the various combinations and sampled every 10 mins. After incubation, the cells were diluted in deionised water and plated in Mueller hinton agar plates. Following 24 h incubation of the plates at 37°C, the percentage of viable cells was determined relative to incubation without added antibiotics. Biofilm assay: To test the susceptibility of the P. aeruginosa strain to various antibiotics in the biofilms mode of growth, overnight cultures of P. aeruginosa were diluted 1:100 into fresh medium supplemented with magnesium chloride, glucose and casamino acids. Aliquots of the dilution were dispensed into a 96 well dish and incubated (37°C, 24 h). Excess broth was removed and the number of colony forming units per milliliter (CFU/mL) of the planktonic bacteria was quantified. The biofilms were then washed and stained with 0.1% (w/v) crystal violet for 15 mins at room temperature. Following vigorous washing with water, the stained biofilms were solubilized in 30% acetic acid and the absorbance at 550nm of a 125 µL aliquot was determined in a microplate reader (Multiskan spectrum, Thermo Scientific) using 30% acetic acid in water as the blank. Aliquots of the broth prior to staining were used as an indicator of the level of planktonic growth. RESULTS AND DISCUSSION Following spray drying, the mean yield, volume weighted mean diameter and moisture content of lactoferrin powder were measured and were as follows (Table 1 and table 2); Table 1: Spray drying parameters FormulationInlet temp (°C)Outlet temp (°C)Airflow rate (L/hr)Mean yield (%)Moisture content (%) SD Lactoferrin18099 - 10060645.2 ±2.75.9 ±0.4 SD Apo Lactoferrin180100 - 10260657.8 ±1.85.7 ±0.2 Tobramycin180102 - 10460682.1 ±2.23.2 ±0.4 Lactoferrin + Tobramycin180104 - 10660687.5 ±1.43.7 ±0.2 Apo Lactoferrin + Tobramycin180103 - 10460676.3 ±2.43.3 ±0.5 Gentamicin18099 - 10260685.4 ±1.34.0 ±0.2 Lactoferrin + Gentamicin180102 - 10460687.3 ±2.13.9 ±0.3 Apo Lactoferrin + Gentamicin18099 -10360680.1±1.93.4 ±0.4 Table 2: Particle size distribution d10 d50d90 SD Lactoferrin1.384.9111.08 SD Apo Lactoferrin1.284.7911.04 SD Tobramycin1.254.9011.29 SD Lactoferrin + Tobramycin1.175.2715.23 SD Apo Lactoferrin + Tobramycin1.115.0614.31 SD Gentamicin1.406.0614.38 SD Lactoferrin + Gentamicin1.476.2314.41 SD Apo Lactoferrin + Gentamicin1.465.1511.53 The bactericidal activity of the various combinations were tested against P. aeruginosa PAO1 following a 60 minute incubation period (Figure 1 and Figure 2). While 2 µg/mL of a 1:1 combination of spray dried apo lactoferrin and Gentamicin was able to completely kill all bacterial cells within 40 mins, the same concentration was not as effective for the other antibiotic combinations. However, there was an overall reduction of bacterial cells by over 3 log units by the other combinations within 60 mins. Figure 1: Logarithmic plot of bacterial cell viability of various combinations of tobramycin and lactoferrin preparations at 2µg/mL (n = 3). Figure 2: Logarithmic plot of bacterial cell viability of various combinations of gentamicin and lactoferrin preparations at 2µg/mL (n = 3). Crystal violet staining showed that biofilm formation by P. aeruginosa PAO1 was significantly (ANOVA, p < 0.05) inhibited in the presence of the different lactoferrin preparations. Interestingly, apo lactoferrin and spray dried lactoferrin exhibited greater inhibition of both biofilm formation and biofilm persistence (Figure 2). Figure 2: Crystal violet staining of residual biofilms of P. aeruginosa following a 24hr incubation with the various combinations of antibiotics and an exposure to 48 hr formed biofilms. CONCLUSION In conclusion, combination therapy comprising of an antimicrobial peptide (lactoferrin) and an aminoglycosides (tobramycin or gentamicin) provides a feasible and alternative approach to monotherapy since the various combinations are more efficient than the respective monotherapy in the eradication of both planktonic and biofilms of P. aeruginosa. ACKNOWLEDGEMENT The authors would like to thank Mr. John Swarbrick and Friesland Campina for their generous donation of the Lactoferrin. REFERENCES 1.Hassett, D.J., Sutton, M.D., Schurr, M.J., Herr, A.B., Caldwell, C.C. and Matu, J.O. (2009), "Pseudomonas aeruginosa hypoxic or anaerobic biofilm infections within cystic fibrosis airways". Trends in Microbiology, 17, 130-138. 2.Trust, C.F. (2009), "Antibiotic treatment for cystic fibrosis". Report of the UK Cystic Fibrosis Trust Antibiotic Working Group. Consensus document. London: Cystic Fibrosis Trust. 3.Garcia-Contreras, L. and Hickey, A.J. (2002), "Pharmaceutical and biotechnological aerosols for cystic fibrosis therapy". Advanced Drug Delivery Reviews, 54, 1491-1504. 4.O'May, C.Y., Sanderson, K., Roddam, L.F., Kirov, S.M. and Reid, D.W. (2009), "Iron-binding compounds impair Pseudomonas aeruginosa biofilm formation, especially under anaerobic conditions". J Med Microbiol, 58, 765-773. 5.Reid, D.W., Carroll, V., O'May, C., Champion, A. and Kirov, S.M. (2007), "Increased airway iron as a potential factor in the persistence of Pseudomonas aeruginosa infection in cystic fibrosis". European Respiratory Journal, 30, 286-292. 6.Xu, G., Xiong, W., Hu, Q., Zuo, P., Shao, B., Lan, F., Lu, X., Xu, Y. and Xiong, S. (2010), "Lactoferrin-derived peptides and Lactoferricin chimera inhibit virulence factor production and biofilm formation in Pseudomonas aeruginosa". J Appl Microbiol, 109, 1311-1318

Measuring the flow properties of small powder samples using an avalanche tester

The feasibility of using a small-scale avalanche tester to measure the flow properties of pharmaceutical lactose powders was examined. The modes of behavior observed in larger systems were displayed and showed a clear distinction between angular, free-flowing particles and more spherical particles of similar flow characteristics. Angular Lactohale LH100 particles showed slumping behavior at a rotational frequency of 0.33 Hz that disappeared at higher frequencies. Spherical lactose powder with a similar flow function to LH100 only showed rolling behavior under the same conditions, as did more cohesive powders LH200 and LH300. Further investigation of the LH100 data using fast Fourier analysis showed that the slumping frequency was one tenth of the rotational frequency

The efficacy of downhill running as a method to enhance running economy in trained distance runners

© 2018 European College of Sport Science Running downhill, in comparison to running on the flat, appears to involve an exaggerated stretch-shortening cycle (SSC) due to greater impact loads and higher vertical velocity on landing, whilst also incurring a lower metabolic cost. Therefore, downhill running could facilitate higher volumes of training at higher speeds whilst performing an exaggerated SSC, potentially inducing favourable adaptations in running mechanics and running economy (RE). This investigation assessed the efficacy of a supplementary 8-week programme of downhill running as a means of enhancing RE in well-trained distance runners. Nineteen athletes completed supplementary downhill (−5% gradient; n = 10) or flat (n = 9) run training twice a week for 8 weeks within their habitual training. Participants trained at a standardised intensity based on the velocity of lactate turnpoint (vLTP), with training volume increased incrementally between weeks. Changes in energy cost of running (E C ) and vLTP were assessed on both flat and downhill gradients, in addition to maximal oxygen uptake (⩒O 2max). No changes in E C were observed during flat running following downhill (1.22 ± 0.09 vs 1.20 ± 0.07 Kcal kg −1  km −1 , P = .41) or flat run training (1.21 ± 0.13 vs 1.19 ± 0.12 Kcal kg −1  km −1 ). Moreover, no changes in E C during downhill running were observed in either condition (P  >  .23). vLTP increased following both downhill (16.5 ± 0.7 vs 16.9 ± 0.6 km h −1 ,P = .05) and flat run training (16.9 ± 0.7 vs 17.2 ± 1.0 km h −1 , P = .05), though no differences in responses were observed between groups (P = .53). Therefore, a short programme of supplementary downhill run training does not appear to enhance RE in already well-trained individuals

A case-study investigating the physicochemical characteristics that dictate the function of a liposomal adjuvant

A range of particulate delivery systems have been considered as vaccine adjuvants. Of these systems, liposomes offer a range of advantages including versatility and flexibility in design format and their ability to incorporate a range of immunomodulators and antigens. Here we briefly outline research, from within our laboratories, which focused on the systematic evaluation of cationic liposomes as vaccines adjuvants. Our aim was to identify physicochemical characteristics that correlate with vaccine efficacy, with particular consideration of the interlink between depot-forming action and immune responses. A variety of parameters were investigated and over a range of studies we have confirmed that cationic liposomes, based on dimethyldioctadecylammonium bromide and trehalose 6,6'-dibehenate formed a depot at the injection site, which stimulates recruitment of antigen presenting cells to the injection site and promotes strong humoral and cell-mediated immune responses. Physicochemical factors which promote a strong vaccine depot include the combination of a high cationic charge and electrostatic binding of the antigen to the liposome system and the use of lipids with high transition temperatures, which form rigid bilayer vesicles. Reduction in vesicle size of cationic vesicles did not promote enhanced drainage from the injection site. However, reducing the cationic nature through substitution of the cationic lipid for a neutral lipid, or by masking of the charge using PEGylation, resulted in a reduced depot formation and reduced Th1-type immune responses, while Th2-type responses were less influenced. These studies confirm that the physicochemical characteristics of particulate-based adjuvants play a key role in the modulation of immune responses

A qualitative study of prescription contraception use: the perspectives of users, general practitioners and pharmacists

Background: The oral contraceptive pill (OCP) remains the most popular form of prescription contraception in many countries, despite adherence difficulties for many. Uptake of long acting reversible contraceptives (LARCs), which are less reliant on user adherence, remains low. The aim of this study was to explore the experiences of, and attitudes towards, prescription contraception amongst samples of contraception users, general practitioners (GPs) and pharmacists.Methodology and Finding: We conducted a qualitative study using semi-structured interviews with 18 contraception users, 18 GPs and 9 pharmacists. The study took place in Galway, Republic of Ireland between June and September 2014. Thematic analysis was used to analyse the data. Overall, contraception users were more familiar with the OCP, and all the women interviewed began their prescription contraception journey using this method. All participants identified episodes of poor adherence throughout the reproductive life course. The identified barriers for use of LARCs were lack of information, misconceptions, lack of access and high cost. In contrast, GPs believed that adherence to the OCP was good and stated they were more likely to prescribe the OCP than other methods, as they were most familiar with this option.Barriers to prescribing LARCs were time, cost to practice, training and deskilling. Pharmacists also believed that adherence to the OCP was generally good and that their role was limited to dispensing medication and providing information when asked.Discussion and Conclusion: There are contrasting perspectives between contraception service providers and contraceptive users. Training for healthcare providers is required to support informed contraceptive choice and adherence. It is necessary to address the practice barriers of cost and lack of time, to promote better communication around adherence issues and prescription contraception options. There is a need for more easily-accessible public health information to promote awareness on all methods of prescription contraception.<br/

Acute effects of Vitamin D3 supplementation on muscle strength in Judoka athletes: a randomized placebo-controlled, double-blind trial

Objective: Indoor athletes have been shown to be prone to vitamin D3 deficiency. The aim of the study was to examine the acute effects of vitamin D supplementation on muscle function using isokinetic dynamometry. Design: Randomized placebo-controlled, double-blind study. Setting: Institutional. Participants: Adult male white national level judoka athletes (n = 22) who were involved in full-time training. Exclusion criteria were vitamin supplementation, overseas travel to sunny climes, and/or an injury incurred during the last 3 months before testing. Interventions: Subjects were randomly allocated to the treatment (150 000IU vitamin D3) or placebo and given blinded supplements by an independent researcher. Participants were tested twice, 8 days apart, on a Monday morning before the start of judo training and after 2 days of rest. A 5 to 7 mL of blood sample was collected followed by isokinetic concentric quadriceps and hamstring muscle function assessments on the right leg at 30 and 200°·s. Main outcome measures: Repeated-measures analysis of variance was used to analyze isokinetic muscle force and serum 25(OH)D3. Regression to the mean was used to examine changes in 25(OH)D3 levels over the study period. Results: The treatment group demonstrated a significant increase in serum 25(OH)D levels (34%, P ≤ 0.001) and muscle strength (13%, P = 0.01) between days 1 and 8. No significant differences were found for the placebo group for the same period. Conclusions: A single bolus of 150 000IU vitamin D3 had a significant positive effect on serum 25(OH)D levels and muscle function in vitamin D insufficient elite indoor athletes. Clinical relevance: Serum 25(OH)D3 levels of indoor athletes should be monitored throughout the year and especially during winter months. Beneficial responses, in muscle strength and serum 25(OH)D3, to 1 dose of vitamin D3 supplementation can be observed within 1 week of ingestion. Muscle strength is linked to serum 25(OH)D levels. Acute Effects of Vitamin D3 Supplementation on Muscle Strength in Judoka Athletes: A Randomized Placebo-Controlled, Double-Blind Trial (PDF Download Available). Available from: https://www.researchgate.net/publication/283499805_Acute_Effects_of_Vitamin_D3_Supplementation_on_Muscle_Strength_in_Judoka_Athletes_A_Randomized_Placebo-Controlled_Double-Blind_Trial [accessed May 10, 2016]

Articulatory Rate and Stuttering

The effect of speech rate on stuttering frequency was investigated with 20 stutterers. Subjects read two different 300 syllable passages at a normal and fast speech rate. Stuttering counts and articulatory rate was determined for each speech sample. Articulatory rates were derived from portions of the passages which were perceptually fluent. No statistically significant difference in stuttering frequency was found between the two speech rate conditions (p = .16) while a significant difference was observed for articulatory rate (p = .0007). These findings suggest that increased articulatory rate does not determine stuttering frequency with the same consistency as does decreased articulatory rate. It was concluded that a single explanation of the relationship between speech rate and stuttering frequency in terms of speech timing complexity is inadequate

The HERO review: harnessing efficiencies, rethinking outcomes: the future of the defence estate

The HERO review: harnessing efficiencies, rethinking outcomes: the future of the defence estat