Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

Quality of interhospital transport of critically ill patients: a prospective audit

INTRODUCTION: The aim of transferring a critically ill patient to the intensive care unit (ICU) of a tertiary referral centre is to improve prognosis. The transport itself must be as safe as possible and should not pose additional risks. We performed a prospective audit of the quality of interhospital transports to our university hospital-based medical ICU. METHODS: Transfers were undertaken using standard ambulances. On departure and immediately after arrival, the following data were collected: blood pressure, heart rate, body temperature, oxygen saturation, arterial blood gas analysis, serum lactic acid, plasma haemoglobin concentration, blood glucose, mechanical ventilation settings, use of vasopressor/inotropic drugs, and presence of venous and arterial catheters. Ambulance personnel completed forms describing haemodynamic and ventilatory data during transport. Data were collected by our research nurse and analyzed. RESULTS: A total of 100 consecutive transfers of ICU patients over a 14-month period were evaluated. Sixty-five per cent of patients were mechanically ventilated; 38% were on vasoactive drugs. Thirty-seven per cent exhibited an increased number of vital variables beyond predefined thresholds after transport compared with before transport; 34% had an equal number; and 29% had a lower number of vital variables beyond thresholds after transport. The distance of transport did not correlate with the condition on arrival. Six patients died within 24 hours after arrival; vital variables in these patients were not significantly different from those in patients who survived the first 24 hours. ICU mortality was 27%. Adverse events occurred in 34% of transfers; in 50% of these transports, pretransport recommendations given by the intensivist of our ICU were ignored. Approximately 30% of events may be attributed to technical problems. CONCLUSION: On aggregate, the quality of transport in our catchment area carried out using standard ambulances appeared to be satisfactory. However, examination of the data in greater detail revealed a number of preventable events. Further improvement must be achieved by better communication between referring and receiving hospitals, and by strict adherence to checklists and to published protocols. Patients transported between ICUs are still critically ill and should be treated as such

Rifampicin and clarithromycin (extended release) versus rifampicin and streptomycin for limited Buruli ulcer lesions: a randomised, open-label, non-inferiority phase 3 trial.

BACKGROUND: Buruli ulcer is a neglected tropical disease caused by Mycobacterium ulcerans infection that damages the skin and subcutis. It is most prevalent in western and central Africa and Australia. Standard antimicrobial treatment with oral rifampicin 10 mg/kg plus intramuscular streptomycin 15 mg/kg once daily for 8 weeks (RS8) is highly effective, but streptomycin injections are painful and potentially harmful. We aimed to compare the efficacy and tolerability of fully oral rifampicin 10 mg/kg plus clarithromycin 15 mg/kg extended release once daily for 8 weeks (RC8) with that of RS8 for treatment of early Buruli ulcer lesions. METHODS: We did an open-label, non-inferiority, randomised (1:1 with blocks of six), multicentre, phase 3 clinical trial comparing fully oral RC8 with RS8 in patients with early, limited Buruli ulcer lesions. There were four trial sites in hospitals in Ghana (Agogo, Tepa, Nkawie, Dunkwa) and one in Benin (Pobè). Participants were included if they were aged 5 years or older and had typical Buruli ulcer with no more than one lesion (caterories I and II) no larger than 10 cm in diameter. The trial was open label, and neither the investigators who took measurements of the lesions nor the attending doctors were masked to treatment assignment. The primary clinical endpoint was lesion healing (ie, full epithelialisation or stable scar) without recurrence at 52 weeks after start of antimicrobial therapy. The primary endpoint and safety were assessed in the intention-to-treat population. A sample size of 332 participants was calculated to detect inferiority of RC8 by a margin of 12%. This study was registered with ClinicalTrials.gov, NCT01659437. FINDINGS: Between Jan 1, 2013, and Dec 31, 2017, participants were recruited to the trial. We stopped recruitment after 310 participants. Median age of participants was 14 years (IQR 10-29) and 153 (52%) were female. 297 patients had PCR-confirmed Buruli ulcer; 151 (51%) were assigned to RS8 treatment, and 146 (49%) received oral RC8 treatment. In the RS8 group, lesions healed in 144 (95%, 95% CI 91 to 98) of 151 patients, whereas lesions healed in 140 (96%, 91 to 99) of 146 patients in the RC8 group. The difference in proportion, -0·5% (-5·2 to 4·2), was not significantly greater than zero (p=0·59), showing that RC8 treatment is non-inferior to RS8 treatment for lesion healing at 52 weeks. Treatment-related adverse events were recorded in 20 (13%) patients receiving RS8 and in nine (7%) patients receiving RC8. Most adverse events were grade 1-2, but one (1%) patient receiving RS8 developed serious ototoxicity and ended treatment after 6 weeks. No patients needed surgical resection. Four patients (two in each study group) had skin grafts. INTERPRETATION: Fully oral RC8 regimen was non-inferior to RS8 for treatment of early, limited Buruli ulcer and was associated with fewer adverse events. Therefore, we propose that fully oral RC8 should be the preferred therapy for early, limited lesions of Buruli ulcer. FUNDING: WHO with additional support from MAP International, American Leprosy Missions, Fondation Raoul Follereau France, Buruli ulcer Groningen Foundation, Sanofi-Pasteur, and BuruliVac

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Delayed tracking and inequality of opportunity: Gene-environment interactions in educational attainment

There are concerns that ability tracking at a young age increases unequal opportunities for children of different socioeconomic background to develop their potential. To disentangle family influence and potential ability, we applied moderation models to twin data on secondary educational track level from the Netherlands Twin Register (N = 8847). Delaying tracking to a later age is associated with a lower shared environmental influence and a larger genetic influence on track level in adolescence. This is in line with the idea that delaying tracking improves equality of opportunity. Our results further suggest that this is mostly because delaying tracking reduces the indirect influence of family background on track level via the test performance of students. Importantly, delaying tracking improves the realization of genetic potential especially among students with low test scores, while it lowers shared environmental influence on track level for students of all test performance levels

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Iso-osmotic regulation of nitrate accumulation in lettuce (Lactuca sativa L.)

Concerns about possible health hazards arising from human consumption of lettuce and other edible vegetable crops with high concentrations of nitrate have generated demands for a greater understanding of processes involved in its uptake and accumulation in order to devise more sustainable strategies for its control. This paper evaluates a proposed iso-osmotic mechanism for the regulation of nitrate accumulation in lettuce (Lactuca sativa L.) heads. This mechanism assumes that changes in the concentrations of nitrate and all other endogenous osmotica (including anions, cations and neutral solutes) are continually adjusted in tandem to minimise differences in osmotic potential of the shoot sap during growth, with these changes occurring independently of any variations in external water potential. The hypothesis was tested using data from six new experiments, each with a single unique treatment comprising a separate combination of light intensity, N source (nitrate with or without ammonium) and nitrate concentration carried out hydroponically in a glasshouse using a butterhead lettuce variety. Repeat measurements of plant weights and estimates of all of the main soluble constituents (nitrate, potassium, calcium, magnesium, organic anions, chloride, phosphate, sulphate and soluble carbohydrates) in the shoot sap were made at intervals from about 2 weeks after transplanting until commercial maturity, and the data used to calculate changes in average osmotic potential in the shoot. Results showed that nitrate concentrations in the sap increased when average light levels were reduced by between 30 and 49 % and (to a lesser extent) when nitrate was supplied at a supra-optimal concentration, and declined with partial replacement of nitrate by ammonium in the external nutrient supply. The associated changes in the proportions of other endogenous osmotica, in combination with the adjustment of shoot water content, maintained the total solute concentrations in shoot sap approximately constant and minimised differences in osmotic potential between treatments at each sampling date. There was, however, a gradual increase in osmotic potential (ie a decline in total solute concentration) over time largely caused by increases in shoot water content associated with the physiological and morphological development of the plants. Regression analysis using normalised data (to correct for these time trends) showed that the results were consistent with a 1:1 exchange between the concentrations of nitrate and the sum of all other endogenous osmotica throughout growth, providing evidence that an iso-osmotic mechanism (incorporating both concentration and volume regulation) was involved in controlling nitrate concentrations in the shoot

Selected Soybean Plant Introductions with Partial Resistance to \u3ci\u3eSclerotinia sclerotiorum\u3c/i\u3e

Sclerotinia stem rot, caused by Sclerotinia sclerotiorum, is a major soybean (Glycine max) disease in north-central regions of the United States and throughout the world. Current sources of resistance to Sclerotinia stem rot express partial resistance, and are limited in number within soybean germ plasm. A total of 6,520 maturity group (MG) 0 to IV plant introductions (PIs) were evaluated for Sclerotinia stem rot resistance in the United States and Canada in small plots or in the greenhouse from 1995 to 1997. Selected PIs with the most resistance were evaluated for resistance in the United States and Canada in replicated large plots from 1998 to 2000. The PIs in the MG I to III tests in Urbana, IL were evaluated for agronomic traits from 1998 to 2000. The selected PIs also were evaluated with an excised leaf inoculation and petiole inoculation technique. After the 1995 to 1997 evaluations, all but 68 PIs were eliminated because of their susceptibility to Sclerotinia stem rot. In field tests in Urbana, higher disease severity in selected MG I to III PIs was significantly (P \u3c 0.05) associated with taller plant heights and greater canopy closure. All other agronomic traits evaluated were not associated or were inconsistently associated with disease severity. MG I to III PIs 153.282, 189.931, 196.157, 398.637, 417.201, 423.818, and 561.331 had high levels of resistance and had canopies similar to the resistant checks. The resistance ratings from the petiole inoculation technique had a high and significant (P \u3c 0.01) correlation with disease severity in the MG I and II field tests. The partially resistant PIs identified in this study can be valuable in incorporating Sclerotinia stem rot resistance into elite germ plasm

Histopathologic Features of Mycobacterium ulcerans Infection

Because of the emergence of Buruli ulcer disease, the World Health Organization launched a Global Buruli Ulcer Initiative in 1998. This indolent skin infection is caused by Mycobacterium ulcerans. During a study of risk factors for the disease in Ghana, adequate excisional skin-biopsy specimens were obtained from 124 clinically suspicious lesions. Buruli ulcer disease was diagnosed in 78 lesions since acid-fast bacilli (AFB) were found by histopathologic examination. Lesions with other diagnoses included filariasis (3 cases), zygomycosis (2 cases), ulcerative squamous cell carcinomas (2 cases), keratin cyst (1 case), and lymph node (1 case). Thirty-seven specimens that did not show AFB were considered suspected Buruli ulcer disease cases. Necrosis of subcutaneous tissues and dermal collagen were found more frequently in AFB-positive specimens compared with specimens from suspected case-patients (p<0.001). Defining histologic criteria for a diagnosis of Buruli ulcer disease is of clinical and public health importance since it would allow earlier treatment, leading to less deforming sequelae

Hyperglycemia Activates Caspase-1 and TXNIP-Mediated IL-1β Transcription in Human Adipose Tissue

Contains fulltext : 96993.pdf (publisher's version ) (Closed access)OBJECTIVE: Obesity is characterized by elevated levels of proinflammatory cytokines, including interleukin (IL)-1beta, that contribute to the development of insulin resistance. In this study, we set out to investigate whether hyperglycemia drives IL-1beta production and caspase-1 activation in murine and human adipose tissue, thus inducing insulin resistance. RESEARCH DESIGN AND METHODS: ob/ob animals were used as a model to study obesity and hyperglycemia. Human adipose tissue fragments or adipocytes were cultured in medium containing normal or high glucose levels. Additionally, the role of thioredoxin interacting protein (TXNIP) in glucose-induced IL-1beta production was assessed. RESULTS: TXNIP and caspase-1 protein levels were more abundantly expressed in adipose tissue of hyperglycemic ob/ob animals as compared with wild-type mice. In human adipose tissue, high glucose resulted in a 10-fold upregulation of TXNIP gene expression levels (P < 0.01) and a 10% elevation of caspase-1 activity (P < 0.05), together with induction of IL-1beta transcription (twofold, P < 0.01) and a significant increase in IL-1beta secretion. TXNIP suppression in human adipocytes, either by a small interfering RNA approach or a peroxisome proliferator-activated receptor-gamma agonist, counteracted the effects of high glucose on bioactive IL-1 production (P < 0.01) mainly through a decrease in transcription levels paralleled by reduced intracellular pro-IL-1beta levels. CONCLUSIONS: High glucose activates caspase-1 in human and murine adipose tissue. Glucose-induced activation of TXNIP mediates IL-1beta mRNA expression levels and intracellular pro-IL-1beta accumulation in adipose tissue. The concerted actions lead to enhanced secretion of IL-1beta in adipose tissue that may contribute to the development of insulin resistance