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In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on nonholomorphic generating series. We establish a divisibility result for such nonholomorphic congruences of Hurwitz class numbers. The two key tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences., Competing Interests: The authors declare no competing interest.

The adhesion strength of a contact between a rotationally symmetric indenter and an elastic half-space is analysed analytically and numerically using an extension of the method of dimensionality reduction for superimposed normal/tangential adhesive contacts. In particular, the dependence of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The fracture criterion used coincides with that suggested by Johnson. In this paper, it is used to develop a method that is applicable straightforwardly to adhesive contacts of arbitrary bodies of revolution with compact contact area., Competing Interests: We declare we have no competing interests.

Previous research demonstrated that arrays of vertically aligned carbon nanotubes (VACNTs) exhibit strong frictional properties. Experiments indicated a strong decrease of the friction coefficient from the first to the second sliding cycle in repetitive measurements on the same VACNT spot, but stable values in consecutive cycles. VACNTs form clusters under shear applied during friction tests, and self-organization stabilizes the mechanical properties of the arrays. With increasing load in the range between 300 µN and 4 mN applied normally to the array surface during friction tests the size of the clusters increases, while the coefficient of friction decreases. To better understand the experimentally obtained results, we formulated and numerically studied a minimalistic model, which reproduces the main features of the system with a minimum of adjustable parameters. We calculate the van der Waals forces between the spherical friction probe and bunches of the arrays using the well-known Morse potential function to predict the number of clusters, their size, instantaneous and mean friction forces and the behaviour of the VACNTs during consecutive sliding cycles and at different normal loads. The data obtained by the model calculations coincide very well with the experimental data and can help in adapting VACNT arrays for biomimetic applications.

Microstructures responsible for temporary arresting of contacting surfaces are widely distributed on surfaces in different organisms. Recent morphological studies show that these structures have different density of outgrowths and not ideal distribution pattern on both complementary parts of the contact. One can suggest that this difference is optimized by natural selection to get stronger mechanical arrest within the system. In this paper, we simulate such a system numerically, both in the frames of continuous contact and discrete dynamical models to prove this hypothesis and elucidate other aspects of optimization of such mechanical adhesive systems., (© 2014 The Author(s) Published by the Royal Society. All rights reserved.)

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock theta functions.

Hemorrhagic shock results in inadequate tissue oxygenation. Plasma lactate (L) can characterize the degree of systemic oxygen debt (OD), but gives no information on local changes. The aim of this study was to characterize different degrees of hemorrhagic shock by microdialysis measurement of L and histamine (H) in small bowel circulation. Thirty-eight pigs were randomized to five groups of increasing OD (< 50 --> 120 ml/kg). The OD was accrued by hemorrhage over 60 min and was followed by retransfusion and observation for 3 days. In parallel to plasma probes, subserosa(ss)-, submucosa(sm)-, and intraluminal(il)-L- and H-probes were obtained by small bowel microdialysis every 30 min for 210 min. Ss- and sm-L increased during hemorrhage from 1.2 +/- 0.06 and 1.18 +/- 0.06 to 2.57 +/- 0.15 and 2.96 +/- 0.27 mmol/L. Highest mean L > 3.5mmol/L resulted 90 and 120 min after induction of hemorrhage. Although ss- and sm- levels hardly differed, il-L was significantly decreased with 0.27 +/- 0.02 mmol/L at 0 min and highest mean il-L at 120 min: 2.45 +/- 0.51 mmol/L. Sm-L was significantly increased after 60, 90, 120, and 150 min of highest hemorrhage severity (OD > 100 mL/kg). In parallel, systemic L increased significantly during hemorrhage and correlated well with the severity of shock. Although systemic H increased significantly during hemorrhage (from 1.3 +/- 0.31 to 15.2 +/- 0.67 ng/mL), H-dialysates showed no effect either over time nor with the degree of hemorrhage. In conclusion, microdialysis allows evaluation of local L changes in small bowel circulation in pig hemorrhagic shock. Sm-L levels appear to correlate with the degree of shock. Local H changes were not observed during hemorrhagic shock in this study.

"Uncontrolled bleeding," "a controlled prefixed bleeding volume," or "controlled decrements in blood pressure" are traditional models of experimental hemorrhagic shock. They are influenced by compensatory mechanisms and do not adequately reflect the severity of the cellular insult as a major target for therapeutic strategies. The aim of this study was to develop an animal model that uses oxygen debt (OD) and metabolic acidemia as indicators of hemorrhage severity. Twenty-five female pigs (mean weight: 23.8 kg) were anesthesized and randomized to 1 of 5 groups of increasing OD (<50 through >120 mL/kg). The predetermined OD was accrued by hemorrhage uniformly over 60 min and followed by retransfusion. The animals were allowed to recover under anesthesia for 200 min and were then observed for 3 days. The extent of metabolic derangements were quantified by arterial base excess (BE) and plasma lactate (LAC) measurements. OD, BE, and LAC were shown to be superior as predictors of outcome in comparison with traditional variables ("bleeding volume," "blood pressure," "cardiac output") in correlation and regression. Of the analyzed predictors of outcome, BE and LAC showed the highest correlation to levels of OD (r = -0.78, 0.8 respectively; P < 0.0001), and regression models were developed. The LD50 for OD was 95.0 mL/kg, for BE -15.3 mmol/L and for LAC 7.7 mmol/L. By using the developed regression models, it is possible to estimate accurately the actual level of OD from BE and LAC values obtained during hemorrhagic shock. OD, BE, and LAC appear to be optimal indicators of severity for a pig hemorrhagic shock model.

This prospective, multi-center, observational study of 2069 multiple trauma patients evaluated the prognostic significance of the posttrauma base deficit (BD) on hospital and intensive care unit (ICU) admission to hemodynamic changes, volume and transfusion requirements, lactate and coagulation, as well as mortality. Furthermore, the importance of the BD development throughout a patient's course of critical illness from the time of injury to ICU admission is analyzed as a prognostic factor for fatal outcome. The data were obtained by the trauma registry of the 'Deutsche Gesellschaft für Unfallchirurgie.' The patients were subdivided into five categories of increasing BD values on hospital and ICU admission: Category I, BD < or = -2; Category II, -2 < BD < or = 2; Category III, 2 < BD < or = 6; Category IV, 6 < BD < or = 10; and Category V, BD > 10. A statistical analysis was performed by means of the ANOVA and chi-square tests. In 1264 (61.1%) of 2069 multiple trauma patients (age 39 +/- 19 years, 70.0% males, injury severity score 22 +/- 13, 18.6% mortality), the BD was documented on hospital and in 1536 (74.2%) patients on ICU admission. At both points in time, an increase in the BD category was associated with a significant decrease in systolic blood pressure and prothrombin time as well as increases in heart rate, lactate level and mortality (P < 0.0001). Also transfusion requirements (Category I: 4.5 +/- 7.7 and Category V: 13.7 +/- 13.0 packed red blood cells) increased significantly on hospital admission (P < 0.0001) with a worsening in the BD category. Mortality increased significantly (P < 0.0001) with a worsening of BD from hospital to ICU admission (from a mortality of 13% in patients with a hospital and an ICU admission BD of <6 to 45% in patients with a hospital and an ICU admission BD of >6). These data show that the base deficit is an early available important indicator to identify trauma patients with hemodynamic instability, high transfusion requirements, metabolic and coagulatory decompensation, as well as a high probability of death. The base deficit development may help to guide an early and aggressive therapy for the trauma/hemorrhage induced tissue hypoxia.

Malaria vaccines are being developed against different stages in the parasite's life cycle, each increasing the opportunity to control malaria in its diverse settings. Sporozoite vaccines are designed to prevent mosquito-induced infection; first generation recombinant or synthetic peptide vaccines have been tested in humans. Asexual erythrocytic stage vaccines, developed to prevent or reduce the severity of disease, have been tested in animals and in humans. A third strategy is to produce sexual stage vaccines that would induce antibodies which would prevent infection of mosquitoes when ingested in a bloodmeal containing sexual stage parasites. Although not directly protective, the sexual stage vaccine combined with a sporozoite or asexual stage vaccine (protective component) could prolong the useful life of the protective component by reducing transmission of resistant vaccine-induced mutants. In areas of low endemnicity, the sexual stage vaccine could reduce transmission below the critical threshold required to maintain the infected population, thereby assisting in the control or eradication of malaria. Transmission of Plasmodium falciparum, the major human malaria, can be blocked by monoclonal antibodies against three sexual stage-specific antigens. We have cloned the gene encoding the surface protein of relative molecular mass Mr 25,000 (25K; Pfs25), expressed on zygotes and ookinetes of P. falciparum. The deduced amino-acid sequence consists of a signal sequence, a hydrophobic C-terminus, and four tandem epidermal growth factor EGF-like domains.