On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift

We consider the Kudla-Millson lift from elliptic modular forms of weight (p+q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p,q). We study the L²-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian place. For locally symmetric spaces associated to even unimodular lattices, we obtain an explicit formula for the L²-norm of the lift, which often implies that the lift is injective. For O(p,2) we discuss how such injectivity results imply the surjectivity of the Borcherds lift.

Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

Twisted Reidemeister torsion for twist knots

The aim of this paper is to give an explicit formula for the SL2(C)-twisted Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables given approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.

A protocol guided by transpulmonary thermodilution and lactate levels for resuscitation of patients with severe burns.

Over-resuscitation is deleterious in many critically ill conditions, including major burns. For more than 15 years, several strategies to reduce fluid administration in burns during the initial resuscitation phase have been proposed, but no single or simple parameter has shown superiority. Fluid administration guided by invasive hemodynamic parameters usually resulted in over-resuscitation. As reported in the previous issue of Critical Care, Sánchez-Sánchez and colleagues analyzed the performance of a 'permissive hypovolemia' protocol guided by invasive hemodynamic parameters (PiCCO, Pulsion Medical Systems, Munich, Germany) and vital signs in a prospective cohort over a 3-year period. The authors' results confirm that resuscitation can be achieved with below-normal levels of preload but at the price of a fluid administration greater than predicted by the Parkland formula (2 to 4 mL/kg per% burn). The classic approach based on an adapted Parkland equation may still be the simplest until further studies identify the optimal bundle of resuscitation goals.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.

Pizgrischite, (Cu,Fe)Cu14PbBi17S35, a new sulfosalt from the Swiss Alps: Description, crystal structure and occurrence

Pizgrischite, (Cu,Fe)Cu14PbBi17S35, is a new mineral species named after the type locality, Piz Grisch Mountain, Val Ferrera, Graubunden, Switzerland. This sulfosalt occurs as thin, striated, metallic lead-grey blades measuring up to I cm in length, embedded in quartz and associated with tetrahedrite, chalcopyrite, pyrite, sphalerite, emplectite and derivatives of the aikinite-bismuthinite series. In plane-polarized light, the new species is brownish grey with no perceptible pleochroism; under crossed nicols in oil immersion, it presents a weak anisotropy with dark brown tints. Minimum and maximum reflectance values (in %) in air are: 40.7-42.15 (470 nm), 41.2-43.1 (546 nm), 41.2-43.35 (589 nm) and 40.7-43.3 (650 nm). Cleavage is perfect along 001 I and well developed on {010}. Abundant polysynthetic twinning is observed on (010). The mean micro-indentation hardness is 190 kg/mm(2) (Mohs hardness 3.3), and the calculated density is 6.58 g/cm(3). Electron-microprobe analyses yield (wt%; mean result of seven analyses): Cu 16.48, Pb 2.10, Fe 0.77, Bi 60.70, Sb 0.35, S 19.16, Se 0.04, total 99.60. The resulting empirical chemical formula is (Cu15.24Fe0.80Pb0.60)(Sigma 16.64)(Bi17.07Sb0.17)(Sigma 17.24)(S35.09Se0.03)(Sigma 35.12), in accordance with the formula derived from the single-crystal refinement of the structure, (Cu,Fe)Cu14PbBi17S35. Pizgrischite is monoclinic, space group C2/m, with the following unit-cell parameters: a 35.054(2), b3.91123(I), c43.192(2) angstrom, beta 96.713(4)degrees, V5881.24 angstrom(3), Z=4. The strongest seven X-ray powder-diffraction lines [d in angstrom (I)(hkl)] are: 5.364(40)((6) over bar 04), 4.080(50)((8) over bar 05), 3.120(40)(118), 3.104(68)((3) over bar 18), 2.759(53) ((9) over bar 11),2.752(44)(910) and 1.956(100)(020). The crystal structure is an expanded monoclinic derivative of kupcikite. Pizgrischite belongs to the cuprobismutite series of bismuth sulfosalts but, sensu stricto, it is not a homologue of cuprobismutite. At the type locality. pizarischite is the result of the Alpine metamorphism under greenschist-facies conditions of pre-Tertiary hydrothermal Cu-Bi mineralization.

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

BORN AT 27 WEEKS OF GESTATION WITH CLASSICAL PKU: CHALLENGES OF DIETETIC MANAGEMENT IN A VERY PRETERM INFANT

Only few cases of classical phenylketonuria (PKU) in premature infants have been reported. Treatment of these patients is challenging due to the lack of a phenylalanine-free amino acid solution for parenteral infusion. The boy was born at 27 weeks of gestation with a weight of 1000 g (P10). He received parenteral nutrition with a protein intake of 3 g/kg/day. On day 7 he was diagnosed with classical PKU (genotype IVS10-11G>A/IVS12+ 1G>A) due to highly elevated phenylalanine (Phe) level in newborn screening (2800 micromol/L). His maximum plasma Phe level reached 3696 micromol/L. Phe intake was stopped for 4 days. During this time the boy received intravenous glucose and lipids as well as little amounts of Phe-free formula by a nasogastric tube. Due to a deficit of essential amino acids and insufficient growth, a parenteral nutrition rich in branched-chain amino-acids and relatively poor in Phe was added, in order to promote protein synthesis without overloading in Phe. Under this regimen, Phe plasma levels normalized on day 19 when intake of natural protein was started. The boy has now a corrected age of 2 years. He shows normal growth parameters and psychomotor development. Despite a long period of highly elevated Phe levels in the postnatal period our patient shows good psychomotor development. The management of premature infants with PKU depends on the child's tolerance to enteral nutrition. It demands an intensive follow-up by an experienced team and dedicated dietician. Appropriate Phe-free parenteral nutrition would be necessary especially in case of gastro-intestinal complications of prematurity.

Age, smoking and overweight contribute to the development of intestinal metaplasia of the cardia.

AIM: To assess the role of Helicobacter pylori (H. pylori), gastroesophageal reflux disease (GERD), age, smoking and body weight on the development of intestinal metaplasia of the gastric cardia (IMC).¦METHODS: Two hundred and seventeen patients scheduled for esophagogastroduodenoscopy were enrolled in this study. Endoscopic biopsies from the esophagus, gastroesophageal junction and stomach were evaluated for inflammation, the presence of H. pylori and intestinal metaplasia. The correlation of these factors with the presence of IMC was assessed using logistic regression.¦RESULTS: IMC was observed in 42% of the patients. Patient age, smoking habit and body mass index (BMI) were found as potential contributors to IMC. The risk of developing IMC can be predicted in theory by combining these factors according to the following formula: Risk of IMC = a + s - 2B where a = 2,...6 decade of age, s = 0 for non-smokers or ex-smokers, 1 for < 10 cigarettes/d, 2 for > 10 cigarettes/d and B = 0 for BMI < 25 kg/m² (BMI < 27 kg/m² in females), 1 for BMI > 25 kg/m² (BMI > 27 kg/m² in females). Among potential factors associated with IMC, H. pylori had borderline significance (P = 0.07), while GERD showed no significance.¦CONCLUSION: Age, smoking and BMI are potential factors associated with IMC, while H. pylori and GERD show no significant association. IMC can be predicted in theory by logistic regression analysis.

Seigniorage-maximizing inflation

What is the seigniorage-maximizing level of inflation? Four models formulae for the seigniorage maximizing inflation rate (SMIR) are compared. Two sticky-price models arrive at very different quantitative recommendations although both predict somewhat lower SMIRs than Cagan’s formula and a variant of a .ex-price model due to Kimbrough (2006). The models differ markedly in how inflation distorts the labour market: The Calvo model implies that inflation and output are negatively related and that output is falling in price stickiness whilst the Rotemberg cost-of-price-adjustment model implies exactly the opposite. Interestingly, if our version of the Calvo model is to be believed, the level of inflation experienced recently in advanced economies such as the USA and the UK may be quite close to the SMIR.

Bargaining one-dimensional policies and the efficiency of super majority rules

We consider negotiations selecting one-dimensional policies. Individuals have single-peaked preferences, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. The existence and uniqueness of stationary subgame perfect equilibrium is established, and its explicit characterization provided. We supply an explicit formula to determine the unique alternative that prevails, as impatience vanishes, for each majority. As an application, we examine the efficiency of majority rules. For symmetric distributions of peaks unanimity is the unanimously preferred majority rule. For asymmetric populations rules maximizing social surplus are characterized.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Tractable valuations under uncertainty

I put forward a concise and intuitive formula for the calculation of the valuation for a good in the presence of the expectation that further, related, goods will soon become available. This valuation is tractable in the sense that it does not require the explicit resolution of the consumerís life-time problem.

Detecting and measuring deprivation in primary care: development, reliability and validity of a self-reported questionnaire: the DiPCare-Q.

OBJECTIVES: Advances in biopsychosocial science have underlined the importance of taking social history and life course perspective into consideration in primary care. For both clinical and research purposes, this study aims to develop and validate a standardised instrument measuring both material and social deprivation at an individual level. METHODS: We identified relevant potential questions regarding deprivation using a systematic review, structured interviews, focus group interviews and a think-aloud approach. Item response theory analysis was then used to reduce the length of the 38-item questionnaire and derive the deprivation in primary care questionnaire (DiPCare-Q) index using data obtained from a random sample of 200 patients during their planned visits to an ambulatory general internal medicine clinic. Patients completed the questionnaire a second time over the phone 3 days later to enable us to assess reliability. Content validity of the DiPCare-Q was then assessed by 17 general practitioners. Psychometric properties and validity of the final instrument were investigated in a second set of patients. The DiPCare-Q was administered to a random sample of 1898 patients attending one of 47 different private primary care practices in western Switzerland along with questions on subjective social status, education, source of income, welfare status and subjective poverty. RESULTS: Deprivation was defined in three distinct dimensions: material (eight items), social (five items) and health deprivation (three items). Item consistency was high in both the derivation (Kuder-Richardson Formula 20 (KR20) =0.827) and the validation set (KR20 =0.778). The DiPCare-Q index was reliable (interclass correlation coefficients=0.847) and was correlated to subjective social status (r(s)=-0.539). CONCLUSION: The DiPCare-Q is a rapid, reliable and validated instrument that may prove useful for measuring both material and social deprivation in primary care.