Asymptotic Implied Volatility at the Second Order with Application to the SABR Model

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.Comment: 27 pages; v2: typos fixed and a few notation changes; v3: published version, typos fixed and comments added. in Large Deviations and Asymptotic Methods in Finance, Springer (2015) 37-6

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Bell Correlations and the Common Future

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

High (but Not Low) Urinary Iodine Excretion Is Predicted by Iodine Excretion Levels from Five Years Ago

Background: It has not been investigated whether there are associations between urinary iodine (UI) excretion measurements some years apart, nor whether such an association remains after adjustment for nutritional habits. The aim of the present study was to investigate the relation between iodine-creatinine ratio (ICR) at two measuring points 5 years apart. Methods: Data from 2,659 individuals from the Study of Health in Pomerania were analyzed. Analysis of covariance and Poisson regressions were used to associate baseline with follow-up ICR. Results: Baseline ICR was associated with follow-up ICR. Particularly, baseline ICR >300 mu g/g was related to an ICR >300 mu g/g at follow-up (relative risk, RR: 2.20; p < 0.001). The association was stronger in males (RR: 2.64; p < 0.001) than in females (RR: 1.64; p = 0.007). In contrast, baseline ICR <100 mu g/g was only associated with an ICR <100 mu g/g at follow-up in males when considering unadjusted ICR. Conclusions: We detected only a weak correlation with respect to low ICR. Studies assessing iodine status in a population should take into account that an individual with a low UI excretion in one measurement is not necessarily permanently iodine deficient. On the other hand, current high ICR could have been predicted by high ICR 5 years ago. Copyright (C) 2011 S. Karger AG, Base

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

The role of rigidity in adaptive and maladaptive families assessed by FACES IV: the points of view of adolescents

Previous studies using Olson’s Circumplex Model and FACES IV, the self-report assessing family functioning, did not clarify the role of rigidity, a dimension of this model. Rigidity emerged as ambiguous: it was considered either as a functional or as a dysfunctional dimension. Building upon the results of previous studies, we provided a contribution intended to disambiguate the role of rigidity considering adolescents’ perceptions and using a non-a priori classification analysis. 320 Italian adolescents (13–21 years) participated in this study and responded to a questionnaire containing scales of the study variables. A latent class analysis was performed to identify the association of rigidity with the other dimensions of Olson’s model and with indicators of adaptive family functioning in adolescence: parental monitoring and family satisfaction. We found six clusters corresponding to family typologies and having different levels of functioning. Rigidity emerged as adaptive in the typologies named rigidly balanced and flexibly oscillating; it was associated with positive dimensions of family functioning, i.e. flexibility, cohesion, parental monitoring, and high levels of family satisfaction. Differently, when rigidity was associated with disengagement, low cohesion and flexibility, and lack of parental supervision, emerged as maladaptive. This was the case of two typologies: the rigidly disengaged and the chaotically disengaged. Adolescents of these families reported the lowest levels of satisfaction. In the two last typologies, the flexibly chaotic and the cohesively disorganized, rigidity indicated a mid-range functionality as these families were characterized by emotional connectedness but lack of containment. Clinical implications are discussed

Survival Rate, Fracture Strength and Failure Mode of Ceramic Implant Abutments After Chewing Simulation

The aim of this study was to compare titanium-reinforced ZrO2 and pure Al2O3 abutments regarding their outcome after chewing simulation and static loading. Forty-eight standard diameter implants with an external hexagon were divided into three groups of 16 implants each and restored with three different types of abutments (group A: ZrO2 abutments with titanium inserts; group B: densely sintered high-purity Al2O3 abutments; group C: titanium abutments). All abutments were fixated on the implants with gold-alloy screws at 32 Ncm torque, and metal crowns were adhesively cemented onto the abutments. The specimens were exposed to 1.2 million cycles in a chewing simulator. Surviving specimens were subsequently loaded until fracture in a static testing device. Fracture loads (N) and fracture modes were recorded. A Wilcoxon Rank test to compare fracture loads among the 3 groups and a Fisher exact test to detect group differences in fracture modes were used for statistical evaluation (

Novel European free-living, non-diazotrophic Bradyrhizobium isolates from contrasting soils that lack nodulation and nitrogen fixation genes - a genome comparison

The slow-growing genus Bradyrhizobium is biologically important in soils, with different representatives found to perform a range of biochemical functions including photosynthesis, induction of root nodules and symbiotic nitrogen fixation and denitrification. Consequently, the role of the genus in soil ecology and biogeochemical transformations is of agricultural and environmental significance. Some isolates of Bradyrhizobium have been shown to be non-symbiotic and do not possess the ability to form nodules. Here we present the genome and gene annotations of two such free-living Bradyrhizobium isolates, named G22 and BF49, from soils with differing long-term management regimes (grassland and bare fallow respectively) in addition to carbon metabolism analysis. These Bradyrhizobium isolates are the first to be isolated and sequenced from European soil and are the first free-living Bradyrhizobium isolates, lacking both nodulation and nitrogen fixation genes, to have their genomes sequenced and assembled from cultured samples. The G22 and BF49 genomes are distinctly different with respect to size and number of genes; the grassland isolate also contains a plasmid. There are also a number of functional differences between these isolates and other published genomes, suggesting that this ubiquitous genus is extremely heterogeneous and has roles within the community not including symbiotic nitrogen fixation