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

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

High Prevalence of Methanobrevibacter smithii and Methanosphaera stadtmanae Detected in the Human Gut Using an Improved DNA Detection Protocol

Background: The low and variable prevalence of Methanobrevibacter smithii and Methanosphaera stadtmanae DNA in human stool contrasts with the paramount role of these methanogenic Archaea in digestion processes. We hypothesized that this contrast is a consequence of the inefficiencies of current protocols for archaeon DNA extraction. We developed a new protocol for the extraction and PCR-based detection of M. smithii and M. stadtmanae DNA in human stool. Methodology/Principal Findings: Stool specimens collected from 700 individuals were filtered, mechanically lysed twice, and incubated overnight with proteinase K prior to DNA extraction using a commercial DNA extraction kit. Total DNA was used as a template for quantitative real-time PCR targeting M. smithii and M. stadtmanae 16S rRNA and rpoB genes. Amplification of 16S rRNA and rpoB yielded positive detection of M. smithii in 95.7% and M. stadtmanae in 29.4% of specimens. Sequencing of 16S rRNA gene PCR products from 30 randomly selected specimens ( 15 for M. smithii and 15 for M. stadtmanae) yielded a sequence similarity of 99-100% using the reference M. smithii ATCC 35061 and M. stadtmanae DSM 3091 sequences. Conclusions/Significance: In contrast to previous reports, these data indicate a high prevalence of the methanogens M. smithii and M. stadtmanae in the human gut, with the former being an almost ubiquitous inhabitant of the intestinal microbiome