Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal 1/f1/f noise

To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By employing the thermodynamic formalism we predict the characteristic scale and the precise scaling form of the distribution of number of points above a given level. We demonstrate that the powerlaw forward tail of the probability density, with exponent controlled by the level, results in an important difference between the mean and the typical values of the counting function. This can be further used to determine the typical threshold $x_m$ of extreme values in the pattern which turns out to be given by $x_m^{(typ)}=2-c\ln{\ln{M}}/\ln{M}$ with $c=3/2$. Such observation provides a rather compelling explanation of the mechanism behind universality of $c$. Revealed mechanisms are conjectured to retain their qualitative validity for a broad class of disorder-generated multifractal fields. In particular, we predict that the typical value of the maximum $p_{max}$ of intensity is to be given by $-\ln{p_{max}} = \alpha_{-}\ln{M} + \frac{3}{2f'(\alpha_{-})}\ln{\ln{M}} + O(1)$, where $f(\alpha)$ is the corresponding singularity spectrum vanishing at $\alpha=\alpha_{-}>0$. For the $1/f$ noise we also derive exact as well as well-controlled approximate formulas for the mean and the variance of the counting function without recourse to the thermodynamic formalism.Comment: 28 pages; 7 figures, published version with a few misprints corrected, editing done and references adde

Fully secure functional encryption with general relations from the decisional linear assumption

This paper presents a fully secure functional encryption scheme for a wide class of relations, that are specified by non-monotone access structures combined with inner-product relations. The security is proven under a standard assumption, the decisional linear (DLIN) assumption, in the standard model. The proposed functional encryption scheme covers, as special cases, (1) key-policy, ciphertext-policy and unified-policy (of key and ciphertext policies) attribute-based encryption with non-monotone access structures, and (2) (hierarchical) predicate encryption with inner-product relations and functional encryption with non-zer

Nebulized Anticoagulants Limit Coagulopathy But Not Inflammation in Pseudomonas Aeruginosa-Induced Pneumonia in Rats

Disturbed alveolar fibrin turnover is a characteristic feature of pneumonia. Inhibitors of coagulation could exert lung-protective effects via anticoagulant (inhibiting fibrin deposition) and possibly anti-inflammatory pathways, but could also affect host defense. In this randomized controlled in vivo laboratory study, rats were challenged intratracheally with Pseudomonas aeruginosa, inducing pneumonia, and randomized to local treatment with normal saline (placebo), recombinant human activated protein C (rh-APC), plasma-derived antithrombin (AT), heparin, or danaparoid. Induction of P. aeruginosa pneumonia resulted in activation of pulmonary coagulation and inhibition of pulmonary fibrinolysis, as reflected by increased pulmonary levels of thrombin-AT complexes and fibrin degradation products and decreased pulmonary levels plasminogen activator activity. Pseudomonas aeruginosa pneumonia was accompanied by systemic coagulopathy, since systemic levels of thrombin-AT complexes increased, and systemic levels of plasminogen activator activity decreased. Although rh-APC and plasma-derived AT potently limited pulmonary coagulopathy, neither heparin nor danaparoid affected net pulmonary fibrin turnover. Recombinant human APC also displayed systemic anticoagulant effects. Neither bacterial clearance nor pulmonary inflammation was affected by anticoagulant therapy. Nebulization of rh-APC or plasma-derived AT attenuated pulmonary coagulopathy, but not bacterial clearance or inflammation, in a rat model of P. aeruginosa pneumoni