Simulating Auxiliary Inputs, Revisited

For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In folklore this problem is known as \emph{simulating auxiliary inputs}. This idea of simulating auxiliary information turns out to be a powerful tool in computer science, finding applications in complexity theory, cryptography, pseudorandomness and zero-knowledge. In this paper we revisit this problem, achieving the following results: \begin{enumerate}[(a)] We discuss and compare efficiency of known results, finding the flaw in the best known bound claimed in the TCC'14 paper "How to Fake Auxiliary Inputs". We present a novel boosting algorithm for constructing the simulator. Our technique essentially fixes the flaw. This boosting proof is of independent interest, as it shows how to handle "negative mass" issues when constructing probability measures in descent algorithms. Our bounds are much better than bounds known so far. To make the simulator $(s,\epsilon)$-indistinguishable we need the complexity $O\left(s\cdot 2^{5\ell}\epsilon^{-2}\right)$ in time/circuit size, which is better by a factor $\epsilon^{-2}$ compared to previous bounds. In particular, with our technique we (finally) get meaningful provable security for the EUROCRYPT'09 leakage-resilient stream cipher instantiated with a standard 256-bit block cipher, like $\mathsf{AES256}$.Comment: Some typos present in the previous version have been correcte

Modified low-cycle fatigue (LCF) test

The fatigue test results obtained by the common low-cycle fatigue test (LCF) and its modified MLCF counterpart were presented. A satisfactory agreement of results was achieved for the two selected materials. With the MLCF method it is possible to examine from ten to twenty parameters using one single sample only. These parameters characterise the tested material in terms of its mechanical properties under the conditions of mechanical loads. Simultaneously, the study shows the implementation of the modified low-cycle fatigue test in practice

Volterra-Prabhakar derivative of distributed order and some applications

The paper studies the exact solution of two kinds of generalized Fokker-Planck equations in which the integral kernels are given either by the distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or the distributed order Prabhakar function $k_{2}(\alpha, \gamma; \lambda; t) = \int_{0}^{1} e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t) d\mu$, where the Prabhakar function is denoted as $e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t)$. Both of these integral kernels can be called the fading memory functions and are the Stieltjes functions. It is also shown that their Stieltjes character is enough to ensure the non-negativity of the mean square values and higher even moments. The odd moments vanish. Thus, the solution of generalized Fokker-Planck equations can be called the probability density functions. We introduce also the Volterra-Prabhakar function and its generalization which are involved in the definition of $k_{2}(\alpha, \gamma; \lambda; t)$ and generated by it the probability density function $p_2(x, t)$

The Effect of Marinating on Fatty Acid Composition of Sous-Vide Semimembranosus Muscle from Holstein-Friesian Bulls

The aim of the study was to evaluate the effect of two commercial oil marinades on marinated bovine semimembranosus muscles’ (n = 12) fatty acid composition. Fatty acids were determined in unmarinated raw and sous-vide beef and marinated muscles with two different marinades. The application of marinating changed the fatty acid composition in sous-vide beef. The sum of saturated fatty acids (SFA) and n-6/n-3 ratio decreased. However, the sum of monounsaturated fatty acids (MUFA) and polyunsaturated fatty acids (PUFA), including n-6 and n-3, increased in marinated sous-vide beef, while a proportion of conjugated linoleic acid (CLA) and arachidonic acid (AA) de-creased. The concentration (mg/100 g) of the sum of SFA and CLA in sous-vide beef was unaffected by marinating; however, the treatment significantly increased the sum of MUFA, PUFA, n-6 fatty and n-3 fatty acid concentrations. Using marinades containing canola oil and spices prior to the sous-vide treatment of beef was effective in improving its fatty acid composition