Parameterized Complexity of Secluded Connectivity Problems

The Secluded Path problem models a situation where a sensitive information has to be transmitted between a pair of nodes along a path in a network. The measure of the quality of a selected path is its exposure, which is the total weight of vertices in its closed neighborhood. In order to minimize the risk of intercepting the information, we are interested in selecting a secluded path, i.e. a path with a small exposure. Similarly, the Secluded Steiner Tree problem is to find a tree in a graph connecting a given set of terminals such that the exposure of the tree is minimized. The problems were introduced by Chechik et al. in [ESA 2013]. Among other results, Chechik et al. have shown that Secluded Path is fixed-parameter tractable (FPT) on unweighted graphs being parameterized by the maximum vertex degree of the graph and that Secluded Steiner Tree is FPT parameterized by the treewidth of the graph. In this work, we obtain the following results about parameterized complexity of secluded connectivity problems. We give FPT-algorithms deciding if a graph G with a given cost function contains a secluded path and a secluded Steiner tree of exposure at most k with the cost at most C. We initiate the study of "above guarantee" parameterizations for secluded problems, where the lower bound is given by the size of a Steiner tree. We investigate Secluded Steiner Tree from kernelization perspective and provide several lower and upper bounds when parameters are the treewidth, the size of a vertex cover, maximum vertex degree and the solution size. Finally, we refine the algorithmic result of Chechik et al. by improving the exponential dependence from the treewidth of the input graph.Comment: Minor corrections are don

Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates

We study the following computational problem: for which values of k, the majority of n bits MAJ_n can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJ_k o MAJ_k. We observe that the minimum value of k for which there exists a MAJ_k o MAJ_k circuit that has high correlation with the majority of n bits is equal to Theta(sqrt(n)). We then show that for a randomized MAJ_k o MAJ_k circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n^(2/3+o(1)). We show a worst case lower bound: if a MAJ_k o MAJ_k circuit computes the majority of n bits correctly on all inputs, then k <= n^(13/19+o(1)). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k= O(n^(2/3)) can compute MAJ_n correctly on all inputs

Circuit Size Lower Bounds and #SAT Upper Bounds Through a General Framework

Most of the known lower bounds for binary Boolean circuits with unrestricted depth are proved by the gate elimination method. The most efficient known algorithms for the #SAT problem on binary Boolean circuits use similar case analyses to the ones in gate elimination. Chen and Kabanets recently showed that the known case analyses can also be used to prove average case circuit lower bounds, that is, lower bounds on the size of approximations of an explicit function. In this paper, we provide a general framework for proving worst/average case lower bounds for circuits and upper bounds for #SAT that is built on ideas of Chen and Kabanets. A proof in such a framework goes as follows. One starts by fixing three parameters: a class of circuits, a circuit complexity measure, and a set of allowed substitutions. The main ingredient of a proof goes as follows: by going through a number of cases, one shows that for any circuit from the given class, one can find an allowed substitution such that the given measure of the circuit reduces by a sufficient amount. This case analysis immediately implies an upper bound for #SAT. To~obtain worst/average case circuit complexity lower bounds one needs to present an explicit construction of a function that is a disperser/extractor for the class of sources defined by the set of substitutions under consideration. We show that many known proofs (of circuit size lower bounds and upper bounds for #SAT) fall into this framework. Using this framework, we prove the following new bounds: average case lower bounds of 3.24n and 2.59n for circuits over U_2 and B_2, respectively (though the lower bound for the basis B_2 is given for a quadratic disperser whose explicit construction is not currently known), and faster than 2^n #SAT-algorithms for circuits over U_2 and B_2 of size at most 3.24n and 2.99n, respectively. Here by B_2 we mean the set of all bivariate Boolean functions, and by U_2 the set of all bivariate Boolean functions except for parity and its complement

The revised method for retrieving daytime distributions of atomic oxygen and odd-hydrogens in the mesopause region from satellite observations

Atomic oxygen (O) and atomic hydrogen (H) in the mesopause region are critical species, governing chemistry, airglow, and energy budget. However, they cannot be directly measured by satellite remote sensing techniques and so inference techniques, by airglow observations, are used. In this work, we retrieved daytime O and H distributions at ~ 77 km–100 km from the data of observations by the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) instrument at the TIMED (Thermosphere Ionosphere Mesosphere Energetics and Dynamics) satellite in 2003–2015. The retrieval approach considered the reaction H + O3 → O2 + OH in the ozone balance equation. Moreover, we revised all quenching and spontaneous emission coefficients according to latest published data. We then calculated daytime distributions of OH and HO2 at these altitudes with the use of their conditions of photochemical equilibrium

Radiative Decay Width of Neutral non-Strange Baryons from PWA

An overview of the GW SAID and ITEP groups effort to analyze pion photoproduction on the neutron-target will be given. The disentanglement the isoscalar and isovector EM couplings of N* and Delta* resonances does require compatible data on both proton and neutron targets. The final-state interaction plays a critical role in the state-of-the-art analysis in extraction of the gamma n --> pi N data from the deuteron target experiments. It is important component of the current JLab, MAMI-C, SPring-8, ELSA, and ELPH programsComment: 7 pages, 7 figures, 1 table; Proceedings of International Conference Dark Matter, Hadron Physics and Fusion Physics, Messina, Italy, Sept. 2014; will be published in EPJ Web of Conference

PHARMACOKINETIC RESEARCH OF POTENTIAL HYGOGLICEMIC DRUGS С7070

Introduction: The development of effective drugs for the treatment of diabetes is one of the urgent problems of modern medicine; we conducted pharmacokinetic studies of the innovative hypoglycemic drug - C7070, in rabbits and rats. Materials and Methods: The object of the study was substance C7070. Two methods of administration have been studied: intravenously and intragastrically. The concentration of C7070 is determined in blood plasma by a sensitive and selective HPLC method with tandem mass spectrometry detection. The range of detection was from 0.02 μg to 3876.00 μg in 1 ml of plasma in the animals under study. Chromatographic separation was performed on a 150 × 3.0 mm column of Zorbax Eclipce XDB C18 with a particle size of 3.0 μm (Agilent technologies, USA). To obtain stable results, a Zorbax Eclipce XDB C18 (Agilent technologies, USA) protection column of 12.5 × 3.0 mm with a particle size of 5.0 μm was used at 40 ° C for all analytical cycles. Ballast proteins in the test solutions were precipitated with acetonitrile followed by extraction of the analyte with ultrasound. Results and its Discussion: With intragastric administration, the maximum concentration (Cmax) of C7070 in blood plasma reached, on average, in rabbits through (tmax) 60 ± 0.1 minutes, in rats after 170.0 ± 79.8 minutes and was 34.6 ± 7.3 μg/ml and 17.6 ± 1.4 μg/ml, respectively. The half-life (t1/2) was prolonged and was 291.8 ± 17.1 minutes for rabbits and 225.2 ± 12.4 minutes for rats. The absolute bioavailability (fa) of C7070 in rabbits was 78.2 ± 1.0%, in rats 18.1 ± 2.0%. When administered intravenously, Cmax C7070 in blood plasma averaged 123.1 ± 23.7 μg/ml in rabbits and 337.6 ± 40.5 μg/ml in rats. The half-life period (t1/2) was prolonged and amounted to 225.5 ± 15.9 minutes for rabbits and 154.1 ± 5.1 minutes for rats. The Conclusion: The pharmacokinetic characteristics of a potential hypoglycemic drug C7070 in animals (rats, rabbits) under two routes of administration, intra-gastrointestinal and intravenous, were studied. The parameters obtained can be useful for clinical application and further studies of C7070 drugs based on it. Key words: C7070, diabetes mellitus, hypoglycemic agents, blood plasma of rabbits and rats, high-performance liquid chromatography, pharmacokinetics