On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions

AbstractLet f:{0,1}n→{0,1} be a monotone Boolean function whose value at any point x∈{0,1}n can be determined in time t. Denote by c=⋀I∈C⋁i∈Ixi the irredundant CNF of f, where C is the set of the prime implicates of f. Similarly, let d=⋁J∈D⋀j∈Jxj be the irredundant DNF of the same function, where D is the set of the prime implicants of f. We show that given subsets C′⊆C and D′⊆D such that (C′,D′)≠(C,D), a new term in (C⧹C′)∪(D⧹D′) can be found in time O(n(t+n))+mo(logm), where m=|C′|+|D′|. In particular, if f(x) can be evaluated for every x∈{0,1}n in polynomial time, then the forms c and d can be jointly generated in incremental quasi-polynomial time. On the other hand, even for the class of ∧,∨-formulae f of depth 2, i.e., for CNFs or DNFs, it is unlikely that uniform sampling from within the set of the prime implicates and implicants of f can be carried out in time bounded by a quasi-polynomial 2polylog(·) in the input size of f. We also show that for some classes of polynomial-time computable monotone Boolean functions it is NP-hard to test either of the conditions D′=D or C′=C. This provides evidence that for each of these classes neither conjunctive nor disjunctive irredundant normal forms can be generated in total (or incremental) quasi-polynomial time. Such classes of monotone Boolean functions naturally arise in game theory, networks and relay contact circuits, convex programming, and include a subset of ∧,∨-formulae of depth 3

Thermodynamic aspects of materials' hardness: prediction of novel superhard high-pressure phases

In the present work we have proposed the method that allows one to easily estimate hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, that has been performed for diamond and cubic boron nitride. The correctness of this approach has been shown for the recently synthesized superhard diamond-like BC5. It has been predicted that the hypothetical forms of B2O3, diamond-like boron, BCx and COx, which could be synthesized at high pressures and temperatures, should have extreme hardness

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.Comment: 18 page

Using Strategy Improvement to Stay Alive

We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides solving an MPG in the usual sense, our algorithm computes more information about the game, information that is important with respect to applications. The weights of the edges of an MPG can be thought of as a gained/consumed energy -- depending on the sign. For each vertex, our algorithm computes the minimum amount of initial energy that is sufficient for player Max to ensure that in a play starting from the vertex, the energy level never goes below zero. Our algorithm is not the first algorithm that computes the minimum sufficient initial energies, but according to our experimental study it is the fastest algorithm that computes them. The reason is that it utilizes the strategy improvement technique which is very efficient in practice

The heats of formation of the haloacetylenes XCCY [X, Y = H, F, Cl]: basis set limit ab initio results and thermochemical analysis

The heats of formation of haloacetylenes are evaluated using the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects, and (where relevant) first-order spin-orbit coupling. The heats of formation determined using W2 theory are: \hof(HCCH) = 54.48 kcal/mol, \hof(HCCF) = 25.15 kcal/mol, \hof(FCCF) = 1.38 kcal/mol, \hof(HCCCl) = 54.83 kcal/mol, \hof(ClCCCl) = 56.21 kcal/mol, and \hof(FCCCl) = 28.47 kcal/mol. Enthalpies of hydrogenation and destabilization energies relative to acetylene were obtained at the W1 level of theory. So doing we find the following destabilization order for acetylenes: FCCF $>$ ClCCF $>$ HCCF $>$ ClCCCl $>$ HCCCl $>$ HCCH. By a combination of W1 theory and isodesmic reactions, we show that the generally accepted heat of formation of 1,2-dichloroethane should be revised to -31.8$\pm$0.6 kcal/mol, in excellent agreement with a very recent critically evaluated review. The performance of compound thermochemistry schemes such as G2, G3, G3X and CBS-QB3 theories has been analyzed.Comment: Mol. Phys., in press (E. R. Davidson issue

Some Peculiarities in the Dose Dependence of Separate and Combined In Vitro Cardiotoxicity Effects Induced by CdS and PbS Nanoparticles With Special Attention to Hormesis Manifestations

Spherical nanoparticles (NPs) of cadmium and lead sulfides (diameter 37 ± 5 and 24 ± 4 nm, respectively) have been found to be cytotoxic for HL-1 cardiomyocytes as evidenced by decrease in adenosine triphosphate–dependent luminescence. Cadmium sulfide (CdS)-NPs were discovered to produce a much greater cytotoxic impact than lead sulphide (PbS)-NP. Given the same dose range, CdS-NP reduced the number of calcium spikes. A similar effect was observed for small doses of PbS-NP. In addition to cell hypertrophy under the impact of certain doses of CdS-NP and PbS-NP, doses causing cardiomyocyte size reduction were identified. For these 3 outcomes, we obtained both monotonic “dose–response” functions (well approximated by the hyperbolic function) and different variants of non-monotonic ones for which we found adequate mathematical expressions by modifying certain models of hormesis available in the literature. Data analysis using a response surface linear model with a cross-term provided new support to the previously established postulate that a diversity of types of joint action characteristic of one and the same pair of damaging agents is one of the important assertions of the general theory of combined toxicity. © The Author(s) 2020

Manifestation of systemic toxicity in rats after a short-time inhalation of lead oxide nanoparticles

Outbred female rats were exposed to inhalation of lead oxide nanoparticle aerosol produced right then and there at a concentration of 1.30 ± 0.10 mg/m3 during 5 days for 4 h a day in a nose-only setup. A control group of rats were sham-exposed in parallel under similar conditions. Even this short-time exposure of a relatively low level was associated with nanoparticles retention demonstrable by transmission electron microscopy in the lungs and the olfactory brain. Some impairments were found in the organism’s status in the exposed group, some of which might be considered lead-specific toxicological outcomes (in particular, increase in reticulocytes proportion, in δ-aminolevulinic acid (δ-ALA) urine excretion, and the arterial hypertension’s development). © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Funding: This work was funded by the budget of the Ekaterinburg Medical Research Center for Prophylaxis and Health Protection in Industrial Workers