Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

The effects of enhanced Z penguins on lepton polarizations in B→Xsℓ+ℓ−B \to X_s \ell^+ \ell^-

The sensitivity of the $B \to \pi K$ mode to electroweak penguins and the recent experimental data for the $B \to \pi \pi$, $\pi K$ modes has given rise to what is known as the ``$B \to \pi K$ puzzle''. Recently it has been observed that this {\sl puzzle} can be resolved by considering the new physics which can enter via $Z^0$ penguins. In this note we analyze the effect of this enhanced $Z^0$ penguins on the lepton polarization asymmetries of $b \to s \ell^+ \ell^-$.Comment: Published versio

h\to \gamma \gamma In Inert Higgs Doublet Model

Motivated by the recent result reported from LHC on the di-photon search for a Standard Model (SM) Higgs-like boson. We discuss the implications of this possible signal in the framework of the Inert Higgs Doublet Model (IHDM), taking into account previous limits from Higgs searches at LEP, the Tevatron and the LHC as well as constraints from unitarity, vacuum stability and electroweak precision tests. We show that the charged Higgs contributions can interfere constructively or destructively with the W gauge bosons loops leading to enhancement or suppression of the di-photon rate with respect to SM rate. We show also that the invisible decay of the Higgs, if open, could affect the total width of the SM Higgs boson and therefore suppress the di-photon rate.Comment: 15 pages, added reference

Marketing innovative service solutions with inter-organizational service networks: opportunities and threats

--

Charge imbalance resolved R\'enyi negativity for free compact boson: Two disjoint interval case

In this paper, we study the symmetry decomposition of R\'enyi negativity into charge imbalance sectors for the 1+1 dimensional free compact boson field with a global U(1) symmetry in the ground state for the case of two disjoint intervals. We obtain multi-charged and charged R\'enyi negativity moments by computing the four-point correlator of flux-generating vertex operators on the Riemann surface. We then obtain charge imbalance resolved R\'enyi negativity by taking the Fourier transform of the charged moments. Finally, we match our results against the tight-binding model as a numerical check.Comment: v2, 27 pages, 9 figures. New references added. Accepted for publication in JHE

X-ray Flux and Spectral Variability of Blazar H 2356-309

We present the results of timing and spectral analysis of the blazar H 2356-309 using XMM-Newton observations. This blazar is observed during 13 June 2005-24 December 2013 in total nine observations. Five of the observations show moderate flux variability with amplitude 1.7-2.2 percent. We search for the intra-day variability timescales in these five light curves, but did not find in any of them. The fractional variability amplitude is generally lower in the soft bands than in the hard bands, which is attributed to the energy dependent synchrotron emission. Using the hardness ratio analysis, we search for the X-ray spectral variability along with flux variability in this source. However, we did not find any significant spectral variability on intra-day timescales. We also investigate the X-ray spectral curvature of blazar H 2356-309 and found that six of our observations are well described by the log parabolic model with alpha=1.99-2.15 and beta=0.03-0.18. Three of our observations are well described by power law model. The break energy of the X-ray spectra varies between 1.97-2.31 keV. We investigate the correlation between various parameters that are derived from log parabolic model and their implications are discussed.Comment: 13 pages, 4 figures, published in the special issue "X-Ray Flux and Spectral Variability of Blazars" of Galaxies journa