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

A novel fermentor system optimized for continuous production of pullulan

A novel fermentor system containing Aureobasidium pullulans in polyurethane foam was designed to achieve continuous production of pullulan. A. pullulans cells were immobilized in 10 to 20 g polyurethane foam with pore size of 1000 Ǻ. The system has specialized aeration provision with 80 perforations of 4 mm. Pullulan production achieved was approximately 37g/l in 18 cycles at 42°C, pH 5.5 and at aeration rate of 0.5 vvm. The concentration of sucrose and ammonium sulphate was 3 and 0.5%, respectively. This novel design could serve as an excellent fermentor system in industries for large scale continuous production of pullulan.Key words: Aureobasidium pullulans, polyurethane foam, pullulan, immobilized cells

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

Role of a Cytotoxic-T-Lymphocyte Epitope-Defined, Alternative gag Open Reading Frame in the Pathogenesis of a Murine Retrovirus-Induced Immunodeficiency Syndrome

LP-BM5 murine leukemia virus-infected C57BL/6 mice develop profound immunodeficiency and B-cell lymphomas. The LP-BM5 complex contains a mixture of defective (BM5def) and replication-competent helper viruses among which BM5def is the primary causative agent of disease. The BM5def primary open reading frame (ORF1) encodes the single gag precursor protein (Pr60gag). Our lab has recently demonstrated that a novel immunodominant cytotoxic-T-lymphocyte (CTL) epitope (SYNTGRFPPL) is expressed from a +1-nucleotide translational open reading frame of BM5def during the course of normal retrovirus expression. The SYNTGRFPPL CTL epitope may be generated from either of two initiation methionines present, ORF2a or ORF2b, located downstream of the ORF1 initiation site. This study investigates the role(s) of the alternative ORF2-derived gagprotein(s) of BM5def in viral pathogenesis. We have examined the disease-inducing capabilities of mutant viruses in which the translational potential of either the initiating ORF2a or ORF2b AUG has been disrupted. Although these mutated viruses are capable of wild-type ORF1 expression, they are unable to induce disease. Our data strongly suggest the existence of a novel ORF2 product(s) that is required for LP-BM5-induced pathogenesis and have potentially broad implications for other retroviral diseases

Spiders (Araneae) from Agricultural fields near foothill of Satpura Mountain ranges of Amravati District, Maharashtra, India.

This paper deals with the study of spider distribution in agricultural fields adjoining the Satpura Mountain Ranges of the Amravati district. The total collection of spiders comprises 12 families, 37 genera and 76 species. The Araneidae and Thomisidae families were dominant, followed by Saltisidae from the selected agricultural area. Lycosidae and Tetragnathidae were also found in a decreasing number of species due to their specific habitation. The analysis of guild structure revealed six feeding guilds. Orb web weavers and Ambushers constituted the dominant feeding guild representing 33% and 22% of the total collection respectively. Stalkers and ground runners represent 20% and 17% and foliage hunters and sheet web weavers represent 5% and 3% respectively. A new species of genus Sassacus (Beetle like spider), family Saltisidae was found for the first time in the Vidarbha region. The richness of spider diversity is a sign of the overall biodiversity which is a useful indicator of the species richness of the agro-ecosystem.
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The Hard X-ray emission of the blazar PKS 2155--304

The synchrotron peak of the X-ray bright High Energy Peaked Blazar (HBL) PKS 2155$-$304 occurs in the UV-EUV region and hence its X-ray emission (0.6--10 keV) lies mostly in the falling part of the synchrotron hump. We aim to study the X-ray emission of PKS 2155$-$304 during different intensity states in 2009$-$2014 using XMM$-$Newton satellite. We studied the spectral curvature of all of the observations to provide crucial information on the energy distribution of the non-thermal particles. Most of the observations show curvature or deviation from a single power-law and can be well modeled by a log parabola model. In some of the observations, we find spectral flattening after 6 keV. In order to find the possible origin of the X-ray excess, we built the Multi-band Spectral Energy distribution (SED). We find that the X-ray excess in PKS 2155--304 is difficult to fit in the one zone model but, could be easily reconciled in the spine/layer jet structure. The hard X-ray excess can be explained by the inverse Comptonization of the synchrotron photons (from the layer) by the spine electrons.Comment: 14 pages, 7 Figures, Accepted for publication in Ap

Looking for the Harappan Ports around Dholavira, Khadir Bet, Kachchh, Gujarat

1769-1773The rise of Harappan settlement at Dholavira is attributed to multidimensional factors which may include industrial activities, overseas trade and commerce and distribution of resources available in the Kachchh to other parts of the Harappan domain. The very location of the site is highly intriguing because presently the area is surrounded by marshy land which is called as Rann of Kachchh. However, various studies have indicated the different environmental and morphological conditions in the area and have been suggested that during Harappan time Rann was navigable. Though there is a remote possibility of any port installation close to ancient Dholavira town but a few potential sites in the proximity such as Jhandiasar, Saran and Bambhanka might have played a decisive role in the rise of Harappan settlement at Dholavira. The present study is based on the preliminary surface exploration undertaken in the recent past at above-mentioned sites

Conductivity of Highly Concentrated Aqueous Electrolyte Solutions: Ammonium Nitrate-Water System

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