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

Role Of Social & Psychological Factors In Drug Default In Patients Of Pulmonary Tuberculosis

Research Problem: What is the influence of social and psychological factors on drug default in patients of pul­monary tuberculosis? Objective: To assess the role of social and psychological factors in drug default in patients of pulmonary tubercu­losis. Study Design: Hospital - based study by questionnaire method Setting and Participants: Patients of pulmonary tubercu­losis attending Out Patient Department of Tuberculosis and Respiratory Diseases, J.N. Medical College Hospital, A.M.U., Aligarh. Sample Size: 136 defaulters and 86 treated cases of pulmonary tuberculosis. Study Variables: Social factors, psychological factors, drug default and pulmonary tuberculosis. Outcome Variables: Association of social and psycho­logical factors with drug default in pulmonary tuberculo­sis patients. Statistical Analysis: By chi - square test and significance at 5% level. Result: Important social factors influencing drug default were joint family (74.27%), lack of money (22.06%) and uncooperative family (11.7%). Psychiatric morbidity among defaulters was significantly high (68.39%). Conclusion: Patient compliance depends on many psy­chological (e.g. psychiatric morbidity, type of personal­ity), and sociological,factors (including economic status of patient, nature of family, its environment, interaction between patient and doctor and patient's own attitude and idea about his disease). Age, sex, residence, religion and education did not show any significant contribution towards drug default

Clockwise rotation of the Brahmaputra Valley relative to India: Tectonic convergence in the eastern Himalaya, Naga Hills, and Shillong Plateau

GPS data reveal that the Brahmaputra Valley has broken from the Indian Plate and rotates clockwise relative to India about a point a few hundred kilometers west of the Shillong Plateau. The GPS velocity vectors define two distinct blocks separated by the Kopili fault upon which 2–3 mm/yr of dextral slip is observed: the Shillong block between longitudes 89 and 93°E rotating clockwise at 1.15°/Myr and the Assam block from 93.5°E to 97°E rotating at ≈1.13°/Myr. These two blocks are more than 120 km wide in a north‐south sense, but they extend locally a similar distance beneath the Himalaya and Tibet. A result of these rotations is that convergence across the Himalaya east of Sikkim decreases in velocity eastward from 18 to ≈12 mm/yr and convergence between the Shillong Plateau and Bangladesh across the Dauki fault increases from 3 mm/yr in the west to \u3e8 mm/yr in the east. This fast convergence rate is inconsistent with inferred geological uplift rates on the plateau (if a 45°N dip is assumed for the Dauki fault) unless clockwise rotation of the Shillong block has increased substantially in the past 4–8 Myr. Such acceleration is consistent with the reported recent slowing in the convergence rate across the Bhutan Himalaya. The current slip potential near Bhutan, based on present‐day convergence rates and assuming no great earthquake since 1713 A.D., is now ~5.4 m, similar to the slip reported from alluvial terraces that offsets across the Main Himalayan Thrust and sufficient to sustain a Mw ≥ 8.0 earthquake in this area

Prioritization of candidate genes in "QTL-hotspot" region for drought tolerance in chickpea (Cicer arietinum L.)

A combination of two approaches, namely QTL analysis and gene enrichment analysis were used to identify candidate genes in the "QTL-hotspot" region for drought tolerance present on the Ca4 pseudomolecule in chickpea. In the first approach, a high-density bin map was developed using 53,223 single nucleotide polymorphisms (SNPs) identified in the recombinant inbred line (RIL) population of ICC 4958 (drought tolerant) and ICC 1882 (drought sensitive) cross. QTL analysis using recombination bins as markers along with the phenotyping data for 17 drought tolerance related traits obtained over 1-5 seasons and 1-5 locations split the "QTL-hotspot" region into two subregions namely "QTL-hotspot_a" (15 genes) and "QTL-hotspot_b" (11 genes). In the second approach, gene enrichment analysis using significant marker trait associations based on SNPs from the Ca4 pseudomolecule with the above mentioned phenotyping data, and the candidate genes from the refined "QTL-hotspot" region showed enrichment for 23 genes. Twelve genes were found common in both approaches. Functional validation using quantitative real-time PCR (qRT-PCR) indicated four promising candidate genes having functional implications on the effect of "QTL-hotspot" for drought tolerance in chickpea.Sandip M Kale, Deepa Jaganathan, Pradeep Ruperao, Charles Chen, Ramu Punna, Himabindu Kudapa, Mahendar Thudi, Manish Roorkiwal, Mohan AVSK Katta, Dadakhalandar Doddamani, Vanika Garg, P B Kavi Kishor, Pooran M Gaur, Henry T Nguyen, Jacqueline Batley, David Edwards, Tim Sutton and Rajeev K Varshne

Optical and Radio Variability of BL Lacertae

We observed the prototype blazar, BL Lacertae, extensively in optical and radio bands during an active phase in the period 2010--2013 when the source showed several prominent outbursts. We searched for possible correlations and time lags between the optical and radio band flux variations using multifrequency data to learn about the mechanisms producing variability. During an active phase of BL Lacertae, we searched for possible correlations and time lags between multifrequency light curves of several optical and radio bands. We tried to estimate any possible variability timescales and inter-band lags in these bands. We performed optical observations in B, V, R and I bands from seven telescopes in Bulgaria, Georgia, Greece and India and obtained radio data at 36.8, 22.2, 14.5, 8 and 4.8 GHz frequencies from three telescopes in Ukraine, Finland and USA. Significant cross-correlations between optical and radio bands are found in our observations with a delay of cm-fluxes with respect to optical ones of ~250 days. The optical and radio light curves do not show any significant timescales of variability. BL Lacertae showed many optical 'mini-flares' on short time-scales. Variations on longer term timescales are mildly chromatic with superposition of many strong optical outbursts. In radio bands, the amplitude of variability is frequency dependent. Flux variations at higher radio frequencies lead the lower frequencies by days or weeks. The optical variations are consistent with being dominated by a geometric scenario where a region of emitting plasma moves along a helical path in a relativistic jet. The frequency dependence of the variability amplitude supports an origin of the observed variations intrinsic to the source.Comment: 10 pages, 9 figures, Accepted for publication in A&

Plant vigour QTLs co-map with an earlier reported QTL hotspot for drought tolerance while water saving QTLs map in other regions of the chickpea genome

Background Terminal drought stress leads to substantial annual yield losses in chickpea (Cicer arietinum L.). Adaptation to water limitation is a matter of matching water supply to water demand by the crop. Therefore, harnessing the genetics of traits contributing to plant water use, i.e. transpiration rate and canopy development dynamics, is important to design crop ideotypes suited to a varying range of water limited environments. With an aim of identifying genomic regions for plant vigour (growth and canopy size) and canopy conductance traits, 232 recombinant inbred lines derived from a cross between ICC 4958 and ICC 1882, were phenotyped at vegetative stage under well-watered conditions using a high throughput phenotyping platform (LeasyScan). Results Twenty one major quantitative trait loci (M-QTLs) were identified for plant vigour and canopy conductance traits using an ultra-high density bin map. Plant vigour traits had 13 M-QTLs on CaLG04, with favourable alleles from high vigour parent ICC 4958. Most of them co-mapped with a previously fine mapped major drought tolerance “QTL-hotspot” region on CaLG04. One M-QTL was found for canopy conductance on CaLG03 with the ultra-high density bin map. Comparative analysis of the QTLs found across different density genetic maps revealed that QTL size reduced considerably and % of phenotypic variation increased as marker density increased. Conclusion Earlier reported drought tolerance hotspot is a vigour locus. The fact that canopy conductance traits, i.e. the other important determinant of plant water use, mapped on CaLG03 provides an opportunity to manipulate these loci to tailor recombinants having low/high transpiration rate and plant vigour, fitted to specific drought stress scenarios in chickpea

A peculiar multi-wavelength flare in the Blazar 3C 454.3

The blazar 3C454.3 exhibited a strong flare seen in gamma-rays, X-rays, and optical/NIR bands during 3--12 December 2009. Emission in the V and J bands rose more gradually than did the gamma-rays and soft X-rays, though all peaked at nearly the same time. Optical polarization measurements showed dramatic changes during the flare, with a strong anti-correlation between optical flux and degree of polarization (which rose from ~ 3% to ~ 20%) during the declining phase of the flare. The flare was accompanied by large rapid swings in polarization angle of ~ 170 degree. This combination of behaviors appear to be unique. We have cm-band radio data during the same period but they show no correlation with variations at higher frequencies. Such peculiar behavior may be explained using jet models incorporating fully relativistic effects with a dominant source region moving along a helical path or by a shock-in-jet model incorporating three-dimensional radiation transfer if there is a dominant helical magnetic field. We find that spectral energy distributions at different times during the flare can be fit using modified one-zone models where only the magnetic field strength and particle break frequencies and normalizations need change. An optical spectrum taken at nearly the same time provides an estimate for the central black hole mass of ~ 2.3 * 10^9 M_sun. We also consider two weaker flares seen during the $\sim 200$ d span over which multi-band data are available. In one of them, the V and J bands appear to lead the $\gamma$-ray and X-ray bands by a few days; in the other, all variations are simultaneous.Comment: 11 pages, 4 figures, 2 tables; MNRAS in pres