Spontaneous Supersymmetric Generation of an Indeterminate Mass Scale and a Possible Light Sterile Neutrino

If a global continuous symmetry of a supersymmetric field theory is spontaneously broken while preserving the supersymmetry, the resulting theory has a massless superfield. One of its two bosonic degrees of freedom is the familiar phase rotation of the usual massless Nambu-Goldstone boson, but the other is a scale transformation. An indeterminate mass scale is thus generated. In the fermion sector, a seesaw texture appears which may be suitable for a possible light sterile neutrino. This feature persists even after the gauging of the continuous symmetry or the breaking of the supersymmetry to resolve the aforementioned mass-scale ambiguity.Comment: 9 pages, expanded to include the discussion of a possible sterile neutrin

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

Locating a New Family Activity Centre: A Recreational Development Application of GIS

Loch Lomond and The Trossachs were established as a national park in 2001. Loch Lomond, UK’s second largest lake, is situated within 50 km of Glasgow (a major UK city) and has long been an important recreational centre for water sports, hill and forest walking, mountain biking, etc. A long distance path crosses the area (The West Highland Way), taking walkers, in five days, from Glasgow to Glen Nevis (the location of the UK’s highest mountain). The lake’s cultural and ecological significance has long been recognized. As one of Europe’s deepest lakes [Hydromod, 2003; www.hydromod.de/Eurolakes/] it is an important natural freshwater habitat; our university also has an internationally recognized field study centre on the lake’s shores [SCENE, 2009; http://www.gla.ac.uk/scene/]. Our university offers four one-year Geomatics MSc programmes which attract UK and international students. Coursework, September to April, precedes the students’ six-month research project. As part of their coursework, those students with little background in GIS must find a suitable location for a “Family Activity Centre” on the lake, using GIS. Students must submit an individual report on their methods used. Many illustrate their report with their own photos - so the task reviews and explores GIS skills, and encourages visits to an important location near our city

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

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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Multi-Band Intra-Night Optical Variability of BL Lacertae

We monitored BL Lacertae frequently during 2014 - 2016 when it was generally in a high state. We searched for intra-day variability for 43 nights using quasi-simultaneous measurements in the B, V, R, and I bands (totaling 143 light curves); the typical sampling interval was about eight minutes. On hour-like timescales, BL Lac exhibited significant variations during 13 nights in various optical bands. Significant spectral variations are seen during most of these nights such that the optical spectrum becomes bluer when brighter. The amplitude of variability is usually greater for longer observations but is lower when BL Lac is brighter. No evidence for periodicities or characteristic variability time-scales in the light curves was found. The color variations are mildly chromatic on long timescales.Comment: 15 pages, 5 Figures, 3 Tables; Accepted for publication in Galaxies; a special issue on Microvariability of Blazar

Multi-band optical variability of three TeV Blazars on Diverse Timescales

We present our optical photometric observations of three TeV blazars, PKS 1510-089, PG 1553+113 and Mrk 501 taken using two telescopes in India, one in Bulgaria, one in Greece and one in Serbia during 2012 - 2014. These observations covered a total of 95 nights with a total of 202 B filter frames, 247 images in V band, 817 in R band while 229 images were taken in the I filter. This work is focused on multi-band flux and colour variability studies of these blazars on diverse timescales which are useful in understanding the emission mechanisms. We studied the variability characteristics of above three blazars and found all to be active over our entire observational campaigns. We also searched for any correlation between the brightness of the sources and their colour indices. During the times of variability, no significant evidence for the sources to display spectral changes correlated with magnitude was found on timescales of a few months. We briefly discuss the possible physical mechanisms most likely responsible for the observed flux variability.Comment: 11 pages, 7 figures, 9 tables. Accepted for publication in MNRA