The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We show how the Chabauty–Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a non-abelian generalisation of Coleman’s effective Chabauty theorem.

Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava and Shankar studying the average sizes of $n$ -Selmer groups, have given new upper bounds on the average algebraic rank in families of elliptic curves over $\mathbb{Q}$ , ordered by height. We describe databases of elliptic curves over $\mathbb{Q}$ , ordered by height, in which we compute ranks and $2$ -Selmer group sizes, the distributions of which may also be compared to these theoretical results. A striking new phenomenon that we observe in our database is that the average rank eventually decreases as height increases.

Given a sextic CM field $K$ , we give an explicit method for finding all genus- $3$ hyperelliptic curves defined over $\mathbb{C}$ whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an approximation of their Rosenhain invariants. Building on the work of Weng [J. Ramanujan Math. Soc. 16 (2001) no. 4, 339–372], we give an algorithm which works in complete generality, for any CM sextic field $K$ , and computes minimal polynomials of the Rosenhain invariants for any period matrix of the Jacobian. This algorithm can be used to generate genus-3 hyperelliptic curves over a finite field  $\mathbb{F}_{p}$ with a given zeta function by finding roots of the Rosenhain minimal polynomials modulo  $p$ .

The Coleman integral is a $p$ -adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

Starfish are echinoderms that live among corals and occur from the supra-littoral to the hadal zone. Deviation from pentamerism is a rare phenomenon in starfish and was observed in the red-knobbed starfish (Protoreaster linckii) collected from the Tuticorin coast, India. Eighty-five specimens were collected and, among these, one was found to be abnormal and had only four arms. The reasons for this abnormality may be due to the changes that occur during larval metamorphosis or caused by an abnormal regeneration of the arm.

The Andaman & Nicobar Islands are a group of 572 large and small islands & islets in the southeastern part of the Bay of Bengal. This preliminary study reports on husbandry practices and phenotypic characterization of indigenous Nicobari pig, in its home tract (Nicobar group of islands). A total of 377 families were surveyed in randomly selected villages on Car Nicobar, Nancowrie, Teressa, Katchal and Chowra islands. Results of the study revealed that Nicobari pigs were mostly semi feral in nature and reared under a free range system. Pigs were fed mainly with coconut and other locally available resources. The Nicobari pigs appeared short with long body. They showed high prolificacy with an average litter size of 8–10 numbers. These pigs were considered as a family asset among the Nicobari tribe. No commercial farms and slaughter was practiced by the tribes. It is concluded that the Nicobari pigs are considered as an indigenous pig breed/germplasm (Sus scrofa Nicobaricus) belonging to this island territory. Owing to its adaptation and performance under resource-driven island ecosystem, Nicobari pig warrants conservation and improvement. In addition, genetic characterization this pig using SNP would help to confirm their genetic distinctiveness and recognition as a new breed for conservation and sustainable utilization.

Acquisition of the gastrointestinal microbiota at birth may have long-term health impacts. We longitudinally characterised major microbial communities in the faeces of a cohort of infants using molecular methods. Faecal samples were prospectively obtained at several time points after birth from eighty-three infants. Real-time PCR using SYBR green and primers targeted at 16S rRNA gene sequences were used to quantify Bifidobacterium, Lactobacillus acidophilus group, Bacteroides–Prevotella group, Enterobacteriaceae, Enterococcus, Clostridium coccoides–Eubacterium rectale group, Clostridium leptum group and Staphylococcus. Microbial community abundance was expressed relative to amplification of sequences conserved universally for domain bacteria. Faecal copy number of 16S rRNA genes increased non-significantly from a mean of 4·1 × 109/g on day 1 to 1·1 × 1010/g on day 4. All microbial communities were detected from day 1 after birth. Enterobacteriaceae and lactobacilli predominated on day 1, while bifidobacteria and staphylocci increased on day 4. Bacteroides–Prevotella and C. coccoides–E. rectale increased by day 180. C. leptum was detected in half of the cohort at birth and in a slightly larger percentage by 6 months. Caesarean section was associated with delayed colonisation by several bacterial communities. Higher socio-economic status was associated with more abundant lactobacilli and Bacteroides–Prevotella at 90 and 180 d. Supplemental feeding was associated with a reduction in Enterobacteriaceae. Microbial colonisation of the gut was well established on the first day of birth, and relative abundance of microbial communities was influenced by mode of delivery, socio-economic status and supplemental feeding. These findings may have relevance to infant nutrition and growth.

During a routine survey, the scalloped hammerhead shark, Sphyrna lewini was caught from Nagapattinam coastal waters, south-east coast of India. It is the second time this species has occurred after a long period along the Indian coast, and this substantiates the possibility of its entry from another place.

In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.

The effect of vegetarian diets on faecal microbiota has been explored largely through culture-based techniques. The present study compared the faecal microbiota of vegetarian and omnivorous young women in southern India. Faecal samples were obtained from thirty-two lacto-vegetarian and twenty-four omnivorous young adult women from a similar social and economic background. Macronutrient intake and anthropometric data were collected. Faecal microbiota of interest was quantified by real-time PCR with SYBR Green using primers targeting 16S rRNA genes of groups, including: Clostridium coccoides group (Clostridium cluster XIVa), Roseburia spp.–Eubacterium rectale, Bacteroides–Prevotella group, Bifidobacterium genus, Lactobacillus group, Clostridium leptum group (Clostridium cluster IV), Faecalibacterium prausnitzii, Ruminococcus productus–C. coccoides, Butyrivibrio, Enterococcus species and Enterobacteriaceae. The groups were matched for age, socio-economic score and anthropometric indices. Intake of energy, complex carbohydrates and Ca were significantly higher in the omnivorous group. The faecal microbiota of the omnivorous group was enriched with Clostridium cluster XIVa bacteria, specifically Roseburia–E. rectale. The relative proportions of other microbial communities were similar in both groups. The butyryl-CoA CoA-transferase gene, associated with microbial butyrate production, was present in greater amounts in the faeces of omnivores, and the levels were highly correlated with Clostridium cluster XIVa and Roseburia–E. rectale abundance and to a lesser extent with Clostridium leptum and F. prausnitzii abundance and with crude fibre intake. Omnivores had an increased relative abundance of Clostridium cluster XIVa bacteria and butyryl-CoA CoA-transferase gene compared with vegetarians, but we were unable to identify the components of the diet responsible for this difference.

An alternative high temperature structural alloy system based on the X-X3Si eutectic compositions of chromium and vanadium is put forward. These low-density (~6g/cm3) eutectics have a bcc solid-solution to increase alloy fracture toughness, and a A15 X3Si as the high temperature load-bearing phase. (½Cr,½V)-(½Cr,½V)3Si was used as the base alloy for further element additions, and is represented by the symbol 山 10at.% tantalum and aluminium were substituted for vanadium as quaternary and quinary alloy additions.

Microstructure, elemental phase partitioning, compression creep and oxidation results will be discussed. Cr-Cr3Si has a tidy, fine lamellar microstructure. Vanadium coarsens and destabilises the lamellae to a limited extent. Tantalum addition causes two distinct populations of eutectic to form; one population having finer lamellae than the other. Aluminium does not coarsen or destabilise the lamellar microstructure. High temperature compression tests at 1200°C and 1300°C show that 山 is stronger than the binary alloys, and of similar strength to the quaternary and quinary alloys.

Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.

Fe deficiency in women contributes significantly to maternal and child morbidity in India. The intestinal bacterial flora may facilitate absorption of Fe from the caecum and proximal colon. The present study investigated the possibility that intestinal microbiota of anaemic young women may differ from that of women with normal Hb levels. The microbiota was quantified by real-time PCR in faeces of eight anaemic (Hb ≤ 100 g/l) and twenty-six normohaemic (Hb ≥ 120 g/l) women aged 18–25 years. Sequences of 16S ribosomal DNA (rDNA) specific to Bifidobacterium genus, Lactobacillus acidophilus group, Bacteroides–Prevotella–Porphyromonas group, Clostridium leptum group and Eubacterium rectale were amplified and expressed (as relative difference) relative to the universally conserved bacterial 16S rDNA sequences. Dietary intakes of energy, carbohydrate, fibre and Fe were ascertained by maintenance of a diet diary for a week. Faecal lactobacilli were significantly lower in anaemic women (median 6·6 × 10− 8, relative difference compared with total bacteria) than in the reference group (2·9 × 10− 6; P = 0·001, unpaired t test with logarithmic transformation). There was no difference between the two groups with respect to any of the other bacteria that were examined. Intakes of energy, carbohydrate, fibre, Fe and milk were similar in both the groups. Fe deficiency in young women in south India was associated with low levels of lactobacilli in the faeces. The relationship between lactobacilli and Fe deficiency needs to be explored further.

Gut bacteria contribute to energy conservation in man through their ability to ferment unabsorbed carbohydrate. The present study examined the composition of predominant faecal microbiota in obese and non-obese children. The participants (n 28) aged 11–14 years provided fresh faecal samples and completed a dietary survey consisting of 24 h diet recall and a FFQ of commonly used foods taken over the previous 3 months. Faecal bacteria were quantitated by real-time PCR using primers targeted at 16S rDNA. Of the participants, fifteen (seven female) were obese, with median BMI-for-age at the 99th percentile (range 97 to>99) while thirteen participants (seven female) were normal weight, with median BMI-for age being at the 50th percentile (range 1–85). Consumption of energy, carbohydrates, fat and protein was not significantly different between the obese and non-obese participants. There was no significant difference between the two groups in faecal levels of Bacteroides–Prevotella, Bifidobacterium species, Lactobacillus acidophilus group or Eubacterium rectale. Levels of Faecalibacterium prausnitzii were significantly higher in obese children than in non-obese participants (P = 0·0253). We concluded that the finding of increased numbers of F. prausnitzii in the faeces of obese children in south India adds to the growing information on alterations in faecal microbiota in obesity.

Extended abstract of a paper presented at Microscopy and Microanalysis 2009 in Richmond, Virginia, USA, July 26 – July 30, 2009

We present analytical models and experimental results to describe low-defect density growth (∼ 6 × 105/cm2) of highly mismatched antimonides on Si and GaAs substrates, with strain relief achieved at the growth interface through periodic, 90° interfacial misfit dislocations (IMF). We use molecular mechanics (MM) based modeling techniques to understand, at the atomic level, the spontaneous formation and energetics of these IMF. We have modeled, grown and characterized two systems extensively, these are - AlSb on Si with ∼ 13% mismatch and GaSb on GaAs with 7.83% lattice mismatch. Growth of these materials by molecular beam epitaxy (MBE) and subsequent High-Resolution Transmission Electron Microscopy (HR-TEM) has indicated that there is no tetragonal distortion in these two systems despite the high lattice mismatch. Instead, the mismatched epi-layers spontaneously form periodic IMF arrays that run along both [110] and [1-10] directions and relieve almost 100% of the strain in a few monolayers of deposition. To model this form of strain relief, we use existing theories of strain relief adapted for very high strain conditions and we also use bond energetics to model the strain-relieving interface. The IMFs in these systems are periodic and so is the deviation in bond lengths and bond angles, which restricts our calculation space to a finite number of elements. We shall also demonstrate extensive growth and characterization results of the materials grown with a particular emphasis on the strain-relieving interface to show excellent agreement of the experimental data with the proposed models. The high quality and low-defect density in AlSb grown on Si, has helped us demonstrate optically pumped IR VCSELs and edge emitters monolithically on Si (001) and this data will also be presented.