Online Steiner Tree with Deletions

In the online Steiner tree problem, the input is a set of vertices that appear one-by-one, and we have to maintain a Steiner tree on the current set of vertices. The cost of the tree is the total length of edges in the tree, and we want this cost to be close to the cost of the optimal Steiner tree at all points in time. If we are allowed to only add edges, a tight bound of $\Theta(\log n)$ on the competitiveness is known. Recently it was shown that if we can add one new edge and make one edge swap upon every vertex arrival, we can maintain a constant-competitive tree online. But what if the set of vertices sees both additions and deletions? Again, we would like to obtain a low-cost Steiner tree with as few edge changes as possible. The original paper of Imase and Waxman had also considered this model, and it gave a greedy algorithm that maintained a constant-competitive tree online, and made at most $O(n^{3/2})$ edge changes for the first $n$ requests. In this paper give the following two results. Our first result is an online algorithm that maintains a Steiner tree only under deletions: we start off with a set of vertices, and at each time one of the vertices is removed from this set: our Steiner tree no longer has to span this vertex. We give an algorithm that changes only a constant number of edges upon each request, and maintains a constant-competitive tree at all times. Our algorithm uses the primal-dual framework and a global charging argument to carefully make these constant number of changes. We then study the natural greedy algorithm proposed by Imase and Waxman that maintains a constant-competitive Steiner tree in the fully-dynamic model (where each request either adds or deletes a vertex). Our second result shows that this algorithm makes only a constant number of changes per request in an amortized sense.Comment: An extended abstract appears in the SODA 2014 conferenc

Topological phase in a dx2−y2+(p+ip)d_{x^2-y^2}+(p+ip) superconductor in presence of spin-density-wave

We consider a mean-field Hamiltonian for a $d_{x^2-y^2}+(p+ip)$ superconductor(SC) in presence of spin-density-wave(SDW) order. This is due to the fact that the non-commutativity of any two orders produces the third one. The energy spectrum of such a Hamiltonian is shown to be gapped and it yields a topological phase in addition to the conventional one. A phase diagram characterizing different topological phases is construted. The Chern numbers and hence the nature of the topological phases are determined. The edge state spectrum and the possibility of whether the vortex state harbouring the zero modes are discussed.Comment: 5 pages, 3 figure

On Constant-Round Concurrent Zero-Knowledge from a Knowledge Assumption

In this work, we consider the long-standing open question of constructing constant-round concurrent zero-knowledge protocols in the plain model. Resolving this question is known to require non-black-box techniques. We consider non-black-box techniques for zero-knowledge based on knowledge assumptions, a line of thinking initiated by the work of Hada and Tanaka (CRYPTO 1998). Prior to our work, it was not known whether knowledge assumptions could be used for achieving security in the concurrent setting, due to a number of significant limitations that we discuss here. Nevertheless, we obtain the following results: 1. We obtain the first constant round concurrent zero-knowledge argument for \textbf{NP} in the plain model based on a new variant of knowledge of exponent assumption. Furthermore, our construction avoids the inefficiency inherent in previous non-black-box techniques such that those of Barak (FOCS 2001); we obtain our result through an efficient protocol compiler. 2. Unlike Hada and Tanaka, we do not require a knowledge assumption to argue the soundness of our protocol. Instead, we use a discrete log like assumption, which we call Diffie-Hellman Logarithm Assumption, to prove the soundness of our protocol. 3. We give evidence that our new variant of knowledge of exponent assumption is in fact plausible. In particular, we show that our assumption holds in the generic group model. 4. Knowledge assumptions are especially delicate assumptions whose plausibility may be hard to gauge. We give a novel framework to express knowledge assumptions in a more flexible way, which may allow for formulation of plausible assumptions and exploration of their impact and application in cryptography.Comment: 30 pages, 3 figure

SLOW AND STEADY WINS THE ORGANIC RACE

Organic production is carried out under an extensive regulatory setup because organic products are sold as value-added products with certified organic labelling in developed countries. Production is strictly monitored at every step in production chain. Organic production apart from being eco-friendly offers higher net returns per unit area compared to conventional agriculture. Organic production uses traditional tillage systems, crop rotations, crop residues, animal manures, legumes, green manures, off-farm organic wastes, mineral bearing rocks, and biological pest and weed control to maintain soil productivity. Thus, an organic farm should be a self contained system of production with minimal dependence on external inputs. Those farms having dairy as one of the active components will have to convert to organic livestock management so that manures supplied are as per requirements for organic production. The dairy products can also be certified organic to fetch higher prices. Organic farming is a highly labour intensive enterprise. Some of the major organic accreditation agencies are IFOAM (International Federation of Organic Agriculture Movements), FiBL, Demeter and many more. APEDA has also developed national standards for organic production. Indian farmers face many challenges in adoption of certified organic production. Some of the important organic production requirements as per national standards for organic production have been developed by APEDA.Genetically engineered cultivars or plant materials are not permitted in organic production. Some of the important organic production requirements as per national standards for organic production have been developed by APEDA. Some of the important organic production requirements as per national standards for organic production have been developed by APEDA.Before products from a farm/project can be certified as organic, inspection shall be carried out during the conversion period. To ensure a clear separation between organic and conventional production, the certification programme (agency) shall inspect, where appropriate, the whole production system. Organic production is one area of agriculture which can convert India’s ‘Green Revolution’ into ‘Evergreen Revolution’

280 Birds with One Stone: Inducing Multilingual Taxonomies from Wikipedia using Character-level Classification

We propose a simple, yet effective, approach towards inducing multilingual taxonomies from Wikipedia. Given an English taxonomy, our approach leverages the interlanguage links of Wikipedia followed by character-level classifiers to induce high-precision, high-coverage taxonomies in other languages. Through experiments, we demonstrate that our approach significantly outperforms the state-of-the-art, heuristics-heavy approaches for six languages. As a consequence of our work, we release presumably the largest and the most accurate multilingual taxonomic resource spanning over 280 languages

Prokaryotic metallothionein locus and cadmium tolerance in Synechococcus PCC 6301

The aim of this study was to investigate the molecular mechanism of Cd-tolerance in the cyanobacterium Synechococcus PCC 6301 and to establish whether the prokaryotic metallothionein (MT) locus, smt, is involved. Cd-tolerant cell lines of Synechococcus PCC 6301 were developed by step-wise selection, of a culture that had undergone prolonged maintenance in liquid medium. The Cd-tolerant cell lines AO.8, A1.3 and A1.7 (tolerant to 0.8, 1.3, 1.7 µM Cd, respectively) were phenotypically different to the non-selected line AO. Genomic DNA from AO and the Cd-tolerant lines AO.8, A1.3 and A1.7 was analysed by Southern hybridisation. A ca. 4-fold increase in hybridisation to radiolabelled smtA (prokaryotic metallothionein gene), relative to AO, was observed in genomic DNA from A1.7. Equivalent amounts of DNA were loaded onto each track, and no difference in hybridisation to a control gene, psaE (photosystem I gene), was observed. Indeed, the hybridisation of DNA from Al .7 to psaE was slightly less than that observed in AO. Genomic DNA isolated from AO, AO. 8, A1.3 and A1.7 was also analysed after 2, 4, 7 and 12 subcultures in the presence of the respective Cd concentrations. An increase in hybridisation to smtA, relative to AO, was observed in DNA from all Cd-tolerant cell lines. Additionally, unique additional restriction fragments, both larger and smaller than that in AO, were observed in DNA from A1.3 and A1.7. A similar restriction pattern was observed in 3 independent restrictions of DNA from A1.3 after 2 subcultures. Cd-tolerant cell lines were also developed from a 'clonal' culture of Synechococcus PCC 6301. An increase in tolerance was marked by an increase in growth lag, which reduced upon subsequent maintenance of the Cd-tolerant line in the presence of Cd. Genomic DNA from the non-selected line CO and Cd-tolerant lines C1.4, CI.8, C2.6 and C3.2 (tolerant to 1.4, 1.8, 2.6, 3.2 µM Cd, respectively) were analysed after 1, 2, 3, 4 and 5 subcultures. In all the Cd-tolerant lines, an increase in hybridisation to smtA, and additional larger (ca. 11 kb) and smaller (ca. 5.45 kb) restriction fragments, relative to CO (ca. 5.8 kb), were observed. However, amplification and rearrangement in DNA from CI .4 were evident only after 2 subcultures. Additionally, restriction fragment equivalent in size to that observed in CO was lost in CI.8, C2.6 and C3.2, and the presence of Cd did not affect DNA restriction with Sah under in vitro and short term in vivo conditions. The rearrangement in Cd-tolerant line C3 .2 was observed on a minimal HindIII-SalI fragment (ca. 350 bp smaller than that in CO) and isolated from size-fractionated genomic libraries. The alteration was mapped by PCR to a 600 bp region in the 5' flank of smtA. Nucleotide sequence analysis of the clones identified a deletion of 352 bp within a region of 360 bp encoding the C- terminal end of smtB (repressor of smtA transcription), rendering it non-functional. Increased basal level of smtA expression (derepressed expression) and indications for complete loss of the excised fragment were observed in Cd-tolerant line C3.2. Rearrangement was detected in DNA from C3.2 even after maintenance in the absence of Cd for 3 subcultures. The clone bank pPLAN Bal-Ba7 and pPLAN B2 (carrying Bamm restriction fragments of Synechococcus PCC 7942 plasmids) were used to study the plasmid/chromosomal localisation of smtA. Weak hybridisation of pPLAN Ba2 to smtA was observed, but further Southern analysis of plasmid and genomic DNA suggested chromosomal localisation of smtA. PCR and Southern hybridisation were used to detect homologues of smtA in other cyanobacterial strains. Putative homologues were identified in Synechococcus PCC 7942, Synechococcus D562, Oscillatoria D814 and Synechocystis D840 (= PCC 6803) by heterologous probing. However, no hybridisation to smtA was observed in DNA isolated from Calothrix D184 and Microchaete D578