Blackbox identity testing for bounded top fanin depth-3 circuits: the field doesn't matter

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called sps(k,d,n) circuits) over base field F. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runs in time poly(nd^k), regardless of the base field. The only field for which polynomial time algorithms were previously known is F=Q (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-3 circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a sps(k,d,n) circuit to k variables, but preserves the identity structure.Comment: 14 pages, 1 figure, preliminary versio

Meromorphic Functions and the Topology of Giant Gravitons

Using Mikhailov's map from holomorphic functions to supersymmetric D3-brane solutions, we show how to construct giant gravitons in AdS5 x S5 with toroidal topologies. In the 1/4-BPS sector we show that these are always of the form #^K (S2 x S1), and in the limit in which this becomes a set of m+n perpendicular spherical giants re-connected near to their intersections, we find K in terms of m,n. In the 1/8-BPS sector we find a similar class of solutions.Comment: 10 pages, 8 figure

Factors influencing decisions on delay claims in construction contracts for Indian scenario

  Construction industry in India is second largest next to agriculture. In current era of infrastructure development construction projects occupy a key position. In any construction project contract time and cost overrun is a common feature, which gives rise to claims leading to disputes. These disputes if not handled properly tend to consume time and money of all parties to the contract. To resolve the dispute in optimum time, it is essential to understand the root cause of disputes as early as possible. Hence there is a need of analyzing the disputes scientifically.  The present study reveals from the study of arbitration awards that the causes for delay claims can be grouped in domains and the probable decisions to the disputes can be traced through the probing questions considered by decision makers. This paper attempts to identify questions related to disputes for Indian scenario through literature, arbitration awards, court cases and discussions with professionals

Prolongation of a pregnancy with second trimester severe oligohydramnios to term: a case report

The occurrence of oligohydramnios complicating a pregnancy is seen in 0.8 to 5.5 % of pregnancies. Severe Oligohydramnios, though not clearly defined, but clinically with an AFI of less than 5 cm appears to be an important predictor for an abnormal fetal outcome. In general, the prognosis of mid trimester oligohydramnios is still poor. Hence we report a case with a very favourable neonatal outcome following severe oligohydramnios documented in early pregnancy. The aim of this case report is to add our experience to the currently limited literature regarding the best treatment of this unique obstetrical problem

EVALUTION OF ANALGESIC ACTIVITY OF LEAF EXTRACTS OF PERGULARIA DAEMIA [FORSK] IN EXPERIMENTAL ANIMALS

Objective: Pergularia daemia [Forsk] has been used from long time in traditional medicine. The main objective of this work is to evaluate analgesic activity of leaf of Pergularia daemia [Forsk] Methods: Analgesic activity of petroleum ether and methanol extract of leaf of Pergularia daemia [Forsk] was evaluated by using Eddy's hot plate and tail immersion method. Results: Preliminary Phytochemical investigation of Petroleum ether extract of leaf of Pergularia daemia [Forsk] shows presence of steroids, terpenoids, sterols while methanolic extract of leaf of Pergularia daemia [Forsk] shows presence of alkaloids, glycosides, flavonoids, tannins and phenolic component. The petroleum ether extract [300 mg/kg] shows delayed action in paw licking as well as in jumping whereas in the tail immersion method there was delayed time taken for flicking of tail out of water was recorded. Conclusion: The methanol extract was found to be more potent than petroleum ether extract. The result indicate that the petroleum ether and methanol extract contain such Phytochemical constituents which are responsible for analgesic activity

EVALUTION OF ANTIARTHRITIC ACTIVITY OF LEAF EXTRACTS OF PERGULARIA DAEMIA [FORSK] PLANT IN EXPERIMENTAL ANIMALS

Objective: Pergularia daemia [Forsk] has been used from the long time in traditional medicine. The main objective of this work is to evaluate anti-rheumatic activity of leaf of Pergularia daemia [Forsk] Methods: Anti- arthritic activity of petroleum ether and methanol extracts of leaf of Pergularia daemia [Forsk] was evaluated by using Freund's complete adjuvant model. Results: Preliminary Phytochemical investigation of Petroleum ether extract of leaf of Pergularia daemia [Forsk] shows presence of steroids, terpenoids, sterols while methanolic extract of leaf of Pergularia daemia [Forsk] shows presence of alkaloids, glycosides, flavonoids, tannins and phenolic component. The petroleum ether and methanol extract of leaf of Pergularia daemia [300 mg/kg] shows an improvement in arthritis condition by reducing hind paw inflammation. Conclusion: The methanolic extract was found to be more potent than petroleum ether extract. The result indicates that the petroleum ether and methanol extract contain such phytochemical constituents which are responsible for analgesic and anti-rheumatic activity