Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs

A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program (ABP) where each variable occurs in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity $n^{O(\log n)}$. In both the cases, our time complexity is double exponential in the number of ROABPs. ROABPs are a generalization of set-multilinear depth-$3$ circuits. The prior results for the sum of constantly many set-multilinear depth-$3$ circuits were only slightly better than brute-force, i.e. exponential-time. Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration. We relate basis isolation to rank concentration and extend it to a sum of two ROABPs using evaluation dimension (or partial derivatives).Comment: 22 pages, Computational Complexity Conference, 201

Identity Testing for Constant-Width, and Commutative, Read-Once Oblivious ABPs

We give improved hitting-sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known variable order. The best hitting-set known for this case had cost (nw)^{O(log(n))}, where n is the number of variables and w is the width of the ROABP. Even for a constant-width ROABP, nothing better than a quasi-polynomial bound was known. We improve the hitting-set complexity for the known-order case to n^{O(log(w))}. In particular, this gives the first polynomial time hitting-set for constant-width ROABP (known-order). However, our hitting-set works only over those fields whose characteristic is zero or large enough. To construct the hitting-set, we use the concept of the rank of partial derivative matrix. Unlike previous approaches whose starting point is a monomial map, we use a polynomial map directly. The second case we consider is that of commutative ROABP. The best known hitting-set for this case had cost d^{O(log(w))}(nw)^{O(log(log(w)))}, where d is the individual degree. We improve this hitting-set complexity to (ndw)^{O(log(log(w)))}. We get this by achieving rank concentration more efficiently

COVID-19 Vaccination status among Health care workers diagnosed with COVID-19 in a tertiary care institute of Uttarakhand: A Cross-sectional Study

Background: Vaccines are considered as the one of the main pillars in halting and ending the presently on-going coronavirus disease (COVID-19 disease) pandemic which has spread globally since it was first detected in Wuhan, China in December 2019. In the absence of specific therapy, infection prevention practices and mass vaccination remains the mainstay in controlling the disease. Objectives: Objective of the study was to assess COVID-19 vaccination status, socio-demographic and clinical profile among healthcare workers diagnosed with COVID-19. Methodology: A cross-sectional survey from 1st March 2021 to 30th June 2021 among healthcare workers who were diagnosed with COVID-19 in a tertiary care institute of Uttarakhand, India was conducted, and universal sampling was used. Institutional Ethics Committee approved this study. Results: Total 662 healthcare workers were diagnosed with COVID-19. 429 (64.8%) of these COVID-19 diagnosed healthcare workers had received either single (129,30%) or both dose (300,70%) of COVID-19 vaccine while remaining 233 (35.2%) belonged to non-vaccinated group. History of exposure to COVID-19 positive patients was higher in vaccinated (66.4%) than in non-vaccinated group (55%) (p = 0.004). Hospitalisation was found to be higher among non-vaccinated (5.6%) than vaccinated group (2.3%) (p = 0.029). Conclusions: This study concludes that being vaccinated against COVID-19 disease provides protection against severe infection and reduces the need for hospitalization

Prevention of endotoxin-induced uveitis in rabbits by Triphala, an Ayurvedic formulation

Purpose: Triphala (TA) is an Ayurvedic formulation used to treat various disorders. The present study was designed to investigate the anti-inflammatory effect of TA aqueous extract on experimental uveitis in the rabbit. Methods: Anterior uveitis was induced in rabbits by intravitreal injection of lipopolysaccharide from Eschericha coli after pretreatment with TA aqueous extract. Subsequently the anti-inflammatory activity of TA was evaluated by grading the clinical signs and estimating the inflammatory cell count, protein, and TNF-α level in the aqueous humour. Results: The anterior segment inflammation in the control group was significantly higher than in TA and prednisolone treated groups, as observed by clinical grading. The inflammatory cell count in the control group was 31.23 ± 0.80 × 105cells/ml, whereas it was 3.29 ± 0.47 × 105cells/ml (P < 0.0001 vs. control) and 1.31 ± 0.31 × 105 (P < 0.0001 vs. control) cells/ml in the TA and prednisolone treated groups, respectively. The protein content of the aqueous humour was 15.43 ± 0.54, 3.13 ± 0.35 (P < 0.0001 vs. control), and 1.96 ± 0.39 (P < 0.0001 vs. control) mg/ml in the control, TA and prednisolone treated groups respectively. The aqueous TNF- α level in the control group was 942.20 ± 6.46 pg/ml and was 261.30 ± 13.60 (P < 0.001 vs. control) and 104.00 ± 4.50 (P < 0.0001 vs. control) pg/ml in the TA and prednisolone treated groups, respectively. \ud Conclusions: Topical administration of aqueous extract of TA prevented uveitis in endotoxin-induced experimental rabbits.\u

Organogenesis in anise (Pimpinella anisum L.)

High frequency organogenesis was achieved in anise (Pimpinella anisum L.) using hypocotyl explants from in vitro germinated seedlings. Both cytokinins, benzylaminopurine and kinetin induced shoot regeneration but the effect of benzylaminopurine was more pronounced. High frequency shoot regeneration (45 shoots explant-1) was obtained on benzylaminopurine 1 mg l-1. Both cytokinins were also tested in combination with auxins (naphthaleneacetic acid/indoleacetic acid). Interaction of benzylaminopurine/kinetin with naphthaleneacetic acid/indoleacetic acid increased the length of regenerated shoots. Different kinds of callus morphology was observed but it had no relationship with regeneration potential. The regenerated plants were normal and healthy. &nbsp

Organogenesis in anise (Pimpinella anisum L.)

High frequency organogenesis was achieved in anise (Pimpinella anisum L.) using hypocotyl explants from in vitro germinated seedlings. Both cytokinins, benzylaminopurine and kinetin induced shoot regeneration but the effect of benzylaminopurine was more pronounced. High frequency shoot regeneration (45 shoots explant-1) was obtained on benzylaminopurine 1 mg l-1. Both cytokinins were also tested in combination with auxins (naphthaleneacetic acid/indoleacetic acid). Interaction of benzylaminopurine/kinetin with naphthaleneacetic acid/indoleacetic acid increased the length of regenerated shoots. Different kinds of callus morphology was observed but it had no relationship with regeneration potential. The regenerated plants were normal and healthy. &nbsp