The Defect Sequence for Contractive Tuples

We introduce the defect sequence for a contractive tuple of Hilbert space operators and investigate its properties. The defect sequence is a sequence of numbers, called defect dimensions associated with a contractive tuple. We show that there are upper bounds for the defect dimensions. The tuples for which these upper bounds are obtained, are called maximal contractive tuples. The upper bounds are different in the non-commutative and in the com- mutative case. We show that the creation operators on the full Fock space and the co ordinate multipliers on the Drury-Arveson space are maximal. We also study pure tuples and see how the defect dimensions play a role in their irreducibility.Comment: 16 Pages. To appear in Linear Algebra and its Application

Standard noncommuting and commuting dilations of commuting tuples

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly there is the minimal isometric dilation consisting of isometries with orthogonal ranges and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on Boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of Cuntz algebra O_n coming from dilations of commuting tuples.Comment: 18 pages, Latex, 1 commuting diagra

AN EXPLORATORY STUDY ON THE CENTRAL NERVOUS SYSTEM EFFECTS OF KOPSIA FRUTICOSA ON LABORATORY ANIMALS

Drugs bearing indole alkaloids are known to produce important pharmacological effects. Kopsia fruticosa (KF), member of thee Genus Kopsia containing four indole alkaloids possesses central nervous system (CNS) pharmacological effects. This study was conducted to explore the CNS effects of KF in rodents.Materials and Methods: The propylene glycolic solution (KF1) and aqueous solution (KF2) were prepared from the dried extract of the leaves of KF. Evaluation of hexobarbitone induced sleeping time in mice, analgesic effect by Tail flick response on thermal stimulus in rats, locomotor activity by Spontaneous motor activity and rotarod method in rats, sedative ataxic score by inclined plane method in mice and behavioural activity by Gross behavioural effects, Conditional Avoidance response, and cataleptic effects in rats were performed at 2, 4, 8,16 mg/kg of body weight respectively.Results: KF1 reduced the spontaneous locomotor activity and exploratory behaviour in mice (p<0.001-0.01) more than KF2. KF1 in all doses potentiated the hypnotic dose (p<0.001) of hexobarbitone and sub-hypnotic dose (upto 80% potentiation) of hexabarbitone as compared to only 40% potentiation by KF2. Anti-nociception effect was found to be absent at all doses. KF1 possesses moderate sedative ataxic effect (p<0.001) and KF2 at 8mg/kg b.w. revealed mild effect (p<0.05) when compared to pentobarbitone. KF1 induced a moderate degree of catalepsy and potentiated cataleptic and sub-cataleptic doses of haloperidol at all doses (p<0.001).Conclusion: The present study has revealed that the propylene glycolic extract of the leaves Kopsia fruticosa possesses profound action on the CNS thereby paving the way to further research

Photobase effect for just-in-time delivery in photocatalytic hydrogen generation

Carbon dots (CDs) are a promising nanomaterial for photocatalytic applications. However, the mechanism of the photocatalytic processes remains the subject of a debate due to the complex internal structure of the CDs, comprising crystalline and molecular units embedded in an amorphous matrix, rendering the analysis of the charge and energy transfer pathways between the constituent parts very challenging. Here we propose that the photobasic effect, that is the abstraction of a proton from water upon excitation by light, facilitates the photoexcited electron transfer to the proton. We show that the controlled inclusion in CDs of a model photobase, acridine, resembling the molecular moieties found in photocatalytically active CDs, strongly increases hydrogen generation. Ultrafast spectroscopy measurements reveal proton transfer within 30ps of the excitation. This way, we use a model system to show that the photobasic effect may be contributing to the photocatalytic H-2 generation of carbon nanomaterials and suggest that it may be tuned to achieve further improvements. The study demonstrates the critical role of the understanding the dynamics of the CDs in the design of next generation photocatalysts

Prescribing trends of anti glaucoma medication usage in treatment naive patients of primary open angle glaucoma in a tertiary care hospital in Eastern India

Background: Primary open angle glaucoma remains a high magnitude healthcare problem due to its prevalence and chronicity. The real world scenario of anti glaucoma medical therapy needs periodical auditing as far as drug prescriptions are concerned for formulation of treatment guidelines. Few studies from India have taken a longitudinal approach in this respect. This study was undertaken to identify such lacunae.Methods: This was an open label, prospective, observational study. Each treatment naive patient was followed up for a period of 6 months, where their prescriptions were scanned for the type of the anti glaucoma medications, total number of medications, route of administration, their duration of use and their frequency of dosage and change in medications if any, in each visits.Results: A gradual shift from monotherapy towards combination therapy was observed. Overall averages for prescriptions were topped by monotherapy at 44.25 followed by fixed dose combinations at 38.25, and then combination-polytherapy at 36 and the least number of prescriptions were for concurrent polytherapy at 17.5. Amongst all monotherapy agents, beta blockers were the most frequently prescribed drugs at baseline but their share of prescriptions was almost halved at the end of our study. The prostaglandin analogs on the other hand saw an upsurge in prescriptions from their baseline to the end of this study. Prostaglandin analogs andbeta blockers as fixed dose combination was a popular prescription over the entire study duration.Conclusions: Prescribing trends were remarkable for the shift from primary monotherapy towards fixed dose combinations as the study concluded. The decline in the number of beta blocker prescriptions and a rise in prostaglandin analog prescriptions is a testament to their better effectiveness and tolerability. The future of open angle glaucoma pharmacotherapy lies in prescribing more efficacious drugs either in monotherapy or in fixed combinations

A comprehensive model to predict mitotic division in budding yeasts

High-fidelity chromosome segregation during cell division depends on a series of concerted interdependent interactions. Using a systems biology approach, we built a robust minimal computational model to comprehend mitotic events in dividing budding yeasts of two major phyla: Ascomycota and Basidiomycota. This model accurately reproduces experimental observations related to spindle alignment, nuclear migration, and microtubule (MT) dynamics during cell division in these yeasts. The model converges to the conclusion that biased nucleation of cytoplasmic microtubules (cMTs) is essential for directional nuclear migration. Two distinct pathways, based on the population of cMTs and cortical dyneins, differentiate nuclear migration and spindle orientation in these two phyla. In addition, the model accurately predicts the contribution of specific classes of MTs in chromosome segregation. Thus we present a model that offers a wider applicability to simulate the effects of perturbation of an event on the concerted process of the mitotic cell division