We propose a discrete analogue of null geodesics in causal sets that are approximated by 𝕄^2 , in the spirit of Kronheimer and Penrose’s ”grids” and ”beams” for an abstract causal space. The causal set analogues are “ladder molecules”, whose rungs are linked pairs of elements corresponding loosely to Barton et al’s horizon bi-atoms [1]. In 𝕄^2 a ladder molecule traps a ribbon of null geodesics corresponding to a thickened or fuzzed out horizon. The existence of a ladder between linked pairs of elements in turn provides a generalisation of the horismotic relation to causal sets. Simulations of causal sets approximated by a region of 𝕄^2 show that ladder molecules are fairly dense in the causal set, and provide a light-cone like grid. Moreover, similar to the uniqueness of null geodesics between horismotically related events in 𝕄^2 , in such causal sets there is a unique ladder molecule between any two linked pairs which are related by the generalised horismotic relation.

We study different aspects of observer independent formulation of quantum field theory (QFT) in curved spacetime background. This thesis is broadly divided into two parts, in the first part we study an observer independent scalar field vacuum, called as the Sorkin-Johnston (SJ) vacuum for a small mass scalar field in a 2d causal diamond, and conformally coupled scalar field in spacetimes which are conformally related to ultrastatic spacetime with time dependent conformal factor. We study several properties of the SJ vacuum in these spacetimes and compare with the known vacua. In the second part of the thesis we study a spacetime formulation of entanglement entropy, called as the Sorkin Spacetime Entanglement Entropy (SSEE), in curved spacetime, which makes use of the Wightman function restricted to the region of interest and the spacetime field commutator. We study SSEE in cylinder slab spacetimes and compare the result with the Calabrese-Cardy entanglement entropy. We also study SSEE of de Sitter and black hole horizons and compared with known results.

We review some recent results on Sorkin’s spacetime formulation of the entanglement entropy (SSEE) for a free quantum scalar field both in the continuum and in manifold-like causal sets. The SSEE for a causal diamond in a 2d cylinder spacetime has been shown to have a Calabrese–Cardy form, while for de Sitter and Schwarzschild de Sitter horizons in dimensions $$d>2$$ , it matches the mode-wise von-Neumann entropy. In these continuum examples the SSEE is regulated by imposing a UV cut-off. Manifold-like causal sets come with a natural covariant spacetime cut-off and thus provide an arena to study regulated QFT. However, the SSEE for different manifold-like causal sets in $$d=2$$ and $$d=4$$ has been shown to exhibit a volume rather than an area law. The area law is recovered only when an additional UV cut-off is implemented in the scaling regime of the spectrum which mimics the continuum behaviour. We discuss the implications of these results and suggest that a volume-law may be a manifestation of the fundamental non-locality of causal sets and a sign of new UV physics.

In the present investigation, the chloroformic and hydro-alcoholic extracts of leaves and female cones of Cycas revoluta were screened for its antimicrobial potential and in urge for isolation and characterization of the potent molecule responsible for antimicrobial potential against pathogenic and drug resistant strains. The results showed that both the leaves and female cones of Cycas revoluta are potent antimicrobial agents. It was found that chloroformic extracts of the cones was having potent antimicrobial activity in comparison to the chloroformic extracts of leaves. The studies report the isolation and characterization of a novel molecule, 2, 3-dihydro-4′-O-methyl-amentoflavone from the chloroformic extracts of leaves and female cones of the plant. The molecule was found to be promising antimicrobial agent against Methicillin resistant Staphylococcus aureus (MRSA), E. coli, Salmonella abony, Aspergillus niger, Candida albicans, and other pathogens reported in the study. The results hereby concluded that the extracts or the molecule can be utilized in formulating new antimicrobials which can be utilized in treating several infections caused by drug resistant pathogens. However further studies are however needed to study and evaluate its broad spectrum profile and to screen other different pharmacological activities.

In the present study, the pectin, a natural gelling plant polysaccharide was extracted from pomace portion of apples and oranges. Further the antimicrobial, antioxidant and anti-inflammatory activities of pectin extracts were investigated. It was found that the yield of pectin content extracted was predominant in apples (20.60 %) in comparison to that of oranges (10.56%). The pectin samples extracted from apples and oranges were qualitatively evaluated for characteristic properties. Further the phytochemical constituents were qualitatively determined by conventional procedures. The results confirmed the presence of alkaloids, flavanoids, reducing sugars, steroids and cardiac glycosides in orange pectin while alkaloids, reducing sugars, steroids, cardiac glycosides and anthraquinones were present in apple pectin. Tannins, saponin and anthraquinones were absent in orange pectin while tannins, flavanoids and saponin were absent in apple pectin. In separation of pectin extracts by TLC, the Rf values of the pectin samples were found to be similar viz. Apple pectin (0.62), Orange pectin (0.62) to that of standard pectin (procured from Ranchem), 0.63. The apple pectin and orange pectin showed almost similar retention time viz. 1.821 minutes and 1.757 minutes specifically on HPLC chromatogram. The FT-IR spectra of extracted pectin samples were determined using a computerized FTIR spectrometer in the range of 4400–400 cm 1 by the KBr pellet technique. Two outstanding features of the infrared spectra of pectinate are bands at 1745-1743 and at 1607-1604 cm -1 . One other feature which should be mentioned is a band, beyond the afore mentioned range, appearing at 1418-1417 cm -l

In the present study, the hydro-alcoholic and hexane extracts of the plant, Rheum australes (Family: Polygonaceae) were screened for antimicrobial activity against pathogenic and drug resistant strains. The non polar extracts did not showed any activity against any of the pathogenic strains. Amongst these extracts the hydro-alcoholic extracts of the plant, Rheum australes, showed potent antimicrobial activity against almost all the pathogens studied. These extracts also showed potent antibacterial activity against multidrug resistant Staphylococcus aureus and Pseudomonas aeruginosa in the ranges from 0.3 mg/ml to 0.7 mg/ml. The potent hydro-alcoholic extract was further subjected for isolation and characterization of potent antimicrobial compound via chromatographic and spectroscopic techniques. The pure antimicrobial compound isolated and characterized was Revandichinone. The compound was isolated as bright yellow needles, mp 214 0 C. The IR spectrum showed absorption bands at 3441 cm _1 (–OH), 1625 cm _1 (chelated-C¼O) and 1749 cm _1 (ester–C¼O). The compound isolated was further subjected for antimicrobial screening against pathogens at varying concentrations.

Chitin, a predominant polysaccharide besides cellulose is present as an important constituent of exoskeleton of arthropods and crustaceans. It is also found as the important component of fungal hyphae. Chitin and its derivatives had a great significance and importance in pharmacological, medical and food dealing fields. In the present investigation, chitinous wastes were collected from the fresh water areas of Dehradun and Rishikesh of Uttarakhand State. The bacterium, Bacillus sp. isolated from soil produces chitinase enzyme responsible for degradation of chitin obtained from chitinous wastes. Further the chitinases enzyme was utilized to degrade the chitinous wastes into chito-oligosaccharides. The chitin active molecule present in the chitinous waste at another stage was deacetylated to chitosan. Further the antifungal activity of chitinases, chitin, chitosan and chito-oligosaccharides was determined in vitro by well diffusion method against Aspergillus niger and Candida albicans. Amongst the test fungal cultures, the chitinase showed maximum inhibition against Aspergillus niger (diameter of zone of inhibition: 24 mm) followed by Candida albicans (diameter of zone of inhibition: 14 mm). Deacetylated form of chitin i.e chitosan showed potent antifungal activity against Candida albicans (diameter of zone of inhibition: 24 mm) followed by Aspergillus niger (diameter of zone of inhibition: 18 mm). The chitin extracted showed almost similar antifungal activity against Aspergillus niger and Candida albicans (diameter of zone of inhibition: 15 mm) respectively. The low molecular weight derivatives viz. chito-oligosaccharide showed significant antifungal activity against Aspergillus niger (diameter of zone of inhibition: 14 mm) but no activity was found against Candida albicans.

GCF is a serum transudate or inflammatory exudate that is derived from the periodontal tissues and can be collected at the orifice or from within the gingival crevice.(1) The potential diagnostic importance of gingival fluid was recognized more than 60 years ago and serious investigation of the dynamics of GCF production did not begin until the late 1950s with the reports of Brill and co-workers.(2,3) The fluid component of GCF derives primarily from microvascular leakage. Additions to the fluid volume are made from the intercellular fluid and cellular cytoplasm. The gingival tissue is constantly subjected to mechanical and bacterial aggregation.Resistance to these actions is provided by saliva, sulcular fluid, epithelial surface keratinisation and initial stages of inflammation.(4) The origin,composition and clinical significance of gingival crevicular fluid have significantly helped us in understanding the pathogenesis of periodontal disease.The need to find a non-invasive test method in periodontitis drew attention to the sulcus fluid that is produced in small quantities even in a completely healthy periodontium, and its composition is near similar to that of blood plasma.

We calculate Sorkin’s manifestly covariant entanglement entropy S for a massive and massless minimally coupled free Gaussian scalar field for the de Sitter horizon and Schwarzschild de Sitter horizons, respectively, in d > 2. In de Sitter spacetime we restrict the Bunch–Davies vacuum in the conformal patch to the static patch to obtain a mixed state. The finiteness of the spatial L 2 norm in the static patch implies that S is well defined for each mode. We find that S for this mixed state is independent of the effective mass of the scalar field, and matches that of Higuchi and Yamamoto (2018 Phys. Rev. D 98 065014), where, a spatial density matrix was used to calculate the horizon entanglement entropy. Using a cut-off in the angular modes we show that S ∝ A c , where A c is the area of the de Sitter cosmological horizon. Our analysis can be carried over to the black hole and cosmological horizon in Schwarzschild de Sitter spacetime, which also has finite spatial L 2 norm in the static regions. Although the explicit form of the modes is not known in this case, we use the boundary conditions of Qiu and Traschen (2020 Class. Quantum Grav. 37 135012) for a massless minimally coupled scalar field, to find the mode-wise S b , c , where b , c denote the black hole and de Sitter cosmological horizons, respectively. As in the de Sitter calculation we see that S b , c ∝ A b , c after taking a cut-off in the angular modes.

The excessive use of pesticides causesmaximum soil stress and infertile conditions. The present study was performed in order to explore and identify the novel microbial source for the biodegradation of monocrotophos pesticides. Soil samples (approx. 500 g) were collected using some clean,dry, and sterile polythene bags along with a sterile spatula, marking pen rubber band, and other accessories. These samples were air-dried for 1 week, crushed, and sieved. The sieved soils were then used for Actinomycetes isolation. A totalof 120 Soil samples were aseptically collected from different field regions of Uttarakhand viz. Tehri-Garhwal, Chamoli, Srinagar, Uttarkashi, and Haridwar havedominant usage of monocrotophos pesticides. Amongst these samples, A total of 280 microbes were isolated; out of which 24 isolates of Actinobacteria (8.57 %) were isolated. The results revealed the strains of the genera viz. Micromonospora (65%), Actinomycetes (25%,) and Streptomyces (10%)are meant to be responsible for the biodegradation of monocrotophos pesticides.

Received 28 July 2021DOI:https://doi.org/10.1103/PhysRevD.104.089901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum fields in curved spacetimeQuantum gravityParticles & FieldsGravitation, Cosmology & Astrophysics

In causal set theory the gravitational path integral is replaced by a path-sum over a sample space Ω n of n-element causal sets. The contribution from non-manifold-like orders dominates Ω n for large n and therefore must be tamed by a suitable action in the low energy limit of the theory. We extend the work of Loomis and Carlip on the contribution of sub-dominant bilayer orders to the causal set path-sum and show that the ‘link action’ suppresses the dominant Kleitman–Rothschild orders for the same range of parameters.

Plants are found to be the significant bioreactors of versatile phytochemicals and nutraceuticals responsible for significant antimicrobial, antioxidant and other pharmacological activities.These molecules are thus an exemplary source of formulation of drugs and thus the ayurvedic extracts of plant (s) or plant part (s) are in traditional use to combat any infection and immunomodulating activity in the living being.In the present study, the fruit extracts of Myrica esculenta were prepared in different solvents viz.80% methanol, hydro-alcohol, hexane and chloroform.The results of the study revealed significant antimicrobial and antioxidant activities as determined by conventional procedures.The results showed, extracts viz.80% methanolic extract, hydro-alcoholic extract and hexane extract at 1 mg/ml concentration had significant antimicrobial potential against E. coli, Salmonella abony and Staphylococcus epidermidis while no antimicrobial activity was determined against Micrococcus luteus, Aspergillus niger and Candida albicans.The chloroformic extracts possessed no activity against any of the organism studied.antioxidant activity of the solvent extracts follows the order viz 80% methanolic extract>hydro-alcoholic extract>hexane extract>chloroformic extract.

We calculate Sorkin's spacetime entanglement entropy of a Gaussian scalar field for complementary regions in the 2d cylinder spacetime and show that it has the Calabrese-Cardy form. We find that the cut-off dependent term is universal when we use a covariant UV cut-off as in [1]. In addition, we show that the relative size-dependent term exhibits complementarity. Its coefficient is however not universal and depends on the choice of pure state. It asymptotes to the universal form within a natural class of pure states.

The aim of the present review is to study the effect of plant growth promoting rhizobacteria (PGPR) on crops. These PGPRs are meant to be the natural and alternate substitute of chemicals in agriculture. The plant growth promoting rhizobacteria are the naturally occurring soil bacteria which enhance the plant growth, also protect plant in stress condition without causing any adverse effect on the environment. The use of PGPRs for sustainable and safe agriculture has increased globally in last couple of decades. PGPRs are meant to reduce the soil toxicity which occurs due to surplus use of chemicals and pesticides. Scientific researches involve multidisciplinary approaches to understand the working of PGPR, effects on plant growth and physiology, biocontrol of plant pathogens, induced systematic resistance and phyto-stimulation. PGPR had shown both antagonistic and synergistic interaction with their surrounding microorganism to boost the plant favorably. The present review has tried to describe all the important aspects of PGPRs and thus can be described as revolutionized tools for farmers for sustainable agriculture.

Medicinal plants are the potential sources of different natural molecules having wide pharmacological activities. The fruits and parts of these plants are also the sources of significant antioxidants and nutraceuticals having potent antioxidant potential and significant immuno-modulatory activities. The present study is the first report on wild edible food supplements that are endowed with various medicinal properties and significant antidiabetic, anticancer and anti-nephrolithiasis properties. The study was performed to determine the nutritional, mineral profile and phytochemical analysis of seven (7) medicinal plants viz. Cajanus indicus, Dolichos biflorus, Glycine soja, Benincasa cerifera, Setaria italica, Cleome viscosa and Hordeum vulgare for exploring and development of new, safe and potent drugs. The extraction was performed by fractionation with different solvents, while the nutrients and minerals present in all these plants were studied using Association of Official Analytical Chemists (AOAC) method and Inductively coupled plasma-mass-spectrometry (ICP-MS) techniques. The results of the study revealed the presence of significant nutrients and minerals in all the seven (7) plants studied. The present study revealed that, carbohydrates/glycosides were present in Cajanus indicus, Dolichos biflorus, Glycine soja, Benincasa cerifera, Setaria italica, Cleome viscosa and Hordeum vulgare while alkaloids were observed by Mayer’s test only in Cajanus indicus, Dolichos biflorus and Glycine soja. The flavonoids were observed in Cajanus indicus, Glycine soja, Benincasa cerifera, Cleome viscosa and Hordeum vulgare. The saponins were observed in Cajanus indicus, Glycine soja, Benincasa cerifera, Setaria italica and Hordeum vulgare. The tannins were observed as pyrogallol and catechol in Cajanus indicus, Glycine soja, Benincasa cerifera and Cleome viscosa. The unsaturated sterol and triterpene were observed by Liebermann Burchard test and Salkowski test in all the seven plants studied. The varied levels of mineral content were observed in Cajanus indicus, Dolichos biflorus, Glycine soja, Benincasa cerifera, Setaria italica, Cleome viscosa and Hordeum vulgare. The nutritional value of Cajanus indicus, Dolichos biflorus, Glycine soja, Benincasa cerifera, Setaria italica, Cleome viscosa and Hordeum vulgare.

Silicon is the second most abundant element in the earth's crust, and hence is plentiful in most soils.Silica is absorbed by plants as silicic acid, with cereals and grasses containing the highest concentrations (0.2-2.0%).Most soils contain significant quantities of silica, but continuous cropping, particularly with crops that accumulate significant quantities of silica, can reduce plant available levels of Si to the point that supplemental Si fertilization is required.There appears to be a need for Si amendments in temperate as well as tropical crop production systems, and Si fertilizers are applied to crops in several countries for increased productivity and sustainable production.High silica uptake has been shown to improve drought resistance, increase resistance to fungi and other pathogens, and increase plant growth rate and yield.However, its essentiality as a micronutrient for higher plants is difficult to prove, partly due to the fact that many positive effects of Si are most apparent in cases of abiotic stresses.Silica amendments have also been shown to correct soil toxicities resulting from high levels of soluble Mn 2+ , Fe 2+ , and Al 3+ .Most plants groups are known to deposit silica between the cells and tissues in solid form creating amorphous structures called Phytoliths or Silica bodies.Phytoliths are formed after absorbing silica in soluble form, as is offered in Biological silica.They provide mechanical strength and rigidity to plant parts and act as defence system against insects, pests and fungal infestations as well as improve water balance, plant growth and yield, rates of photosynthesis and reproduction.Silica acts as immune-stimulator within crops thus enable the enhancement of defence mechanism in crops.Silica enables the plants build up a physical mineral barrier lining the cell.This makes it difficult for biting and sucking bugs to damage the plants.Naturally this reduces the food intake, growth longevity and population growth ofxylem feeding insects and other pathogens.It has been observed that plants accumulate Silica around fungal infected sites.If the plant has sufficient silica level, it creates an active defence against fungal infections as well.From last few decade silicon is getting great attention due to its abundance and non-hazardous nature.Silicon nutrition is found to be very helpful providing resistance to crops against biotic and abiotic stresses.Silicon also provide resistance to the plants against pathogens.The present review is thus attempted to define nature of silica, its compatibility with crops and applications of silica in enhancement of agricultural productivity in terms of sustainable agriculture.

The medicinal plants are the resources of novel molecules and phytochemicals of wide pharmacological significance.Such novel agents in medicinal plants are significant as these play a key role in our body's vital needs.There is still a need to explore surplus biodiversity of medicinal plants and different novel agents that can be utilized pharmacologically.The present study was performed to prepare different formulations of anti-ageing cream using ethanolic extracts of fruits of Martynia annua.The cream formulations (F1-F6) prepared was having softness, whitening and antiseptic effects on the skin.These formulations can be safely used on the skin.The research work suggests that, the ethanolic extract of Martynia annua can be used to prepare an ideal face cream.The study finally concludes that, the composition of the extract and the base of the cream F5 and F6 were found to be more stable and safer in terms of all respect.

Aim: Clinical evaluation of aspartate aminotransferase (AST) in gingival crevicular fluid (GCF) with and without laser biostimulation as an adjunctive to non-surgical periodontal therapy (NSPT). Materials and Methods: This is a split-mouth randomized trial. Ten patients (20 sites) were diagnosed with chronic periodontitis as per the American Academy of Periodontology (AAP) classification (1999), and radiographic evidence of horizontal bone loss was provided. Scaling and root planning (SRP) was performed in both the test groups. One of the test groups was treated with low-level laser therapy (LLLT) along with SRP and another with only SRP. GCF collection was done at baseline, during the third and sixth months by using microcapillary tubes for the estimation of AST. Quantification of AST was done by a Semi-automated Clinical Chemistry Analyzer. The data were subjected to statistical analysis by an independent t-test, Kruskal–Wallis test, Mann–Whitney U test, Wilcoxon signed-rank test, and post hoc pairwise comparison. Results: The results revealed a statistically significant reduction in pocket probing depth (PPD) (P < 0.001) and relative attachment gain (P < 0.001) at the test sites when compared from baseline till six months. Similarly, there was a statistically significant reduction in AST levels in GCF at the sites treated with laser biostimulation along with NSPT (P < 0.001). Conclusion: Laser biostimulation along with NSPT has shown propitious results as per clinical and biochemical marker analysis and evaluation.