On the spectrum of Random Simplicial Complexes in Thermodynamic Regime

Linial-Meshulam complex is a random simplicial complex on $n$ vertices with a complete $(d-1)$-dimensional skeleton and $d$-simplices occurring independently with probability p. Linial-Meshulam complex is one of the most studied generalizations of the Erd\H{o}s-R{\'e}nyi random graph in higher dimensions. In this paper, we discuss the spectrum of adjacency matrices of the Linial-Meshulam complex when $np \rightarrow \lambda$. We prove the existence of a non-random limiting spectral distribution(LSD) and show that the LSD of signed and unsigned adjacency matrices of Linial-Meshulam complex are reflections of each other. We also show that the LSD is unsymmetric around zero, unbounded and under the normalization $1/\sqrt{\lambda d}$, converges to standard semicircle law as $\lambda \rightarrow \infty$. In the later part of the paper, we derive the local weak limit of the line graph of the Linial-Meshulam complex and study its consequence on the continuous part of the LSD.Comment: 32 Pages, 7 Figures, 1 Tabl

A non-Gaussian limit for linear eigenvalue statistics of Hankel matrices

This article focuses on linear eigenvalue statistics of Hankel matrices with independent entries. Using the convergence of moments we show that the linear eigenvalue statistics of Hankel matrices for odd degree monomials with degree greater than or equal to three does not converge in distribution to a Gaussian random variable. This result is a departure from the known results, Liu, Sun and Wang (2012), Kumar and Maurya (2022), of linear eigenvalue statistics of Hankel matrices for even degree monomial test functions, where the limits were Gaussian random variables.Comment: 22 Pages, 3 figure

Induced hypotension for functional endoscopic sinus surgery: comparison between dexmedetomidine and nitro-glycerine

Background: Functional endoscopic sinus surgery (FESS) is a minimally invasive technique used to restore sinus ventilation and normal function by opening sinus air cells and ostia. FESS requires bloodless field, several techniques and drugs have been used in the past for achieving controlled hypotension such as nitroglycerine, esmolol, remifentanil, dexmedetomidine, isoflurane, propofol. Therefore, this study was conducted to compare between dexmedetomidine and nitroglycerine for controlled hypotension for FESS. Primary aim to compare quality of surgical field using average category scale and surgeon satisfaction and secondary aim to compare arterial pressure and heart rate changes between dexmedetomidine and nitroglycerine when used to induce hypotension.Methods: This study was conducted in 40 consenting adult patients posted for FESS and were randomly divided into two groups, group D received dexmedetomidine 1 mcg/kg and group N received nitroglycerine 0.5 mcg/kg/min, both infusions started 10 min after induction. Parameters such as quality of surgical field by average category scale, heart rate and mean arterial pressure (MAP) recorded every 10 minutes.Results: Dexmedetomidine and nitroglycerine both had comparable quality of surgical field. ACS grading of 1 or 2 were found among both the groups. Dexmedetomidine group had better mean arterial pressure at 10th, 20th, 30th, 40th, 50th, 60th and 70th min and heart rate at 10th, 20th, 30th, 40th, 50th, 60th and 70th min when compared to nitroglycerine group.Conclusions: Dexmedetomidine and nitroglycerine both were found to be safe to use for controlled hypotension in functional endoscopic sinus surgeries

Identification of lunar volcanic tubes, a potential site for human settlement using 3D Chandrayaan-1 TMC data

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Future Indian earth observation systems

Indian Earth Observation (EO) capability has increased manifold since the launch of Bhasakra-I in 1979 to Cartosat-Z in 2007. Improvements are not only in spatial, spectral. temporal and radiometric resolutions but also in their coverage and value added products. It has also entered into the arena of passive and active microwave remote sensing. stereo viewing and viewing from the geo-synchronous platform at moderately high resolution. Observations specific to oceans and atmosphere are getting further emphasis. Demand for a constellation of satellites for monitoring disaster situations is strongly made. In this context, India has made extensive plans for continuity and enhancement in EO capability. not only towards its OWn national needs. but also as a contributing participant towards Global Earth Observation System of Systems (GEOSS). Major emphasis of the future plan has been to consolidate theme-specific satellites. in order to fill the gaps in observation including those for disaster monitoring and mitigation, and also to develop synergy with international missions for complementing and supplementing Indian missions. The future Indian EO systems include those for land applications-Resourcesat witli wide swath LlSS- Ill, high resolution Cartosat (0.3 m) and Imaging Radar (RISAT: C-band, multi- polarization). It also proposes to develop space based hyper-spectral sensor and atmospheric corrector. The future ocean application sensors include improved Ocean Color Monitor, Ku band scatterometer and a thermal IR sensor. The two major satellites dedicated for atmospheric observations are INSAT-3D with 6 channel imager and 19 channel sounder. and the ISRO-CNES joint venture Megha Tropiques with three sensors viz. MADRAS, SAPHIRE and ScaRab. Satellite for Argos and Ka band radio altimeter (SA RA I,). a joint ISRO-CNES mission is also underway. L-band polarimetric radiometer. hyper spectral sounder. rain radar, millimeter wave sounder, high resolution imager from geo-synchronous platform are some of the sensors being considered for future missions

Harnessing ornamental fisheries resources for sustainable growth and development: A trade perspective from Kerala, India

Ornamental fish trade has gained paramount importance with more than 125 countries involved in the freshwater and marine fishes. The global trade is estimated to be around US $ 450 million registering a growth rate of ten percent since 2001. Asia caters up to 60 per cent of the global trade while India stands with a dismal 0.9 per cent with a portfolio of 30-35 fresh water species. The ornamental fish resources of Kerala has huge potential with untapped and unexploited resources. However the performance of the sector is not worthy and production is much below the demand. The SWOL analysis - Strengths, Weaknesses, Opportunities and Limitations analysis - is done to analyse the status of ornamental fish industry in Kerala. The results indicated that good export market, high demand, availability of under-utilized marine resources, potential for rural development, low cost effort, efficiency of ornamental fish marketers, institutional support for development and promotions were the major strengths. Dependence on wild caught species, inadequate data on resources, wastage of resources, unwillingness towards marine fishes, lack of trained/ skilled manpower and organized trade, lack of adept technologies, poor marketing facilities, backwardness in international market, weak market image and lack of fishing regulations were the major inherent weaknesses. The major opportunities were enhancement of species portfolio, increasing market value, less capital intensive, high popularity and demand, breeding and culture of indigenous fishes, faster market growth, entry to new market destinations, increased awareness of international buyers and support of government. Technological backwardness, technology transfer, insufficient awareness programmes, adverse government policies, competitions from neighboring countries, sustainability of resources and drastic drop in fish prices were the major limitations. The study suggests concerted efforts by the different stakeholders to enhance the production of the sector

Changes in expression of VE-cadherin and MMPs in endothelial cells: Implications for angiogenesis

The mechanism of cell-cell contact dependent regulation of pericellular proteolysis in angiogenesis was examined by studying the expression of MMPs using isolated HUVECs in culture. Zymography, Immunoblot and RT-PCR analysis showed that the production and secretion of matrixmetalloproteinase-2 and matrixmetalloproteinase-9 by HUVECs in culture were high when they remain as individual cells and significantly decreased during later stages of culture when cells developed cell-cell contact and tubular network-like structure. As MMPs decreased there was significant upregulation of VE-cadherin in cells undergoing angiogenic transition. Investigations to understand the signaling pathways downstream of VE-cadherin showed a relatively high level of β-catenin in the nucleus of endothelial cells in culture during initial stages and decrease in its levels in the nucleus, associated with an increase in the cytosol during later stages of culture. The distribution of β-catenin was found to be regulated by Tyr/Ser phosphorylation status of this protein. Cell-cell contact dependent downregulation of MMPs during angiogenesis was also observed in experiments using proangiogenic substances which caused a rapid rate of downregulation of MMP-2 and MMP-9 and absence of downregulation of MMPs when treated with anti-angiogenic agents