Properties of Hesse derivatives of cubic curves

The Hesse curve or Hesse derivative Hess$(\Gamma_f)$ of a cubic curve $\Gamma_{f}$ given by a homogeneous polynomial $f$ is the set of points $P$ such that $\det \left(H_f (P)\right)=0$, where $H_f (P)$ is the Hesse matrix of $f$ evaluated at $P$. Also Hess$(\Gamma_f)$ is again a cubic curve. We show that for a point $P\in$Hess$(\Gamma_{f})$, all the contact points of tangents from $P$ to the curves $\Gamma_{f}$ and Hess$(\Gamma_{f})$ are intersection points of two straight lines $\ell_1^P$ and $\ell_2^P$ (meeting on Hess$(\Gamma_{f})$) with $\Gamma_{f}$ and Hess$(\Gamma_{f})$, where the product of $\ell_1^P$ and $\ell_2^P$ is the polar conic of $\Gamma_{f}$ at $P$. The operator Hess defines an iterative discrete dynamical system on the set of the cubic curves. We identify the two fixed points of this system, investigate orbits that end in the fixed points, and discuss the closed orbits of the dynamical system.Comment: 14 pages, 3 figure

Analysing the Extent of Misinformation in Cancer Related Tweets

Twitter has become one of the most sought after places to discuss a wide variety of topics, including medically relevant issues such as cancer. This helps spread awareness regarding the various causes, cures and prevention methods of cancer. However, no proper analysis has been performed, which discusses the validity of such claims. In this work, we aim to tackle the misinformation spread in such platforms. We collect and present a dataset regarding tweets which talk specifically about cancer and propose an attention-based deep learning model for automated detection of misinformation along with its spread. We then do a comparative analysis of the linguistic variation in the text corresponding to misinformation and truth. This analysis helps us gather relevant insights on various social aspects related to misinformed tweets.Comment: Proceedings of the 14th International Conference on Web and Social Media (ICWSM-20

Revisiting a family of wormholes: geometry, matter, scalar quasinormal modes and echoes

We revisit a family of ultra-static Lorentzian wormholes which includes Ellis-Bronnikov spacetime as a special case. We first show how the required total matter stress energy (which violates the local energy conditions) may be split into a part due to a phantom scalar and another extra piece (which vanishes for Ellis--Bronnikov) satisfying the Averaged Null Energy Condition (ANEC) along radial null geodesics. Thereafter,we examine the effective potential for scalar wave propagation in a general setting. Conditions on the metric function, for which the effective potential may have double barrier features are written down and illustrated (using this class of wormholes). Subsequently, using numerous methods, we obtain the scalar quasinormal modes (QNMs). We note the behaviour of the QNMs as a function of $n$ (the metric parameter) and $b_0$ (the wormhole throat radius). Thus, the shapes and sizes of the wormholes, governed by the metric parameter $n$ and the throat radius $b_0$ are linked to the variation and the values of the QNMs. Finally, we demonstrate how, for large $n$, the time domain profiles exhibit, expectedly, the occurence of echoes. In summary, our results suggest that this family of wormholes may indeed be used as a template for further studies on the gravitational wave physics of exotic compact objects.Comment: Revised version. Title changed. More compact presentation with additions. To appear in European Physical Journal

Implementation and Optimization of Algal Biomass in Value-Added Products Recovery: A Step towards Algae-Based Green Economy

Algal biomass is a prospective feedstock for the eco-sustainable production of many different products with added value, such as meals, feeds, and fuels. The remaining biomass from the algae can be used as raw material and can be transformed into useful secondary products after the important macromolecules have been removed. By optimizing algal biomass hydrolysate utilizing microbial fermentation, several studies demonstrated the generation of bioenergy (bioalcohol, biogas, and biohydrogen) and biochemicals (organic acids and biopolymers). Since the harvest and maintenance of sustainable algal cultivation incur considerable energy and economical prowess, developing products from algae remains a challenge to be countered in commercial applications. This is a typical bottleneck issue when processing algae for fuels or chemicals at the pilot scale. Implementation of integrated algae biorefinery methods can substantially reduce the cost of production and energy consumption. An algae-based green economy can be financially more viable and utilizable, especially for countries with weaker economies. This review’s goal is to examine the implementation of integrated biorefineries for the recovery of bioproducts generated from algae and potential applications. In this context, the life cycle analysis and business elements of a unified algal biorefinery are also addressed

An observational study of the effect of escitalopram and etizolam in type 2 diabetes mellitus patients with depression

Background: Past decades have witnessed a rapid rise in the prevalence of diabetes mellitus; estimated to affect 415 million adults worldwide and 69.1 million adults in India. There has been an increased prevalence of diabetes associated depression, which can aggravate the symptoms of depression and diabetes associated complications. Use of tricyclic antidepressants (TCA) can disturb the glycemic control. Escitalopram is a selective serotonin reuptake inhibitor (SSRI) and Etizolam is a new safe antianxiety agent. The objective of this study was to study the prevalence of depression and anxiety in type 2 diabetes mellitus patients and to assess the efficacy of escitalopram and etizolam in the treatment of depression and/or anxiety in type 2 diabetes mellitus patients.Methods: Total 125 patients diagnosed with type 2 diabetes mellitus with fulfilling the inclusion and exclusion criteria were included in the study. Informed written consent was obtained from the patients willing to participate in the study. They were screened for the presence of depression with the help of PHQ-9. Their demographic features were recorded and initial laboratory investigations done. Haemogram, blood sugar level - fasting (BSL-F) and postprandial (PP), serum alanine transferase (ALT), serum creatinine and Urine routine analysis. Patients were started on Escitalopram (10 mg) + Etizolam (0.5 mg) daily for 30 days and others were not treated and acted as control; keeping the management of diabetes mellitus unchanged for all. Laboratory investigations were repeated after 30 days.Results: The prevalence of depression with/without anxiety was 35.2%. 51 patients treated with Escitalopram + Etizolam improved clinically and biochemically. There was a significant (P < 0.05) improvement in BSL-F and PP and HbA1C in patients treated with Escitalopram + Etizolam.Conclusions: Prevalence of depression among type 2 diabetes mellitus was found to be 35% in this study. Fifty one patients treated with escitalopram + etizolam improved clinically as well as biochemically. There was significant improvement in BSL-F, BSL-PP and HbA1c. Escitalopram may be considered as antidepressant of choice in such cases

2,4-dihydroxy benzaldehyde derived Schiff bases as small molecule Hsp90 inhibitors: rational identification of a new anticancer lead

Hsp90 is a molecular chaperone that heals diverse array of biomolecules ranging from multiple oncogenic proteins to the ones responsible for development of resistance to chemotherapeutic agents. Moreover they are over-expressed in cancer cells as a complex with co-chaperones and under-expressed in normal cells as a single free entity. Hence inhibitors of Hsp90 will be more effective and selective in destroying cancer cells with minimum chances of acquiring resistance to them. In continuation of our goal to rationally develop effective small molecule azomethines against Hsp90, we designed few more compounds belonging to the class of 2,4-dihydroxy benzaldehyde derived imines (1-13) with our validated docking protocol. The molecules exhibiting good docking score were synthesized and their structures were confirmed by IR, (1)H NMR and mass spectral analysis. Subsequently, they were evaluated for their potential to suppress Hsp90 ATPase activity by Malachite green assay. The antiproliferative effect of the molecules were examined on PC3 prostate cancer cell lines by adopting 3-(4,5-dimethythiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) assay methodology. Finally, schiff base 13 emerged as the lead molecule for future design and development of Hsp90 inhibitors as anticancer agents.Fil: Dutta Gupta, Sayan. Osmania University; India. Jawaharlal Nehru Technological University; IndiaFil: Revathi, B.. Osmania University; IndiaFil: Mazaira, Gisela Ileana. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Biológica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Galigniana, Mario Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Biológica; ArgentinaFil: Subrahmanyam, C. V. S.. Osmania University; IndiaFil: Gowrishankar, N. L.. Swami Vivekananda Institute of Pharmaceutical Sciences; IndiaFil: Raghavendra, N. M.. Osmania University; Indi