Generalized Z2×Z2\mathbb{Z}_2\times \mathbb{Z}_2 in Scaling neutrino Majorana mass matrix and baryogenesis via flavored leptogenesis

We investigate the consequences of a generalized $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry on a scaling neutrino Majorana mass matrix. It enables us to determine definite analytical relations between the mixing angles $\theta_{12}$ and $\theta_{13}$, maximal CP violation for the Dirac type and vanishing for the Majorana type. Beside the other testable predictions on the low energy neutrino parameters such as $\beta\beta_{0\nu}$ decay matrix element $|M_{ee}|$ and the light neutrino masses $m_{1,2,3}$, the model also has intriguing consequences from the perspective of leptogenesis. With the assumption that the required CP violation for leptogenesis is created by the decay of lightest ($N_1$) of the heavy Majorana neutrinos, only $\tau$-flavored leptogenesis scenario is found to be allowed in this model. For a normal (inverted) ordering of light neutrino masses, $\theta_{23}$ is found be less (greater) than its maximal value, for the final baryon asymmetry $Y_B$ to be in the observed range. Besides, an upper and a lower bound on the mass of $N_1$ have also been estimated. Effect of the heavier neutrinos $N_{2,3}$ on final $Y_B$ has been worked out subsequently. The predictions of this model will be tested in the experiments such as nEXO, LEGEND, GERDA-II, T2K, NO$\nu$A, DUNE etc.Comment: 37 pages, 12 figures, 9 tables, version accepted for publication in JHE

Phenomenological implications of the Friedberg-Lee transformation in a neutrino mass model with μτ\mu\tau-flavored CP symmetry

We propose a neutrino mass model with $\mu\tau$-flavored CP symmetry, where the effective light neutrino Lagrangian enjoys an additional invariance under a Friedberg-Lee (FL) transformation on the left-handed flavor neutrino fields, that leads to a highly predictive and testable scenario. While both types of the light neutrino mass ordering, i.e., Normal Ordering (NO) as well as the Inverted Ordering (IO) are allowed, the absolute scale of neutrino masses is fixed by the vanishing determinant of light Majorana neutrino mass matrix $M_\nu$. We show that for both types of mass ordering, whilst the atmospheric mixing angle $\theta_{23}$ is in general nonmaximal ($\theta_{23}\neq \pi/4$), the Dirac CP phase $\delta$ is exactly maximal ($\delta=\pi/2,3\pi/2$) for IO and nearly maximal for NO owing to $\cos\delta\propto \sin\theta_{13}$. For the NO, very tiny nonvanishing Majorana CP violation might appear through one of the Majorana phases $\beta$; otherwise the model predicts vanishing Majorana CP violation. Thus, despite the fact, that from the measurement of $\theta_{23}$, it is difficult to rule out the model, any large deviation of $\delta$ from its maximality, will surely falsify the scenario. For a comprehensive numerical analysis, beside fitting the neutrino oscillation global fit data, we also present a study on the $\nu_\mu\rightarrow \nu_e$ oscillation which is expected to show up Dirac CP violation in different long baseline experiments. Finally, assuming purely astrophysical sources, we calculate the Ultra High Energy (UHE) neutrino flavor flux ratios at neutrino telescopes, such as IceCube, from which statements on the octant of $\theta_{23}$ could be made in our model.Comment: 20 pages, 7 figures, updated with clarifications and minor changes, version published in JHE

Humanitarian Laws and Human Rights Law-Analysis of Existing Differences and Similarities?

The purpose of this article is to make visible the thin line demarcation between humanitarian law and human rights law, which can only be understood by tracing history of both the concepts and analyze there difference at the nanoscopic level. International law offers to States a great scale of means and measures for the peaceful settlement of disputes with a view to an effective abolition of the recourse to war. War is a rot to humanity and involves most brutal and arbitrary violence. However, as human rights law and humanitarian law have totally different historical origins, the codification of these laws has been very recently followed entirely different lines. But still international humanitarian law is increasingly perceived as part of human rights law applicable in the armed conflict. The purpose of this article is to study the origin of humanitarian and law relating to human right, there differences and similarity. Finally the view expressed by Indian Courts over the issue with a conclusion throwing light on the modern approach over the issue

Design and Development Towards a Novel Prosthesis for Total Shoulder Arthroplasty to Reduce Aseptic Glenoid Loosening

Total shoulder arthroplasty (TSA) is the most common surgical solution, that helps in restoring the structural and functional integrity of a diseased glenohumeral (GH) joint with intact rotator-cuff. A 300% increase in the usage of TSA has been observed since 2007, along with 2.5% increase in revision rate. Aseptic glenoid loosening accounts for 37% of postsurgical failures in TSA. Eccentric loading of the prosthetic glenoid cup, leading to the “rocking horse” effect, is one of the prevalent causes of aseptic glenoid loosening. Current anatomical total shoulder prosthesis (ATSP) geometry does not consider all the GH morphometric features, for example the elliptical shape of the humeral head. Moreover, the morphometric studies leading to the initial ATSP design did not consider the GH morphology of any sub-Saharan population. Hence, there exists a gap in understanding of the implications of certain morphometric features on the functionality of a post-TSA GH joint. This thesis had two primary aims to address this gap in knowledge. Firstly, to study the GH morphometric variations between cohorts representing native European (Swiss) and native sub-Saharan (South African) populations. Secondly, to develop anatomically inspired ATSP design concepts and test them using biomechanical and finite element (FE) models, insilico, under standardised testing protocols. The morphometric analysis suggested that an average Swiss humeral head radius of curvature was larger (P28mm or <19mm. Considering both the populations, the inherent shape of an average humeral head was found to be elliptical. The thickest region of the head was found to lie in the posterior region and not at the geometric center. Hertzian contact theory was applied to calculate the GH stresses produced by symmetric and asymmetric elliptical heads. Higher concentric stresses (P<0.001), within the acceptable limit for polyethylene, were observed to be imparted by the asymmetric heads. Population-specific musculoskeletal models were developed to study the post-TSA kinematic variation. When an identical range of motion (RoM) was performed by these models, population-specific variation in muscle moment arms was observed. The novel glenoid designs were not found to alter the post-surgical kinematics. FE models of the biradial, compartmental and pear-shaped glenoid implant designs were subjected to compressive and shear loading according to the American Society for Testing and Materials (ASTM). Using the bi-radial the glenoid cup, with thickened posterior-superior surface, anatomically relevant force distribution patterns could be replicated. Compartmentalising the glenoid prosthesis into concentric and eccentric regions with the gaps, proved to be highly beneficial. When compared to a commercially available glenoid prosthesis, the compartmental prosthesis was able to contain the GH forces to the concentric region for longer, delaying the eccentric loading and therefore potentially reducing the “rocking horse” effect. In the light of the above observations, two conclusions can be drawn from this thesis. Firstly, it would be beneficial if population-specific ATSP were made available for natives of certain geographic locations. Secondly, glenoid prosthesis designs could be compartmentalised to contain the GH joint forces within the concentric regions of the cup which might aid in the reduction of post-TSA complications

TRANSFORMATION AND CLASSIFICATION OF ORDINAL SURVEY DATA

Currently, Machine Learning is being significantly used in almost all of the research domains. However, its applicability in survey research is still in its infancy. We in this paper, attempt to highlight the applicability of Machine Learning in survey research while working on two different aspects in parallel. First, we introduce a pattern-based transformation method for ordinal survey data. Our purpose behind developing such a transformation method is twofold. Our transformation facilitates easy interpretation of ordinal survey data and provides convenience while applying standard Machine Learning approaches. Second, we demonstrate the application of various classification techniques over real and transformed ordinal survey data and interpret their results in terms of their suitability in survey research. Our experimental results suggest that Machine Learning coupled with the Pattern Recognition paradigm has a tremendous scope in survey research

Parameterized Complexity of Path Set Packing

In PATH SET PACKING, the input is an undirected graph $G$, a collection $\cal P$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\cal P$. We study the parameterized complexity of PATH SET PACKING with respect to both natural and structural parameters. We show that the problem is $W[1]$-hard with respect to vertex cover plus the maximum length of a path in $\cal P$, and $W[1]$-hard respect to pathwidth plus maximum degree plus solution size. These results answer an open question raised in COCOON 2018. On the positive side, we show an FPT algorithm parameterized by feedback vertex set plus maximum degree, and also show an FPT algorithm parameterized by treewidth plus maximum degree plus maximum length of a path in $\cal P$. Both the positive results complement the hardness of PATH SET PACKING with respect to any subset of the parameters used in the FPT algorithms

Qualitative Nature of Some Traditional Crude Drugs Available in Commercial Markets of Mumbai, Maharashtra, India

Medicinal plants have been used since ancient times for the treatment of human ailments. Interest in medicinal plants has been shown throughout the world because of the safe and effective constituents of plant products. The increasing demand for herbal medicines, both in the developing and developed countries, has provided the stimulus for the workers in this field to maintain the quality and purity of their herbal raw materials and finished products. The standardization problem relating to herbal drugs arises from the complex composition of drugs that are used in the form of whole plants, plant parts or extracts obtained there from. To ensure reproducible quality of any herbal remedy, proper control of starting material is utmost essential. With this thought in mind, the present preliminary study was conducted in order to discover the qualitative nature of 20 Traditional crude drugs available in the commercial markets of Mumbai, Maharashtra, India

An FPT algorithm for Matching Cut and d-cut

Given a positive integer $d$, the $d$-CUT problem is to decide if an undirected graph $G=(V,E)$ has a non trivial bipartition $(A,B)$ of $V$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). When $d=1$, this is the MATCHING CUT problem. Gomes and Sau, in IPEC 2019, gave the first fixed parameter tractable algorithm for $d$-CUT, when parameterized by maximum number of the crossing edges in the cut (i.e. the size of edge cut). However, their paper doesn't provide an explicit bound on the running time, as it indirectly relies on a MSOL formulation and Courcelle's Theorem. Motivated by this, we design and present an FPT algorithm for the MATCHING CUT (and more generally for $d$-CUT) for general graphs with running time $2^{O(k\log k)}n^{O(1)}$ where $k$ is the maximum size of the edge cut. This is the first FPT algorithm for the MATCHING CUT (and $d$-CUT) with an explicit dependence on this parameter. We also observe a lower bound of $2^{\Omega(k)}n^{O(1)}$ with same parameter for MATCHING CUT assuming ETH