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Multidimensional Child Poverty in the City of Kolkata: Construction and Identification from the Perspective of 8 years old School-going Children
No full textThe Sustainable Development Goal (SDG) 1 aims to end poverty in all its forms, everywhere. Although children experience poverty differently from adults and their needs and expectations are different, child poverty is rarely differentiated from adult poverty, and its special dimensions are often recognised. For the first time, as part of the SDGs, countries have committed to addressing child poverty specifically and directly, which is not derived from household poverty. This article aims to measure multidimensional child specific poverty in India in response to such global norms and trends focusing on the child rather than the household as a whole. We utilise the data collected in the third wave of “Children’s Worlds Survey, 2016–19” for India, which was conducted in the metro city of Kolkata in place of all over the country, bearing in mind the financial as well as the time constraints. This survey allows the yardstick of deprivation informed by subjective opinion of the children, the measure which takes us deeper into the ‘rights based’ approach. Measuring child specific poverty with this approach in the Indian context has not been attempted so far. This article is an effort to contribute to this end. We intend to identify the multidimensional poor school-going 8 years old children from the perspective of themselves following the dual cut-offs approach proposed by Alkire and Foster in 2011. Also, it allows us empirically test three issues like, (i) if the status of these children to be multidimensional poor is significantly gender (boys/girls) sensitive, (ii) if does it depend significantly on the region (northern/southern) the children belong to, and, (iii) if does it depend significantly on the type of school (government/private) the children are enrolled. Our findings show that in the metro city of Kolkata more than fifty percent of 8 years old children, enrolled in government schools, are multidimensional poor, whereas, the situation of private schools are quite better. This is alarming in terms of fulfillment of Sustainable Development Goal 1 targeting the eradication of poverty in all its forms and dimensions. However, we do not find significant gender bias while significant regional disparity is evidenced from our test results
On (n,m)-chromatic numbers of graphs with bounded sparsity parameters
No full textAn (n,m)-graph is characterized by n types of arcs and m types of edges. A homomorphism of an (n,m)-graph G to an (n,m)-graph H, is a vertex mapping that preserves adjacency, direction, and type. The (n,m)-chromatic number of G, denoted by χn,m(G), is the minimum value of |V(H)| such that there exists a homomorphism of G to H. The theory of homomorphisms of (n,m)-graphs have connections with graph theoretic concepts like harmonious coloring, nowhere-zero flows; with other mathematical topics like binary predicate logic, Coxeter groups; and has application to the Query Evaluation Problem (QEP) in graph database. In this article, we show that the arboricity of G is bounded by a function of χn,m(G) but not the other way around. Additionally, we show that the acyclic chromatic number of G is bounded by a function of χn,m(G), a result already known in the reverse direction. Furthermore, we prove that the (n,m)-chromatic number for the family of graphs with maximum average degree less than [Formula presented.], including the subfamily of planar graphs with girth at least 8(2n+m), equals 2(2n+m)+1. This improves upon previous findings, which proved the (n,m)-chromatic number for planar graphs with girth at least 10(2n+m)−4 is 2(2n+m)+1. It is established that the (n,m)-chromatic number for the family T2 of partial 2-trees is both bounded below and above by quadratic functions of (2n+m), with the lower bound being tight when (2n+m)=2. We prove 14≤χ(0,3)(T2)≤15 and 14≤χ(1,1)(T2)≤21 which improves both known lower bounds and the former upper bound. Moreover, for the latter upper bound, to the best of our knowledge we provide the first theoretical proof
On isometric embeddability of Sminto Snpas non-commutative quasi-Banach spaces
No full textThe existence of isometric embedding of Sm into Snp, where 1 ≤p ≠q≤ ∞ and m, n ≥ 2, has been recently studied in. In this article, we extend the study of isometric embeddability beyond the above-mentioned range of p and q. More precisely, we show that there is no isometric embedding of the commutative quasi-Banach space lmq(R) into lnp (R), where (q, p) ∈ (0,∞) × (0, 1) and p ≠ q. As non-commutative quasi-Banach spaces, we show that there is no isometric embedding of Smq into Snp, where (q, p) ∈ (0, 2) \ {1} × (0, 1) ∪{1} × (0, 1) \{1/n : n ∈ N} ∪ {∞} × (0, 1) \{1/n : n ∈ N} and p ≠ q. Moreover, in some restrictive cases, we also show that there is no isometric embedding of Smq into Snp, where (q, p) ∈ [2,∞) × (0, 1). A new tool in our paper is the non-commutative Clarkson\u27s inequality for Schatten class operators. Other tools involved are the Kato-Rellich theorem and multiple operator integrals in perturbation theory, followed by intricate computations involving power-series analysis
Otsu-BRSG: An Effective Algorithm for River Bank Line Detection and Monitoring in the Challenging Terrains of Kaziranga National Park
No full textThe topography of the Kaziranga National Park (KNP), situated in Central Assam, India, is undergoing enormous erosion and accretion as a result of unforeseen changes in the Brahmaputra River’s course. Since monsoon rains and subsequent floods inundate the National Park area annually, the geographical analysis of the riverfront region surrounding the Park has been a laborious effort. The task of detecting the river bank-line becomes quite difficult as the topography of the landscape is continuously changing over the time period. The river course and vegetative parts are primarily affected by the heavy seasonal rainfall in the area. The region of interest consists of bare land which includes sandbar (also known as shoal), different types of vegetation, and water bodies. In such a scenario, extraction of edges using classical edge detection algorithms is quite challenging. A list of multispectral Landsat and Sentinel 2 imagery is used here to determine the river bank line of Brahmaputra which represents the northern boundary of the KNP using the smoothening capability of Savitzky-Goley filter followed by a suitable edge plotting method which is dependant on the locations of the edge pixels with respect to the other pixels in the image. The method suggests the suitability of an Otsu segmentation-based boundary refining algorithm (Otsu-BRSG) that examines the evolution of the above-mentioned bank line region between 2008 and 2018 and also the south-west boundary of Majuli Island as an additional case study between 2018 and 2022. This study explored a detailed comparative analysis of different vegetations in the highly affected regions from the viewpoint of multisource earth observation sensors using changes in bank line edges to measure soil erosion across the study period (2008–2018) along with the changes in riparian vegetation. The analysis revealed a net loss of 540.63 ha of wooded area in the vulnerable region, revealing an alarming trend of erosion
Pairs of inner projections and two applications
No full textOrthogonal projections onto closed subspaces of H2(Dn) of the form φH2(Dn) for inner functions φ on Dn are referred to as inner projections, where H2(Dn) denotes the Hardy space over the open unit polydisc Dn. In this paper, we classify pairs of commuting inner projections. We also present two seemingly independent applications: the first is an answer to a question posed by R. G. Douglas, and the second is a complete classification of partially isometric truncated Toeplitz operators with inner symbols on Dn
Pushforward of structure sheaf and virtual global generation
No full textLet be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle is virtually globally generated. Moreover, is ample if and only if f is genuinely ramified
Q factor: A measure of competition between the topper and the average in percolation and in self-organized criticality
No full textWe define the Q factor in the percolation problem as the quotient of the size of the largest cluster and the average size of all clusters. As the occupation probability p is increased, the Q factor for the system size L grows systematically to its maximum value Qmax(L) at a specific value pmax(L) and then gradually decays. Our numerical study of site percolation problems on the square, triangular, and simple cubic lattices exhibits that the asymptotic values of pmax, though close, are distinct from the corresponding percolation thresholds of these lattices. We also show, using scaling analysis, that at pmax the value of Qmax(L) diverges as Ld (d denoting the dimension of the lattice) as the system size approaches its asymptotic limit. We further extend this idea to nonequilibrium systems such as the sandpile model of self-organized criticality. Here the Q(ρ,L) factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches, with ρ the drop density of the driving mechanism. This study was prompted by some observations in sociophysics
Relationships between cumulative entropy/extropy, Gini mean difference and probability weighted moments
No full textIn this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative past extropy are also established. We then show that several entropy and extropy measures discussed here can be brought into the framework of probability weighted moments, which would facilitate finding estimators of these measures
Relationships between inflation, output growth, and uncertainty in the era of inflation stabilization: a multicountry study
No full textSince the 1990s, central banks in many industrialized and developing countries have adopted similar policy strategies for stabilizing inflation. In this context, it has been argued that during common policy periods, the relationships between inflation, output growth, and their uncertainties are stable and more uniform across countries. We intend to verify this for 19 countries using both linear and non-linear bivariate GARCH-in-mean models. According to our findings, the non-linear regime-dependent model performs better in most of the sampled countries. It has been observed that inflation uncertainty has a significant impact on inflation, particularly in developing countries. Nominal and real uncertainty affect output growth primarily during periods of economic contraction. Although nominal uncertainty inhibits output growth, real uncertainty has mixed effects. In most countries, negative growth shocks result in greater output growth volatility than positive growth shocks. Furthermore, in some countries, output growth significantly increases inflation only in high-inflation regimes
Robust Clustering with Normal Mixture Models: A Pseudo β-Likelihood Approach
No full textAs in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust alternative to the ordinary likelihood approach for this estimation problem is proposed which performs simultaneous estimation and data clustering and leads to subsequent anomaly detection. To invoke robustness, the methodology based on the minimization of the density power divergence (or alternatively, the maximization of the β-likelihood) is utilized under suitable constraints. An iteratively reweighted least squares approach has been followed in order to compute the proposed estimators for the component means (or equivalently cluster centers) and component dispersion matrices which leads to simultaneous data clustering. Some exploratory techniques are also suggested for anomaly detection, a problem of great importance in the domain of statistics and machine learning. The proposed method is validated with simulation studies under different set-ups; it performs competitively or better compared to the popular existing methods like K-medoids, TCLUST, trimmed K-means and MCLUST, especially when the mixture components (i.e., the clusters) share regions with significant overlap or outlying clusters exist with small but non-negligible weights (particularly in higher dimensions). Two real datasets are also used to illustrate the performance of the newly proposed method in comparison with others along with an application in image processing. The proposed method detects the clusters with lower misclassification rates and successfully points out the outlying (anomalous) observations from these datasets