Indian Statistical Institute
  • Baranagar, West Bengal, India
Recent publications
Background Birt-Hogg-Dubé syndrome (BHDS) is a rare monogenic condition mostly associated with germline mutations at FLCN . It is characterized by either one or more manifestations of primary spontaneous pneumothorax (PSP), skin fibrofolliculomas and renal carcinoma (chromophobe). Here, we comprehensively studied the mutational background of 31 clinically diagnosed BHDS patients and their 74 asymptomatic related members from 15 Indian families. Results Targeted amplicon next-generation sequencing (NGS) and Sanger sequencing of FLCN in patients and asymptomatic members revealed a total of 76 variants. Among these variants, six different types of pathogenic FLCN mutations were detected in 26 patients and some asymptomatic family members. Two of the variants were novel mutations: an 11-nucleotide deletion ( c.1150_1160delGTCCAGTCAGC ) and a splice acceptor mutation ( c.1301-1G > A ). Two variants were Clinvar reported pathogenic mutations: a stop-gain ( c.634C > T ) and a 4-nucleotide duplication ( c.1329_1332dupAGCC ). Two known variants were: hotspot deletion ( c.1285delC ) and a splice donor mutation ( c.1300 + 1G > A ). FLCN mutations could not be detected in patients and asymptomatic members from 5 families. All these mutations greatly affected the protein stability and FLCN-FNIP2 interaction as observed by molecular docking method. Family-based association study inferred pathogenic FLCN mutations are significantly associated with BHDS. Conclusion Six pathogenic FLCN mutations were detected in patients from 10 families out of 15 families in the cohort. Therefore, genetic screening is necessary to validate the clinical diagnosis. The pathogenic mutations at FLCN affects the protein–protein interaction, which plays key roles in various metabolic pathways. Since, pathogenic mutations could not be detected in exonic regions of FLCN in 5 families, whole genome sequencing is necessary to detect all mutations at FLCN and/or any undescribed gene/s that may also be implicated in BHDS.
The inherently stochastic nature of community detection in real-world complex networks poses an important challenge in assessing the accuracy of the results. In order to eliminate the algorithmic and implementation artifacts, it is necessary to identify the groups of vertices that are always clustered together, independent of the community detection algorithm used. Such groups of vertices are called constant communities. Current approaches for finding constant communities are very expensive and do not scale to large networks. In this paper, we use binary edge classification to find constant communities. The key idea is to classify edges based on whether they form a constant community or not. We present two methods for edge classification. The first is a GCN-based semi-supervised approach that we term Line-GCN. The second is an unsupervised approach based on image thresholding methods. Neither of these methods requires explicit detection of communities and can thus scale to very large networks of the order of millions of vertices. Both of our semi-supervised and unsupervised results on real-world graphs demonstrate that the constant communities obtained by our method have higher F1-scores and comparable or higher NMI scores than other state-of-the-art baseline methods for constant community detection. While the training step of Line-GCN can be expensive, the unsupervised algorithm is 10 times faster than the baseline methods. For larger networks, the baseline methods cannot complete, whereas all of our algorithms can find constant communities in a reasonable amount of time. Finally, we also demonstrate that our methods are robust under noisy conditions. We use three different, well-studied noise models to add noise to the networks and show that our results are mostly stable.
The disjointness problem—where Alice and Bob are given two subsets of {1,⋯,n}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{1, \dots, n\}$$\end{document} and they have to check if their sets intersect—is a central problem in the world of communication complexity. While both deterministic and randomized communication complexities for this problem are known to be Θ(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta(n)$$\end{document}, it is also known that if the sets are assumed to be drawn from some restricted set systems then the communication complexity can be much lower. In this work, we explore how communication complexity measures change with respect to the complexity of the underlying set system. The complexity measure for the set system that we use in this work is the Vapnik—Chervonenkis (VC) dimension. More precisely, on any set system with VC dimension bounded by d, we analyze how large can the deterministic and randomized communication complexities be, as a function of d and n. The d-sparse set disjointness problem, where the sets have size at most d, is one such set system with VC dimension d. The deterministic and the randomized communication complexities of the d-sparse set disjointness problem have been well studied and are known to be Θdlogn/d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta \left( d \log \left({n}/{d}\right)\right)$$\end{document} and Θ(d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta(d)$$\end{document}, respectively, in the multi-round communication setting. In this paper, we address the question of whether the randomized communication complexity of the disjointness problem is always upper bounded by a function of the VC dimension of the set system, and does there always exist a gap between the deterministic and randomized communication complexities of the disjointness problem for set systems with small VC dimension. We construct two natural set systems of VC dimension d, motivated from geometry. Using these set systems, we show that the deterministic and randomized communication complexity can be Θ~dlogn/d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widetilde{\Theta}\left(d\log \left( n/d \right)\right)$$\end{document} for set systems of VC dimension d and this matches the deterministic upper bound for all set systems of VC dimension d. We also study the deterministic and randomized communication complexities of the set intersection problem when sets belong to a set system of bounded VC dimension. We show that there exist set systems of VC dimension d such that both deterministic and randomized (one-way and multi-round) complexities for the set intersection problem can be as high as Θdlogn/d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta\left( d\log \left( n/d \right) \right)$$\end{document}.
Research is a planned and scientific method of increasing knowledge that is typically funded by a country's government or funding agencies. Research activity produces valuable data. Research Data Services (RDS) or Research Data Management (RDM) services are considered vital services provided by an academic library and are focused on the management, archiving, processing, and reuse of critical research data. This study evaluates the current status of the adaptation of RDS or RDM services in Indian academic libraries (which includes a total of 186 institutions, including all of India's Central Universities (54) and Institutes of National Importance (132)). A method triangulation approach was used for the data collection, including a literature survey, library website study, online survey, and telephonic interview with LIS professionals from Indian academic libraries. Academic libraries in India are yet to keep up with those in developed countries in adopting RDM services owing to a lack of RDM policy, institutional support, and technological challenges, according to the data. The study also presents suggestions to decision-makers, higher authorities of academic institutions, and the government to develop a strong RDM policy at both the institutional and national levels defining the role and duties of the libraries in RDM.
In this paper, we consider a two-dimensional random amplitude chirp signal model. It is assumed that the additive error is independent and identically distributed. This is an extension of the one dimensional random amplitude chirp model proposed by Besson et al. (IEEE Trans Signal Process 47(12):3208–3219, 1999) to two-dimension. The random amplitudes can be thought of as a multiplicative error and are assumed to be independent and identically distributed with non-zero mean such that the fourth order moment exists. The parameters are estimated by maximizing a two-dimensional chirp periodogram like function and discuss their theoretical properties. The proposed estimators are consistent and we obtain the asymptotic distribution as multivariate normal. Under normality of the additive error, the proposed estimator attains the Cramer–Rao lower bound. We propose a general multicomponent two-dimensional model of similar form. The performances of the proposed estimators for finite samples are evaluated based on numerical experiments and are reported graphically.
Fueter and Polya proved that the only quadratic polynomials giving a bijection between N and N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2}$$\end{document} are the two Cantor polynomials. It is conjectured that there is no bijection from N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document} onto N given by a polynomial of degree at least 3. A similar problem arises when the domain of the map is replaced by the set of integral points in some sector in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}. Rational sectors were considered by Nathanson and Stanton. Here, we study and solve the case of general irrational sectors. In fact, our method enables us also to recover the results on rational sectors and also answer a question posed by Nathanson.
This study aims to undertake the Participatory Livelihood Vulnerability Assessment (PLVA) of forest dwellers in the Jharkhand and Odisha states of eastern Indian region. The study covers 15 tribes that included 8 Particularly Vulnerable Tribal Groups (PVTGs) and 7 other tribes from eight districts of Jharkhand and Odisha. The authors combined both participatory and survey-based approaches and used the simple indexing method for PLVA. They observed that landless families were among the most vulnerable. The forest dwellers have poor access to education and health. Both minor forest produce and social-welfare measures are important safety nets for the forest dwellers. There is, however, better access to banking, pukka houses, toilets and so on. Furthermore, attention is required to strengthen livelihood opportunities for the forest dwelling communities.
With the advent of nanoscience, nanotechnology and their applications in various fields, mesoporous silica nanoparticles have gained popularity due to their stability, biocompatibility, unique honeycomb-like structures - ordered and random by nature, large surface to volume ratio, porosity, active surfaces, high loading capacity, ease of interactions with solvent, solute and suspended particles. These multitudes of intrinsic properties have motivated us towards an interdisciplinary detailed study on applications of mesoporous silica with an intention in increasing efficacy of productivity, growth if any, in plant life. This study aims at finding modus operandi of the structural uniqueness and eccentricity of various types of mesoporous silica in maneuvering their own functionality as a potential regulator for growth of seedlings of model plant Vigna radiata. We undertook characterization of surface, morphology, epitome of porosity for MCM 41 and MCM 48 using various experimental techniques followed by application of the same to growing seedlings at various dosages. It turned out that mesoporous silica nanoparticles, inarguably have higher efficacy in promoting plant growth, reducing stress, and enhancing basic metabolic rates at optimum dosage. Optimal operation point was determined at effective dosages for MCM 41 and MCM 48 those are being much lower than that of conventional silica nanoparticles. This optimum dosage is attributed to the structures of the nanoparticles used and implied further that higher pore volume, higher surface to volume ratio in case of MCM 41 at higher dosage lead to better adsorption of ions and functionality in contrast to that of MCM 48.
A model-independent sensitivity analysis for (deep) neural network, Bilateral sensitivity analysis (BiSA), is proposed to measure the relationship or dependency between neurons and layers. For any feed-forward neural networks including deep networks, we have defined the BiSA between a pair of layers as well as the same between any pair neurons in different layers. This sensitivity can quantify the influence or contribution from any layer to any other higher level layer. It provides a helpful tool to interpret the learned model. The BiSA can also measure the influence from any neuron to another neuron in a subsequent layer and it is critical to analyze the relationship between neurons in different layers. Then the BiSA from any input to any output of the network is easily defined to assess the strength of connection between the inputs and outputs. We have applied BiSA to characterize the well connectivity in oil fields—a very important and challenging problem in reservoir engineering. Given a network trained by Water Injection Rates and Liquid Production Rates data, the well connectivity can be efficiently discovered through BiSA. The empirical results verify the effectiveness of BiSA. Our comparison with exiting methods demonstrates the robustness and the superior performance. Besides, we also investigate the effectiveness of BiSA for a feature selection task using a deep neural network. The experimental results on MNIST data set demonstrate a satisfactory performance of BiSA on this issue with 1,536,640,000 parameters in the neural network.
In this paper, we study the problem of estimation of parameters of multichannel sinusoidal model. In multichannel sinusoidal model, the inherent frequencies from distinct channels are same with different amplitudes. It is assumed that the errors in individual channel are independently and identically distributed, whereas the signal from different channels is correlated. We first propose to minimize the sum of residual sum of squares to estimate the unknown parameters, and they can be easily obtained. Next we propose to use more efficient generalized least squares estimators which become the maximum likelihood estimators also when the errors follow multivariate Gaussian distribution. Both the estimators are strongly consistent and asymptotically normally distributed. We have provided the implementation of the generalized least squares estimators. Simulation experiments have been performed to compare the performances of the least squares estimators and generalized least squares estimators. It is observed that the variances of the maximum likelihood estimators reach the Cramer–Rao lower bound even for moderate sample sizes. We have extended the methods of estimation and the associated results of the two-channel model to an arbitrary m-channel model. It is observed that the computational complexity does not increase significantly with the increase in number of channels.
We study extreme values of group-indexed stable random fields for discrete groups G acting geometrically on spaces X in the following cases: (1) G acts properly discontinuously by isometries on a CAT(-1) space X, (2) G is a lattice in a higher rank Lie group, acting on a symmetric space X, and (3) G is the mapping class group of a surface acting on its Teichmüller space. The connection between extreme values and the geometric action is mediated by the action of the group G on its limit set equipped with the Patterson–Sullivan measure. Based on motivation from extreme value theory, we introduce an invariant of the action called extremal cocycle growth which measures the distortion of measures on the boundary in comparison to the movement of points in the space X and show that its non-vanishing is equivalent to finiteness of the Bowen–Margulis measure for the associated unit tangent bundle U(X/G) provided X/G has non-arithmetic length spectrum. As a consequence, we establish a dichotomy for the growth-rate of a partial maxima sequence of stationary symmetric α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-stable (0<α<2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0< \alpha < 2$$\end{document}) random fields indexed by groups acting on such spaces. We also establish analogous results for normal subgroups of free groups.
Thermotectonic evolution of the rocks of the Central Indian Tectonic Zone (CITZ) is crucial to understand the growth of the Indian shield and its response to the supercontinental cycles of the Earth. In this study we present field, petrology, geochemistry, in-situ U-Pb zircon and Th-U-total Pb monazite dates from a suite of felsic orthogneisses from the least studied Makrohar Granulite Belt (MKGB) of the CITZ. Petrology and geochemical data identify two rock groups: charnockitic orthogneiss (COG) and garnet orthogneiss (GOG). Geochemical fingerprints suggest that the magmatic protoliths of the gneisses are S-type granitoids, formed in a continental arc setting. In situ U-Pb zircon dates yield the time of arc magmatism at ca. 1400–1350 Ma. This is the first report of mid-Mesoproterozoic arc magmatism in the CITZ. These arc granites were subsequently metamorphosed at granulite facies condition that culminated at ∼800–850 °C, 7–7.5 kbar. A prominent gneissic (migmatitic) fabric was formed with garnet ± orthopyroxene + plagioclase + K-feldspar + quartz as peak metamorphic assemblages. After reaching the recorded P-T maxima, the studied rocks followed a decompression and cooling path to 4 kbar and 500 °C. The inferred clockwise P-T path is consistent with reworking of the Mesoproterozoic arc granites in a continent–continent collisional setting. In-situ Th-U-total Pb monazite and in-situ U-Pb ages of zircon overgrowth constrain the age of deformation and metamorphism in the span of ca. 974–913 Ma. In combination with the published information, the results of this study are consistent with the views that (a) the Indian shield participated as a coherent block in the Columbia supercontinent since ca. 1450 Ma (or before), (b) the ca. 1400–1350 Ma arc magmatism is presumably linked to collapse or closure of a basin (either north or south of the MKGB) in the CITZ in response to the prolonged accretionary phase of the Columbia supercontinent and (c) during the assembly of the Rodinia supercontinent, localized dismembered fragments of the Columbia got re-amalgamated during late Mesoproterozoic to early Neoproterozoic. Archean cratons got fused along the Proterozoic mobile belts (such as Central Indian Tectonic Zone, Eastern Ghats Mobile Belt). Different units within these mobile belts also experienced local compression during this time frame of the Grenvillian orogeny in the Indian subcontinent.
Female comparative disadvantage refers to the mismatch of the female with respect to achievements in different dimensions of human well-being in comparison with the corresponding achievements of the male. This paper axiomatically derives a general family of female comparative disadvantage indicators which has very important policy implications. The axioms employed are shown to be ‘independent’. An empirical illustration of the general index is provided using the UNDP data on mean years of schooling, life expectancy at birth and gross national income per capita in 2018. Results show that female comparative disadvantage is not necessarily related to standard measures of human development, such as the HDI, and is present even in countries reaching very high human development. The factor where policy intervention is needed the most is income.
The pattern of active deformation of frontal structures in Darjeeling Himalaya is complex with out‐of‐sequence reactivations in the chain and development of scarps associated to earthquake ruptures reaching the surface in the piedmont. To clarify the distribution of active deformation in this area, we analyze passive seismic records by the Horizontal‐to‐Vertical Spectral Ratio method along three NS trending profiles. We image the Siwalik sedimentary rocks / recent deposits interface under the piedmont and show folded and faulted geometries. Two of these faults are located under scarps of about ten meters affecting the 3.7 ± 0.7 ka old surface of the Tista megafan. Such features imply that about half of the convergence is expressed south of the Himalayan front while the other part occurs out‐of‐sequence in the chain, suggesting a very limited activity of the Main Frontal Thrust itself.
Quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC) are two important branches of quantum cryptography, where one can transmit a secret message securely without encrypting it by a prior key. In the practical scenario, an adversary can apply detector-side-channel attacks to get some non-negligible amount of information about the secret message. Measurement device–independent (MDI) quantum protocols can remove this kind of detector-side-channel attacks, by introducing an untrusted third party, who performs all the measurements during the protocol with imperfect measurement devices. In this paper, we put forward the first MDI-QSDC protocol with user identity authentication, where both the sender and the receiver first check the authenticity of the other party and then exchange the secret message. Then, we extend this to an MDI quantum dialogue protocol, where both the parties can send their respective secret messages after verifying the identity of the other party. Along with this, we also report the first MDI-DSQC protocol with user identity authentication. Theoretical analyses prove the security of our proposed protocols against common attacks.
In 1979, Pang proved that within the class of semimonotone matrices, R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}-matrices are Q-matrices and conjectured that the converse is also true. Jeter and Pye gave a counterexample when n=5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=5$$\end{document} for the converse; namely, they gave a semimonotone matrix that is in Q but not in R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}. In this paper, we prove this conjecture for semimonotone matrices of order n≤3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \le 3$$\end{document} and provide a counterexample when n>3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n> 3$$\end{document}, showing the sharpness of the result. We also provide an application of this result.
Given a digraph G, a set X⊆V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\subseteq V(G)$$\end{document} is said to be an absorbing set (resp. dominating set) if every vertex in the graph is either in X or is an in-neighbour (resp. out-neighbour) of a vertex in X. A set S⊆V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S\subseteq V(G)$$\end{document} is said to be an independent set if no two vertices in S are adjacent in G. A kernel (resp. solution) of G is an independent and absorbing (resp. dominating) set in G. The problem of deciding if there is a kernel (or solution) in an input digraph is known to be NP-complete. Similarly, the problems of computing a minimum cardinality dominating set or absorbing set or kernel, and the problems of computing a maximum cardinality independent set or kernel, are all known to be NP-hard for general digraphs. We explore the algorithmic complexity of these problems in the well known class of interval digraphs. A digraph G is an interval digraph if a pair of intervals (Su,Tu)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(S_u,T_u)$$\end{document} can be assigned to each vertex u of G such that (u,v)∈E(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u,v)\in E(G)$$\end{document} if and only if Su∩Tv≠∅\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_u\cap T_v\ne \emptyset $$\end{document}. Many different subclasses of interval digraphs have been defined and studied in the literature by restricting the kinds of pairs of intervals that can be assigned to the vertices. We observe that several of these classes, like interval catch digraphs, interval nest digraphs, adjusted interval digraphs and chronological interval digraphs, are subclasses of the more general class of reflexive interval digraphs—which arise when we require that the two intervals assigned to a vertex have to intersect. We see as our main contribution the identification of the class of reflexive interval digraphs as an important class of digraphs. We show that while the problems mentioned above are NP-complete, and even hard to approximate, on interval digraphs (even on some very restricted subclasses of interval digraphs called point-point digraphs, where the two intervals assigned to each vertex are required to be degenerate), they are all efficiently solvable, in most of the cases linear-time solvable, in the class of reflexive interval digraphs. The results we obtain improve and generalize several existing algorithms and structural results for subclasses of reflexive interval digraphs. In particular, we obtain a vertex ordering characterization of reflexive interval digraphs that implies the existence of an O(n+m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n+m)$$\end{document} time algorithm for computing a maximum cardinality independent set in a reflexive interval digraph, improving and generalizing the earlier known O(nm) time algorithm for the same problem for the interval nest digraphs. (Here m denotes the number of edges in the digraph not counting the self-loops.) We also show that reflexive interval digraphs are kernel-perfect and that a kernel in such digraphs can be computed in linear time. This generalizes and improves an earlier result that interval nest digraphs are kernel-perfect and that a kernel can be computed in such digraphs in O(nm) time. The structural characterizations that we show for point-point digraphs, apart from helping us construct the NP-completeness/APX-hardness reductions, imply that these digraphs can be recognized in linear time. We also obtain some new results for undirected graphs along the way: (a) We describe an O(n(n+m))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n(n+m))$$\end{document} time algorithm for computing a minimum cardinality (undirected) independent dominating set in cocomparability graphs, which slightly improves the existing O(n3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^3)$$\end{document} time algorithm for the same problem by Kratsch and Stewart; and (b) We show that the Red-Blue Dominating Set problem, which is NP-complete even for planar bipartite graphs, is linear-time solvable on interval bigraphs, which is a class of bipartite (undirected) graphs closely related to interval digraphs.
The gathering over meeting nodes problem requires the robots to gather at one of the pre-defined meeting nodes. This paper investigates the problem with respect to the objective function that minimizes the total number of moves made by all the robots. In other words, the sum of the distances traveled by all the robots is minimized while accomplishing the gathering task. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. The robots do not agree on a global coordinate system and operate under an asynchronous scheduler. A deterministic distributed algorithm has been proposed to solve the problem for all those solvable configurations, and the initial configurations for which the problem is unsolvable have been characterized. The proposed gathering algorithm is optimal with respect to the total number of moves performed by all the robots in order to finalize the gathering.
Variable selection is a well-studied problem in linear regression, but the existing works mostly deal with continuous responses. However, in many applications, we come across data with categorical responses. In the classical (frequentist) approach there exists penalized regression methods (e.g. logistic Lasso) which can be used for variable selection when we have a categorical response, and a large number of predictors. In this paper, we compare the performance of three alternative approaches for handling data with a single categorical response and multiple continuous (or count) predictors. In addition to the well-known logistic Lasso, we consider a model-based Bayesian approach, and a model-free approach for variable selection. We consider a binary response, and a response with three categories. Through extensive simulation studies we compare the performance of these three competing methods. We observe that the model-based methods can often accurately identify the important predictors, but sometimes fail to detect the unimportant ones. Also the model-based approaches are computationally expensive whereas the model-free approach is extremely fast. For misspecified models, the model-free method really outperforms in prediction. However, when the predictors are correlated (moderately or substantially) then the model-based methods perform better than the model-free method. We analyse the well-known Pima Indian Diabetes dataset for illustrating the effectiveness of three competing methods under consideration.
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1,084 members
Kishor Satpathy
  • Library, Documentation and Information Sciences Division
Malay Kumar Kundu
  • Machine Intelligence Unit (MIU)
Vasulu TS
  • Biological Anthropology Unit (BAU)
Saurabh Das
  • Center for Soft Computing Research: A National Facility (CSCR)
Nilabja Sikdar
  • Human Genetics Unit (HGU)
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Professor Sanghamitra Bandyopadhyay (Director)
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