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Conditions for A to be Noetherian are being investigated. Neena Gupta and N. There are examples where m need not be zero. A minimal lower bound for this integer m is being investigated. I have been focusing on problems related to the Euler class group. Two papers published in the year involve exploring the relation between the Euler class group of a ring and that of its polynomial extension. Double structures appear in connection with Poisson Geometry, namely in the context of Poisson groupoids.

We have observed that similar double structures also arise in the context of Jacobi groupoids and Jacobi vector bundles. We also observe that the Poissonisation functor can be extended to double structures. The work has been done in collaboration with Neeta Pandey.

Mahuya Datta Operator Theory Currently I am studying representation theory of planar algebras, a pictorial invariant for subfactors. We have proved a conjecture of Kevin Walker and Vaughan Jones relating affine representations of subfactor planar algebras to the Drinfeld center of a bimodule category coming from the subfactor.

Moral hazard problems and incentives. Spectral inference. Spectral properties of large dimensional random matrices. Ratan Dasgupta Stat-Math Unit, Delhi Martingale problems and Markov Processes — Necessary and sufficient conditions for an operator to be the generator of a semigroup of a Markov process, taking values in a complete separable metric space have been identified. These conditions are on the lines of the Hille-Yosida theorem.

Abhay G. Bhatt The evolvement or supression of separability or entanglement in its various levels in quantum dynamical semigroups has been studied arXiv. Jointly with Sibasish Ghosh tags associated with unitary bases for matrix algebras have been defined and a fan representation for them has been obtained; it is then related to maximally entangled vectors basis, mutually unbiased bases and orthogonal latin squares.

Jointly with M. Filali and M. Sangani Monfared, a trivolution on a complex algebra A has been defined and studied in the context of Banach algebras, second duals of certain group algebras and the duals of some topologically introverted spaces.

Ajit Iqbal Singh Research was carried out in the following areas: i Factorial and fractional factorial designs, ii second order response surface designs, iii use of block designs in finding optimal key predistribution schemes for distributed sensor networks and iv nested orthogonal arrays. Aloke Dey i On standard deviations estimates for tree order restricted models; ii Connectivity threshold of random geometric graphs with canter distributed vertices; iii On the nearest neighbor algorithm for mean field traveling salesman problem; iv On Poly urn schemes with infinitely many colors; v Random Walks on i.

Antar Bandyopadhyay Probability, random graphs, random directed trees, the Brownian web and extreme value theory has been continued. Anish Sarkar The work on a problem of random matrix with entries from a heavy-tailed moving average process has been continued.

Arijit Chakrabarty and Parthanil Roy Investigation on new approaches to high dimensional two-sample testing using bootstrap has been continued. The study of higher order accuracy of bootstrap for adaptive lasso estimators in high dimensions has been continued and remarkable improvements over existing approaches have been shown. The study on the techniques related to model selection using robust adaptive lasso estimators in spatial settings has been continued. Arindam Chatterjee 10 Research Activities Earlier work on noncommutative geometry have been continued, in particular on the geometry of quantum groups and their homogeneous spaces.

Deepayan Sarkar Worked on bounds for coherent systems based on signatures. Studied discrete concepts of ageing and looking at tests for them. Working on quantile density estimation and tests based on quantiles. Modelling of competing risks data. Isha Dewan The work on Genus numbers in computing this invariant for classical groups and some exceptional groups has been continued. Further work on this is still in progress. Maneesh Thakur Random threshold graphs, random directed trees and the Brownian web has been continued.

Rahul Roy Work on properties of graphs related to matrices was continued. It is known that the adjacency matrix of the line graph of a tree has nullity at most one. It was shown that this property holds for a graph with an odd number of spanning trees. Bapat Several inequalities for positive linear maps and for matrix means were obtained. A striking extension of the fundamental matrix polar decomposition was discovered. Rajendra Bhatia Worked on the irreducibility of polynomials, particularly Hermite-Laguerre polynomials and got some results.

Also worked on an implication of abc-Conjecture on some well known problems and wrote a paper. Revisited a diophantine equation coming for a conjecture of Erdos and got some new insights. Shanta Laishram Working on a monograph on Statistical Signal Processing which mainly deals with frequency estimation.

Worked on two-dimensional frequency estimation in stable error and estimating the parameters of bivariate exponential distribution under random censoring using EM algorithm.

The work on burst signal model in stationary errors has been continued. Rajarama Bhat A versal deformation theory of algebras over quadratic operads has been developed, where the parameter space is a complete local algebra and a construction of a distinguised deformation of this type, which induces all other deformations of a type of algebras, has been provided.

Anita Naolekar, Alice Fialowski and Goutam Mukherjee Strong relative property T for pair of groups was considered and conditions on the action of the semisimple Levy subgroup on the radical was obtained so that the corresponding pair consisting of semismple Levy subgroup and the radical has strong relative property T. Also, strong relative property T was considered for actions on solenoids and interesting results were proved.

Explored and proved various results concerning contraction groups, distality and unimodularity of closed subgroups and polynomial growth. Raja and R.

Shah A ruin problem was formulated, which is appropriate to a multidimensional renewal type insurance network in an orthant with a risk-diversifying treaty whose dynamics are governed by Skorokhod equations.

In the special case of Cramer-Lundberg type network, connection between probability of ruin of the network and a family of "boundary value problems" for certain first order integro-partial differential operators was also established. Ramasubramanian Work continued in Geometry of Banach spaces. A Garkavi type theorem was proved for M-ideals by exhibiting classes of Banach spaces in which any M ideal of finite codimension is an intersection of hyperplanes, each of which is again a M-ideal.

Rao Explored a relationship between certain invariants of quotient Hilbert modules in the Cowen Douglas class. Also issues of similarity and isomorphism of such modules has been analyzed. Introduced a concrete model of doubly commuting operator tuples acting on a separable Hilbert space.

Jaydeb Sarkar Work on the polarities of geometries of type, maximal subgroups of groups of type F4, ovoids in projective 3-spaces over a field of characteristic 2 and codes related to rank 2 — geometries were studied. Sastry On a lemma of Raghunathan which leads to a simplification of one of the principal results in a joint paper of Mason-Premet-Sury-Zalesskii has been elaborated.

By applying this to S-arithmetic lattices of rank 1 groups over a global field of positive characteristic, it also provides a lower estimate for the number of subgroups of a given index in such a lattice which are not S-congruence. Sury and Alec W. Mason Obtained results on triangular factorizations and Gauss decomposition of Chevalley groups over rings.

In particular, it was shown that over a ring of stable rank 1, one has short length 4 unitriangular factorisations for any Chevalley group. Sury, A. Smolensky and N. Vavilov 12 Research Activities A classical result of Erdos and Selfridge shows that a product of two or more consecutive integers is never a perfect power. Sury and Manisha Kulkarni Several results on generating functions and asymptotics of sums of moments of reciprocals of binomial coefficients were obtained.

In another collaborative work with 4 others, obtained 6 different interpretations and evaluations of a certain sum involving binomial coefficients. Sury, H. Belbachir and M. Rahmani Maximal ideals in the ring of continuous functions were shown to be uncountably generated. During the year , a new unit viz. Bayesian and Interdisciplinary Research Unit was created within this Division.

During a third unit, the Sampling and Official Statistics Unit was created within this Division. The following are the research and other activities of the Applied Statistics Division during the year. The members of the faculty conduct research in various areas of statistics, mathematics and computer science, with special emphasis on applications.

Sample Surveys Following the Report on the pilot survey executed in districts of Mumbai, Amritsar and Imphal, the Government of India constituted a fresh committee with Arijit Chaudhuri as the chairman and Prabal Chaudhuri and Debasis Sengupta as non-government members. The recommendations of this committee are with the Government of India and expected to be followed up soon.

Theoretical research was conducted on i random data gathering on sensitive issues, and ii constraining network sampling techniques Arijit Chaudhuri and Kajal Dihidar An advantageous randomized response model was considered for estimating the sensitive quantitative population mean based on simple random sampling with replacement for selecting the respondents, for which the estimator and the variance estimator are free of the known parameters of the scrambling variable.

Irrespective of how a sample of respondents is chosen, allowing a direct or a randomized response without revealing the option explored has been found to improve estimation 13 Research Activities procedure by the usual model. In the context of missing data, the problem of estimating the population mean under unequal probability sampling scheme was considered, taking into account the doubtful random nonresponse.

The proposed estimators were compared with the usual estimators of population mean in presence of random nonresponse through numerical simulations. Kajal Dihidar In connection with a pilot study conducted by NSSO for Periodic Labour Force Survey with mixed panel data, the problem of estimation of unemployment rate was considered with two-quarter penal data in a volatile labour market.

It was observed that the regression estimator has more variance with increased volatility. Sample size needed to achieve a fixed mean squared error has also been worked out. Shibdas Bandyopadhyay Reliability and Survival Analysis The problem of estimating the distribution of quality adjusted lifetime under some illness-death models with dependent sojourn time distributions was considered.

An improved calibration procedure for graphical comparison of two life distributions was proposed. The problem of estimating regression parameters and baseline cause specific hazards in competing risks framework with general missing pattern is being investigated.

A discrete-time software reliability growth model for the analysis of software testing data with periodic debugging schedule was considered, in addition to some extensions of Jelinski-Moranda model incorporating nested error structure. A NHPP model has been developed and analysed for a particular data set of software failure from industry.

New parametric models and tests for Accelerated Life Testing problems using parametric models were studied based on conditional specifications. Change-point problems with multivariate non-normal observations on cancer patients were studied.

A new broad-spectrum construction method was proposed for efficient key predistribution schemes for distributed sensor networks based on combinations of duals of block designs. Explicit expressions were obtained for various metrics and properties of these schemes were studied. Various types of response-adaptive designs were investigated. The problem of optimal allocation of units, with given prognostic variates or covariates, among different treatments was studied.

Optimal compound designs in the context of dose-response studies of phase II clinical trials were studied. Some problems related to model selection and parameter estimation for a class of completing models were investigated. Mausumi Bose, Anup Dewanji and Atanu Biswas Signal Processing A practical constraint that comes in the way of spectrum estimation of a continuous time-stationary stochastic process is the minimum separation between successively observed samples of the process. When the underlying process is not band-limited, sampling at any uniform rate leads to aliasing, while 14 Research Activities certain stochastic sampling schemes, including Poisson process sampling, are rendered infeasible by the constraint of minimum separation.

It has been proved that, subject to this constraint, no point process sampling scheme is alias-free for the class of all spectra. It was observed that point process sampling under this constraint can be alias-free for band-limited spectra, though the usual construction of a consistent spectrum estimator does not work in such a case.

It was established through simulations that a commonly used estimator, which is consistent in the absence of this constraint, performs poorly when the constraint is present. These results are expected to help practitioners in rationalizing their expectations from point process sampling as far as spectrum estimation is concerned, and motivate researchers to look for appropriate estimators of band-limited spectra. Debasis Sengupta Multivariate analysis Tests for multivariate Scatter or Overall Variability were constructed in a nonparametric framework.

The scope for incorporating information from auxiliary data in nonparametric estimation of multivariate density was investigated, and a suitable method was developed for this purpose. Several applications of this technique were pointed out and a data analytic illustration was given.

Bayesian methods for Growth Curve analysis and for Change-point problems were enhanced. Ashis SenGupta Categorical Data Analysis A detailed study in the context of a general model for longitudinal categorical data is going on.

Atanu Biswas Time series of discrete data Time series for discrete data were studied. A study to compare several stationery processes for categorical data with finite numbers of categories was conducted. Time series of zero-inflated count data were also investigated Atanu Biswas Directional Data Analysis Constructions of and inference for axial distributions, asymmetric circular distributions and multivariate directional distributions have been given.

Models and inference for directional inverse regression analysis have been enhanced. Bayesian analysis of Growth curves for possibly multivariate data have been enhanced.

Generalized wrapped stable distributions, symmetric and asymmetric, have been derived and related inference procedures have been developed. Some test procedures for circular data are carried out in the context of cataract surgery data. Also modeling and analysis of multivariate circular data in the context of some galaxy data are under study.

Included among these are theoretical aspects of hash functions, study of weak keys for RSA, correlation and biases in RC4, Boolean functions, key pre-distribution in sensor networks, broadcast encryption and modes of operations of a block cipher. The faculty members also actively participated in the program committees and organizations of several international conferences.

Ashis SenGupta Clinical Trials Response-adaptive designs were carried out in clinical trials to allocate a larger number of patients to the better treatment, leading to ethical gain. Some work related to several response-adaptive designs in different set-ups was carried out. In particular, a study to obtain optimal target allocation was initiated.

Inference on treatment difference in clinical trials was studied in the presence of surrogate responses when not all the true responses are available. The existing results were improved upon in the case of binary treatment responses.

Distributions of log odds-ratio and comparison of several standard estimation procedures in this context were studied for such surrogate-augmented data. It was observed that the efficient use of surrogate data improves the inference. Asymptotic closeness of Mantel-Haenszel estimator and profile log-likelihood estimator are under study. The problem of investigating Adverse Drug Reaction ADR associated with a specific drug from the post-market spontaneous response database is being studied.

In addition, research was also conducted on some mathematical problems, and the Integral Value Transformation IVT , a discrete transformation from to , was developed. Depending on the convergence property of IVT, an analogous version of the Collatz Conjecture was formulated and proved. Also, studies of affine discrete dynamical systems in the light of the Collatz function have been made.

An inverse of the IVT, for finding the pre-image of a number, has been obtained for some special cases, and applied to a network design. Multistage Stratified Sampling Schemes were used. On the basis of geographical locations and availability of infrastructural health facilities 4 strata were formed, namely, municipal, rural, municipal rural combined and riverine. Using structured questionnaires, patient-related information was collected from the TB register and Treatment card available in TUs, as 16 Research Activities well as from the households of the selected patients.

Data processing has been completed. Geostatistical analysis is in progress. The members of the faculty conduct research in various areas of Applied and Theoretical Statistics. Critical Sets in Equiorthogonal Frequency Squares A study of critical sets in a pair of equiorthogonal Frequency Squares has been carried out.

Using this stronger definition of orthogonality, a pair of equiorthogonal Frequency Squares is classified into one of the three classes depending on the isomorphism or orthogonality of the corresponding rows and columns.

The structural pattern of any Frequency Square having an equiorthogonal mate with isomorphic corresponding rows and columns have been identified.

A general result determining the size of the critical set of a pair of such equiorthogonal Frequency Squares has been obtained. For the other possible patterns of corresponding rows and columns in a pair of equiorthogonal Frequency Squares, some general investigations have been made with a detailed study of the conditions for the existence of an equiorthogonal mate and the size of a critical set for a pair of squares of order 8 based on 2 symbols.

This was done by comparing an observed velocity distribution of stars at an unknown location with respect to the centre of the galaxy with simulated velocity distributions at known with respect to the centre of the galaxy locations the simulations being done under four different astrophysical models.

The location of the best matching simulated distribution was proposed as an estimate for the location of the observed velocity distribution, which can be used to obtain an estimate for the location of the centre of the Milky Way. The findings over four different astrophysical models have been compared to determine which one best explains the observed distribution.

The affinity measure based on the familiar Hellinger distance has been used to quantify the closeness of two estimated densities. A validation test has also been implemented in order to judge the suitability of this approach. Ayanendranath Basu Robust Tests of Hypothesis Based on the Density Power Divergence A class of robust tests of hypothesis, with good asymptotic power but significantly improved robustness properties compared to the likelihood ratio test, has been developed.

This purely nonparametric technique was tested on a wide range of simulated and real datasets. This simple method was found to be quite competitive with other established sophisticated classification techniques. This adaptive and nonparametric classification technique Generalized Quadratic Discriminant Analysis, GQDA performed extremely well when the underlying distributions are not Gaussian which is a necessary assumption for the QDA framework.

Smarajit Bose, Rita Saharay and Amita Pal Statistical Issues in Content Based Image Retrieval In the context of content-based Image retrieval, algorithms have been developed by combining conventional and segmentation-based approaches for significant improvement in retrieval performance.

Coupled with relevance feedback, the resultant algorithms achieved excellent retrieval accuracy on several benchmark datasets. The EM algorithm was used for successful implementation of the theory. This algorithm is effective in the case of bimodality in the count data which shows evidence of under- or overdispersion. Since the input to the classifier is independent of sequence lengths, the approach is especially useful when sequences to be classified are of differing lengths and homology-based methods tend to fail.

The performance of a number of different feature subsets has been demonstrated on human olfactory receptor sequences, which are classified into one of two classes, namely, functional genes and pseudogenes. Among several classifiers explored, a multilayer perceptron MLP with 4 hidden nodes performed best on an average. Arni S. Srinivasa Rao Estimating population numbers required annually for Biometric Cards in India India has launched a massive project on biometric cards which is expected to be useful for residents in several ways, from obtaining driving license to passports etc.

Several deterministic approaches are 18 Research Activities being developed in estimating annual requirements of new cards for the governments. How do we account for missing population so that a unique identity is provided, is investigated.

Srinivasa Rao Mathematical Models in Insurance Methodology of estimating the impact of health insurance on life expectancies in India has been investigated. There has been increase in private insurance schemes for more than a decade in the country and our methods are dealt with indirect estimation models, osculatory methods. Srinivasa Rao Population Coverage Errors Large undercount in census leads to a great problems in planning and growth of every country.

We are working on this very untouched area for coverage error estimation in Indian Census. Using Post Enumeration Survey PES we are trying to give some robust coverage error estimates through probabilistic model. Kiranmoy Chatterjee and Arni S. Srinivasa Rao Child Mortality estimation in India We perform Bayesian analysis on the child mortality data obtained from three round of National Family Health Surveys , and Reetabrata Bhattacharya and Arni S.

Problems related to prime numbers and distance between individual and group of prime numbers are explored in deterministic and probabilistic ways. Srinivasa Rao Some problems related to Complex dynamics and applications Application of complex analysis methods in biology is being investigated. Our long term goal is to obtain relationship with simply connected regions and Monte Carlo methods which could have role to play with massive data sets.

Srinivasa Rao Trans-dimensional MCMC Algorithms Based on Deterministic Transformations Dutta and Bhattacharya developed a novel MCMC methodology that uses simple deterministic transformations of some arbitrary, one-dimensional random variable to update high-dimensional random variables in a single block.

Then, inversion of such measurements can help us learn the parameters that describe such Milky Way features. A Bayesian inverse problem approach has been proposed, where the available stellar velocity information matrix is modelled as an unknown function of the Milky Way model parameters, where this function is inverted using Bayesian techniques to predict the model parameters. This unknown function turns out to be matrix-variate, which is modeled as a matrix-variate Gaussian Process.

We develop a general method to perform inverse, nonparametric learning, using matrix-variate Gaussian Processes. Application of our method to observed stellar velocity data results in estimates that are consistent with those in astrophysical literature.

That these results could be obtained using far smaller data sets compared to those required for the calibration approach is encouraging in terms of projected applications to external galaxies. Dalia Chakrabarty, Munmun Biswas and Sourabh Bhattacharya Circular Bayesian Non-parametric State-Space Models The approach in the earlier work on Bayesian Non-parametric State-Space Models has been extended to the far more complicated and challenging situation where the state-space equations correspond to unknown functions where the inputs and the outputs lie on circles.

We develop a novel methodology for Bayesian inference in these models. Satyaki Mazumdar and Sourabh Bhattacharya Nonstationary Semiparametric Spatio-Temporal Bayesian Modelling using Kernel Convolution of Order-Based Dependent Dirichlet Process Spatio-temporal processes are important modeling tools for many problems of environmental science, biological science, geographical science, etc.

However, it is usually and somewhat unrealistically assumed that the underlying model is parametric and that the covariance function is stationary and separable.

All the previous attempts to construct nonparametric processes with covariance functions that are neither stationary nor separable fail to satisfy some desirable properties. We show that suitable kernel convolution of order-based dependent Dirichlet processes rectify all the problems and have many attractive theoretical properties.

Moumita Das and Sourabh Bhattacharya Prior and posterior MISE convergence rates of mixture models based on Dirichlet processes: asymptotic comparison and choice of parameters In terms of MISE Mean Integrated Squared Error , the posterior rate of convergence of the Dirichlet process-based mixture models proposed by Escobar and West and Bhattacharya has been calculated, and it has been shown that the latter converges much faster. The prior MISE convergence rate of the Bhattacharya has been computed with respect to M and a under suitable assumptions on the base measure, and the resultant choices of M and a have been compared with those associated with the posterior convergence rate.

Sabyasachi Mukhopadhyay and Sourabh Bhattacharya Perfect simulation in clustering of categorical time series with unknown number of clusters For the first time, a methodology has been proposed for clustering in categorical time series with unknown number of clusters and the perfect sampling theory of mixtures of unknown number of components has been applied for exact Bayesian inference in this case.

Sabyasachi Mukhopadhyay and Sourabh Bhattacharya 20 Research Activities Recent advances in perfect sampling A comprehensive review of the recent advances of perfect simulation theory has been provided, showing that many challenging realistic Bayesian problems can be handled via perfect simulation, completely eliminating the problems of assessment of MCMC convergence. Sabyasachi Mukhopadhyay and Sourabh Bhattacharya Nonstationary nonparametric space-time processes using Hamiltonian dynamics A novel methodology using the Hamiltonian dynamics has been proposed to construct a nonstationary, nonparametric spatio-temporal process having desirable properties.

To construct the process, an isotropic Gaussian process was used as the starting point and Hamiltonian dynamics was applied to create a new process that is neither stationary nor Gaussian. The resultant process is highly structured in space and time, and yet possesses desirable properties, not enjoyed by the spatiotemporal processes existing in the literature. Moumita Das and Sourabh Bhattacharya Nonstationary nonparametric space-time processes using compositions of processes Gaussian A novel methodology has been proposed for construction of nonparametric, non-stationary processes using compositions of isotropic Gaussian processes.

Moreover, the process has many attractive theoretical and computational properties. This methodology is proposed to be extended for constructing space-time processes on spheres, which is important when considering spatio-temporal data collected from all over the world.

Since the data will be massive, we need cuttingedge computational methods for Bayesian inference. Asymmetric Information and Middlemen Margins—an Experiment with Indian Potato Farmers The role of asymmetric information in potato production and trade was investigated in some selected markets of West Bengal. An experiment was conducted to provide two types of information public and private to randomly selected farmers in treatment villages, while the control villages remained unaffected.

A large-scale survey was conducted to understand the impact. Information provision could bring no change in average margins, but the private information intervention caused farmgate prices and traded quantities to co-move more with wholesale prices. The evidence is inconsistent with long-term implicit contracts allowing risk to be shared between farmers and traders. Instead, the results are explained by a model of expost bargaining, in which low outside options of farmers prevent informational interventions from having significant impacts.

Sandip Mitra, Dilip Mookherjee, Sujata Visaria and Maximo Torero 21 Research Activities Borrower Selection and Impacts of Agent Intermediate versus Group Based Lending: Theory and Evidence In this study, which is a departure from traditional microfinance in that it advocates doorstep credit through agent Intermediaries, a model of credit market with adverse selection has been developed, in which borrowers vary with respect to unobservable project risk and observable landholdings, and the informal market is locally segmented.

The model generates detailed predictions concerning informal interest rates, borrower selection, take-up and repayment patterns with respect to both risk and landholding categories. The predictions of the model were successfully tested using data from a randomized evaluation currently being con-ducted in West Bengal, with traditional group-based joint liability loans GBL serving as the control.

The proposed approach TRAIL was found to be more successful in targeting low-risk clients, thereby generating higher repayment rates, unlike GBL which is more successful in targeting landless households. It was also seen to achieve higher take-up rates, thereby managing to overcome problems faced by microfinance clients inherent in group-based lending and monitoring.

The study further aims at looking into the differential impacts of information and credit intervention across various villages. Relative Incentives—an Experiment Targeting Child Malnutrition in Slums of Kolkata Improvement in worker efficiency has been an area of great focus in the private sector and industry, where incentives appear to matter for profitability and improved performance. However, there is almost no evidence on the impact of performance pay for public sector workers in a controlled experiment.

This study was made with the objective of examining the impact of providing monetary incentives or introducing competition among Anganwadi workers, along with uniformly providing nutritional information to mothers, in reducing child malnutrition. Analysis was made of i the complementarity effect for the same level of performance incentive as well as a higher incentive, to derive an estimate of the elasticity of the complementarity effect with respect to the incentive; ii the absolute incentive scheme against a relative incentive scheme where workers compete against each other for a larger piece of the total prize.

Recent literature on institutional economics has indicated that the ability of the state to effectively deliver basic goods and services is an important determinant of economic growth. However, public institutions in India have often failed to deliver efficiently.

Arguments have therefore been made in favour of direct cash transfer to beneficiaries, triggering debate between two schools: pro- cash transfer and anti-cash transfer.

Attempts have been made to understand the apparent conflicts through theoretical and empirical exercises, conducted in the state of Bihar. Sandip Mitra, Maitreesh Ghatak and Chinmay Kumar Taxing the Informal Sector An attempt has been made to provide an innovative mechanism to enable the State Government to generate revenue from street vendors, to contain extortion and to provide social protection without 22 Research Activities assigning any kind of property right to public space and hurting their means of livelihood.

Similar mechanisms have been experimented with success in several African and South-east Asian countries without any political backlash. Street vendors pay substantial extortion and illegal fees to various agents and spots are transferred from one vendor to another in exchange for huge payments.

Thus though they are effectively being taxed all the time, the Government does not receive this tax. At the same time, there is absolutely no legitimacy to such trading activities, and these traders are always at the mercy of extortionists.

This study has proposed a strategy for converting a part of the illegal fees into legal taxes or license fees of some kind, with the objective of empowering the urban poor with social dignity and, at the same time, providing the State with much needed resources on a regular basis. This has been a unique study in the context of India. Sandip Mitra and Sugata Marjit Computer and Communication Sciences Division Advanced Computing and Microelectronics Unit The research activities of the Advanced Computing and Microelectronics Unit ACMU comprise theoretical and applied research in the areas of high performance computing, pervasive and mobile computing, wireless and sensor networks, VLSI design tools and electronic design automation, logic synthesis and testing, error correction and fault-tolerance, physical design of microchips, embedded systems, system-on-a-chip, low-power architectures, computational geometry, algorithms and data structures, computational biology, hardware for image processing, nano-technology and giga-scale integration techniques, hardware and software validation.

Existing algorithms for physical design of 2D chips are inadequate to tackle additional constraints due to through-silicon-via and thermal vias required for 3D ICs. Few research groups are focussing on this topic. This project aims at designing efficient algorithms for physical design of 3D ICs. Simulated Annealing based algorithms and genetic algorithms for floorplanning in 3D ICs have been explored. Newer and very fast methods of estimating thermal parameters of circuits were developed for thermal simulation.

Results suggest that simulated annealing coupled with heuristics performed consistently better than without them. Each colored chip can move to an adjacent vertex, provided the vertex it is moving to was previously empty.

Thus no vertex of the graph hosts more than one chip at any particular instant. Once a red chip reaches that particular vertex, it can be removed from the graph, thus making that particular vertex empty. Thus the number of empty vertices in the graph increases as colored chips are brought to their respective receptors.

The goal is to empty the graph by taking all the colored chips to their respective receptors with a minimum number of moves.

Subhas C. Nandy Partitioning and Covering Problem of Polygon in 2D Dividing or partitioning polygonal regions satisfying some specific criteria helps to solve many problems in facility location, VLSI, robotics domain. Competitive facility location is concerned with the favorable placement of facilities by competing market players, and has been studied in several contexts.

In such a scenario, when the users choose the facilities based on the nearest-neighbor rule, the optimization criteria is to maximize the cardinality or the area of the service zone depending on whether the demand region is discrete or continuous, respectively. A game-theoretic analogue of this problem gives rise to the notion of the Voronoi game, which has been studied mostly for continuous demand regions. At first P1 chooses a facility f1 following which P2 chooses another facility f2 such that maximum payoff of P2 is attained at the point f2 whereas optimum payoff of P1 is attained at point f1.

Optimal location can be determined in polynomial time. In the area of cognitive radio networks CRN , we have addressed the problem of channel sensing, channel allocation and transmission of multimedia signals, while maintaining the required QoS constraints. Depending on the type of signal and QoS requirements, different types of multimedia signals need different bandwidths for communication. In typical wireless systems, unless a contiguous frequency band in the spectrum with width at least equal to the required bandwidth is obtained, multimedia communication can not occur with the desired QoS.

Our approach is based on utilizing several frequency 24 Research Activities bands, each of smaller width than the required bandwidth but whose sum total equals at least the required bandwidth. Algorithms for channel reservation, channel sensing and allocation along with protocols for transmission and reception have been developed.

Our approach also ensures preemption of secondary users by the primary users as typically demanded in a cognitive radio based communication environment.

We have also proposed a novel scheme for multi-path routing in a CRN for multimedia communication, based on an extension of the idea of SDM as given for single-hop communication, even when a contiguous band of required width is not available for some or one of the hops in the route.

Each data packet of the multimedia signal is split into several sub-packets each of which needs much smaller bandwidth than the original packet, and these sub-packets are sent through all these routes to be eventually received by the destination node with the desired QoS. Bhabani P. It has gargantuan application in different areas of computer science. We proposed a method of constructing this data structure in an in-place manner such that all the rudimentary query operations performed on this structure can also be implemented as efficiently as in the original one.

We used this data structure, to compute the maximum area empty axis-parallel rectangle with the same point set that runs in O R log n time using O 1 extra-space, where R is the number of maximal empty rectangles present on the floor. Optimization Problems of Geometric Intersection Graphs: In sophisticated database query and VLSI physical design, several optimization problems are formulated using the intersection graph of axis-parallel rectangles. Similarly, the disk graph plays an important role in formulating different problems in mobile ad hoc networks.

Most of the optimization problems like finding maximum independent set, minimum dominating set are NP-hard. Approximation algorithms are available for these problems. We are investigating whether inplace approximation algorithms for these problems are possible or not.

On the other hand, finding maximum clique for both rectangles intersection graphs and unit disk graphs are polynomially solvable.

We proposed efficient in-place algorithms for these problems with O 1 additional space. Arijit Bishnu and Subhas C. Although mathematical formulations for UMTS network planning have been derived in the literature considering many system features such as base station selection and configuration, power assignment, traffic requirement, cell load, little has been done to address the soft handover issue explicitly.

We have argued that the incorporation of soft handover remains an important component for definitive investigation in optimization models for cell planning because it can provide gain to the user.

We have then quantified the benefits obtainable with soft handoff, as opposed to merely stating them on qualitative reasoning. For that, first we have developed an optimization model for transmission site selection and configuration in UMTS networks by taking advantage of the maximum ratio combining soft handover SHO gain that can arise due to fade margins.

Then, we have measured the coverage improvement that can be achieved due to the fade margin on the soft handover with respect to the coverage without soft handover. We have demonstrated that incorporation of soft handover leads to improved coverage in UMTS network planning.

The speed of network evaluation is a binding constraint on the performance of meta-heuristic techniques used for the planning tasks. Consequently in large-scale scenarios, tractability is significantly impeded by the number of test points that requires to be evaluated. We are attempting to improve the tractability of planning problem by changing the resolution of the problem scenario by reducing the number of test points that required to be evaluated.

Our goal is to improve the tractability significantly while marginal reduction in quality of network evaluation may be sacrificed. We are also attempting to develop efficient power control mechanism and efficient technique to cope up with mobility of the users. Sasthi C. Ghosh 25 Research Activities Computer-Aided Design and Testing of Digital Microfluidic Nano-Biochips Completed A lab-on-a-chip combines microfluidics, bio chemistry, electronic and optical sensors, and microchip fabrication technology.

We have studied several optimization issues involving sample preparation, testing and contamination wash in digital microfluidic biochips.

These algorithms are specially important for low-cost dilution and mixture preparation - an essential step towards automation of bioassays. New procedures for faster testing and contamination cleaning have been developed and evaluated. These results will provide an enabling platform for viable implementation a large class of nanobiochips for a variety of healthcare applications. CS students of the Institute. With uniform node distribution and continuous traffic model without data fusion, no routing strategy, in general, can avoid the creation of an energy hole around the sink.

However, nearly balanced energy consumption can be achieved by using non-uniform deterministic node distribution where nodes are placed in predetermined positions.

For a random graded node distribution, we develop a simple static distributed algorithm for data gathering with an attempt to distribute the traffic uniformly to maximize the lifetime of the network. It requires just a one-time computation during the initialisation of the network. Simulation studies show that for non-uniform random distribution of nodes the proposed algorithm with less information and less computing can enhance network lifetime significantly compared to earlier algorithms.

Nabanita Das Automated Debugging for Evolving Programs Debugging denotes the process of detecting root causes of unexpected observable behaviour in programs such as a program crash, an unexpected output value being produced or an assertion violation. Debugging program errors is a difficult process, and often takes a significant fraction of the time in the program development stage.

Even today, debugging remains much of a manual activity, with the actual debugging time dependent on the size and complexity of the program being debugged, the nature of manifestation of the bug and the level of familiarity and expertise of the programmer.

The standard practice of debugging till date in the software community is to manually inspect the execution trace exhibiting the bug inside a debugger and try and locate the error cause s from an observed error.

It is a widely accepted reality in any large-scale development that a complex piece of program is never written from scratch. Usually a program evolves from one version to another.

This is termed as program evolution where one program version evolves to a new version. When we change a program version to produce a new version, we may introduce bugs. The main objective of this work is to devise efficient means for debugging change-induced bugs, which are absent in an earlier version of a program but present in a modified buggy version of the same.

Design of efficient quantum computing hardware architectures is mandatory for building real quantum computing machines. Most of the work focuses on binary logic whereas multi-valued logic has the advantages of less hardware cost. Defining ternary logic in quantum domain has been achieved and utilized for synthesis of ternary logic quantum circuits.

Recently, synthesis methods for quaternary logic have also been devised which yield more circuits with lower quantum gate cost. Susmita Sur-Kolay Distributed Algorithms for Geometric Problems for Robot Swarms A robot swarm is a system of multiple autonomous mobile robots engaged in collaborative tasks. Robots are usually autonomous, oblivious, and homogeneous. Most of the existing works consider the robot to be dimensionless or a point.

Algorithm for Gathering fat robots a robot is represented as a unit disc has been reported for three and four robots. We have shown that if the robots are orderable in a distributed fashion, they can be gathered. We characterize the positions, when the robots are orderable.

Some other problems in this domain that we plan to consider are arbitrary pattern formation, pattern formation in the presence of obstacles, etc. Krishnendu Mukhopadhyaya Computer Vision and Pattern Recognition Unit Multi-Script Document Recognition In graphical or artistic documents the text lines are annotated in multiple orientations or curvilinear way to illustrate different locations or symbols.

We propose a novel method to segment such text lines and the method is based on the foreground and background information of the text components. Touching character segmentation problem becomes complex when touching strings are multi-oriented. We also presented a scheme towards the segmentation of English multi-oriented touching strings into individual characters. A dataset containing 26, handwritten legal amount words written in Hindi and Marathi languages Devanagari script is developed and a training-free technique is developed to recognize such handwritten legal amounts.

We proposed a symbol spotting technique through hashing the shape descriptors of graph paths Hamiltonian paths. Although for postal automation there are many pieces of work towards street name recognition on non-Indian languages, to the best of our knowledge there is no work on street name recognition on Indian languages and we have developed a system for recognition of Indian street name written in Bangla script.

We also proposed an effective staff line detection and removal method from musical scores. For handwritten text line segmentation, databases for Bangla, Kannada, Persian and Oriya script have been developed. These databases are available freely for research purpose. Umapada Pal, R. Mandal and Souvik Bhowmick Stemming for Information Retrieval Stemming is a mechanism that is used to normalize morphologically related words. In an information retrieval task, a stemmer serves two main purposes.

Naturally, the role of a stemmer is more useful if the concerned language is morphologically more complex. A number of stemmers of varying spirit and flavor have been developed over the decades. By contrast, corpus based stemmers find groups using the ambient corpus, obviating the language specific knowledge. Some corpus based stemmers use only the lexicon of the corpus, whereas others use the co-occurrences of the words to find semantically more homogeneous groups.

We have developed a number of fully automatic stemming algorithms using the target corpus on which search is performed. Our first algorithm focuses primarily on the execution speed of the algorithm in producing the stems while not sacrificing the retrieval effectiveness. In our second algorithm we came up with a novel graph based stemming algorithm which boosts retrieval performance significantly over the state of the art algorithm with low computational cost. Our third algorithm, unlike the previous two algorithms, uses the document level co-occurrence statistics as the primary form of evidence to find the desired groups of morphologically related words.

In this work we propose a strongest neighbour based clustering algorithm which automatically finds the cluster of words without the specification of any similarity threshold. The experimental results confirm the effectiveness of our algorithms on these collections.

Paik, M. Mitra, D. Pal and S. Automatic Reading of Texts in Camera Captured Images We developed a robust scheme for detection of Devanagari or Bangla texts in scene images improving our previous algorithm for the same purpose and the present approach is primarily based on two major characteristics of such texts - i variations in stroke thickness for text components of a script are low compared to their non-text counterparts and ii presence of a headline along with a few vertical downward strokes originating from this headline.

We use the Euclidean distance transform to verify the general characteristics of texts in i. Also, we apply the probabilistic Hough line transform to detect the characteristic headline of Devanagari and Bangla texts.

Further, similarity and adjacency measures are applied to identify text regions, which do not satisfy the verification in ii. The proposed approach has been simulated on a repository of images taken from Indian roads. Finally, we studied a novel zone-based segmentation approach for Bangla texts extracted from scene images. Extracted scene texts are often affected by artefacts and our segmentation algorithm can detect them efficiently. Bhattacharya and S. Parui Online Handwriting Recognition — Bangla Developed a GUI-based semi-automatic scheme for annotation of unconstrained mixed cursive online handwritten Bangla words at character boundary levels and another scheme for XML representation of such annotated data.

A holistic recognition scheme based on a novel approach of combining MLP and SVM classifiers is studied for such unconstrained handwriting. Also, we identified 75 stroke classes present in a publicly available large database of online handwritten isolated Bangla basic characters and developed a separate database of the above handwritten strokes. This is the first such database for Bangla script. Additionally, we designed certain efficient features on the basis of their extremum.

We studied an efficient two-stage recognition approach based on the above feature and a hidden Markov model HMM classifier. First, a probability distribution is estimated for each stroke class using the stroke features and then an HMM based character classifier is designed using each stroke class as a state. Finally, we designed a personalized handwriting recognition system that is acceptably fast, light-weight, possessing a user-friendly interface with minimally-intrusive correction and auto-personalization mechanisms for Android based devices.

Parui, U. Bhattacharya, P. Banik, C. Biswas, S. Baral, R. De, S. Bhattacharya and O. Samanta, 28 Research Activities Blind quality assessment of image and video The provision of blind quality assessment is an important requirement for modern multimedia and communication systems.

Fragile watermarking techniques have been proposed earlier for this purpose. A novel approach which makes use of both fragile and robust watermarking techniques has been developed. The embedded fragile watermark is used to assess the degradation undergone by the transmitted images.

Robust image features, on the other hand, are used to construct the reference watermark from the received image, for assessing the amount of degradation of the fragile watermark. Construction of the watermark from the image itself dispenses with the need for embedding an extraneous watermark which must be made known to the user separately, a significant contribution in image quality assessment.

The validity of the proposed approach has been verifed through extensive simulations using different kinds of gray-scale and color images. A different approach, completely blind, has been proposed for the quality assessment of images undergoing JPEG compression. Simulations on a large number of well-known images have been used to demonstrate the performance. Image tamper detection, localization and correction An approach for detecting tampering in images and also capable of restoring back the image, based on watermarking, has been proposed.

Besides being able to detect and correct the usual forms of tampering such as the cut-and-paste attack, it is also sensitive to the more complex vector quantization attack and can effectively detect and recover the image from the tampered one. The watermark constructed from the image has two parts, one having the purpose of tamper detection while the other part is used for recovering the untampered image. The second part uses fragile image features which change with tampering. The entire watermark is embedded using a robust technique so that it is not affected by tampering.

Extensive experiments on standard images have been performed to test the performance of this approach and the results found to be very satisfactory. Palit and A. This research is now being extended to Hindi text.

Machine Authentication of Security Documents In the field of computational forensics, machine authentication of security paper documents is attempted. Because of the easy availability of technological help, increasing amount of counterfeit documents is posing a serious threat to our society. Therefore, automatic and low cost authentication tool is needed to combat this evil. This research is aimed at developing techniques for quick and easy authentication of security paper documents.

Image processing and pattern recognition principles form the basis of this authentication technique. The goal is two-fold: i to check security features in a document in question in order to establish its authenticity, and at the same time ii analysis of security features to grade them according to their vulnerability against counterfeiting effort in order to help the designers for preparing of such security documents in future.

As part of this research the basic NLP tools are being developed first. After developing morphological analyzer, part-of-speech tagger, and chunker for Bangla, a dependency parsing is attempted. The demand frames for Bangla verbs are considered as a general linguistics resource that has been developed under this research. Both the rule based and statistical frameworks are being explored. A new approach for pronominal anaphora resolution in Bangla has been formulated.

In a separate attempt, text-to-diagram conversion problem is targeted by integrating artificial intelligence and NLP tools. Under this research, machine is able to draw the diagram described in a piece of text e. This research has been extended for the Blind people so that they can perceive the diagrams on a Braille print out. This has resulted in a noteworthy advancement in the field of OCR of math expressions, a task required for automatic conversion of scientific paper documents into electronic ones.

Documentation, Research and Training Centre DRTC , Bangalore The main areas of research in which the DRTC Faculty were engaged during the period are furnished below Knowledge Organization The focus of Knowledge Organization has transformed substantially in the last one decade and as a direct consequence of the emergence of digital resources, digital libraries and the World Wide Web. Knowledge organization, today, has to meet the twin objectives of facilitating organization of information resources for effective retrieval while at the same time look at ways and means of effective tagging of the huge volume of digital resources to support retrieval at tolerable levels of precision.

Madalli The revised e of Colon Classification is in progress. A revised edition of the scheme in Kannada was completed and published by the Central Institute of Languages in The issues related to multilingual thesauri and lateral relations especially in the Humanities and culture-specific domains are being studied.

A few papers have been published based on these studies. The problems and issues in building the digital collection of resources in Kanada and Tamil with focus on full-text indexing are being studied.

Raghavan 30 Research Activities Digital Libraries and Semantic Web Research carried out in faceted ontologies in social and media research. The main objective of the project is to develop ontologies using faceted approach, in order to provide folksonomies which should facilitate visualizations to the end-user. The ultimate goal is to develop context based search mechanisms combined with inference engines.

Devika P Madalli Library and Information Technology In the recent past, several technology applications to library and information work have been demonstrated. As a part of this kind of research, a LiveCD called Liblivecd had been released. As of May, more than downloads have taken place. In these servers, authors would deposit their pre-prints.

It thus provided readers worldwide with a quick access to research outputs. These types of servers began as informal vehicles for the dissemination of preliminary research and those literatures which were not peer reviewed.

However, the last decade witnessed the rapid evolution of these into increasingly important media for dissemination of research results in certain fields. Study the adequacy of existing standards in this regard especially for scholarly material in Indian languages and scripts. Design an end user interface for browsing, navigating through and searching the Institutional Repository.

Prasad and M. Bibliometrics and Scientometrics Attempts were made to study the growth of literature and its impact on library collection development. Different scientometric measures such as h-index, g-index and impact factors were also studied. A project was also under taken to study the pattern of downloading of online literature. It is well known that any trust based communication is associated with uncertainty that changes over time.

An effort is being taken to model such data as a probabilistic temporal Database. Bagchi Access Control over Digital Library Ontology Modifying a digital library ontology to support multiple inheritance, an effort is being taken to develop a suitable access control model.

In this case the segmentation is done by dividing the video stream into shots, which may be treated as smallest semantic unit. For that purpose a model based shot boundary detection technique using frame transition parameters is proposed. The method produces well accepted results. For the human action recognition from video, problem of recognition of Indian classical dance is chosen as a case study.

Chanda Image processing and Analysis Producing high resolution image from low resolution ones is an important task to overcome hardware limitations. The technique is known as super resolution SR image reconstruction. We have developed multi-frame SR image reconstruction algorithm based morphological regularization.

Unlike with lang. Home Lady Alphabet School. Thank you for 13 13MB Read more. Greek Alphabet Greek alphabet From Wikipedia, the free encycopedia This article contains special characters. Without proper rendering su 32 4 KB Read more. German Alphabet German Alphabet Learning the German alphabet is very important because its structure is used in every day conversation.

Arabic Alphabet Arabic alphabet and word list There are twenty-eight letters in the Arabic alphabet. Remember, Arabic is read from right 35 KB Read more. Alphabet Rules Learn English Pronunciation Pronunciation can be a tricky matter when it comes to the English language.

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