IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Fine particulate matter (PM2.5, aerodynamic diameter ≤2.5 µm) impacts the climate, reduces visibility and severely influences human health. The Indo-Gangetic Plain (IGP), home to about one-seventh of the world’s total population and a hotspot of aerosol loading, observes strong enhancements in the PM2.5 concentrations towards winter. We performed high-resolution (12 km × 12 km) atmospheric chemical transport modeling (WRF-Chem) for the post-monsoon to winter transition to unravel the underlying dynamics and influences of regional emissions over the region. Model, capturing the observed variations to an extent, reveals that the spatial distribution of PM2.5 having patches of enhanced concentrations (≥100 µgm−3) during post-monsoon, evolves dramatically into a widespread enhancement across the IGP region during winter. A sensitivity simulation, supported by satellite observations of fires, shows that biomass-burning emissions over the northwest IGP play a crucial role during post-monsoon. Whereas, in contrast, towards winter, a large-scale decline in the air temperature, significantly shallower atmospheric boundary layer, and weaker winds lead to stagnant conditions (ventilation coefficient lower by a factor of ~4) thereby confining the anthropogenic influences closer to the surface. Such changes in the controlling processes from post-monsoon to winter transition profoundly affect the composition of the fine aerosols over the IGP region. The study highlights the need to critically consider the distinct meteorological processes of west-to-east IGP and changes in dominant sources from post-monsoon to winter in the formulation of future pollution mitigation policies.

Department Of Civil Engineering

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Department of Ocean Engineering

Department Of Chemical Engineering

Department of Mathematics

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Scientific Reports

On the widespread enhancement in fine particulate matter across the Indo-Gangetic Plain towards winter

In the conventional design of reinforced concrete (RC) rectangular slabs in beam-slab systems subject to gravity loading, it is assumed that the code-specified moment coefficients (derived based on yield line theory, assuming non-deflecting supports at the edges) can be used, provided the beams provided at the edges are adequately stiff. Recent experimental and theoretical studies have established that such designs turn out to be over-conservative, as the assumed yield line mechanism of the slab does not occur. In general, a combined beam-slab collapse mechanism occurs at the limit state of collapse, in which the yield lines in the slab connect to plastic hinges in the supporting beams. With a proper understanding of possible collapse mechanisms and estimation of the lowest collapse load, using yield line theory, a more rational and economical design of the beam-slab system is possible. Considerable savings in steel can be achieved, while fully complying with the strength and serviceability requirements of the code. © 2020, Associated Cement Companies Ltd. All rights reserved.

Indian Concrete Journal

Economical and rational design of ‘one-way’ RC beam-slab systems

Arnoldi method approximates exterior eigenvalues of a large sparse matrix, but may fail to approximate corresponding eigenvectors. The refined Arnoldi method approximates an eigenpair by solving a related singular value problem. In this paper, we propose a new procedure to extract an approximate eigenpair from a Krylov subspace in Arnoldi method, using a minimization problem. Unlike the refined Arnoldi method, the suggested procedure requires solving a linear system. © 2018 Elsevier B.V.

Journal of Computational and Applied Mathematics

A new variant of Arnoldi method for approximation of eigenpairs

We present a ball game that can be continued as long as we wish. It looks as though the game would never end. But by applying a result on trees, we show that the game nonetheless ends in some finite number of moves. We then point out some deep results on the natural number system connected with the game. © 2017, Indian Academy of Sciences.

Resonance

From a ball game to incompleteness

In this paper we survey different methods of computation of prime implicants and implicates in prepositional, first order and modal logic and their applications in electrical engineering, truth maintenance systems and Diagnosis. © 2014 CRL Publishing Ltd.

Computer Systems Science and Engineering

A survey on computing prime implicants and implicates in classical and non-classical logics

It is generally believed that the Ritz vectors do not coincide with the refined Ritz vectors in the Arnoldi method for computing eigenvalues of matrices. We show that this coincidence is theoretically possible. We provide a necessary and sufficient condition for this coincidence to happen and give examples to illustrate the same. Using Lanczos polynomials, we give a polynomial characterization of refined Ritz vectors of symmetric matrices that is different from the one available in the literature. © 2014 Elsevier Ltd. All rights reserved.

Computers and Mathematics with Applications

On refined Ritz vectors and polynomial characterization

We propose a novel multichannel image restoration scheme based on Bayesian maximum a posteriori estimation. Restoration schemes for mono-channel images fail in the case of multichannel images since they do not take into account the cross channel relations present. We propose a robust M-estimator based Gibbs prior which uses not only spatial but also interchannel term for multichannel image data modelled as a Markov random field. Regularized total variation potential function is used as a robust M-estimator in each channel and a weighted inter-channel coupling term with Gaussian prior is used to capture the cross-correlations of the given image. We prove the well-posedness of the corresponding minimization in the bounded variation space. This variational Bayesian scheme reduces the channel mixup artifacts and preserves color edges when compared with other schemes on real and noisy multidimensional images. © 2010 by IJTS.

International Journal of Tomography and Statistics

Multichannel image restoration using combined channel information and robust M-estimator approach

We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. By incorporating edges found at multiple scales via an adaptive edge detector-based indicator function, the proposed scheme removes noise while respecting salient boundaries. We create a smooth transition region around probable edges found and reduce the diffusion rate near it by a gradient-based diffusion coefficient. In contrast to the previous anisotropic diffusion schemes, we prove the well-posedness of our scheme in the space of bounded variation. The proposed scheme is general in the sense that it can be used with any of the existing diffusion equations. Numerical simulations on noisy images show the advantages of our scheme when compared to other related schemes. Copyright © 2010 V. B. S. Prasath and A. Singh.

Journal of Applied Mathematics

Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising

We propose a new hybrid model for variational image restoration using an alternative diffusion switching non-quadratic function with a parameter. The parameter is chosen adaptively so as to minimize the smoothing near the edges and allow the diffusion to smooth away from the edges. This model belongs to a class of edge-preserving regularization methods proposed in the past, the φ{symbol}-function formulation. This involves a minimizer to the associated energy functional. We study the existence and uniqueness of the energy functional of the model. Using real and synthetic images we show that the model is effective in image restoration. © 2009 Elsevier Inc. All rights reserved.

Applied Mathematics and Computation

A hybrid convex variational model for image restoration

A novel way to denoise multispectral images is proposed via an anisotropic diffusion based partial differential equation (PDE). A coupling term is added to the divergence term and it facilitates the modelling of interchannel relations in multidimensional image data. A total variation function is used to model the intrachannel smoothing and gives a piecewise smooth result with edge preservation. The coupling term uses weights computed from different bands of the input image and balances the interchannel information in the diffusion process. It aligns edges from different channels and stops the diffusion transfer using the weights. Well-posedness of the PDE is proved in the space of bounded variation functions. Comparison with the previous approaches is provided to demonstrate the advantages of the proposed scheme. The simulation results show that the proposed scheme effectively removes noise and preserves the main features of multispectral image data by taking channel coupling into consideration. © 2010 Taylor & Francis.

International Journal of Remote Sensing

Multispectral image denoising by well-posed anisotropic diffusion scheme with channel coupling

Image deblurring and denoising are the main steps in early vision problems. A common problem in deblurring is the ringing artifacts created by trying to restore the unknown point spread function (PSF). The random noise present makes this task even harder. Variational blind deconvolution methods add a smoothness term for the PSF as well as for the unknown image. These methods can amplify the outliers correspond to noisy pixels. To remedy these problems we propose the addition of a first order reaction term which penalizes the deviation in gradients. This reduces the ringing artifact in blind image deconvolution. Numerical results show the effectiveness of this additional term in various blind and semi-blind image deblurring and denoising problems. © 2009 IEEE.

Proceedings of the 7th International Conference on Advances in Pattern Recognition, ICAPR 2009

Ringing artifact reduction in blind image deblurring and denoising problems by regularization methods

In this paper we study how Lavrentiev regularization can be used in the context of learning theory, especially in regularization networks that are closely related to support vector machines. We briefly discuss formulations of learning from examples in the context of ill-posed inverse problem and regularization. We then study the interplay between the Lavrentiev regularization of the concerned continuous and discretized ill-posed inverse problems. As the main result of this paper, we give an improved probabilistic bound for the regularization networks or least square algorithms, where we can afford to choose the regularization parameter in a larger interval. © 2009 World Scientific Publishing Company.

Asian-European Journal of Mathematics

An error analysis of Lavrentiev regularization in learning theory

Using the edge detection techniques we propose a new enhancement scheme for noisy digital images. This uses inhomogeneous anisotropic diffusion scheme via the edge indicator provided by well known edge detection methods. Addition of a fidelity term facilitates the proposed scheme to remove the noise while preserving edges. This method is general in the sense that it can be incorporated into any of the nonlinear anisotropic diffusion methods. Numerical results show the promise of this hybrid technique on real and noisy images.© 2008 IEEE.

Proceedings - 6th Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2008

Edge detectors based anisotropic diffusion for enhancement of digital images

A new class of variational-PDE based models is proposed for edge preserving image enhancement. Using the equivalence relation between regularization and PDEs we propose a general class of models which restore noisy images with selective enhancement. It contains a controlled inverse diffusion term which sharpens the image. Experiments show the effectiveness of the model with real and MRI images. © 2008 IEEE.

Proceedings - 1st International Conference on Emerging Trends in Engineering and Technology, ICETET 2008

Controlled inverse diffusion models for image restoration and enhancement

In this paper, a modified version of Newton's Iteration (also called Quasilinearization) for nonlinear systems of ordinary differential equations is considered. Under certain conditions, a simple proof of quadratic convergence of the iteration is derived.&nbsp;

International Journal of Computer Mathematics

A modified version of newton's iteration

In this paper, a numerical method is proposed to solve singularly perturbed systems of nonlinear two-point boundary-value problems. First, Newton's iteration is used to linearize such problems, reducing these to a sequence of linear singularly perturbed two-point boundary-value problems. Then, a difference scheme is applied to solve the linear systems. The difference scheme is accurate up to O(h2). Test examples are included to demonstrate the efficiency of the method. © 1989, Taylor & Francis Group, LLC. All rights reserved.

A numerical method for solving singularly perturbed systems of nonlinear two-point boundary-value problems

An algorithm based on consensus method to compute the set of prime implicates of a quantifier free first order formula X was presented in an earlier work. In this paper the notion of prime implicates is extended to theory prime implicates in the first order case. We provide an algorithm to compute the theory prime implicates of a Knowledge base X with respect to another knowledge base Y where both X and Y are assumed to be unquantified first order formulas. The partial correctness of the algorithm is proved. Copyright © 2007 Inderscience Enterprises Ltd.

VIT Unitversity

International Journal of Information and Communication Technology

An algorithm for computing theory prime implicates in first order logic

In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Viewing it as an ill-posed problem, Showalter's regularization method is applied to approximate the solution. Convergence of the regularized solution to the original is proved. A numerical example has been included for illustrating the method. © 2003 Elsevier Inc. All rights reserved.

Showalter regularization of a singularly perturbed PDE

Knowledge compilation techniques are usually applied for prepositional knowledge bases. In this article, an extension of the notion of prime implicants of aknowledge base using first order formulas in Skolem conjunctive normal form is suggested. The method of transversal clauses used earlier for computing prime implicants of a propositional formula in conjuctive normal form is adopted to the first order case via substitutions. Partial correctness of the algorithm is proved. The algorithm is adopted heuristically for computing approximate prime implicants.

Prime implicants of first order formulas via transversal clauses

This paper considers a reaction-diffusion equation with a small parameter multiplied with the derivatives. Considering this as an ill-posed problem, Lavrentiev regularization method is used to formulate the related well-posed problem. Pointwise a priori estimates of the regularized solutions and of the regularization error are also derived. The regularized equations are solved numerically via the central difference scheme. It is suggested that any other suitable discretization might also be used to solve the regularized problems. Also it is found that with a comparatively small number of grid points, the numerical solution of the regularized equation comes up as a good approximation to the original solution. © 2002 Elsevier Inc. All rights reserved.