Department of Mathematics

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In this paper, we investigate various stochastic orderings for series and parallel systems with independent and heterogeneous components having lifetimes following the proportional odds model. We also investigate comparisons between a system with heterogeneous components and that with homogeneous components. This paper also studies relative ageing orders for two systems in the framework of components having lifetimes following the proportional odds model. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.

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Reliability study of series and parallel systems of heterogeneous component lifetimes following proportional odds model

In this paper, a novel graph theoretic image segmentation technique is proposed, which utilizes forest concept for clustering. The core idea is to obtain a forest from the image followed by construction of average value super pixels. Thereafter, a merging criterion is proposed to merge these super pixels into two big classes thereby binarizing and thresholding the image separating background from foreground. Extensive experimentation and comparative analysis are finally performed on a diverse set of images to validate the technique and have noted the significant improvements. © Springer Nature Singapore Pte Ltd 2020.

Communications in Computer and Information Science

A novel graph theoretic image segmentation technique

The aim of this study was to investigate whether parameters from an instrumented one-leg stance (OLS) on a force plate could provide relevant information related to fall risk in older people. Forty-two community dwelling older people including 17 fallers and 25 nonfallers, and 25 young subjects performed a OLS while standing on a force plate, with parameters related to transferring weight onto one leg and postural sway in singe-leg stance evaluated. No differences were observed between older fallers and nonfallers and the younger participants for any of the weight transfer parameters. The younger participants were able to reduce their postural sway during the OLS test after the first 0-2 s period, unlike older participants who swayed the same amount throughout the test. The older fallers swayed significantly more than both nonfallers and younger participants throughout the 10-s of OLS evaluated. When the tests were used to classify older participants as fallers, the instrumented OLS achieved 100% accuracy, compared to 69.0% classification accuracy for the five times sit-to-stand test, 61.9% for the standard OLS, and 47.6% for the timed-up-and-go test. These findings suggest that the standard OLS test might not be suitable to detect fall risk. In contrast, an instrumented version of the OLS could provide valuable additional information that could identify older fallers. Future work will include a prospective study of the instrumented OLS in a larger population of older people. © 2020 BMJ Publishing Group. All rights reserved.

Department of Electrical Engineering

Journal of Biomechanical Engineering

A Pilot Study to Detect Balance Impairment in Older Adults Using an Instrumented One-Leg Stance Test

The Sit-to-Stand (STS) is a widely used test of physical function to screen older people at risk of falls and frailty and is also one of the most important components of standard screening for sarcopenia. There have been many recent studies in which instrumented versions of the STS (iSTS) have been developed to provide additional parameters that could improve the accuracy of the STS test. This systematic review aimed to identify whether an iSTS is a viable alternative to a standard STS to identify older people at risk of falling, frailty, and sarcopenia. A total of 856 articles were found using the search strategy developed, with 12 articles retained in the review after screening based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Six studies evaluated the iSTS in fallers, five studies in frailty and only one study in both fallers and frailty. The results showed that power and velocity parameters extracted from an iSTS have the potential to improve the accuracy of screening when compared to a standard STS. Future work should focus on standardizing the segmentation of the STS into phases to enable comparison between studies and to develop devices integrated into the chair used for the test to improve usability. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Bioengineering

Instrumented analysis of the sit-to-stand movement for geriatric screening: A systematic review

The sit-to-stand test (STS) is a simple test of function in older people that can identify people at risk of falls. The aim of this study was to develop two novel methods of evaluating performance in the STS using a low-cost RGB camera and another an instrumented chair containing load cells in the seat of the chair to detect center of pressure movements and ground reaction forces. The two systems were compared to a Kinect and a force plate. Twenty-one younger subjects were tested when performing two 5STS movements at self-selected slow and normal speeds while 16 older fallers were tested when performing one 5STS at a self-selected pace. All methods had acceptable limits of agreement with an expert for total STS time for younger subjects and older fallers, with smaller errors observed for the chair (-0.18 ± 0.17 s) and force plate (-0.19 ± 0.79 s) than for the RGB camera (-0.30 ± 0.51 s) and the Kinect (-0.38 ± 0.50 s) for older fallers. The chair had the smallest limits of agreement compared to the expert for both younger and older participants. The new device was also able to estimate movement velocity, which could be used to estimate muscle power during the STS movement. Subsequent studies will test the device against opto-electronic systems, incorporate additional sensors, and then develop predictive equations for measures of physical function. © 2001-2011 IEEE.

IEEE Transactions on Neural Systems and Rehabilitation Engineering

A Comparison of Four Approaches to Evaluate the Sit-to-Stand Movement

In this paper, a straightforward design technique is presented for designing broadband, polarization-insensitive meta-surface for wideband radar cross-section (RCS) reduction. Two different unit cell structures, one dual resonance unit cell composed of a circular patch and circular loop and, a square patch are selected for enhancing the phase bandwidth and covering 2π range. Three different metasurfaces i.e.Triangular checkerboard metasurface, random triangular checkerboard metasurface and aperiodic metasurface are designed and characterized. Enhanced performance, both in terms of diffused reflection and wideband RCS reduction, is achieved by aperiodic metasurface compared to the other two metasurfaces. The proposed aperiodic metasurface significantly reduce the RCS for wide operational bandwidth and demonstrate features such as polarization insensitivity and low design complexity. © 2020 Indian Radio Science Society.

2020 URSI Regional Conference on Radio Science, URSI-RCRS 2020 - Proceedings

Aperiodic Metasurface for Broadband RCS Reduction

We study the multi-boundary entanglement structure of the states prepared in (1+1) and (2+1) dimensional Chern-Simons theory with finite discrete gauge group G. The states in (1+1)-d are associated with Riemann surfaces of genus g with multiple S1 boundaries and we use replica trick to compute the entanglement entropy for such states. In (2+1)-d, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple T2. We present a quantitative analysis of the entanglement structure for both abelian and non-abelian groups. For all the states considered in this work, we find that the entanglement entropy for direct product of groups is the sum of entropy for individual groups, i.e. EE(G1× G2) = EE(G1) + EE(G2). Moreover, the reduced density matrix obtained by tracing out a subset of the total Hilbert space has a positive semidefinite partial transpose on any bi-partition of the remaining Hilbert space. © 2020, The Author(s).

Journal of High Energy Physics

Multi-boundary entanglement in Chern-Simons theory with finite gauge groups

In this paper, we discuss the superconvergence of the Galerkin solutions for second kind nonlinear integral equations of Volterra–Hammerstein type with a smooth kernel. Using Legendre polynomial bases, we obtain order of convergence O(n-r) for the Legendre Galerkin method in both L2-norm and infinity norm, where n is the highest degree of the Legendre polynomial employed in the approximation and r is the smoothness of the kernel. The iterated Legendre Galerkin solutions converge with the order O(n-2r) , whose convergence order is the same as that of the multi-Galerkin solutions. We also prove that iterated Legendre multi-Galerkin method has order of convergence O(n-3r) in both L2-norm and infinity norm. Numerical examples are given to demonstrate the efficacy of Galerkin and multi-Galerkin methods. © 2019, Forum D'Analystes, Chennai.

Journal of Analysis

Legendre spectral Galerkin and multi-Galerkin methods for nonlinear Volterra integral equations of Hammerstein type

In this article, we consider a class of derivative dependent Fredholm-Hammerstein integral equations i.e., the integral equation, where the nonlinear function inside the integral sign is dependent on derivative and the kernel function is of Green's type. We propose the piecewise polynomial based Galerkin and iterated Galerkin methods to solve these type of derivative dependent Fredholm-Hammerstein integral equations. We discuss the convergence and error analysis of the proposed methods and also obtain the superconvergence results for iterated Galerkin approximations. Some numerical results are given to illustrate this improvement. © 2019 Elsevier B.V.

Journal of Computational and Applied Mathematics

Convergence analysis for derivative dependent Fredholm-Hammerstein integral equations with Green's kernel

This article deals with the existence of the following quasilinear degenerate singular elliptic equation: (Pλ){-div(w(x)|∇u|p-2∇u)=gλ(u),u&gt;0inΩ,u=0on∂Ω,where Ω ⊂ Rn is a smooth bounded domain, n≥ 3 , λ&gt; 0 , p&gt; 1 , and w is a Muckenhoupt weight. Using variational techniques, for gλ(u) = λf(u) u-q and certain assumptions on f, we show existence of a solution to (Pλ) for each λ&gt; 0. Moreover, when gλ(u) = λu-q+ ur, we establish existence of at least two solutions to (Pλ) in a suitable range of the parameter λ. Here, we assume q∈ (0 , 1) and r∈(p-1,ps∗-1). © 2020, Springer Nature Switzerland AG.}, author_keywords={Multiple weak solutions; Singular nonlinearity; Variational method; Weighted p-Laplacian}, references={Arcoya, D., Boccardo, L., Multiplicity of solutions for a Dirichlet problem with a singular and a supercritical nonlinearities (2013) Differ. Integral Equ., 26 (1-2), pp. 119-128; Arcoya, D., Moreno-Mérida, L., Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity (2014) Nonlinear Anal., 95, pp. 281-291; Bal, K., Garain, P., (2017) Multiplicity Results for a Quasilinear Equation with Singular Nonlinearity; Boccardo, L., A Dirichlet problem with singular and supercritical nonlinearities (2012) Nonlinear Anal., 75 (12), pp. 4436-4440; Boccardo, L., Orsina, L., Semilinear elliptic equations with singular nonlinearities (2010) Calc. Var. Partial Differ. Equ., 37 (3-4), pp. 363-380; Canino, A., Sciunzi, B., Trombetta, A., Existence and uniqueness for p -Laplace equations involving singular nonlinearities (2016) NoDEA Nonlinear Differ. Equ. Appl., 23 (2), p. 18. , Art. 8; Crandall, M.G., Rabinowitz, P.H., Tartar, L., On a Dirichlet problem with a singular nonlinearity (1977) Commun. Partial Differ. Equ., 2 (2), pp. 193-222; Quasilinear elliptic equations with degenerations and singularities (1997) De Gruyter Series in Nonlinear Analysis and Applications, 5. , Walter de Gruyter & Co., Berlin; Fabes, E.B., Kenig, C.E., Serapioni, R.P., The local regularity of solutions of degenerate elliptic equations (1982) Commun. Partial Differ. Equ., 7 (1), pp. 77-116; Garain, P., On a degenerate singular elliptic problem (2018) Arxiv; Ghergu, M., Rădulescu, V.D., Singular elliptic problems: Bifurcation and asymptotic analysis (2008) Oxford Lecture Series in Mathematics and Its Applications, 37. , The Clarendon Press, Oxford University Press, Oxford; Giacomoni, J., Schindler, I., Takác, P., Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation (2007) Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6 (1), pp. 117-158; Haitao, Y., Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem (2003) J. Differ. Equ., 189 (2), pp. 487-512; Heinonen, J., Kilpeläinen, T., Martio, O., (1993) Nonlinear Potential Theory of Degenerate Elliptic Equations, , Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York; Hirano, N., Saccon, C., Shioji, N., Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities (2004) Adv. Differ. Equ., 9 (1-2), pp. 197-220; Kilpeläinen, T., Weighted Sobolev spaces and capacity (1994) Ann. Acad. Sci. Fenn. Ser. A I Math, 19 (1), pp. 95-113; Eunkyung, K., Eun, K.L., Shivaji, R., Multiplicity results for classes of infinite positone problems (2011) Z. Anal. Anwend., 30 (3), pp. 305-318; Lazer, A.C., McKenna, P.J., On a singular nonlinear elliptic boundary-value problem (1991) Proc. Am. Math. Soc., 111 (3), pp. 721-730; Lindqvist, P., (2006) Notes on the P -Laplace Equation, 102. , Report, University of Jyväskylä Department of Mathematics and Statistics. University of Jyväskylä, Jyväskylä; Muckenhoupt, B., Weighted norm inequalities for the Hardy maximal function (1972) Trans. Am. Math. Soc., 165, pp. 207-226; Peral, I., Multiplicity of Solution for P-Laplacian, , ICTP lecture notes; Wu, L., Niu, P., Harnack inequalities for weighted subelliptic p -Laplace equations constructed by Hörmander vector fields (2017) Math. Rep. (Bucur.), 19 (69), pp. 313-337. , 3}, correspondence_address1={Garain, P.; Department of Mathematics and Systems Analysis, Otakaari 1, Finland; email: pgarain92@gmail.com}, publisher={Birkhauser}, issn={16605446}, language={English}, abbrev_source_title={Mediterr. J. Math.}, document_type={Article}, source={Scopus},