Hi, I'm Manaswita, a Doctoral Researcher from The Math-O-Genic World!




Mathematics gives us hope that  'Every Problem Has A Solution', which is a hard-core truth in our life!

Educational Qualifications..

B.Sc. In Mathematics - Alipurduar College, West Bengal, India

M.Sc. In Mathematics - Techno India University, Kolkata, India

B.Ed. - Maharshi Dayanand University, Haryana, India

Ph.D. Study Program in Geometry & Topology - Comenius University, Bratislava, Slovakia

M.SC. Thesis

WAVELET POWER SPECTRUM ANALYSIS OF A NON-STATIONARY NON-LINEAR TIME SERIES

The significant wave height (SWH) data variability is studied for the Bay of Bengal region for the period 1996-2000 using continuous wavelet power spectrum. The averaged SWH time series were normalized by their standard deviation and then decomposed using the Morlet wavelet function. The normalized wavelet power spectrum are generated with the cone of influence, where edge effects become important. The 95% confidence level for the SWH data is shown by the black contours. For a red-noise process the significance levels were computed with a lag-1 coefficient of 0.99. For white-noise process similar contours were generated with a lag-1 coefficient of 0.00 since they are uncorrelated in time. For the year 1996 the red-noise wavelet power spectrum shows two bands of oscillations, one in the 5-20 days period and the other one in the 32-64 days period. Except for the year 2000 the maximum power is concentrated in the June-August months for the 32-64 day period. Inspite of the above fact significant region is noted only in the year 1996 for the 32-64 day period. Hence the red-noise wavelet power spectra effectively captures the oscillations in the SWH data which corresponds to seasonal variations. 

If you want to look at the full paper, you can do so by clicking here! 

Publication- TTIC, 2020. Vol. 4, 35-41

Ph.D. Exploration...

Subgraphs Of Multicriteria Optimized Triangulation

We are on the way of exploring new extensions and generalizations of Delaunay triangulation in the plane for triangulations with one or more special criteria. The results should lead to new or faster algorithms.

The properties of application-useful subgraphs of standard planar Delaunay triangulation (DT) are relatively well known, which is not the case for analogous subgraphs of specialized triangulations and their generalization into multicriteria triangulations. Several of the edges of DT subgraphs can be characterized directly, declaratively (eg by empty space criteria) or procedurally (eg Urquhart graph, minimum spanning tree). The aim of this work is to expand the theory, study the properties and relationships of subgraphs and analyze the computational complexity. Understanding the declarative characteristics of subgraph edges could lead to faster algorithms for constructing special triangulations or their approximations.

Multicriteria triangulations [2] can be applied to data in many application areas [3], [1], [5]. Deterministic algorithmic strategies make it possible to construct part of triangulations and their application-significant subgraphs, for the subgraphs of planar Delaunay triangulation [4], [5], [6] their hierarchy was described by Veltkamp [8]. Stochastic algorithmic strategies (simulated annealing, genetic algorithms) make it possible to approximate each triangulation using the Lawson flipping procedure and its stochastic uses, e.g. [9] and dozens of other authors, citing [2]. We summarize the necessary theory and use appropriate data to design experiments to investigate the algorithm acceleration hypothesis.


Recent Activities (in the process of Ph.D.).. 

References..

[1] DAS, M., SINHA, M. 2020. Wavelet Power Spectrum Analysis of a Non-Stationary NonLinear Time Series Data; TIU Transactions on Intelligent Computing (TTIC) Journal, 2020, Vol. 4, 35-41.

[2] KOLINGEROVÁ, I -  FERKO, A. 2001. Multicriteria-optimized triangulations.The Visual Computer 17 (6), 380-395.

[3] KRÜGER, B. 2016.  Simulating Triangulations: Graphs, Manifolds and (Quantum) Spacetime. Erlangen: FAU University Press.

[4] AURENHAMMER F et al. 2013. Voronoi Diagrams and Delaunay Triangulations. World Scientific Publishing Company.

[5] EDELSBRUNNER, H. 2011.  Alpha shapes --- a survey. In Tessellations in the Sciences...  http://pub.ist.ac.at/~edels/Papers/2011-B-03-AlphaShapes.pdf.


[6] PREPARATA, F.P, SHAMOS, M. I. 1985. Computational Geometry, An Introduction, Springer Verlag 1985.

[7] EDELSBRUNNER, H – HARER, J. 2010. Computational Topology. An Introduction. Amer. Math. Soc., Providence, RI.


[8] VELTKAMP, R.C. 1991.The gamma-neighborhood Graph. Computational Geometry: Theory and Applications  Volume 1Issue 4 April 1992 pp 227–246 https://doi.org/10.1016/0925-7721(92)90003-B.

[9] RODRÍGUEZ, N., SILVEIRA, R. I.. 2017. Implementing Data-Dependent Triangulations with Higher Order Delaunay Triangulations. ISPRS Int. J. Geo-Inf. 2017, 6(12), 390; https://doi.org/10.3390/ijgi6120390 

Contact Details :

Name: Manaswita Das

Room: M144

Department: Katedra algebry a geometrie


University: Fakulta matematiky, fyziky a informatiky Univerzity Komenskeho Mlynska Dolina, 842 48, Bratislava

Phone: +421 (0)2 602 95642 (office) 

Email: manaswita.das@fmph.uniba.sk

ORCID: https://orcid.org/0000-0001-8446-8871


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