Research Experience

Has total twenty two years experience in research work. Has done Ph.D. research work on ‘Some Problems of Brown Dwarf Stars’ under the supervision of Late Prof. Probhas Raychaudhuri, Department of Applied Mathematics, University of Calcutta, Kolkata, India and the Ph.D. degree was awarded in 12.10.2004. In addition to this has done works on the polytropes, on the collapse of rotating stellar cores in the presence of magnetic field, mass transfer in binary stars, fractal nature and time variations in the solar neutrino flux data obtained from different detectors, on the accretion discs of rotating stellar bodies and on the evolution of planets. At present apart from the research works in astrophysics is also engaged in research in the field of time series analysis; statistical signal processing; mathematical modelling on spread of epidemic diseases, mathematical modelling in behavioural and social sciences and pattern classification. In a nutshell his research areas are

i) Stellar and Substellar Astrophysics

ii) Analysis of Time Series and Statistical Signal Processing (Applications in Solar Signals and Financial Time Series)

iii) Nonlinear Systems and Dynamics

iv) Mathematical Modelling in Biological Systems, Social and Behavioural Sciences

v) Pattern Recognition

Google Scholar Profile: https://scholar.google.co.in/citations?user=G76XekUAAAAJ&hl=en

ResearchGate Profile: https://www.researchgate.net/profile/Koushik-Ghosh-14

ORCID ID: https://orcid.org/0000-0003-2138-6320

Web of Science Researcher ID: P-1037-2019

Statement of Research:

I. In the Field of Pattern Recognition:

A new affinity function has been introduced for distance measure between a test point and a training point which is an approach based on local learning in k-nearest neighbour (kNN) algorithm. A new similarity function using this affinity function has also been proposed for the classification of the test patterns. The average classification accuracy, obtained from proposed method has been found to exceed some well-known clustering algorithms.

It has been showed that the performance of the kNN classifier improves significantly from the use of (training) class-wise group-statistics based two criteria during pairwise comparison of features in a given dataset. Granger causality has been employed to assign preferences to each criterion. Analytic Hierarchy Process (AHP) has been applied to obtain weights for different features from the two criteria and their preferences. These weights have been used to build a weighted distance function for the kNN classification. Comprehensive experimentation on different benchmark datasets of the UCI Machine Learning Repository clearly reveals the supremacy of the proposed Granger causality driven AHP induced kNN algorithm over the kNN method with many different distance metrics, and, with various feature selection strategies. In addition, the proposed method has also shown to perform well on high-dimensional face and hand-writing recognition datasets.

Again, presence of outliers critically affects many pattern classification tasks. A novel dynamic outlier detection method has been proposed based on neighbourhood rank difference. In particular, reverse and the forward nearest neighbor rank difference has been employed to capture the variations in densities of a test point with respect to various training points. In the first step of the proposed method, the influence space for a given dataset has been determined. A score for outlierness has been proposed in the second step using the rank difference as well as the absolute density within this influence space. Experiments on synthetic and some UCI machine learning repository datasets clearly indicate the supremacy of the proposed method over some contemporary approaches.

II. In the Field of Astrophysics:

II a) Binary Stars:

Mass Transfer is a regular event in contact binaries. During the process of mass transfer in the contact binaries the mass ratio between the donor and gainer star, the angular momentum and the internal configurations of the binary system are likely to change in case of non-conservative mass transfer. Moreover in case of non-conservative mass transfer the rate of accretion of mass by the gainer star may exhibit a decreasing profile with respect to time as well as the gain in its mass. In addition to this reverse flow of mass may sometimes occur simultaneously with the regular mass transfer in contact binaries with lower angular momentum directed towards the donor as a result of large scale circulation encircling the entire donor and a prominent part of the gainer. To address these issues, separate theoretical models of non-conservative mass transfer has been proposed in contact binaries with lower angular momentum and with both uniform as well as non uniform mass accretion rate of the gainer where the reverse flow of mass directed towards the donor star has also been taken into account along with the regular flow of mass from donor to gainer.

Magnetic braking is a significant cause of angular momentum loss in contact binary stars. The effect of differential rotation in binary stars can be very important in case of generation of magnetic field in companion stars. However, interestingly, the generated magnetic field usually puts a brake in the existing rotation rate. The changing profiles of magnetic field strength, braking in rotation rate due to the magnetic field strength as well as effective angular velocity at different latitudes for each of the components have been analyzed for contact binary system.

II b) Brown Dwarf:

Jupiter is by far the most massive object in our solar system after the Sun having mass of about 10⁻³ M⊙, M⊙ being the mass of the Sun. Its density is significantly lower than that of the inner planets; just 1.3 g cm⁻³ while the densities of Mercury, Venus, Earth and Mars are respectively 5.4, 5.3, 5.5 and 3.9 g cm⁻³. Jupiter radiates more energy into space than it receives from the Sun. It is proposed that the interior of Jupiter has excess energy stored since the time of its collapse. The heat is also generated by the Kelvin-Helmholtz mechanism, the slow gravitational compression of the configuration. This heat within Jupiter contributes to the unusual motion in the internal rotation in Jupiter. Motions in the interior of Jupiter contribute in a very special way to the development of the powerful and extensive magnetosphere of Jupiter. These observations indicate that the composition of Jupiter is basically different from that of the inner planets and these properties of Jupiter are significantly similar to the features of rotating brown dwarfs under the consideration of magnetic field which are thought to be objects having mass between stars and planets. The stellar bodies with mass less than the lower mass limit of the main sequence become completely degenerate as a consequence of gravitational contraction and consequently they cannot go through normal stellar evolution. Primarily they were named ’Black Dwarf.’ The modern term for these objects is ’Brown Dwarf.’ In their young age (<10⁸ years) they contract rapidly and the gravitational binding energy released makes them quite luminous, but as they age they cool rapidly and make them harder to detect. Calculations have shown a significant similarity between the presently observed configuration of Jupiter with that of the model brown dwarf under the consideration of internal rotation and magnetic field with mass, composition and age same that of Jupiter which leads to a conclusion that Jupiter may be considered as a brown dwarf like object in the solar system.

II c) Solar Signals:

Forbush decrease is a rapid decrease in the observed galactic cosmic ray intensity pattern occurring after a coronal mass ejection. The daily Forbush decrease indices generated in IZMIRAN, Russia have been analyzed. First the entire indices have been smoothened and next an attempt has been made to fit a suitable stochastic model for this signal by means of a necessary number of process parameters. The study has revealed that the signal is governed by a stationary autoregressive process of order 2 with a trace of white noise. Under the consideration of the proposed model it has been shown that chaos is not expected in this signal which opens up the possibility of validation of its forecasting (both short-term and long-term) as well as its multi-periodic behaviour.

A search has been made to detect any sort of nonlinearity and chaos in the solar irradiance data from the Earth Radiation Budget Satellite to investigate the inherent complexity in it. Delay vector variance (DVV) analysis has been applied to trace the nonlinearity; whereas 0–1 test, correlation dimension analysis, information entropy, recurrence plot, and recurrence quantification analysis have been used to explore the signature of chaos in the signal. Investigation has revealed that though nonlinearity is significantly present in the signal, chaotic behavior has not been really observed in it.

The radio frequency emission at 10.7 cm (or 2800 MHz) wavelength (considered as solar flux density) out of different possible wavelengths is usually selected to identify periodicities because of its high correlation with solar extreme ultraviolet radiation as well as its complete and long observational record other than sunspot related indices. The solar radio flux at 10.7 cm wavelength plays a very valuable role for forecasting the space weather because it is originated from lower corona and chromospheres region of the Sun. Also, solar radio flux is a magnificent indicator of major solar activity. The solar radio flux data from observed at the Domimion Radio Astrophysical Observatory in Penticton, British Columbia has been processed using Date Compensated Discrete Fourier Transform (DCDFT) to identify predominant periods within the data along with their confidence levels. Also, the multi-taper method (MTM) for periodicity analysis has been used to validate the observed periods. Investigation exhibits multiperiodicity of the signal of F10.7 solar radio flux data. The observed periods have been also compared with the periods of MgII Index data using same algorithm as MgII Index data has 99.9% correlation with F10.7 Solar Radio Flux data. It can be observed that the MgII index data exhibits similar periodicities with very high confidence levels. Investigation has also been clearly indicated that the computed results are very much confining with the results obtained in different communication for the similar data of 10.7 cm Solar Radio Flux as well as for the other solar activities.

A monthly average solar green coronal index signal collected from NOAA (The National Oceanic and Atmospheric Administration) has been analyzed in perspective of scaling analysis and modelling. Smoothed and de-noising has been performed using suitable mother wavelet as a pre-requisite. The Finite Variance Scaling Method (FVSM), Higuchi method, rescaled range (R/S) and a generalized method have been applied to calculate the scaling exponents and fractal dimensions of the signal. Autocorrelation function (ACF) has been used to find autoregressive (AR) process and Partial autocorrelation function (PACF) has been used to get the order of AR model. A best fit model has been proposed using Yule-Walker Method with supporting results of goodness of fit and wavelet spectrum. The results have revealed an anti-persistent, Short Range Dependent (SRD), self-similar property with signatures of non-causality, non-stationarity and nonlinearity in the signal.

The solar wind speed signal has been preprocessed using simple exponential smoothing, discrete wavelet transform for denoising to investigate the underneath dynamics of it. Recurrence plot and recurrence quantification analysis has revealed that the signal is non-stationary with deterministic chaotic behavior. The Hilbert-Huang Transform has been used in search of the underlying periods of the signal. Investigation has revealed a multiperiodic nature of the signal.

An attempt has been also made to investigate statistical association between solar neutrino flux data (both D₂O and Salt data) collected from Sudbury Neutrino Observatory and solar irradiance data detected by Earth Radiation Budget Satellite. To serve this purpose the Multifractal Detrended Cross Correlation Analysis (MF-DCCA) based on Detrended Fluctuation Analysis (MF-X-DFA) method and the Detrending Moving Average Analysis (MF-X-DMA) has been used which explores the long term power-law cross correlations between these two pairs of data sets. Investigation also has been made to find the frequency and time dependent local phase relationship in each pair of data sets using continuous wavelet transform (CWT) based Semblance Analysis. The Semblance Analysis has revealed that there exists positive phase correlation as well as negative phase correlation between solar irradiance and D₂O data at different time sub-intervals. This type of mixed phase correlation is also experienced between solar irradiance and Salt data at different time sub-intervals. The causal relationship between the D₂O and the solar irradiance signal and that between Salt and solar irradiance signal have been revealed using Singular Spectral Analysis (SSA). Calculations indicate that possibly the solar neutrino flux data (both D2O and Salt data) is supportive to predict the solar irradiance data but may not the vice versa which in turn suggests that the variability of nuclear energy generation process inside the Sun may influence the solar activity.

III. In the Field of Financial Market:

The fractal behaviour of prime Indian stock exchanges, namely Bombay Stock Exchange Sensitivity Index (BSE Sensex) and National Stock Exchange (NSE) have been analyzed. To analyze the monofractality of these indices Higuchi method and Katz method have been used separately. By applying Mutifractal Detrended Fluctuation Analysis (MFDFA) technique the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions have been calculated for these indices. Holder exponents as well as singularity spectra for BSE and NSE have been simulated. It has been observed that both the stock exchanges are possessing self-similarity at different small ranges separately and inhomogeneously. By comparing the multifractal behaviour of the BSE and NSE indices, it has been found that the second one exhibits a richer multifractal feature than the first one.

The behaviour of Indian stock markets has a persistent close association with the behaviour of American stock exchange. An effort in this direction has been made to investigate the periodicity of the two prime Indian stock market indices viz. SENSEX and NIFTY and the prime American stock market indices viz. DOW-JONES and S&P500. Ferraz-Mello method of Date-Compensated Discrete Fourier Transform (DCDFT) has been applied on these four double-smoothed monthly averaged time series. Study has revealed periods for SENSEX of 11, 53 and 142 months; for NIFTY periods of 22, 38, 52 and 139 months; for DOW-JONES periods of 23, 25, 27, 30, 59, 107, 138, 194 and 494 months and for S&P500 periods of 28, 66, 74,149 and 384 months. With this specific periodic behaviour also observed some pseudo-periods have also been observed in these four financial time series which certainly adds to the uncertainty in the process of prediction for the same.