Sawon Pratiher

Sawon Pratiher

This article provides a simple trigonometric method for determining how many roots of a quintic equation are real and how many are complex, without solving the equation. The approach transforms a depressed quintic $t^5 + mt^3 + nt^2 + pt + q = 0$ with $m < 0$ into the trigonometric equation $f(θ) = α\cos^2\!θ+ β\cosθ+ \cos 5θ+ γ= 0$ via the Chebyshev identity $16\cos^5\!θ- 20\cos^3\!θ+ 5\cosθ= \cos 5θ$. The derivation is computationally light and conceptually natural, extending the quartic case to fifth-degree equations. As the Abel--Ruffini theorem forbids a general algebraic solution for the quintic, having a simple trigonometric criterion for the nature of its roots is especially appealing.

Sawon Pratiher, Subhankar Chattoraj, Rajdeep Mukherjee

A novel non-stationarity visualization tool known as StationPlot is developed for deciphering the chaotic behavior of a dynamical time series. A family of analytic measures enumerating geometrical aspects of the non-stationarity & degree of variability is formulated by convex hull geometry (CHG) on StationPlot. In the Euclidean space, both trend-stationary (TS) & difference-stationary (DS) perturbations are comprehended by the asymmetric structure of StationPlot's region of interest (ROI). The proposed method is experimentally validated using EEG signals, where it comprehend the relative temporal evolution of neural dynamics & its non-stationary morphology, thereby exemplifying its diagnostic competence for seizure activity (SA) detection. Experimental results & analysis-of-Variance (ANOVA) on the extracted CHG features demonstrates better classification performances as compared to the existing shallow feature based state-of-the-art & validates its efficacy as geometry-rich discriminative descriptors for signal processing applications.

Sawon Pratiher, Subhankar Chattoraj

Histopathological images (HI) encrypt resolution dependent heterogeneous textures & diverse color distribution variability, manifesting in micro-structural surface tissue convolutions. Also, inherently high coherency of cancerous cells poses significant challenges to breast cancer (BC) multi-classification. As such, multi-class stratification is sparsely explored & prior work mainly focus on benign & malignant tissue characterization only, which forestalls further quantitative analysis of subordinate classes like adenosis, mucinous carcinoma & fibroadenoma etc, for diagnostic competence. In this work, a fully-automated, near-real-time & computationally inexpensive robust multi-classification deep framework from HI is presented. The proposed scheme employs deep neural network (DNN) aided discriminative ensemble of holistic class-specific manifold learning (CSML) for underlying HI sub-space embedding & HI hashing based local shallow signatures. The model achieves 95.8% accuracy pertinent to multi-classification & 2.8% overall performance improvement & 38.2% enhancement for Lobular carcinoma (LC) sub-class recognition rate as compared to the existing state-of-the-art on well known BreakHis dataset is achieved. Also, 99.3% recognition rate at 200X & a sensitivity of 100% for binary grading at all magnification validates its suitability for clinical deployment in hand-held smart devices.

Subhadip Dey, Sawon Pratiher, Saon Banerjee et al.

Effective utilization of photovoltaic (PV) plants requires weather variability robust global solar radiation (GSR) forecasting models. Random weather turbulence phenomena coupled with assumptions of clear sky model as suggested by Hottel pose significant challenges to parametric & non-parametric models in GSR conversion rate estimation. Also, a decent GSR estimate requires costly high-tech radiometer and expert dependent instrument handling and measurements, which are subjective. As such, a computer aided monitoring (CAM) system to evaluate PV plant operation feasibility by employing smart grid past data analytics and deep learning is developed. Our algorithm, SolarisNet is a 6-layer deep neural network trained on data collected at two weather stations located near Kalyani metrological site, West Bengal, India. The daily GSR prediction performance using SolarisNet outperforms the existing state of art and its efficacy in inferring past GSR data insights to comprehend daily and seasonal GSR variability along with its competence for short term forecasting is discussed.

Sabyasachi Mukhopadhyay, Soham Mandal, Sawon Pratiher et al.

Our proposed hyper kurtosis based histogram equalized DIC images enhances the contrast by preserving the brightness. The evolution and development of precancerous activity among tissues are studied through S-transform (ST). The significant variations of amplitude spectra can be observed due to increased medium roughness from normal tissue were observed in time-frequency domain. The randomness and inhomogeneity of the tissue structures among human normal and different grades of DIC tissues is recognized by ST based timefrequency analysis. This study offers a simpler and better way to recognize the substantial changes among different stages of DIC tissues, which are reflected by spatial information containing within the inhomogeneity structures of different types of tissue.

Sabyasachi Mukhopadhyay, Soham Mandal, Sawon Pratiher et al.

In this paper, a comparative study between proposed hyper kurtosis based modified duo-histogram equalization (HKMDHE) algorithm and contrast limited adaptive histogram enhancement (CLAHE) has been presented for the implementation of contrast enhancement and brightness preservation of low contrast human brain CT scan images. In HKMDHE algorithm, contrast enhancement is done on the hyper-kurtosis based application. The results are very promising of proposed HKMDHE technique with improved PSNR values and lesser AMMBE values than CLAHE technique.

Sabyasachi Mukhopadhyay, Nandan K. Das, Soham Mandal et al.

In this paper, we have carried out the detail studies of pre-cancer by wavelet coherency and multifractal based detrended fluctuation analysis (MFDFA) on differential interference contrast (DIC) images of stromal region among different grades of pre-cancer tissues. Discrete wavelet transform (DWT) through Daubechies basis has been performed for identifying fluctuations over polynomial trends for clear characterization and differentiation of tissues. Wavelet coherence plots are performed for identifying the level of correlation in time scale plane between normal and various grades of DIC samples. Applying MFDFA on refractive index variations of cervical tissues, we have observed that the values of Hurst exponent (correlation) decreases from healthy (normal) to pre-cancer tissues. The width of singularity spectrum has a sudden degradation at grade-I in comparison of healthy (normal) tissue but later on it increases as cancer progresses from grade-II to grade-III.