Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations

We demonstrate the existence of complex solitary wave and periodic solutions of the Kortweg de-vries (KdV) and modified Kortweg de-Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity ($\cal{P}$) and time-reversal ($\cal{T}$) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The $\cal{PT}$-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental $sech^2$ solution through supersymmetry

Application of spectral and spatial indices for specific class identification in Airborne Prism EXperiment (APEX) imaging spectrometer data for improved land cover classification

Hyperspectral remote sensing's ability to capture spectral information of targets in very narrow bandwidths gives rise to many intrinsic applications. However, the major limiting disadvantage to its applicability is its dimensionality, known as the Hughes Phenomenon. Traditional classification and image processing approaches fail to process data along many contiguous bands due to inadequate training samples. Another challenge of successful classification is to deal with the real world scenario of mixed pixels i.e. presence of more than one class within a single pixel. An attempt has been made to deal with the problems of dimensionality and mixed pixels, with an objective to improve the accuracy of class identification. In this paper, we discuss the application of indices to cope with the disadvantage of the dimensionality of the Airborne Prism EXperiment (APEX) hyperspectral Open Science Dataset (OSD) and to improve the classification accuracy using the Possibilistic c–Means (PCM) algorithm. This was used for the formulation of spectral and spatial indices to describe the information in the dataset in a lesser dimensionality. This reduced dimensionality is used for classification, attempting to improve the accuracy of determination of specific classes. Spectral indices are compiled from the spectral signatures of the target and spatial indices have been defined using texture analysis over defined neighbourhoods. The classification of 20 classes of varying spatial distributions was considered in order to evaluate the applicability of spectral and spatial indices in the extraction of specific class information. The classification of the dataset was performed in two stages; spectral and a combination of spectral and spatial indices individually as input for the PCM classifier. In addition to the reduction of entropy, while considering a spectral-spatial indices approach, an overall classification accuracy of 80.50% was achieved, against 65% (spectral indices only) and 59.50% (optimally determined principal component

Invariance Properties of Statistical Tests for Dependent Observations

In this dissertation we assume that the observations are from normal populations but are correlated and study the problem of characterizing the class of covariance structures such that the distributions of the popular test statistics remain invariant, that is, they remain the same except for a constant factor. We first obtain some simple extensions and variations of the well known Cauchy-Schwarz inequality. Incidentally, several inequalities that are useful in the detection of outliers can be deduced from our results. Our main result is a characterization of the class of all nonnegative definite solutions W to the matrix equation AWA = B, where A is a symmetric and B is a nonnegative definite matrix. We illustrate the proof of this characterization by considering a special case where A = B = A* = I - 1/n ee\u27, I is the identity matrix and e is a vector of ones. We thus have an elegant characterization of the class of all nonnegative definite g-inverses of the centering matrix A*. Next we present the statistical applications of our matrix theoretic results. For example, we show that the usual two sample t-statistic has a t-distribution if the observations in one of the samples are positively equicorrelated and those in the other sample are negatively equicorrelated with the same correlation in absolute value. More generally, we have a complete characterization of the class of covariance matrices for which the distributional properties of the quadratic forms in ANOVA problems remain invariant. These results are contained in Chapter 3. In Chapters 4 and 5, we generalize our results to the multivariate test statistics, first considering a special covariance structure that occurs in repeated measurements and later for an arbitrary covariance structure. These include invariance properties of the distributions of quadratic forms in MANOVA problems and one- and two-sample Hotelling\u27s T2 statistics. As preliminaries to the multivariate results, we obtain a very general version of the Cochran\u27s theorem concerning the independence and Wishartness of the multivariate quadratic forms

Wishartness and Independence of Matrix Quadratic Forms for Kronecker Product Covariance Structures

Let X be distributed as matrix normal with mean M and covariance matrix W⊗V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran’s theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor. © 2003 Elsevier Inc. All rights reserved

Analysing Amino Acids in Galanin Graph Theoretical Approach

Graph theoretical analysis is an important area of the research in biological networks. Here first we introduce Pt-graph of peptide/protein based on physicochemical properties and adjacency of amino acids in the corresponding peptide/protein. Based on the Pt-graph, we introduce the graph of species which containing the peptide/protein named as SPt-graph. Finally, we analyze graph theoretically Pt-graphs of fourteen species of animals containing Galanin, a neuropeptide and their SPt-graph. From the graph theoretical analyses of Pt-graph and SPt-graph we get some observations about the relations among the amino acids, physicochemical properties of amino acids, peptide/protein and species containing peptide/protein and it may help in the field of evolution of peptide/protein and drug design in future

Henckelia khasiana, una nueva especie de Gesneriaceae de la India

A new species of Henckelia (Gesneriaceae) is here described and illustrated. It is morphologically most similar to H. oblongifolia but differs in having lanceolate calyx lobes, two prominent longitudinal flaps on the inner surface of the corolla tube, bilobed stigma and tomentose capsules. A detailed description of the new species with colour photographs, affinities and a comparison with related species is given. Based on the present data, the new species is provisionally assessed as Critically Endangered (CR) according to IUCN Red List Categories and Criteria.Se describe e ilustra una nueva especie de Henckelia (Gesneriaceae). Esta nueva especie es similar a H. oblongifolia, de la que se diferencia por tener lóbulos del cáliz lanceolados, dos láminas longitudinales prominentes en la superficie interna del tubo de la corola, estigma bilobulado y cápsulas tomentosas. Se proporciona una descripción detallada de la nueva especie y fotografías en color de sus principales órganos. Sobre la base de los datos actuales, se evalúa provisionalmente como en Peligro Crítico (CR) de acuerdo con las categorías y criterios de la Lista Roja de la IUCN

An audit on usage of fresh frozen plasma in a tertiary care hospital in north western part of India

Background: Every blood Component carries inherent risk of adverse transfusion reactions and transmission of transfusion transmitted disease (TTD). The adverse transfusion reactions are unpredictable and makes transfusion services puzzled, FFP being the most common one, it is therefore necessary that appropriate and rational use of FFP is done to make transfusion safer in terms of patient safety. The objective of the study was to assess the utilisation of FFP in a tertiary care Hospital.Methods: We conducted a retrospective study on 256 patient who received FFP transfusion at our tertiary care hospital over a period of 6 months .The usage was classified as appropriate or inappropriate based on the guidelines for FFP usage by British committee for standards in haematology, 2004 and college of American pathologist, 1994.Results: There were 256 patients in the study period who received 1370 units of FFP transfusions. The male: Female ratio was 162 M & 94 F. Most of the patients belonged to Gastroenterology Department (41.75%) followed by CTVS (15.32%). 29.48% of FFP transfusions were reclassified as inappropriate either due to Lack of indication or inappropriate doses.Conclusions: The study emphasize on the need to incurate rational use of blood components which is FFP in present case for evolving safe transfusion practices in the country. This study highlights no adherence to guidelines among clinicians which is mainly due to lack of knowledge of appropriate usage

Stress Urinary Incontinence post-Holmium Laser Enucleation of the Prostate: a Single-Surgeon Experience.

PURPOSE: To identify incidence and predictors of stress urinary incontinence (SUI) following Holmium laser enucleation of the prostate (HoLEP). MATERIALS AND METHODS: We performed a retrospective review of 589 HoLEP patients from 2012-2018. Patients were assessed at pre-operative and post-operative visits. Univariate and multivariate regression analyses were performed to identify predictors of SUI. RESULTS: 52/589 patients (8.8%) developed transient SUI, while 9/589 (1.5%) developed long-term SUI. tSUI resolved for 46 patients (88.5%) within the first six weeks and in 6 patients (11.5%) between 6 weeks to 3 months. Long-term SUI patients required intervention, achieving continence at 16.4 months on average, 44 men (70.9%) with incontinence were catheter dependent preoperatively. Mean prostatic volume was 148.7mL in tSUI patients, 111.6mL in long-term SUI, and 87.9mL in others (p \u3c 0.0001). On univariate analysis, laser energy used (p \u3c 0.0001), laser on time (p=0.0204), resected prostate weight (p \u3c 0.0001), overall International Prostate Symptom Score (IPSS) (p=0.0005), and IPSS QOL (p=0.02) were associated with SUI. On multivariate analysis, resected prostate weight was predictive of any SUI and tSUI, with no risk factors identified for long-term SUI. CONCLUSION: Post-HoLEP SUI occurs in ~10% of patients, with 1.5% continuing beyond six months. Most patients with tSUI recover within the first six weeks. Prostate size \u3e100g and catheter dependency are associated with increased risk tSUI. Larger prostate volume is an independent predictor of any SUI, and tSUI