The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Bäcklund transformation between TLSCS with different degrees of sources. ...

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimat...

Artificial Neural Networks (ANNs) are very powerful tool in modern quantitative finance and have immerged as a powerful statistical modeling technology. This paper focuses on the problem of estimation of volatility of Indian Stock market. It begins with volatility calculation by Auto Regressive Conditional Heteroscedastic (ARCH), & Generalized Autoregressive Conditional Heteroscedasticity (GARC...

Abstract We present a new generalized algorithm which allows the construction of Bäcklund transformations (BTs) for higher order ordinary differential equations (ODEs). This algorithm is based on the idea of seeking transformations that preserve the Painlevé property, and is applied here to ODEs of various orders in order to recover, amongst others, their autoBTs. Of the ODEs considered here, o...

The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for N -times repeated GBDT are presented. This GBDT provides non-auto-Bäcklund transformation between two KdV equations with different degrees of sources and enable us ...

This paper provides insight into the algebraic and geometric structure of Instantaneous Blind Signal Separation based on the assumptions that the cross-correlation functions of the source signals are zero and that the source auto-correlation functions are linearly independent. The presented viewpoint is unifying in the sense that all kinds of statistical variability in the data, such as tempora...

Image categorization is the problem of classifying images into one or more of several possible categories or classes, which are defined in advance. Classifiers can be trained using machine learning algorithms, but existing machine learning algorithms cannot work with images directly. We consider a representation based on texture segmentation and a similarity measure which has been used successf...

A general approach for modeling the volatility process in continuous-time is based on the convolution of a kernel with a non-decreasing Lévy process, which is non-negative if the kernel is non-negative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary condition for the kernel to be non-negative, and propose a numerical method for ch...

The problem of investigating the minimum set landmarks consisting auto-machines (Robots) in a connected network is studied with concept location number or metric dimension this network. In paper, we study latest type called as local fractional (LFMD) and find its upper bounds for generalized Petersen networks GP(n, 3), where n ≥ 7. For 9. limiting values LFMD 3) are also obtained 1 (bounded) if...