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This paper discusses Bayesian analysis of stochastic conditional duration model when the innovations follow inverse Gaussian distribution. Estimation is carried out by the methods of Markov Chain Monte Carlo. Applications of the model and methods are illustrated through simulation and data analysis.

In this paper, we construct a Darboux transformation and the related Bäcklund transformation for the super-symmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is also worked out. We demonstrate that these are natural extensions of the similar results of the Sawada-Kotera...

Some properties of the four-parameter beta-Cauchy distribution such as the mean deviation and Shannon’s entropy are obtained. The method of maximum likelihood is proposed to estimate the parameters of the distribution. A simulation study is carried out to assess the performance of the maximum likelihood...

Simulation platforms play an important role in helping intelligent vehicle research, especially for the research of cooperative driving due to the high cost and risk of the real experiments. In order to ease and bring more convenience for cooperative driving tests, we introduce an intelligent vehicle...

In the present paper we show that the Gompertz function, the Fisher–Tippett and the Gumbel probability distributions are related to both Stirling numbers of the second kind and Bernoulli numbers. Especially we prove for the Gumbel probability density function an analog of the Grosset–Veselov formula...

The complete symmetry group of a 1 + 1 linear evolution equation has been demon- strated to be represented by the six-dimensional Lie algebra of point symmetries sl(2, R)?s W , where W is the three-dimensional Heisenberg-Weyl algebra. The infinite number of solution symmetries does not play a role in...

The solution of the three-dimensional free Schrödinger equation due to W.M. Shtelen based on the invariance of this equation under the Lorentz Lie algebra so(1,3) of nonlocal transformations is considered. Various properties of this solution are examined, including its extension to n 3 spatial dimensions...

We consider the Recursion Operator approach to the soliton equations related to a auxiliary linear system introduced recently by Gerdjikov, Mikhailov and Valchev (GMV system) and their interpretation as dual of Nijenhuis tensors on the manifold of potentials.

Following Feigin and Fuchs, we compute the first cohomology of the Lie superalgebra 𝒦(1) of contact vector fields on the (1, 1)-dimensional real or complex superspace with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities. We also compute...

The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis...

The tail dependence describes the limiting proportion of exceeding one margin over a certain threshold given that the other margin has already exceeded that threshold. In this paper, we obtain the limit tail dependence coefficient for the generalized hyperbolic distribution.

The model proposed in this paper, is a hybridization of fuzzy neural network (FNN) and a functional link neural system for time series data prediction. The TSK-type feedforward fuzzy neural network does not take the full advantage of the use of the fuzzy rule base in accurate input-output mapping and...

A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Askey-Wilson functions is proved. Applications to finite continuous Askey-Wilson transform are given.

We combined measures of resting-state functional magnetic resonance imaging and diffusion tensor imaging (DTI) to investigate alterations of function-structure relationships in patients with early-onset schizophrenia. DTI analysis revealed reduced fractional anisotropy in right frontal white matter....

Here the theory of finite-dimensional supermanifolds is generalized in two directions. First, we introduce infinite-dimensional supermanifolds “locally isomorphic” to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped...

Recently, Neural Network Language Models have been effectively applied to many types of Natural Language Processing (NLP) tasks. One popular type of tasks is the discovery of semantic and syntactic regularities that support the researchers in building a lexicon. Word embedding representations are notably...

In this paper, we obtain µ -symmetry and µ -conservation law of the extended mKdV equation. The extended mKdV equation dose not admit a variational problem since it is of odd order. First we obtain µ -conservation law of the extended mKdV equation in potential form because it admits a variational problem,...

All systems of (n+1)-dimensional quasilinear evolutional second- order equations invariant under the chain of algebras AG(1.n) AG1(1.n) AG2(1.n) are described. The obtained results are illustrated by examples of nonlinear Schrödinger equations.

This paper proposes a Bayesian approach for the analysis of mixed correlated nominal, ordinal and continuous outcomes with possibility of missing values using a variation of Markov Chain Monte Carlo (MCMC) method named Parameter Expanded and Reparamerized Metropolis Hastings (PX-RPMH) method. A general...

Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schr¨odinger and Heisenberg picture levels. A new quasiexactly solvable difference equation...

Actinobacillus pleuropneumoniae (A. pleuropneumoniae) and Haemophilus parasuis (H. parasuis) are important pathogens of swine, which cause great economic losses in the swine industry and bring great safety hazards to food safety. In this study, we established a duplex Droplet Digital Polymerase Chain...

Berger and Stassen reviewed skein relations for link invariants coming from the simple Lie algebras g. They related the invariants with decomposition of the tensor square of the g-module V of minimal dimension into irreducible components. (If V V , one should also consider the decompositions of V V and...

A relativistic two-particle model with superposition of time-asymmetric scalar and vector interactions is proposed and its symmetries are considered. It is shown that first integrals of motion satisfy nonlinear Poisson-bracket relations which include the Poincaré algebra and one of the algebras so(1,3),...

The q-Weibull distribution is a generalized form of the Weibull distribution and has potential to model complex systems and life time datasets. Bayesian inference is the modern statistical technique that can accommodate uncertainty associated with the model parameters in the form of prior distributions....

We observe that recursion operator of an S-integrable hyperbolic equation that degenerates into a Liouvile-type equation admits a particular factorisation. This observation simplifies the construction of such operators. We use it to find a new quasi-local recursion operator for a triplet of scalar fields....

The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the...

With the overwhelming increase of music, it has become difficult to find music which suits the taste of a listener who is in a certain state of emotion. Focusing on the listener's emotional state, this paper presents an emotion-oriented music recommendation algorithm. First, the listener's similarity...

We analyse the behaviour of the Dirac equation in d = 1 + 1 with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise,...

Traditionally, the last step of edge detection algorithms, which is called scaling-evaluation, produces the final output classifying each pixel as edge or nonedge. This last step is usually done based on local evaluation methods. The local evaluation makes this classification based on measures obtained...

Marshall and Olkin [Biometrika. 84 (1997), 641–652. https://doi.org/10.1093/biomet/84.3.641] introduced a new method of adding parameter to expand a family of distribution. In this paper the Marshall-Olkin extended general class of distribution is used. Further, some recurrence relations for single and...

The rapid detection of ongoing outbreak – and the identification of causative pathogen – is pivotal for the early recognition of public health threats. The emergence and re-emergence of infectious diseases are linked to several determinants, both human factors – such as population density, travel, and...

We report wide class of exact solutions of the modified Gross–Pitaevskii equation (GPE) in “smart” Jacobian elliptic potentials, in the presence of external source. Solitonlike solutions, singular solutions, and periodic solutions are found using a recently developed fractional transform in which all...

In order to solve the problem that traditional short text classification methods do not perform well on short text due to the data sparsity and insufficient semantic features, we propose a short text classification method based on convolutional neural network and semantic extension. Firstly, we propose...

Soft set theory and interval set theory are all mathematical tools for dealing with uncertainties. This paper is devoted to the discussion of soft interval set and its application. The notion of soft interval sets is introduced by combining soft set and interval set. Several operations on soft interval...

The aim of this study is to evaluate the susceptibility of landslides at Klang valley area, Malaysia, using a Geographic Information System (GIS) and remote sensing. Landslide locations were identified in the study area from interpretation of aerial photographs and from field surveys. Topographical and...

The attention of driver traveling along a long straight line of prairie highway is easy to be distracted. In this paper, the correlation of straight line length and driver's attention is studied through laboratory simulation experiment and regression analysis. It can be theoretically concluded that the...

Multi-criteria group decision-making (MCGDM) problems are widespread in real life. However, most existing methods, such as hesitant fuzzy set (HFS), hesitant fuzzy linguistic term set (HFLTS) and inter-valued hesitant fuzzy set (IVHFS) only consider the original evaluation data provided by experts but...

There is limited information of level of drug resistance to first-line and second line anti-tuberculosis agents in treatment naïve pulmonary tuberculosis (PTB) patients from the Indian region. Therefore, the present prospective study was conducted to determine the antimicrobial susceptibility to first-line...

Motivated by the fact that the so-called Weibull generated exponentiated exponential distribution (WGEED) accommodates for non-monotone as well as monotone hazard rate functions (HRFs), we give some properties of this WGEED and explore its use in life testing by obtaining Bayes prediction intervals of...

In this paper we propose a new approach for laser-based environment device control systems based on the automatic design of a Fuzzy Rule-Based System for laser pointer detection. The idea is to improve the success rate of the previous approaches decreasing as much as possible the false offs and increasing...

In this paper, step-stress accelerated life test is considered to obtain the failure time data of highly reliable units in specified conditions. It is assumed that the lifetime data of such units follow Lomax distribution with a scale parameter depends on the stress level and the shape parameter remains...

The poblem of characterizing of discrete probability distributions is an important problem. Recently many new results are obtained in characterization of distributions using kth records. Based on the distributional properties of kth weak and ordinary records some characterizations of geometric and discrete...

The presentation of Lie (super)algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. It is very important, for instance, for investigation of the particular Lie (super)algebras arising in different (super)symmetric...

In a number of situations, for example in biology, psychology and neurosciences, researchers are interested in the ratio of two measured quantities. In this paper, we give an overview of different methods to constructing confidence limits for the ratios. Then by using the limiting theorems, a pivotal...

We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.

In this paper we consider the Poisson algebraic structure associated with a classical r-matrix, i.e. with a solution of the modified classical Yang­Baxter equation. In Section 1 we recall the concept and basic facts of the r-matrix type Poisson orbits. Then we describe the r-matrix Poisson pencil (i.e...

In this paper we compute first integrals of nonlinear ordinary differential equations using the extended Prelle-Singer method, as formulated by Chandrasekar et al in J. Math. Phys. 47 (2), 023508, (2006). We find a new first integral for the Painlev´e-Gambier XXII equation. We also derive the first integrals...

In this paper, text representation and feature selection strategies for Chinese text classification based on n-grams are discussed. Two steps feature selection strategy is proposed which combines the preprocess within classes with the feature selection among classes. Four different feature selection...

In this article, we proposed an efficient estimator for estimating population proportion of individuals possessing sensitive attribute in a finite dichotomous population. We used the Hermite distribution to randomize the responses in the randomization design of Kuk [1]. The relative efficiency results...

In this paper we give a generalized form of the Schrödinger equation in the relativistic case, which contains a generalization of the Klein-Gordon equation. By complex Legendre transformation, the complex Lagrangian of electrodynamics produces a complex relativistic Hamiltonian H of electrodynamics,...