In the paper we show that the general relativity in recent Einstein-Palatini formulation is equivalent to a gauge field. We begin with a bit of information of the Einstein-Palatini formulation and derive Einstein field equations from it. In the next section, we consider general relativity with a positive cosmological constant in terms of the corrected curvature. We show that in terms of the corrected curvature general relativity takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

The present review paper aims at collecting and discussing the research work, numerical and experimental, carried out in the field of Fluid-Structure Interaction (FSI) in one-dimensional (1D) pressurized transient flow in the time-domain approach. Background theory and basic definitions are provided for the proper understanding of the assessed literature. A novel frame of reference is proposed for the classification of FSI models based on pipe degrees-of-freedom. Numerical research is organized according to this classification, while an extensive review on experimental research is presented by institution. Engineering applications of FSI models are described and historical accidents and post-accident analyses documented.

Technology development changes society and society demands new and innovative technology development. We analyze technology to understand society and technology itself. Many researches have been introduced in various fields. Most of them were about patent analysis. This is because detailed and accurate results of research and development are patented. In this paper, we study on new patent analysis method based on count data model and Bayesian regression analysis. Using count data model, we analyze the technological keywords extracted from the collected patent documents. We use the posterior distribution of Bayesian statistics to reflect the experience and knowledge of the relevant technological experts in the analysis model. Moreover, we apply the proposed model to finding sustainable technologies. Finding and developing sustainable technologies is an important activity for companies and research institutes to maintain their technological competitiveness. To illustrate how our modeling could be applied to real domain, we carry out a case study using the patent documents related to artificial intelligence.

We introduce poly-symplectic extension of Souriau Lie groups Thermodynamics based on higher-order model of statistical physics introduced by R.S. Ingarden. This extended model could be used for small data analytics and Machine Learning on Lie groups. Souriau Geometric Theory of Heat is well adapted to describe density of probability (Maximum Entropy Gibbs density) of data living on groups or on homogeneous manifolds. For Small Data Analytics (Rarified Gases , sparse statistical survey,…), density of maximum entropy should consider Higher Order Moments constraints (Gibbs density is not only defined by first moment but fluctuations request 2nd order and higher moments) as introduced by R.S. Ingarden. We use Poly-sympletic model introduced by Christian Günther, replacing the symplectic form by a vector-valued form. The poly-symplectic approach generalizes the Noether theorem, the existence of momentum mappings, the Lie algebra structure of the space of currents, the (non-)equivariant cohomology and the classification of G-homogeneous systems. The formalism is covariant, i.e. no special coordinates or coordinate systems on the parameter space are used to construct the Hamiltonian equations. We underline the contextures of these models, and the process to build these generic structures.

Dispersion tests based on the second order component of smooth test statistics are related to Fisher’s Index of Dispersion test, used for testing for the Poisson distribution when there are no covariates present. Such tests have been recommended in [1] to test for the Poisson distribution when covariates are present. The modified Borel-Tanner (MBT) distribution seems suited to data with extra zeroes, a monotonic decline in counts and longer tails. Here we recommend a dispersion test for the MBT distribution for both when covariates are absent and when they are present.

We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes, this enables a comparison between curves’ shapes and allows then the classification of processes’ measure.

In a wireless network, locations of base stations (BSs)/access points (APs)/sensor nodes can be modeled based on stochastic processes, e.g., a Poisson point process (PPP) or a deterministic pattern planned ahead by providers. While deterministic deployment does not provide tractable interference analysis in general, PPP yields tractable analysis for interference. However, PPP allows APs to be deployed very close to each other and gives pessimistic results compared to the field measurements. In this study, in order to address this issue, Lloyd’s algorithm, which functions as a bridge between random and structural APs deployments, is investigated for analyzing coverage probability in a network. The link distance distribution is modeled as a mixture of Weibull distributions and its parameters are obtained by using the expectation-maximization (EM) algorithm for each iteration of Lloyd’s algorithm. The link distance distribution is further utilized for calculating the coverage probability approximately by exploiting the tractability of PPP.

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

The main focus when developing software is to improve the reliability and stability of a software system. When software systems are introduced, these systems are used in field environments that are the same as or close to those used in the development-testing environment; however, they may also be used in many different locations that may differ from the environment in which they were developed and tested. In this paper, we propose a new software reliability model that takes into account the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models and confidence intervals of all models based on two sets of failure data collected from software applications. The results show that the proposed model fits the data more closely than other existing NHPP models to a significant extent.

Land degradation is a serious impediment to improving rural livelihoods in Eastern Africa. This paper identifies major land degradation patterns and causes, and analyzes the determinants of sustainable land management (SLM) in three countries (Ethiopia, Malawi and Tanzania). The results show that land degradation hotspots cover about 51%, 41%, 23% and 23% of the terrestrial areas in Tanzania, Malawi and Ethiopia respectively. The analysis of nationally representative household surveys shows that the key drivers of SLM in these countries are biophysical, demographic, regional and socio-economic determinants. Secure land tenure, access to extension services and market access are some of the determinants incentivizing SLM adoption. The implications of this study are that policies and strategies that facilities secure land tenure and access to SLM information are likely to incentivize investments in SLM. Local institutions providing credit services, inputs such as seed and fertilizers, and extension services must also not be ignored in the development policies.

Nanopores with irregularities are promising tools for distinguishing nano-size objects by their shape, but the forces on the object that critically influence its axial and rotational movement are unclear. The physics of the situation was described using the Poisson-Nernst-Planck and Navier-Stokes equations. With uniformly charged object the axial Coulomb and dielectric pressure (which opposes it and is surprisingly important), control the object's axial movement and rotation. Even without external pressure the hydrodynamic pressure is significant (negative at its upper and positive at its lower surface), but its total value is almost zero. If the object is charged only on the upper surface the axial upper Coulomb pressure is near zero close to the center, but negative near its end (the pressure is zero at the lower surface). The total axial dielectric pressure, which is largely dominated by the pressure at the upper surface, is positive along the length of the object becoming pronounced near its end. The axial hydrodynamic pressure is negative and significant at the upper surface (zero at the lower surface), diminishes in value near the object's end, critically influencing its axial movement, which becomes much faster. At its end the axial dielectric pressure prevails, and controls its rotation.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

To estimate the recreational value provided by the Foy’s Lake annually using the most applicable model for on-site data is the main objective of this study. Adhere to the objective of this study; Individual Travel Cost Method (ITCM) has been applied and Zero Truncated Poisson Regression Model has been found plausible among other models to estimate consumer surplus. Based on the findings of the study, an estimate of the consumer surplus or recreational benefits per trip per visitor can be recommended as BDT 5,875 or US $ 73.44 and counting the consumer surplus per trip per visitor, the annual recreational value (total consumer surplus) provided by the lake is found to be BDT 321 million or US $ 40.2 million.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

Count data are used in many fields of practice, especially Poisson distribution as a popular choice for the marginal process distribution. If these counts exhibit serial dependence, a popular approach is to use a Poisson INAR(1) model to describe the autocorrelation structure of process. In this paper, the explicit formulas are proposed to evaluate performance characteristics of Double Moving Average control chart (DMA) for Integer valued autoregressive of serial dependence Poisson process. The characteristics of the control chart are frequently measured as Average Run Length (ARL) which means that the average of observations are taken before a system is signaled to be out-of-control. These proposed explicit formulas of ARL are simple and easy to implement for practitioner. The numerical results show that the DMA chart performs better than others when the magnitudes of shift are moderate and large.