Assessment of industrial potential in terms of area’s economic security ensuring

Subject. This article discusses the risk-contributing factors and threats that affect the competitiveness of the area and its economic security in terms of industrial potential. Objectives. Defining the concept of Industrial Potential and its role in ensuring economic security, the article aims to substantiate indicators and threshold values for assessing the industrial potential of the area and testing the methodology using the Rosstat data to identify threats in the industrial sphere of the Republic of Mordovia. Methods. For the study, I used the systems approach, analysis and synthesis, deduction, a combination of historical and logical methods, normalizing constant method, and the indicative analysis. Results. The article describes an approach to assessing the state of the industrial potential of the area based on a system of indicators and their threshold values. This approach helps determine the level and depth of threats to economic security that have arisen or may arise under the influence of corrosive factors. The downward trend in the index of industrial production is a key threat to the economy of the Republic of Mordovia. Conclusions. The development of an area’s industrial complex in the conditions of shortage of capital resources is possible only due to an effective regional industrial policy.

Approximate Variational Estimation for a Model of Network Formation

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations, however convergence may be exponentially slow. We propose a deterministic method, based on a variational mean-field approximation of the ERGM's normalizing constant. We compute lower and upper bounds for the approximation error for any network size, adapting nonlinear large deviations results. This translates into bounds on the distance between true likelihood and mean-field likelihood. Monte Carlo simulations suggest that in practice our deterministic method performs better than our conservative theoretical approximation bounds imply, for a large class of models.

Holonomic extended least angle regression

One of the main problems studied in statistics is the fitting of models. Ideally, we would like to explain a large dataset with as few parameters as possible. There have been numerous attempts at automatizing this process. Most notably, the Least Angle Regression algorithm, or LARS, is a computationally efficient algorithm that ranks the covariates of a linear model. The algorithm is further extended to a class of distributions in the generalized linear model by using properties of the manifold of exponential families as dually flat manifolds. However this extension assumes that the normalizing constant of the joint distribution of observations is easy to compute. This is often not the case, for example the normalizing constant may contain a complicated integral. We circumvent this issue if the normalizing constant satisfies a holonomic system, a system of linear partial differential equations with a finite-dimensional space of solutions. In this paper we present a modification of the holonomic gradient method and add it to the extended LARS algorithm. We call this the holonomic extended least angle regression algorithm, or HELARS. The algorithm was implemented using the statistical software , and was tested with real and simulated datasets.

Sine-skewed toroidal distributions and their application in protein bioinformatics

Summary In the bioinformatics field, there has been a growing interest in modeling dihedral angles of amino acids by viewing them as data on the torus. This has motivated, over the past years, new proposals of distributions on the torus. The main drawback of most of these models is that the related densities are (pointwise) symmetric, despite the fact that the data usually present asymmetric patterns. This motivates the need to find a new way of constructing asymmetric toroidal distributions starting from a symmetric distribution. We tackle this problem in this article by introducing the sine-skewed toroidal distributions. The general properties of the new models are derived. Based on the initial symmetric model, explicit expressions for the shape and dependence measures are obtained, a simple algorithm for generating random numbers is provided, and asymptotic results for the maximum likelihood estimators are established. An important feature of our construction is that no extra normalizing constant needs to be calculated, leading to more flexible distributions without increasing the complexity of the models. The benefit of employing these new sine-skewed toroidal distributions is shown on the basis of protein data, where, in general, the new models outperform their symmetric antecedents.

Refinements of Some Recent Inequalities for Certain Special Functions

The aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no. 2, 124–129] for the incomplete gamma function, Polygamma functions, Exponential integral function, Abramowitz function, Hurwitz-Lerch zeta function and for the normalizing constant of the generalized inverse Gaussian distribution and the Remainder of the Binet’s first formula for ln Γ(x).

The tilt of the local velocity ellipsoid as seen by Gaia

ABSTRACT The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7224 631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Schönrich, McMillan & Eyer. We exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of the Sun. We find that the tilt of the disc-dominated RVS sample is accurately described by the relation $\alpha = (0.952 \pm 0.007)\arctan (|z|/R)$, where (R, z) are cylindrical polar coordinates. This corresponds to velocity ellipsoids close to spherical alignment (for which the normalizing constant would be unity) and pointing towards the Galactic Centre. Flattening of the tilt of the velocity ellipsoids is enhanced close to the plane and Galactic Centre, whilst at high elevations far from the Galactic Centre the population is consistent with exact spherical alignment. Using the LAMOST catalogue cross-matched with Gaia DR2, we construct thin disc and halo samples of reasonable purity based on metallicity. We find that the tilt of thin disc stars straddles $\alpha = (0.909{\!-\!}1.038)\arctan (|z|/R)$, and of halo stars straddles $\alpha = (0.927{\!-\!}1.063)\arctan (|z|/R)$. We caution against the use of reciprocal parallax for distances in studies of the tilt, as this can lead to serious artefacts.