Outlier Detection for Pandemic-Related Data Using Compositional Functional Data Analysis

With accurate data, governments can make the most informed decisions to keep people safer through pandemics such as the COVID-19 coronavirus. In such events, data reliability is crucial and therefore outlier detection is an important and even unavoidable issue. Outliers are often considered as the most interesting observations, because the fact that they differ from the data majority may lead to relevant findings in the subject area. Outlier detection has also been addressed in the context of multivariate functional data, thus smooth functions of several characteristics, often derived from measurements at different time points (Hubert et al. in Stat Methods Appl 24(2):177–202, 2015b). Here the underlying data are regarded as compositions, with the compositional parts forming the multivariate information, and thus only relative information in terms of log-ratios between these parts is considered as relevant for the analysis. The multivariate functional data thus have to be derived as smooth functions by utilising this relative information. Subsequently, already established multivariate functional outlier detection procedures can be used, but for interpretation purposes, the functional data need to be presented in an appropriate space. The methodology is illustrated with publicly available data around the COVID-19 pandemic to find countries displaying outlying trends.

Information Generating Function of Ranked Set Samples

In the present paper, we study the information generating (IG) function and relative information generating (RIG) function measures associated with maximum and minimum ranked set sampling (RSS) schemes with unequal sizes. We also examine the IG measures for simple random sampling (SRS) and provide some comparison results between SRS and RSS procedures in terms of dispersive stochastic ordering. Finally, we discuss the RIG divergence measure between SRS and RSS frameworks.

State feedback containment control of multi-agents system with lipschitz nonlinearity

<p>This paper studies the containment control problem of the leader-follower configuration in a multi-agents system included with a type of nonlinearity such as Lipschitz with respect to continuous-time and directed spanning forest communication network topology. A state feedback containment controller is designed and proposed with control theory and the Laplacian network structure where it utilizes the relative information of each agent. The controller designed ensures that the followers are contained by the leaders that form the convex hull formation. For the containment to happen, a minimum of one leader is needed to have a direct communication trajectory to the followers. Lyapunov stability theory is used to provide the stability conditions after analyzing the network structure. Finally, it has been shown from simulation that the followers are contained successfully with the proposed controller.</p>

Development of an innovative methodology of research of systems on an example of a shadow economy as an invariant of system of economic security of state

The object of research is the shadow economy as structural component (invariant) of economic security of state on example of Ukraine. The level of shadowing of Ukrainian economy requires improvement of both: the system of indicators and mechanism of influence on the level of shadowing on the basis of using of fundamental constants of mathematics of harmony and principle of structural harmony of systems. Under research, fundamental provisions and methods of the theory of safety studies, economic theory, theories of systems and structural harmony of systems, institutionalism, transdisciplinary nature were used. The theme of management of the system of economic security of the state is investigated from various scientific positions of classical science. At the same time, practically ignores the theory of synergetic, which is the synthesis of transdisciplinary approach, price approach, classical theory of systems, structural harmony of systems, theory of fractals and attractors and other components of theory of complexity. Obviously, any system has metric characteristics inherent. The most widespread math constant found in nature is the Phidias number (Golden section). Meаsure is the most important component of all and any knowledge, without it any description of processes and phenomena will be incorrect. The law of measures, or the law of proportional distribution with its derivatives can be defined as law of projecting and organizing sustainable systems at all levels of hierarchical management. The structure of the system is the most conservative characteristic of it as opposed to the state of the system. The properties of the system as a whole are determined not only the properties of its individual elements, but also the properties of the structure of the system as whole. They depend on the existence of the system. The existence of the system retains these parameters in the process of adapting the system to external conditions and thus maintains the existence of the system itself. Matching the metric quality system of economic security of the state and obtaining a conclusion on its stability and abilities to self-organization under the conditions of shadowing of the economy can be carried out by comparison. It is carried out using attractors representing a recurrent number of gold sections: 0.500 ...; 0.618 ...; 0.682 ...; 0.725, as well as – distractors: 0.5698 ...; 0.6540 ...; 0.7053. An integral indicator characterizing the state of any system is the relative information entropy by Shannon. Entropy testing of the system (calculation of relative information entropy) is a logical component of the innovative model of system research.

A multivariate test for detecting fraud based on Benford’s law, with application to music streaming data

Benford’s law became a prevalent concept for fraud and anomaly detection. It examines the frequencies of the leading digits of numbers in a collection of data and states that the leading digit is most often 1, with diminishing frequencies up to 9. In this paper we propose a multivariate approach to test whether the observed frequencies follow the theoretical Benford distribution. Our approach is based on the concept of compositional data, which examines the relative information between the frequencies of the leading digits. As a result, we introduce a multivariate test for Benford distribution. In simulation studies and examples we compare the multivariate test performance to the conventional chi-square and Kolmogorov-Smirnov test, where the multivariate test turns out to be more sensitive in many cases. A diagnostics plot based on relative information allows to reveal and interpret the possible deviations from the Benford distribution.

PLOT SIZE AND SHAPE FOR FIELD TRIALS WITH FORAGE CACTUS PEAR

This study aimed to determine the size and shape of experimental plots that provide maximum precision using relative information method. This trial was conducted at the Federal Institute of Bahia. Plant height, cladode length, cladode width, cladode thickness, cladode area, cladode area index, number of cladodes, cladode total area and yield were measured in the third production cycle, 930 days after planting. The plants, defined as basic units, were arranged in 39 plot sizes so that the crop would fill the whole experimental area. Then, plot shapes with higher relative information and equal plot size in basic units were selected. The experimental plot with eight basic units in size ensures higher efficiency in the experimental evaluation. This combination between size and shape, besides meeting all evaluation requirements of the characteristics normally assessed in studies with forage cactus pear, has the maximum control of soil heterogeneity, thereby decreasing experimental error and significantly increasing precision.