Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem

The k-means problem has been paid much attention for many applications. In this paper, we define the uncertain constrained k-means problem and propose a (1+ϵ)-approximate algorithm for the problem. First, a general mathematical model of the uncertain constrained k-means problem is proposed. Second, the random sampling properties of the uncertain constrained k-means problem are studied. This paper mainly studies the gap between the center of random sampling and the real center, which should be controlled within a given range with a large probability, so as to obtain the important sampling properties to solve this kind of problem. Finally, using mathematical induction, we assume that the first j−1 cluster centers are obtained, so we only need to solve the j-th center. The algorithm has the elapsed time O((1891ekϵ2)8k/ϵnd), and outputs a collection of size O((1891ekϵ2)8k/ϵn) of candidate sets including approximation centers.

THE RELATIONAL APPROACH TO THE MATHEMATICAL MODEL OF MEANING OF INFORMATION

A mathematical model of the meaning of the signal is proposed. The meaning is not the signal itself, but its effect on the recipient. Under the action of the signal, the state of the receiver changes, which is the meaning of the signal. The most general mathematical model is the description of the recipient’s state with the help of some mathematical object, and the meaning is modeled by the action of some operator on this object. Various concrete formalisms are considered: abstract automata, matrix representation, algorithms, Markov chains, parameter spaces. The article deals with finite, countable and continuous meanings, reversible and irreversible meanings, ambiguous meanings, decomposition into elementary meanings.

The Mathematical Model for Research of the UAV Longitudinal Moving

The paper presents one of the perspective directions of the development to modern aviation, which is connected with designing and producing unmanned aerial vehicles (UAV) of various functionalities for applying in both military and civilian spheres. The syntheses of UAV control systems, regardless of their type and purpose presumes creation of adequate mathematical models, first of all adequate aerodynamic mathematical models. In the paper results that forms and justify the aerodynamic mathematical model and as well as the results of building a general mathematical model of the longitudinal movement of the perspective UAV are presented. Also factors that forms the mathematical model on given aerodynamic, geometric, mass and inertial data for a hypothetical perspective altitude long-range UAV are submitted. Assessment of the impact of these data on the dynamic, temporal, and logarithmic frequency response UAV also has been given in this paper.

Dynamics of Working Processes in Automatic Direct-Acting Pressure Regulators of Pneumatic Spacecraft Systems

The purpose of the study was by means of modern software to explore working processes taking place in automatic direct-acting pressure regulators of pneumatic spacecraft systems. As a result, we developed a general mathematical model of the pressure regulator. The design of the regulator is shown in the form of a block diagram, composed of a set of channels, cavities, and stages. The elements of the block diagram are interconnected by the basic laws of conservation of energy and mass. The mathematical model was evaluated in the Amesim software package. Findings of the full-scale and computational experiments led to the conclusions about the effect the heat exchange between the working fluid and the environment produces on the parameters of the pressure regulator, and about the use of the Amesim software package for further research of working processes in the valve units of pneumatic systems.

A MATHEMATICAL PROPOSED MODEL FOR PUBLIC KEY ENCRYPTION ALGORITHMS IN CYBERSECURITY

Information security is a very important science, especially after the continuous increase in cybercrime of all kinds, which caused very large financial, economic and political losses, so it was necessary to find a solution to protect the data and keep it secret. Data encryption is one of the most important solutions to preserve data and reduce cybercrime. The encryption process means converting the plain text using a private key into symbols and numbers that make this text incomprehensible to others. There are many algorithms that are used for encryption, and the public key algorithms are the strongest in the encryption process because they depend on two keys, the public key and the private key. One of the most important problems facing this type of algorithm is the lack of a clear mathematical model that facilitates understanding and how to deal with these keys. In this thesis, a mathematical model has been proposed in which two functions are defined, the public key and the function of the private key, based on the concepts and specific characteristics of the function. A general mathematical model was constructed by defining two functions, one for the public key and the other for the private key, using the properties of a function in mathematics, to produce strong keys used in the public key algorithm, to protect data and keep it secret, and this model was applied to the RSA and ELGamal algorithms. The most important result was that in the case of applying the mathematical model, it is easy to understand and deal with the public key and the private key mathematically.

Stochastic Analysis and Neural Network-Based Yield Prediction with Precision Agriculture

In this paper, we propose a general mathematical model for analyzing yield data. The data analyzed in this paper come from a characteristic corn field in the upper midwestern United States. We derive expressions for statistical moments from the underlying stochastic model. Consequently, we illustrate how a particular feature variable contributes to the statistical moments (and in effect, the characteristic function) of the target variable (i.e., yield). We also analyze the data with neural network techniques and provide two methods of data analysis. This mathematical model and neural network-based data analysis allow for better understanding of the variability within the data set, which is useful to farm managers attempting to make current and future decisions using the yield data. Lenders and risk management consultants may benefit from the insights of this mathematical model and neural network-based data analysis regarding yield expectations.

A General Mechano-Pharmaco-Biological Model for Bone Remodeling Including Cortisol Variation

The process of bone remodeling requires a strict coordination of bone resorption and formation in time and space in order to maintain consistent bone quality and quantity. Bone-resorbing osteoclasts and bone-forming osteoblasts are the two major players in the remodeling process. Their coordination is achieved by generating the appropriate number of osteoblasts since osteoblastic-lineage cells govern the bone mass variation and regulate a corresponding number of osteoclasts. Furthermore, diverse hormones, cytokines and growth factors that strongly link osteoblasts to osteoclasts coordinated these two cell populations. The understanding of this complex remodeling process and predicting its evolution is crucial to manage bone strength under physiologic and pathologic conditions. Several mathematical models have been suggested to clarify this remodeling process, from the earliest purely phenomenological to the latest biomechanical and mechanobiological models. In this current article, a general mathematical model is proposed to fill the gaps identified in former bone remodeling models. The proposed model is the result of combining existing bone remodeling models to present an updated model, which also incorporates several important parameters affecting bone remodeling under various physiologic and pathologic conditions. Furthermore, the proposed model can be extended to include additional parameters in the future. These parameters are divided into four groups according to their origin, whether endogenous or exogenous, and the cell population they affect, whether osteoclasts or osteoblasts. The model also enables easy coupling of biological models to pharmacological and/or mechanical models in the future.

Modeling and Trajectory Planning Optimization for the Symmetrical Multiwheeled Omnidirectional Mobile Robot

Trajectory optimization is the series of actions that are taken into consideration in order to produce the best path such that it improves the overall performances of physical properties or reduces the consumption of the resources where the restriction system remains maintained. In this paper, first, a compact mathematical model for a symmetrical annular-shaped omnidirectional wheeled mobile robot (SAOWMR) is derived and verified. This general mathematical model provides an opportunity to conduct research, experiments, and comparisons on these omnidirectional mobile robots that have two, three, four, six, or even more omnidirectional wheels without the need to switch models or derive a new model. Then, a new computationally efficient method is proposed to achieve improvements in the trajectory planning optimization (TPO) for a SAOWMR. Moreover, the proposed method has been tested in collision-free navigation by incorporation of the path constraints. Numerical tests and simulations are presented aiming to ensure the efficiency and effectiveness of the proposed method.

How individuals change language

Languages emerge and change over time at the population level though interactions between individual speakers. It is, however, hard to directly observe how a single speaker’s linguistic innovation precipitates a population-wide change in the language, and many theoretical proposals exist. We introduce a very general mathematical model that encompasses a wide variety of individual-level linguistic behaviours and provides statistical predictions for the population-level changes that result from them. This model allows us to compare the likelihood of empirically-attested changes in definite and indefinite articles in multiple languages under different assumptions on the way in which individuals learn and use language. We find that accounts of language change that appeal primarily to errors in childhood language acquisition are very weakly supported by the historical data, whereas those that allow speakers to change incrementally across the lifespan are more plausible, particularly when combined with social network effects.

EXPERIMENTAL RESEARCH OF THE ACCURACY OF NAVIGATION GNSS - RECEIVERS IN CONDITIONS OF THE CONSTRUCTED TERRITORY

Use of digital geodetic support technologies with the use of GNSS satellite systems in combination with electronic geodetic instruments, introduction of new methods of construction of geodetic networks, collection of information by ground and aerospace surveying, unification of exchange formats of measurement results based on computer technologies and their application conditions. Substantiation and development of remote methods of spatial information collection requires analysis and consideration of a number of errors in order to improve accuracy. Wikimapia is a map project for shared use with open content, which aims to identify all geographical objects with the introduction of useful information about them. It combines an interactive web map and a Wiki system. One of the features of the Wikimapia resource is that it is possible to determine geographical coordinates. To do this, you need to move the cross cursor on the object of interest and get its coordinates visually. The purpose of the study was to determine the accuracy of the coordinates of GPS receivers Garmin Oregon 450 in the built-up area, using as a basis for calibration, the resource "Wikimapia". In order to determine the accuracy of the location with the help of GARMIN Oregon 450 GPS receivers, GNSS measurements were performed at 30 marker points. Ellipsoidal coordinates were recalculated into spatial rectangles according to known formulas. In order to assess the accuracy of determining the location of marker points, the differences in the coordinates of their position were found and the root mean square error from a number of measurements was found. The average error of coordinate measurements was ± 4.79 m for the GPS receiver. Based on experimental research, the possibility of using the resource "Wikimapia" not only to quickly determine the coordinates of topographic objects, determine their categories, but also with sufficient accuracy to apply for the calibration of navigation GNSS receivers when there is no network of geodetic points. A promising direction in the process of scientific and practical research should be the creation of a general mathematical model for predicting the influence of the plurality on the location and improvement of navigation aids.