Multiloop Multirate Continuous‐Discrete Drone Stabilization System: An Equivalent Single‐Rate Model

The article discusses the UAV lateral motion stabilization system, as a MIMO multiloop multirate continuous-discrete system, specified in the form of an input–output model in the domain of discrete Laplace transform or in the form of a structural diagram. Approaches to the construction of equivalent T and NT single-rate models for MIMO multiloop multirate continuous-discrete systems are considered. Here, T is the largest common divisor of the sampling periods of the system, N is a natural number that is the smallest common multiple of the numbers characterizing the sampling periods of the system. The resulting impulse representations of the outputs of equivalent models are in the form of rational functions. The basis for the construction of these models is a matrix of sampling densities—a structural invariant of sampling chains. An example of the construction of the indicated matrix and an equivalent single-rate model are given. Obtaining equivalent single-rate models for MIMO multiloop multirate systems allows us to extend the methods of research and synthesis of MIMO continuous and continuous-discrete systems to a common theoretical base—the theory of polynomials and rational functions, which are typical elements of the description of these classes of systems.

ARTIFICIAL GENERATION OF 2-D FIBER REINFORCED COMPOSITE MICROSTRUCTURES WITH STATISTICALLY EQUIVALENT FEATURES

Fiber reinforced composites are used widely for their high strength and low weight advantages in various aerospace and automotive applications. While their use may be sought after, modeling of these material requires increasing fidelity at the lower scales to capture accurate material behavior under loading. The first steps in creating statistically equivalent models to real life cases is developing a method of rapid evaluation and artificial microstructure generation. The outlined work is capable of tracking microscale fiber positions and determining regions of localized volume fraction extrema (high and low end). Groupings of high and low volume fraction regions are called clusters and their geometry is used to characterize the microstructure. These cluster features can be evaluated for both artificial models and actual scans, allowing correlation to be established which can ultimately be used to regenerate statistically equivalent models. The results of this work show that if one feature is to be correlated, a model can be generated which matches almost exactly. But once more features are equally taken into account, the regeneration loses accuracy.

DESIGN AND SIMULATION OF NEURON-EQUIVALENTORS ARRAY FOR CREATION OF SELF-LEARNING EQUIVALENT-CONVOLUTIONAL NEURAL STRUCTURES (SLECNS)

In the paper, we consider the urgent need to create highly efficient hardware accelerators for machine learning algorithms, including convolutional and deep neural networks (CNN and DNNS), for associative memory models, clustering, and pattern recognition. We show a brief overview of our related works the advantages of the equivalent models (EM) for describing and designing bio-inspired systems. The capacity of NN on the basis of EM and of its modifications is in several times quantity of neurons. Such neural paradigms are very perspective for processing, clustering, recognition, storing large size, strongly correlated, highly noised images and creating of uncontrolled learning machine. And since the basic operational functional nodes of EM are such vector-matrix or matrix-tensor procedures with continuous-logical operations as: normalized vector operations “equivalence”, “nonequivalence”, and etc. , we consider in this paper new conceptual approaches to the design of full-scale arrays of such neuron-equivalentors (NEs) with extended functionality, including different activation functions. Our approach is based on the use of analog and mixed (with special coding) methods for implementing the required operations, building NEs (with number of synapsis from 8 up to 128 and more) and their base cells, nodes based on photosensitive elements and CMOS current mirrors. Simulation results show that the efficiency of NEs relative to the energy intensity is estimated at a value of not less than 1012 an. op. / sec on W and can be increased. The results confirm the correctness of the concept and the possibility of creating NE and MIMO structures on their basis.

Managerial Leadership and Performance as Fully Mediated by Transformational Leadership through Structural Equation Modeling

This study investigated the relationships among managerial leadership, transformational leadership, and performance of school administrators of Northern Iloilo Polytechnic State College (NIPSC) through Structural Equation Modeling (SEM). Covariance-Based SEM (CB-SEM), Confirmatory Factor Analysis (CFA) with its default Maximum Likelihood Estimation (MLE) were used to test the hypothesized model that managerial leadership covary transformational leadership which were both related to the school administrators’ performance. Results revealed that of the eight alternative models, two equivalent models, one model generates every probability distribution that can be generated by another model, Model B3 and Model D3 were generated, got the smallest Alkaike Information Criterion (AIC) and Bayes Information Criterion (BIC) indicating that both models had relatively better fit. Model B3 and Model D3 have the same degrees of freedom but feature a different configuration of paths among the same variables. However, of the two equivalent models, model B3 was rejected due to discriminant validity concerns while model D3 passed both measurement model and structural model, model D3 was confirmed and retained. As contribution to the fields of education, management and leadership, the researcher confirmed and recommends, through CB-SEM using CFA with its default MLE, the Managerial Leadership and Performance as fully mediated by Transformational Leadership Model.

A Note on the Reality of Incomputable Real Numbers and Its Systemic Significance

We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discretization as arbitrary granularity. In this regard, we focus on Incomputable (lacking an algorithm that computes in finite time) Real Numbers (IRNs). We consider how, for measurements, the usual approach to dealing with IRNs is to approximate to avoid the need for more detailed, unrealistic surveys. In this regard, we contrast effective computation and emergent computation. Furthermore, we consider the alternative option of taking into account the properties of the decimal part of IRNs, such as the occurrence, distribution, combinations, quasi-periodicities, and other contextual properties, e.g., topological. For instance, in correspondence with chaotic behaviors, quasi-periodic solutions, quasi-systems, uniqueness, and singularities, non-computability represents and corresponds to theoretically incomplete properties of the processes of complexity, such as emergence and quantum-like properties. We elaborate upon cases of equivalences and symmetries, characterizing complexity and infiniteness as corresponding to the usage of multiple non-equivalent models that are constructively and theoretically incomplete due to the non-exhaustive nature of the multiplicity of complexity. Finally, we detail alternative computational approaches, such as hypercomputation, natural computing, quantum computing, and analog and hybrid computing. The reality of IRNs is considered to represent the theoretical incompleteness of complex phenomena taking place through collapse from equivalences and symmetries. A world of precise finite values, even if approximated, is assumed to have dynamics that are zippable in analytical formulae and to be computable and symbolically representable in the way it functions. A world of arbitrary precise infinite values with dynamics that are non-zippable in analytical formulae, non-computable, and, for instance, sub-symbolically representable, is assumed to be almost compatible with the coherence of emergence. The real world is assumed to be a continuous combination of the two—functioning and emergent—where the second dominates and is the norm, and the first is the locus of primarily epistemic extracts. Research on IRNs should focus on properties representing and corresponding to those that are detectable in real, even if extreme, phenomena, such as emergence and quantum phenomena.

Oriented Fuzzy Numbers vs. Fuzzy Numbers

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.