Study of electrical circuits using Runge Kutta method of order 4

In this paper, Runge Kutta method of order 4 is used to study the electrical circuits designs through past, intermediate and present voltages. When integrating differential equations with Runge Kutta method of order 4, a constant step size (ℎ) is used until a testing procedure confirms that the discontinuity occurs in the present integration interval. This step size function calculations would take place at the end of the functional calculations, but before the dependent variables were updated. Runge Kutta methods along with convolution are given by array interpretation (Butcher matrix) representation, this leads to identify the equilibrium state. The input parameters indicate the voltage coefficient controlled by current sources and measures it a random periodic time. The output parameters provide stable independent values and calculated from past voltage and current values. Finally solutions are compared with exact values and RK method of order 4 along with Heun, Midpoint and Taylors’s method with various ℎ values.

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.

Variance in Variants: Propagating Genome Sequence Uncertainty into Phylogenetic Lineage Assignment

Genetic sequencing is subject to many different types of errors, but most analyses treat the resultant sequences as if they are known without error. Next generation sequencing methods rely on significantly larger numbers of reads than previous sequencing methods in exchange for a loss of accuracy in each individual read. Still, the coverage of such machines is imperfect and leaves uncertainty in many of the base calls. On top of this machine-level uncertainty, there is uncertainty induced by human error, such as errors in data entry or incorrect parameter settings. In this work, we demonstrate that the uncertainty in sequencing techniques will affect downstream analysis and propose a straightforward method to propagate the uncertainty. Our method uses a probabilistic matrix representation of individual sequences which incorporates base quality scores as a measure of uncertainty that naturally lead to resampling and replication as a framework for uncertainty propagation. With the matrix representation, resampling possible base calls according to quality scores provides a bootstrap- or prior distribution-like first step towards genetic analysis. Analyses based on these re-sampled sequences will include a more complete evaluation of the error involved in such analyses. We demonstrate our resampling method on SARS-CoV-2 data. The resampling procedures adds a linear computational cost to the analyses, but the large impact on the variance in downstream estimates makes it clear that ignoring this uncertainty may lead to overly confident conclusions. We show that SARS-CoV-2 lineage designations via Pangolin are much less certain than the bootstrap support reported by Pangolin would imply and the clock rate estimates for SARS-CoV-2 are much more variable than reported.

Enhancing Linear Algebraic Computation of Logic Programs Using Sparse Representation

Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation to perform logical inference in large-scale knowledge bases. In this paper, we analyze the complexity of the linear algebraic methods for logic programs and propose further improvement by using sparse matrices to embed logic programs in vector spaces. We show its great power of computation in reaching the fixed point of the immediate consequence operator. In particular, performance for computing the least models of definite programs is dramatically improved using the sparse matrix representation. We also apply the method to the computation of stable models of normal programs, in which the guesses are associated with initial matrices, and verify its effect when there are small numbers of negation. These results show good enhancement in terms of performance for computing consequences of programs and depict the potential power of tensorized logic programs.

A new approach to identifying the local structure of multidimensional chaotic time series

The paper is devoted to the solution of the problems of mathematical supply of decision making during multichannel monitoring of large-scaled systems. The work also deals with space-time dynamics of multidimensional time series of different origins. Highly dynamical chaotic processes whose fine structure cannot be revealed by standard spectral methods are regarded. Technologies for dimension reduction based on data matrix representation on the first singular basis and multiple regression in projections’ space are developed.

PROPOSAL OF A DATA MODEL FOR MANAGING BLOKCHAIN-BASED TRUST BETWEEN ACTORS IN AN ELECTORAL PROCESS

In this paper we propose a tool (reference data model) for the improvement of trust, based on blokchain technologies, between the different actors of an electoral process. Our contribution focuses in a first step on the implementation of a data model having all these public attributes and thus public classes whose methods are coupled to cryptographic techniques. In a second step, we propose an underlying formalism of this model using a matrix representation of the different actors, the different transactions and the working criteria allowing to validate these transactions and blockchains. This formalism allows to find a transaction performed by one of the actors of the electoral chain and also the data block in which this transaction is validated. Also, an algorithm allowing to reinforce the trust is proposed.

Structural Analysis of Traditional Chinese Complex Puzzle Locks

The development of barbed-spring locks in ancient China has a history of more than two thousand years. With the development of the design and manufacturing techniques in ancient China, the safety of locks has gotten better and better. Since the 17th century, the puzzle lock, with a complicated structure and a high difficulty in opening, was gradually developed and used. The puzzle lock needs specific steps to be opened. Even if strangers have the correct key, it is still difficult for them to open the lock immediately. Based on the difficulty of the opening process, traditional Chinese puzzle locks can be partition into two sorts, namely, general puzzle locks and complex puzzle locks. As the structure of the puzzle lock will change during the opening process, the puzzle lock belongs to the reconfigurable mechanism. In this paper, a method of topology matrix is provided to analyze the structure of the complex puzzle lock during operation systematically. Firstly, the characteristics and types of general puzzle locks are explained, and then the topology matrix representation is introduced. Finally, four complex puzzle locks are taken as examples, to illustrate the opening process. There are various types of complex puzzle locks, and the mechanism designs are quite ingenious and interesting, which shows the extraordinary technique and ingenuity of the ancient craftsmen.

Implicit Contact Dynamics Modeling With Explicit Inertia Matrix Representation for Real-Time, Model-Based Control in Physical Environment

Model-based control has great potential for use in real robots due to its high sampling efficiency. Nevertheless, dealing with physical contacts and generating accurate motions are inevitable for practical robot control tasks, such as precise manipulation. For a real-time, model-based approach, the difficulty of contact-rich tasks that requires precise movement lies in the fact that a model needs to accurately predict forthcoming contact events within a limited length of time rather than detect them afterward with sensors. Therefore, in this study, we investigate whether and how neural network models can learn a task-related model useful enough for model-based control, that is, a model predicting future states, including contact events. To this end, we propose a structured neural network model predicting a control (SNN-MPC) method, whose neural network architecture is designed with explicit inertia matrix representation. To train the proposed network, we develop a two-stage modeling procedure for contact-rich dynamics from a limited number of samples. As a contact-rich task, we take up a trackball manipulation task using a physical 3-DoF finger robot. The results showed that the SNN-MPC outperformed MPC with a conventional fully connected network model on the manipulation task.

GNOM v1.0: An optimized steady-state model of the modern marine neodymium cycle

Spatially distant sources of neodymium (Nd) to the ocean that carry different isotopic signatures (εNd) have been shown to trace out major water masses, and have thus been extensively used to study large-scale features of the ocean circulation both past and current. While the global marine Nd cycle is qualitatively well understood, a complete quantitative determination of all its components and mechanisms, such as the magnitude of its sources and the paradoxical conservative behavior of εNd, remains elusive. To make sense of the increasing collection of observational Nd and εNd data, we develop the global neodymium ocean model (GNOM) v1, the first inverse model of the global marine biogeochemical cycle of Nd. The GNOM is embedded in a data-constrained steady-state circulation that affords spectacular computational efficiency, which we leverage to estimate biogeochemical parameters via systematic objective optimization. Owing to its matrix representation, the GNOM model is additionally amenable to novel diagnostics that allow us to investigate open questions about the Nd cycle with unprecedented accuracy. The GNOM is open-source and freely accessible, is written in Julia, and its code is easily understandable and modifiable for further developments and experiments.