Optimization of Different Fitness Functions Using Reproduction, Crossover and Mutation of Genetic Algorithm With Binary Number Scheduling

Genetic algorithms are search algorithms based on the mechanics of natural selection and natural genetics. In this paper, we investigate a novel approach to the binary coded testing process based on a genetic algorithm. This paper consists of two parts. Thefirst part addresses the problem in the traditional way of using the decimal number system to define the fitness function to study the variations of counts and the variations of probability against the fitness functions. Second, the initialpopulationsare defined using binary coded digits (genes). For the evaluation of the high fitness function values,three genetic operators, namely, reproduction, crossover and mutation, are randomly used. The results show the importance of the genetic operator, mutation, which yields the peak values for the fitness function based on binary coded numbers performed in a new way.

Dysnumeria in Sign Language: Impaired Construction of the Decimal Structure in Reading Multidigit Numbers in a Deaf ISL Signer

We report on the first in-depth analysis of a specific type of dysnumeria, number-reading deficit, in sign language. The participant, Nomi, is a 45-year-old signer of Israeli Sign Language (ISL). In reading multidigit numbers (reading-then-signing written numbers, the counterpart of reading aloud in spoken language), Nomi made mainly decimal, number-structure errors– reading the correct digits in an incorrect (smaller) decimal class, mainly in longer numbers of 5–6-digits. A unique property of ISL allowed us to rule out the numeric-visual analysis as the source of Nomi's dysnumeria: In ISL, when the multidigit number signifies the number of objects, it is signed with a decimal structure, which is marked morphologically (e.g., 84 → Eight-Tens Four); but a parallel system exists (e.g., for height, age, bus numbers), in which multidigit numbers are signed non-decimally, as a sequence of number-signs (e.g., 84 → Eight, Four). When Nomi read and signed the exact same numbers, but this time non-decimally, she performed significantly better. Additional tests supported the conclusion that her early numeric-visual abilities are intact: she showed flawless detection of differences in length, digit-order, or identity in same-different tasks. Her decimal errors did not result from a number-structure deficit in the phonological-sign output either (no decimal errors in repeating the same numbers, nor in signing multidigit numbers written as Hebrew words). Nomi had similar errors of conversion to the decimal structure in number comprehension (number-size comparison tasks), suggesting that her deficit is in a component shared by reading and comprehension. We also compared Nomi's number reading to her reading and signing of 406 Hebrew words. Nomi's word reading was in the high range of the normal performance of hearing controls and of deaf signers and significantly better than her multidigit number reading, demonstrating a dissociation between number reading, which was impaired, and word reading, which was spared. These results point to a specific type of dysnumeria in the number-frame generation for written multidigit numbers, whereby the conversion from written multidigit numbers to the abstract decimal structure is impaired, affecting both reading and comprehension. The results support abstract, non-verbal decimal structure generation that is shared by reading and comprehension, and also suggest the existence of a non-decimal number-reading route.

On The Implementation of Densely Packed Decimal Number System Based Adder: Prospects and Challenges

Decimal digit number computation, through bit compression methodology, offers space and time saving, which can be incurred by the Chen-Ho and Densely Packed Decimal (DPD) coding techniques. Such coding techniques have a property of bit compression, like, three decimal digits can be represented by 10 bits instead of 12 bits in binary coded decimal (BCD) format. The compression has been obtained through the elimination of the redundant 0’s from BCD representation. This manuscript reports the pros and cons of the techniques mentioned above. The logic level functionalities have been examined through MATLAB, whereas circuit simulation has been erified through Cadence Spectre. Performance parameters (such as delay, power consumption) have been evaluated through CMOS gpdk45 nm technology. Furthermore, the best design has been chosen from them, and the decimal adder design technique has been incorporated in this paper.

Genetic code research: a precognition result (II)

In this second part of the short communication (Ref. 2), we give an argument more in favor of the validity of the precognition status of the final result of my 40 years of genetic code researches. It is shown that the changes in the number of atoms in the system-arrangements of protein amino acids, in relation to the Gaussian number (51) and the Dürer number (34 and 68, respectively), correspond to the changes in the products of number 5 in the Multiplication Table of the decimal number system. On the other hand, with the same changes (in the products of number 5), two unconscious narrations, said in the first part of this communication, correspond one hundred percent.

Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

Third Grade Students’ Use of Relational Thinking

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

Squaring Technique using Vedic Mathematics

Vedic Mathematics provides an interesting approach to modern computing applications by offering an edge of time and space complexities over conventional techniques. Vedic Mathematics consists of sixteen sutras and thirteen sub-sutras, to calculate problems revolving around arithmetic, algebra, geometry, calculus and conics. These sutras are specific to the decimal number system, but this can be easily applied to binary computations. This paper presented an optimised squaring technique using Karatsuba-Ofman Algorithm, and without the use of Duplex property for reduced algorithmic complexity. This work also attempts Taylor Series approximation of basic trigonometric and inverse trigonometric series. The advantage of this proposed power series approximation technique is that it provides a lower absolute mean error difference in comparison to previously existing approximation techniques.

Digital on-board clutch tester

The work is devoted to the creation of a digital type on-board device for diagnosing the clutch of traction vehicles (TV) and allows to accurately determine the slipping of the clutch when failures appear in it. The principle of operation of the device is based on the use of digital technology for measuring the rotational speed (number of pulses) in the digital code of the flywheel and the input shaft of the gearbox (GB). The received digital codes are displayed with the help of light-emitting diodes, showing the number of voltage pulses per second from the flywheel speed sensors and the gearbox primary shaft gear. The received digital codes are converted by the driver (operator) into the decimal number sys-tem. Given that the number of flywheel teeth is greater than the number of gear teeth, the number of pulses from the sensors is adjusted by dividing the number of pulses from the flywheel per revolu-tion by the ratio of the number of flywheel teeth to the number of gear teeth. Next, the difference between the corrected number of pulses from the gear and the flywheel is determined. Further it is compared with the permissible number of pulses and a conclusion about the technical condition of the clutch based on this comparison is made. If the difference is equal to zero or less, the clutch will be considered efficient. The device for diagnosing the clutch includes two digital speed sensors, each of which contains an inductance coil with a magnetic core, rigidly fixed near the flywheel teeth and gears of the input shaft of the gearbox. The first differentiating circuit, with a cut-off diode at the output, by the input is connected to the inductor and is made on the first and second resistors and capacitor. The second differentiating circuit with a cut-off diode at the output is made on a resistor and a capacitor, and the input is connected to the output of the self-oscillating multivibrator. The self-oscillating multivibrator is made on two NAND logical elements, two capacitors, two diodes and two resistors. The output of the second differentiating circuit is connected to the zero-setting inputs of sixteen-bit summing electronic counters. The outputs of the AND logical elements are connected by means of resistors with the counting inputs of two electronic counters, at the out-put of which the digital codes are formed. The codes reflect the rotational speed of the flywheel and gears of the input shaft of the gearbox. An example of calculating the parameters of the elements of the differentiating circuit of an auto-oscillating multivibrator is given.

FROM THE HISTORY OF THE BINARY NUMBER SYSTEM. THOMAS HARRIOT

For the first time in the Russian-language literature, the article analyzes the works of the English mathematician, geographer and astronomer Thomas Harriot (1560–1621) related to the binary number system. The various variants of the binary notation of numbers presented in the works, examples of converting a decimal number to a binary number and vice versa, examples of four arithmetic operations in the binary number system, the execution methods of which coincide with modern ones, as well as an example of multiplication by an original method, the name of which can be translated in Latin as "another method is sequential addition" are given. All this allows us to conclude that Thomas Harriot described the binary number system earlier than the great German scientist Gottfried Wilhelm Leibniz, who did so in his work "Explication de l'Arithmétique Binaire" in 1703.

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

Pattern matching is the area of computer science which deals with security and analysis of data. This work proposes two 2D pattern matching algorithms based on two different input domains. The first algorithm is for the case when the given pattern contains only two symbols, that is, binary symbols 0 and 1. The second algorithm is in the case when the given pattern contains decimal numbers, that is, the collection of symbols between 0 and 9. The algorithms proposed in this manuscript convert the given pattern into an equivalent binary or decimal number, correspondingly find the cofactors of the same dimension and convert these cofactors into numbers if a particular cofactor number matches indicate the matching of the pattern. Furthermore, the algorithm is enhanced for decimal numbers. In the case of decimal numbers, each row of the pattern is changed to its decimal equivalent, and then, modulo with a suitable prime number changes the decimal equivalent into a number less than the prime number. If the number mismatched pattern does not exist, the complexity of the proposed algorithm is very low as compared to other traditional algorithms.