Genetic Algebras Research Articles

OPTIMASI KEUNTUNGAN PRODUK KERIPIK SINGKONG MENGGUNAKAN METODE BRANCH AND BOUND DAN ALGORITMA GENETIKA PADA GNP SNACK

GNP Snack company has problems in making raw material inventories which are sometimes not enough for 0.5 tons of cassava chips to fulfill demand. This will affect the production process carried out every day. Production needs per day 1 - 1.5 tons of production of cassava chips. The company benefits of GNP Snack are not optimal because it only produces an average profit per month of Rp. 2,000,000 therefore the right formula is needed to overcome this problem using the Branch and Bound Method and the Genetic Algebra Method. The calculation results from the branch and bound method show an increase in profits in December 2018 of Rp. 2,018,992 to Rp. 2,531,467 or a 25% increase, in January 2019 amounting to Rp. 2,247,488 to Rp. 4.247.620 or an increase of 89%, and in February 2019 Rp. 1,290,661 to Rp. 1,299,020 or experiencing a 1% increase and the results of calculations using the genetic algorithm method show an increase in profits in December 2018 of Rp. 2,018,992 to Rp. 2,555,477 or a 27% increase, in January 2019 Rp. 2,247,488 to Rp. 2,655,551 or an increase of 18%, and in February 2019 Rp. 1,290,661 to Rp. 2,810,316 or 118% increase.

Evolution train algebras

Through this paper, we show that the criteria for real evolution algebra to be a baric algebra can be extended to any evolution algebra over a commutative field of characteristic ≠2. Then we prove that an evolution algebra E is a train algebra of rank r + 1 if and only if the kernel of its weight function is nil of nil-index r > 1. We also study special train evolution algebra and characterize idempotents, power-associativity and automorphism in evolution train algebra. Finally we classify up to dimension 5, indecomposable evolution nil-algebra of nil-index 4 that are not power-associative.

On Genetic Algebra and its Transformation to some Evolution Algebras in Dimension Four

Genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. This paper investigates the existence of non-associative and derivation of genetic algebra related to some operators generated by ξ (as) − QSO. Moreover, a transformation of genetic algebra to some evolution algebras in dimension four is investigated.

The b-radical of generalised alternative b-algebras I

We prove that if (U,ω) is a finite-dimensional generalised alternative baric algebra I over a field F of characteristic different from 2 and 3, then rad(U) = R(U) ⋂ (U (bar(U))2 + (bar(U))2 U + (bar(U))2).

Classification of exceptional train algebras of rank 3 and type (4, 2)

Classification of exceptional train algebras of rank 3 and type (4, 2)

Derivations and dimensionally nilpotent derivations in Lie triple algebras

In this paper, we first study derivations in non nilpotent Lie triple algebras. We determine the structure of derivation algebra according to whether it admits an idempotent or a pseudo-idempotent. We study the multiplicative structure of non nil dimensionally nilpotent Lie triple algebras. We show that when n=2p+1 the adapted basis coincides with the canonical basis of the gametic algebra G(2p+2,2) or this one obviously associated to a pseudo-idempotent and if n=2p then the algebra is either one of the precedent case or a conservative Bernstein algebra.

Optimization of Genetic Algorithm for Implementation Designing and Modeling in Academic Scheduling

This research was investigated using the Genetic Algebra Method for scheduling lectures and practicums. Genetic algorithms are used to solve problems that are modeled according to evolutionary principles in biological sciences. The application of the Genetic Algebraic Method for Scheduling Lectures and Practices is expected to be further developed into a computerized system that can replace the manual lecture scheduling and practicum methods so that it can produce a more accurate schedule with existing rules in a shorter time. The results of the use of the genetic algorithm method are obtained from the results of the data which are fixed scheduling lecture data and can be recommended for lectures according to the lecture schedule obtained from the results of generating genetic algorithms.

A Method of Generating Timing for a Given Target Current Waveform in Electromagnetic Launch Technology

Under the condition of given charging voltage, by adjusting the timing of the power supply trigger, the electromagnetic emission can produce different discharge current waveforms, and then produce different initial velocity. This paper mainly uses the characteristics of the discharge current in a single power module in electromagnetic launch, by specifying the rising time and the maximum value of the total discharge current; a multipopulation genetic algorithm is used to obtain the optimal trigger timing, and the speed control of electromagnetic launch can be achieved. The specific implementation process of algorithm are as follows: the rising time and the peak value of the expected current are set as the objective function, the timing is set as a variable, and the multiple time series are binary coded to get multiple individuals, and then calculate the degree of survival by crossover, mutation, and heredity among individuals, that is, to judge whether the rising time and the maximum value of the discharge current can reach the expected goal, and to keep the survival of the genes to the next generation and screen repeatedly, and then to select the optimal control timing. The optimal control strategy can be obtained by adjusting the parameters such as genetic algebra and mutation rate. The experimental results show that this method produces the optimal power supply timing, and through the application of digital signal processing control system, the expected discharge current waveform can be obtained in the experiment of electromagnetic launch, which also lay a good foundation for the rate control of electromagnetic launch.

On Genetic and Evolution Algebras

The genetic and evolution algebras generally are non-associative algebra. The concept of evolution and genetic algebras were introduced to answer the question what non-Mendelian genetics offers to mathematics. This paper we review some results of evolution and genetic algebras.

Equations des algèbres Lie triple qui sont des algèbres train

In this paper, we consider equations of Lie triple algebras that are train algebras. We obtain two different types of equations depending on assuming the existence of an idempotent or a pseudo-idempotent.In general Lie triple algebras are not power-associative. However we show that their train equation with an idempotent is similar to train equations of power-associative algebras that are train algebras and we prove that Lie triple algebras that are train algebras of rank ≤4 with an idempotent are Jordan algebras.Moreover, the set of non-trivial idempotents has the same expression in Peirce decomposition as that of e-stable power-associative algebras.We also prove that the algebra obtained by 2-gametization process of a Lie triple algebra is a Lie triple one.

Critère d’existence d’idempotent basé sur les algèbres de Rétrocroisement

ABSTRACTWe study the relationship of backcrossing algebras with mutation algebras and algebras satisfying ω-polynomial identities: we show that in a backcrossing algebra every element of weight 1 generates a mutation algebra and that for any polynomial identity f there is a backcrossing algebra satisfying f. We give a criterion for the existence of idempotent in the case of baric algebras satisfying a nonhomogeneous polynomial identity and containing a backcrossing subalgebra. We give numerous genetic interpretations of the algebraic results.

On discrete evolutionary dynamics driven by quadratic interactions

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of specific changes of basis, we study the evolution and possible stability of some examples. We also consider some examples that cannot be treated using the framework of genetic algebras. Among these are bistochastic matrices.

On genetic and evolution algebras in dimension three

In mathematical genetics genetic algebras are devoted to describe some model in genetics. The genetic algebra usually has a basis corresponding to genetically different gametes, and the structure constant of the algebra used to encode the probabilities of producing offspring of several types. In this paper, we find the connection between the genetic and evolution algebras in dimension three

F-evolution algebra

We consider the evolution algebra of a free population generated by an F-quadratic stochastic operator. We prove that this algebra is commutative, not associative and necessarily power-associative. We show that this algebra is not conservative, not stationary, not genetic and not train algebra, but it is a Banach algebra. The set of all derivations of the F-evolution algebra is described. We give necessary conditions for a state of the population to be a fixed point or a zero point of the F-quadratic stochastic operator which corresponds to the F-evolution algebra. We also establish upper estimate of the ?-limit set of the trajectory of the operator. For an F-evolution algebra of Volterra type we describe the full set of idempotent elements and the full set of absolute nilpotent elements.

On Volterra and orthogonality preserving quadratic stochastic operators

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Moreover, we provide its generalization in continuous setting. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

Irreducible Representations of Power-associative Train Algebras

Train algebras were introduced by Etherington in 1939 as an algebraic framework for treating genetic problems. The aim of this paper is to study the representations and irreducible representations of power-associative train algebras of rank 4. There are three families of such algebras and for two of them we prove that every irreducible representation has dimension one over the ground field. For the third family we give an example of an irreducible representation of dimension three.

The Wedderburn b-decomposition for a class of almost alternative baric algebras

In this paper we deal with the Wedderburn b-decomposition for baric algebras of (γ, δ) type.

Graph in Genetic Code Algebra

Graph in Genetic Code Algebra

Homogamétisation d'algèbres pondérées

We generalize the gametization process introduced in [5]. For this we use not necessarily convex linear combinations of a baric algebra (A,ω) with the gametic algebra defined by the weight ω, we call these combinations homogametizations. After establishing a ponderability condition for a homogametization, we introduce the homogametization operators group and we define two actions of this group on the class of baric algebras and the non-commutative and non-associative algebra K〈X〉 of polynomials with variables in X={x1,…,xn}. When an algebra is defined by an identity, we show that this property is preserved after the group action on the algebra and the identity. We give explicit constructions of elements in K〈X〉 which are invariants or universal invariants for this group action.

Reducing Redundancy of Codons through Total Graph

In this study some algebraic connections in genetic code is being discussed. The genetic code is the rule by which DNA stores the genetic information about formation of protein molecule. Based on the physico-chemical properties of four RNA (or DNA) bases, two orders in the base sets are obtained. This ordering allows us to define a ring structure on the set of 64 codons. Then the total graph in the genetic code algebra is being discussed. It is shown that transition mutations (purine (A, G) to purine or pyrimidine (C, T) to pyrimidine) on the third base position of codons partitions the whole set of codons into disjoint graphs and thereby generates the total graph of the genetic code. The redundancy of the 64 codons coding for the 20 amino acids is reduced by the total graph.