V-МІНІМІЗАЦІЯ БУЛЕВИХ ФУНКЦІЙ ЗА МАТРИЦЕЮ ВІДСТАНЕЙ ТА ЗВЕДЕННЯМ ДО ЗАДАЧІ МАТЕМАТИЧНОГО ПРОГРАМУВАННЯ

2020 ◽  
pp. 123-133
Author(s):  
В. Ф. Сенчуков ◽  
Т. В. Денисова
Keyword(s):  
Mathematical Programming ◽  
Visual Analysis ◽  
Hamming Distance ◽  
Goal Function ◽  
Analytical Description ◽  
Distance Matrix ◽  
Disjunctive Normal Form ◽  
Mathematical Programming Problem ◽  
Letter Form ◽  
The Right

The further development of the analytical method for minimizing Boolean functions (BF) in the class of disjunctive normal forms by the numbers of sets of argument values, called -minimization, is proposed. Such an approach allows to reduce the process of minimizing the BF to the use of an exclusively analytical description of all its steps using functions of the number of the set of the BF argument values. In general, the idea is to develop such a toolkit that allows at all stages of the minimization process to operate only with numerical objects – Boolean vectors, not involve a visual analysis of the results of the intermediate steps, and not resort to attracting letter objects. In the future, the implementation of this idea at the software level for computers is assumed. The article consists of two parts. The first part is about calculating the Hamming distance between two Boolean vectors. Its equality to unity is a necessary and sufficient condition for gluing together the constituents of unity (zero) or elementary conjunctions (disjunctions). The Hamming distance between two sets of variable values was calculated using the Zhegalkin operation (inversion of equivalence), the distance matrix was compiled, and the abbreviated disjunctive normal form (DNF) was determined from it. From the abbreviated DNF deadlock form, and among them the minimal ones, were obtained by sorting out subsets of the set of units of the distance matrix. Deadlock forms are found by the units to which the implicants, covering all units of the set of BF values, correspond. The final result is presented, of course, in letter form. The second part of the article is devoted to the formulation and solution of the problem of minimizing BF as a problem of linear integer mathematical programming. The goal function is the arithmetic sum of all implicants of the abbreviated DNF. The system of restrictions is based on the fact that among the set of simple implicants, it is necessary to choose the smallest number of them so that all constituents of the unit of the original BF are covered. Restrictions are based on how much the constituent of a unit is covered by one or another implicant, and they are written in the form of linear inequalities through the symbol "greater than or equal to" with the right-hand sides equal to unity. The solution of the mathematical programming problem requires the use of a distance matrix. Examples of -minimization of BF are given.

Hamming Distance Model Based Power Analysis for Cryptographic Algorithms

2011 ◽  
Vol 121-126 ◽  
pp. 867-871 ◽  
Author(s):  
Jie Li ◽  
Wei Wei Shan ◽  
Chao Xuan Tian
Keyword(s):  
Integrated Circuit ◽  
Power Analysis ◽  
Hamming Distance ◽  
Data Encryption ◽  
Design Stage ◽  
Early Design Stage ◽  
Model Based ◽  
Cryptographic Algorithms ◽  
Distance Model ◽  
The Right

In order to evaluate the security of Application Specific Integrated Circuit (ASIC) implemented cryptographic algorithms at an early design stage, a Hamming distance model based power analysis is proposed. The Data Encryption Standard (DES) algorithm is taken as an example to illustrate the threats of differential power analysis (DPA) attack against the security of ASIC chip. A DPA attack against the ASIC implementation of a DES algorithm is realized based on hamming distance power model (HD model), and it realized the attack by successfully guessing the right 48-bit subkey. This result indicates that the power analysis attack based on the HD model is simple, rapid and effective for the design and evaluation of security chips.

scholarly journals Formulating Intuitionistic Fuzzy Regression Models: A Mathematical Programming Approach

2021 ◽  
Author(s):  
Sheng-Hsing Nien ◽  
Liang-Hsuan Chen
Keyword(s):  
Mathematical Programming ◽  
Regression Models ◽  
Fuzzy Regression ◽  
Distance Measures ◽  
Programming Approach ◽  
Mathematical Programming Problem ◽  
Explanatory Variables ◽  
Intuitionistic Fuzzy ◽  
Mathematical Programming Approach ◽  
Ordinary Regression

Abstract This study develops a mathematical programming approach to establish intuitionistic fuzzy regression models (IFRMs) by considering the randomness and fuzziness of intuitionistic fuzzy observations. In contrast to existing approaches, the IFRMs are established in terms of five ordinary regression models representing the components of the estimated triangular intuitionistic fuzzy response variable. The optimal parameters of the five ordinary regression models are determined by solving the proposed mathematical programming problem, which is linearized to make the resolution process efficient. Based on the concepts of randomness and fuzziness in the formulation processes, the proposed approach can improve on existing approaches’ weaknesses with establishing IFRMs, such as the limitation of symmetrical triangular membership (or non-membership) functions, the determination of parameter signs in the model, and the wide spread of the estimated responses. In addition, some numerical explanatory variables included in the intuitionistic fuzzy observations are also allowed in the proposed approach, even though it was developed for intuitionistic fuzzy observations. In contrast to existing approaches, the proposed approach is general and flexible in applications. Comparisons show that the proposed approach outperforms existing approaches in terms of similarity and distance measures.

scholarly journals ROLE OF KUHN-TUCKER CONDITIONS IN ELASTICITY EQUATIONS IN TERMS OF STRESSES

2000 ◽  
Vol 6 (2) ◽  
pp. 104-112
Author(s):  
Ela Chraptovič ◽  
Juozas Atkočiūnas
Keyword(s):  
Mathematical Programming ◽  
System Integration ◽  
Minimum Principle ◽  
Functional Space ◽  
Elasticity Problem ◽  
Mathematical Programming Problem ◽  
Variation Principle ◽  
Three Dimension ◽  
Strain Compatibility ◽  
Elasticity Equations

Solution of the elasticity problem in terms of stresses leads to the stress vector six components, satisfying the Beltrami compatibility eqns and boundary conditions, evaluation. A direct integration of the nine differential eqns system in respect of the six stress components is difficult to realise practically. This is the reason why often the Casigliano variation principle to solve the boundary elasticity problem in terms of stresses is applied. An application of the above-mentioned principle ensures the satisfaction of all the six Saint-Venant strain compatibility eqns (see the works of Southwell, Kliushnikov, a.o.). Castigliano variation principle does not define the number of independent strain compatibility eqns. Thus, it is not clear whether the elasticity problem eqns system in terms of stresses is over-defined or not. The strain compatibility eqns for an ideal elastic body is investigated in the article by means of the mathematical programming theory. A mathematical model to evaluate the statically admissible stresses is formulated on the basis of complementary energy minimum principle. It is proved that the strain compatibility eqns mean the Kuhn-Tucker optimality conditions of the mathematical programming problem. The method to formulate the strain compatibility eqns in respect of the statically admissible stresses defining eqns formulation technique is revealed. The proposed method is illustrated to achieve the six component stresses vector in functional space for the three-dimension problem: usually the solution of the elasticity problem in terms of the stresses is realised via the nine eqns system integration. The Kuhn-Tucker conditions allowed to confirm an original but not usually applied Washizu conclusion about Cauchy geometrical compatibility eqns.

Influence of sexual cycle phases on cognitive abilities and physical endurance

2021 ◽  
Vol 23 (2) ◽  
pp. 107-112
Author(s):  
Elena B. Filippova ◽  
Elena M. Lesova ◽  
Natalya V. Murgaeva
Keyword(s):  
Left Hemisphere ◽  
Cognitive Abilities ◽  
Luteal Phase ◽  
Visual Analysis ◽  
Right Hemisphere ◽  
Sexual Cycle ◽  
Physical Endurance ◽  
Sexual Steroids ◽  
The Right ◽  
In The Beginning

We researched the dependence of cognitive abilities, mostly connected to functions of right and left hemispheres, and physical endurance on phases of sexual cycle. We discovered that on the first day of the cycle the number of correct tasks, connected with functions of the right hemisphere, was bigger than in the middle of the cycle, while no difference was detected in tasks, connected with functions of the left hemisphere. In the beginning of the cycle all test subjects correctly answered more "right hemisphere" questions, than during the ovulation phase, in the middle of the cycle the majority of test subjects correctly answered more "left hemisphere" tasks. We assume that sexual steroids moderate functional differences, connected with functions of right and left hemisphere. Precisely, low level of sexual steroids in the beginning of the cycle helps to activate functions of the right hemisphere, while steroids concentration in the middle of the cycle stops those functions. The level of heartbeat under the physical load was bigger in the luteal phase than before the ovulation; with the increase of load the heartbeat decreased before the ovulation and increase in the luteal phase. We assume that increased content of estrogens before the ovulations lead to decrease in physical endurance, while the decrease of concentration of estrogens in the luteal phase increased this endurance. Therefore, influence of sexual steroids helps to activate functions, which characterize specific psychological and physical status of women sex, particularly verbal abilities, lower abilities for visual analysis, and lower physical endurance of women.

Possibilistic Linear Programming Problems involving Normal Random Variables

2016 ◽  
Vol 5 (3) ◽  
pp. 1-13 ◽  
Author(s):  
Suresh Kumar Barik ◽  
M. P. Biswal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Random Variables ◽  
Fuzzy Programming ◽  
Solution Procedure ◽  
Mathematical Programming Problem ◽  
Possibility Distribution ◽  
Linear Programming Problems ◽  
The Right ◽  
Possibilistic Linear Programming

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.

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