An Application of the Eigenproblem for Biochemical Similarity

Abstract

Protein alignment finds its application in refining results of sequence alignment and understanding protein function. A previous study aligned single molecules, making use of the minimization of sums of the squares of eigenvalues, obtained for the antisymmetric Cartesian coordinate distance matrices Dx and Dy. This is used in our program to search for similarities between amino acids by comparing the sums of the squares of eigenvalues associated with the Dx, Dy, and Dz distance matrices. These matrices are obtained by removing atoms that could lead to low similarity. Candidates are aligned, and trilateration is used to attach all previously striped atoms. A TM-score is the scoring function that chooses the best alignment from supplied candidates. Twenty essential amino acids that take many forms in nature are selected for comparison. The correct alignment is taken into account most of the time by the alignment algorithm. It was numerically detected by the TM-score 70% of the time, on average, and 15% more cases with close scores can be easily distinguished by human observation.

The Regulation of an Electric Oven and an Inverted Pendulum

“…Remark 3.In this section, the experimental comparisons between the real signal and simulated signal for the electric oven and inverted pendulum are presented to show that the mathematical models were similar to the real data models. Remark 4.For the experiments, linear mathematical models were considered because linearization allows the transfer functions to be obtained, the transfer functions allow the application of the ztransform, and the z-transform allows use of the Arduino platform for application of the regulators in discrete time [15,16]. It is necessary to add the analog inputs of the sensors to obtain a PWM signal which is sent to the electric power regulator; the inputs are stored within a program.…”

“…Using Equations ( 10) and (21), and the feedback model, the transfer function is found as (22). where the sign function is defined in Equation (16).…”

“…Most of the authors use the Lyapunov method to find the gains of the first-order sliding-mode regulator of [7][8][9] and the second-order sliding-mode regulator of [10][11][12]. In contrast to the previous research, this paper uses the pole assignment method of [15][16][17] as an alternative means of determining the gains of the first-order sliding-mode regulator, and the second-order sliding-mode regulator.…”

“…For the experiments, linear mathematical models were considered because linearization allows the transfer functions to be obtained, the transfer functions allow the application of the z-transform, and the z-transform allows use of the Arduino platform for application of the regulators in discrete time [15,16]. It is necessary to add the analog inputs of the sensors to obtain a PWM signal which is sent to the electric power regulator; the inputs are stored within a program.…”

“…Most authors have used the Lyapunov method to assess the gains associated with the use of first-ordersliding-mode regulators [7][8][9], and of second-ordersliding-mode regulators [10][11][12]. In contrast to the previous research, this paper uses the pole assignment method of [15][16][17], as analternative approach to determining gains associated with the use of first-and second-order sliding-mode regulators Simulation and experimental results are described for an electric oven, considered as an example of a stable linear mathematical model, and for an inverted pendulum, considered as an example of an asymmetric unstable non-linear mathematical model. The electric oven could be used for baking, while the inverted pendulum could be used for the testing of regulators.…”