random sequences
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2022 ◽  
Author(s):  
Artis Linārs ◽  
Ivars Silamikelis ◽  
Dita Gudra ◽  
Ance Roga ◽  
Dāvids Fridmanis

Over the decades the improvement of naturally occurring proteins and creation of novel ones has been the primary goal for many practical biotechnology researchers and it is widely recognized that randomization of protein sequences coupled to various effect screening methodologies is one of the most powerful techniques for fast, efficient and purposeful approach for acquisition of desired improvements. Over the years considerable advancements have been made in this field, however development of PCR based or template guided methodologies has been hampered by the resulting template sequence bias. In this article we present novel whole plasmid amplification based approach, which we named OverFlap PCR, for randomization of virtually any region of the plasmid DNA, without introduction of mentioned bias.


2022 ◽  
Vol 4 (2) ◽  
Author(s):  
Unsub Zia ◽  
Mark McCartney ◽  
Bryan Scotney ◽  
Jorge Martinez ◽  
Ali Sajjad

AbstractPseudo-random number generators (PRNGs) are one of the building blocks of cryptographic methods and therefore, new and improved PRNGs are continuously developed. In this study, a novel method to generate pseudo-random sequences using coupled map lattices is presented. Chaotic maps only show their chaotic behaviour for a specified range of control parameters, what can restrict their application in cryptography. In this work, generalised symmetric maps with adaptive control parameter are presented. This novel idea allows the user to choose any symmetric chaotic map, while ensuring that the output is a stream of independent and random sequences. Furthermore, to increase the complexity of the generated sequences, a lattice-based structure where every local map is linked to its neighbouring node via coupling factor has been used. The dynamic behaviour and randomness of the proposed system has been studied using Kolmogorov–Sinai entropy, bifurcation diagrams and the NIST statistical suite for randomness. Experimental results show that the proposed PRNG provides a large key space, generates pseudo-random sequences and is computationally suitable for IoT devices.


Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 68
Author(s):  
Serhii Haliuk ◽  
Oleh Krulikovskyi ◽  
Dmytro Vovchuk ◽  
Fernando Corinto

This paper suggests an approach to generate pseudo-random sequences based on the discrete-time model of the simple memristive chaotic system. We show that implementing Euler’s and Runge–Kutta’s methods for the simulation solutions gives the possibility of obtaining chaotic sequences that maintain general properties of the original chaotic system. A preliminary criterion based on the binary sequence balance estimation is proposed and applied to separate any binary representation of the chaotic time sequences into random and non-random parts. This gives us the possibility to delete obviously non-random sequences prior to the post-processing. The investigations were performed for arithmetic with both fixed and floating points. In both cases, the obtained sequences successfully passed the NIST SP 800-22 statistical tests. The utilization of the unidirectional asymmetric coupling of chaotic systems without full synchronization between them was suggested to increase the performance of the chaotic pseudo-random number generator (CPRNG) and avoid identical sequences on different outputs of the coupled systems. The proposed CPRNG was also implemented and tested on FPGA using Euler’s method and fixed-point arithmetic for possible usage in different applications. The FPGA implementation of CPRNG supports a generation speed up to 1.2 Gbits/s for a clock frequency of 50 MHz. In addition, we presented an example of the application of CPRNG to symmetric image encryption, but nevertheless, one is suitable for the encryption of any binary source.


2021 ◽  
pp. 494-505
Author(s):  
Alexandr A. Kuznetsov ◽  
Yurii Gorbenko ◽  
Anastasiia Kiian Anastasiia Kiian ◽  
Yuliia V. Ulianovska ◽  
Tetiana Kuznetsova

Pseudo-random number generator is an important mechanism for cryptographic information protection. It can be used independently to generate special data or as the most important element of security of other mechanisms for cryptographic information protection. The application of transformations in a group of points of elliptic and hypereliptic curves is an important direction for the designing of cryptographically stable pseudo-random sequences generators. This approach allows us to build  the resistant cryptographic algorithms in which the problem of finding a private key is associated with solving the discrete logarithm problem. This paper proposes a method for generating pseudo-random sequences of the maximum period using transformations on the elliptic curves. The maximum sequence period is provided by the use of recurrent transformations with the sequential formation of the elements of the point group of the elliptic curve. In this case, the problem of finding a private key is reduced to solving a theoretically complex discrete logarithm problem. The article also describes the block diagram of the device for generating pseudo-random sequences and the scheme for generating internal states of the generator.


2021 ◽  
Author(s):  
Katrin Sutter ◽  
Leonie Oostwoud Wijdenes ◽  
Robert J. van Beers ◽  
W. Pieter Medendorp

Professional golf players spend years practicing, but will still perform one or two practice swings without a ball before executing the actual swing. Why do they do this? In this study we tested the hypothesis that repeating a well-practiced movement leads to a reduction of movement variability. To operationalize this hypothesis, participants were tested in a center-out reaching task with four different targets, on four different days. To probe the effect of repetition they performed random sequences from one to six movements to the same target. Our findings show that, with repetition, movements are not only initiated earlier but their variability is reduced across the entire movement trajectory. Furthermore, this effect is present within and across the four sessions. Together, our results suggest that movement repetition changes the tradeoff between movement initiation and movement precision.


Genes ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 2023
Author(s):  
Dirson Jian Li

Nirenberg’s genetic code chart shows a profound correspondence between codons and amino acids. The aim of this article is to try to explain the primordial formation of the codon degeneracy. It remains a puzzle how informative molecules arose from the supposed prebiotic random sequences. If introducing an initial driving force based on the relative stabilities of triplex base pairs, the prebiotic sequence evolution became innately nonrandom. Thus, the primordial assignment of the 64 codons to the 20 amino acids has been explained in detail according to base substitutions during the coevolution of tRNAs with aaRSs; meanwhile, the classification of aaRSs has also been explained.


2021 ◽  
Vol 62 ◽  
pp. C84-C97
Author(s):  
Xifu Sun ◽  
Barry Croke ◽  
Stephen Roberts ◽  
Anthony Jakeman

A computationally efficient and robust sampling scheme can support a sensitivity analysis of models to discover their behaviour through Quasi Monte Carlo approximation. This is especially useful for complex models, as often occur in environmental domains when model runtime can be prohibitive. The Sobol' sequence is one of the most used quasi-random low-discrepancy sequences as it can explore the parameter space significantly more evenly than pseudo-random sequences. The built-in determinism of the Sobol' sequence assists in achieving this attractive property. However, the Sobol' sequence tends to deteriorate in the sense that the estimated errors are distributed inconsistently across model parameters as the dimensions of a model increase. By testing multiple Sobol' sequence implementations, it is clear that the deterministic nature of the Sobol' sequence occasionally introduces relatively large errors in sensitivity indices produced by well-known global sensitivity analysis methods, and that the errors do not diminish by averaging through multiple replications. Problematic sensitivity indices may mistakenly guide modellers to make type I and II errors in trying to identify sensitive parameters, and this will potentially impact model reduction attempts based on these sensitivity measurements. This work investigates the cause of the Sobol' sequence's determinism-related issues. References I. A. Antonov and V. M. Saleev. An economic method of computing LPτ-sequences. USSR Comput. Math. Math. Phys. 19.1 (1979), pp. 252–256. doi: 10.1016/0041-5553(79)90085-5 P. Bratley and B. L. Fox. Algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft. 14.1 (1988), pp. 88–100. doi: 10.1145/42288.214372 J. Feinberg and H. P. Langtangen. Chaospy: An open source tool for designing methods of uncertainty quantification. J. Comput. Sci. 11 (2015), pp. 46–57. doi: 10.1016/j.jocs.2015.08.008 on p. C90). S. Joe and F. Y. Kuo. Constructing Sobol sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30.5 (2008), pp. 2635–2654. doi: 10.1137/070709359 S. Joe and F. Y. Kuo. Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft. 29.1 (2003), pp. 49–57. doi: 10.1145/641876.641879 W. J. Morokoff and R. E. Caflisch. Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput. 15.6 (1994), pp. 1251–1279. doi: 10.1137/0915077 X. Sun, B. Croke, S. Roberts, and A. Jakeman. Comparing methods of randomizing Sobol’ sequences for improving uncertainty of metrics in variance-based global sensitivity estimation. Reliab. Eng. Sys. Safety 210 (2021), p. 107499. doi: 10.1016/j.ress.2021.107499 S. Tarantola, W. Becker, and D. Zeitz. A comparison of two sampling methods for global sensitivity analysis. Comput. Phys. Com. 183.5 (2012), pp. 1061–1072. doi: 10.1016/j.cpc.2011.12.015 S. Tezuka. Discrepancy between QMC and RQMC, II. Uniform Dist. Theory 6.1 (2011), pp. 57–64. url: https://pcwww.liv.ac.uk/~karpenk/JournalUDT/vol06/no1/5Tezuka11-1.pdf I. M. Sobol′. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7.4 (1967), pp. 86–112. doi: 10.1016/0041-5553(67)90144-9 I. M. Sobol′. Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp 1.4 (1993), pp. 407–414.


Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 336
Author(s):  
András Faragó

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.


2021 ◽  
Vol 14 (1) ◽  
pp. 73-86
Author(s):  
Iaroslav Lytvynenko ◽  
Serhii Lupenko ◽  
Petro Onyskiv ◽  
Andriy Zozulia

Aims: We have developed a new approach to the study of human heart rate, which is based on the use of a vector rhythmocardiosignal, which includes as its component the classical rhythmocardiosignal in the form of a sequence of heart cycle durations in an electrocardiogram. Background: Most modern automated heart rate analysis systems are based on a statistical analysis of the rhythmocardiogram, which is an ordered set of R-R interval durations in a recorded electrocardiogram. However, this approach is not very informative, since R-R intervals reflect only the change in the duration of cardiac cycles over time and not the entire set of time intervals between single-phase values of the electrocardiosignal for all its phases. Objective: The aim of this paper is to present a mathematical model in the form of a vector of stationary and permanently connected random sequences of a rhythmocardiosignal with an increased resolution for its processing problems. It shows how the vector rhythmocardiosignal is formed and processed in diagnostic systems. The structure of probabilistic characteristics of this model is recorded for statistical analysis of heart rate in modern cardiodiagnostics systems. Methods: Based on a new mathematical model of a vector rhythmocardiosignal in the form of a vector of stationary and permanently connected random sequences, new methods for statistical estimation of spectral-correlation characteristics of heart rate with increased resolution have been developed. Results: The spectral power densities of the components of the vector rhythmocardiosignal are justified as new diagnostic features when performing rhythm analysis in modern cardiodiagnostics systems, complementing the known signs and increasing the informative value of heart rate analysis in modern cardiodiagnostics systems. Conclusion: The structure of probabilistic characteristics of the proposed mathematical model for heart rate analysis in modern cardiodiagnostics systems is studied. It is shown how the vector rhythmocardiosignal is formed, and its statistical processing is carried out on the basis of the proposed mathematical model and developed methods.


2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Yaoge Jiao ◽  
Lifang Zhou ◽  
Rui Tao ◽  
Yanhong Wang ◽  
Yun Hu ◽  
...  

AbstractPrime editing (PE) enables efficiently targeted introduction of multiple types of small-sized genetic change without requiring double-strand breaks or donor templates. Here we designed a simple strategy to introduce random DNA sequences into targeted genomic loci by prime editing, which we named random prime editing (Random-PE). In our strategy, the prime editing guide RNA (pegRNA) was engineered to harbor random sequences between the primer binding sequence (PBS) and homologous arm (HA) of the reverse transcriptase templates. With these pegRNAs, we achieved efficient targeted insertion or substitution of random sequences with different lengths, ranging from 5 to 10, in mammalian cells. Importantly, the diversity of inserted sequences is well preserved. By fine-tuning the design of random sequences, we were able to make simultaneously insertions or substitutions of random sequences in multiple sites, allowing in situ evolution of multiple positions in a given protein. Therefore, these results provide a framework for targeted integration of random sequences into genomes, which can be redirected for manifold applications, such as in situ protospacer adjacent motif (PAM) library construction, enhancer screening, and DNA barcoding.


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