Strengthening Quality of Chaotic Bit Sequences

We discuss chaos and its quality as measured through the 0-1 test for chaos. When the 0-1 test indicates deteriorating quality of chaos, because of the finite precision representations of real numbers in digital implementations, then the process may eventually lead to a periodic sequence. A simple method for improving the quality of a chaotic signal is to mix the signal with another signal by using the XOR operation. In this paper, such mixing of weak chaotic signals is considered, yielding new signals with improved quality (with K values from the 0-1 test close to 1). In some sense, such a mixing of signals could be considered as a two-layer prevention strategy to maintain chaos. That fact may be important in those applications when the hardware resources are limited. The 0-1 test is used to show the improved chaotic behavior in the case when a continuous signal (for example, from the Chua, Rössler or Lorenz system) intermingles with a discrete signal (for example, from the logistic, Tinkerbell or Henon map). The analysis is presented for chaotic bit sequences. Our approach can further lead to hardware applications, and possibly, to improvements in the design of chaotic bit generators. Several illustrative examples are included.

The influence of the cardinality of the alphabet on the quality of reconstruction of a symbolic periodic sequence from a sequence with noise

В статье рассмотрена задача восстановления символьных периодических последовательностей, искаженных шумами вставки, а также замены и удаления символов. Поскольку степень детализации символьного описания процесса определяется мощностью алфавита, представляет интерес исследование влияния степени детализации символьного описания на возможность восстановления полной информации об исходной периодической последовательности. Представлено экспериментальное исследование зависимости характеристик качества предложенного авторами метода восстановления периода от мощности алфавита. Для алфавитов разной мощности приводятся доля последовательностей с удовлетворительно восстановленным периодом и относительная погрешность определения длины периода. Качество восстановления оценивается отношением редакционного расстояния от восстановленной периодической последовательности до исходной строго периодической последовательности The relevance of this study is associated with the presence of a wide range of applied problems in real-world data processing and analysis. It is sensible to encode information using symbols from a finite alphabet in such problems. By varying the cardinality of the alphabet, in the description of the process, the symbolic representation provides a level of detail sufficient for real-world data analysis. However, for a number of subject areas in which it is possible to use symbolic coding of trajectories of the examined processes researchers face the presence of distortions, noise, and fragmentation of information. This occurs in bioinformatics, medicine, digital economy, time series forecasting and analysis of business processes. Periodic processes are widely represented in these subject areas. Without noise, these processes correspond to periodic symbolic sequences, i.e. words over a finite alphabet. A researcher often receives a sequence distorted by noises of various origins as the experimental data, instead of the expected periodic symbolic sequence. Under these conditions, when solving the problem of identifying the periodicity, which includes both the determination of a periodically repeating symbolic fragment and its length, hereinafter called the period, the problem requires reducing the effect of noise on the experimental results. The article deals with the problem of recovering periodic sequences, distorted by presence of noise along the replaced and deleted symbols. Since the level of detail in the description of the process depends on the cardinality of the alphabet, it is of interest to study the influence of the level of detail in the symbolic description on the possibility of recovering complete information about the initially periodic sequences. The article experimentally examines the dependence of the cardinality of the alphabet on the quality characteristics of the period recovery method proposed by the authors. For alphabets of different cardinalities, the proportion of sequences with a satisfactorily reconstructed period and the relative error in determining the length of the period are given. The quality of reconstruction of a periodically repeating fragment is estimated by the ratio of the editing distance from the reconstructed periodic sequence to the original sequence distorted by noise

Pseudo-random sequences of non-maximum length on shift registers with reducible and primitive polynomials

Inhomogeneous pseudo-random sequences of non-maximal length formed by shift registers with linear feedbacks based on a characteristic polynomial of degree n of the form ϕ(x)=ϕ1(x)ϕ2(x), where ϕ1(x) = x m1 ⊕ 1, and ϕ2(x) of degree m 2 is primitive (m 1 = 2 k , k is a positive integer, n = m 1 + m 2) are considered. Three schemes that are equivalent in terms of periodic sequence structures were considered. Of the greatest interest are the shift registers connected in an arbitrary way using a modulo-two adder, the feedbacks in which correspond to the multipliers ϕ1(x) and ϕ2(x) the polynomials ϕ(x). In this case, there is a complex process of forming output sequences, which involves both direct and inverse M-sequences. The statement about the singularity of the generated sequences at m 1 = 4 is proved, which is confirmed by their decimation with an index equal to the period of the primitive polynomial.

Reconstruction of a Symbolic Periodic Sequence from a Sequence with Noise

The problem of constructing a periodic sequence consisting of at least eight periods is considered, based on a given sequence obtained from an unknown periodic sequence, also containing at least eight periods, by introducing noise of deletion, replacement, and insertion of symbols. To construct a periodic sequence that approximates a given one, distorted by noise, it is first required to estimate the length of the repeating fragment (period). Further, the distorted original sequence is divided into successive sections of equal length; the length takes on integer values from 80 to 120 % of the period estimate. Each obtained section is compared with each of the remaining sections, a section is selected to build a periodic sequence that has the minimum edit distance (Levenshtein distance) to any of the remaining sections, minimization is carried out over all sections of a fixed length, and then along all lengths from 80 to 120 % of period estimates. For correct comparison of fragments of different lengths, we consider the ration between the edit distance and the length of the fragment. The length of a fragment that minimizes the ratio of the edit distance to another fragment of the same length to the fragment length is considered the period of the approximating periodic sequence, and the fragment itself, repeating the required number of times, forms an approximating sequence. The constructed sequence may contain an incomplete repeating fragment at the end. The quality of the approximation is estimated by the ratio of the edit distance from the original distorted sequence to the constructed periodic sequence of the same length and this length.

AN ANTENNA BASED ON A HYBRID METAL–DIELECTRIC STRUCTURE

Purpose: Nowadays, in the millimeter frequency range, the dielectric waveguides of various modifications have certain advantages over the standard metal waveguides, primarily due to the possibility of creating functional units based on them. This is due to the relative simplicity and low cost of manufacturing the dielectric waveguides and functional units using them, the high degree of their integration with active elements, the use in their manufacture of different dielectrics and polymers with a wide range of material constants and a variety of mechanical properties (in particular, some materials have a significant flexibility). After making a series of physical experiments we have found the possibility of implementing the frequency selection and radiation into free space of electromagnetic waves by a hybrid metal-dielectric structure. Design/methodology/approach: The studied electrodynamic structure belongs to the class of hybrid metal-dielectric structures. It includes a modified inverted dielectric waveguide with a periodic sequence on the dielectric plate of fifteen dielectric rods with metallized coating on one of the faces placed outwards. The structure efficiency was estimated by the voltage standing-wave ratio (VSWR) values and power attenuation in the duct. The measurements were made with the reflectometer method. To estimate the degree of electromagnetic field concentration near the rod inhomogeneities in the near zone, the mobile probe method was used. The field structures were visualized with the method of isolines. Findings: The results of a series of experimental investigations showed the possibility of matching the structure with the external waveguides in the frequency range of 26.5-32.5 GHz with the voltage standing-wave ratio (VSWR) less than 1.8. The frequency dependence of attenuation is oscillatory with clearly expressed frequency ranges with small and large attenuation values. Moreover, the dependence is almost periodic, which is typical of periodic structures. The frequency response slope in the transition zones can be quite high and reach values of 41.26 dB/GHz. The degree of concentration of the electric field near the waveguide dielectric rod and the degree of excitation of the dielectric inhomogeneities was found by directly measured electric field strength in the near zone. Measurements of energy characteristics made under the short-circuit conditions for the main guide and in the mode of matched load of the main guide showed both the ability to control the polarization characteristics and the ability to change the appearance of the pattern and its orientation in space. Conclusions: It has been experimentally proven that a hybrid metal-dielectric structure, being a modified inverted dielectric waveguide with a periodic sequence on the dielectric plate of fifteen dielectric rods with metalized coating on one of the faces placed outwards, can be effectively integrated into a standard transmission line. It is found that this structure can be matched with the external circuits in a fairly wide frequency range. It is also found that in different frequency ranges this hybrid metal-dielectric structure shows the possibility of both efficient frequency selection and radiation in free space. Antenna measurements have shown the beam pattern shape controllability. Key words: inverted dielectric waveguide, periodic sequence, voltage standing-wave ratio (VSWR), attenuation, reflectometer method, mobile probe method, directivity pattern

An Important Source About the Timurid Tree

This article discusses important sources about the Timurid family tree. Historical events by the author year after year (Although the historical data in the source are covered in a periodic sequence, a number of historical data are repeated in the text, in some cases the periodic sequence of months and days being overlooked by the author. This situation makes it necessary to study similar historical data in comparison with other written sources.

On the seismic response of a periodic sequence of three thin layers saturated by two-phase fluids

The conversion of fast to slow diffusion P-waves in fluid-saturated porous media induces attenuation and dispersion of waves at seismic frequencies. This effect, known as wave induced fluid flow, occurs at mesoscopic scales, which are much larger than the average pore size and much smaller than the average fast P-wave wavelength. When analyzing this mechanism in hydrocarbon reservoirs with the pore space saturated by multiphase fluids, it is important to include capillary pressure effects and flow interaction between fluids, which cause additional attenuation and velocity dispersion of P-waves. We present a procedure to determine the phase velocities and dissipation factors in a medium composed of a periodic sequence of three poroelastic thin layers saturated by two-phase fluids. The methodology consists of applying compressibility tests to representative samples of the material, which are defined as boundary-value problems solved using a finite-element (FE) procedure. First, we analyze the case of two-phase fluids saturation on each layer and the results are compared with those of the single-phase (effective) fluid case. Then, several cases of patchy saturation are presented, indicating that residual and wetting fluid saturation play an important role to determine the P-wave velocities and dissipation factors.

Integral Equations of Non-Integer Orders and Discrete Maps with Memory

In this paper, we use integral equations of non-integer orders to derive discrete maps with memory. Note that discrete maps with memory were not previously derived from fractional integral equations of non-integer orders. Such a derivation of discrete maps with memory is proposed for the first time in this work. In this paper, we derived discrete maps with nonlocality in time and memory from exact solutions of fractional integral equations with the Riemann–Liouville and Hadamard type fractional integrals of non-integer orders and periodic sequence of kicks that are described by Dirac delta-functions. The suggested discrete maps with nonlocality in time are derived from these fractional integral equations without any approximation and can be considered as exact discrete analogs of these equations. The discrete maps with memory, which are derived from integral equations with the Hadamard type fractional integrals, do not depend on the period of kicks.