On the universal spectrum of periods in the time series of temperature fluctuations in starlings and rats Diatroptov М.Е.1, Panchelyuga V.A.2, Panchelyuga M.S.2, Seraya O.Yu.2 victor.panchelyuga@gmail.com 1 A.N. Severtsov Institute of Ecology and Evolution, RAS, Moscow, Russia; 2 Institute of Theoretical and Experimental Biophysics, RAS, Pushchino, Russia The paper considers a spectral analysis based on Fourier transform of the time series in the temperature fluctuations in the bodies of common starlings (Sturnus vulgaris) and rats (mature Wistar males). The spectra of the periods in the starlings and rats contain the same sets of harmonics, so on this basis we can tell about a common spectrum. Interesting to note that the spectrum coincides with a previously revealed spectrum of the periods, obtained with the use of local fractal analysis by the all permutations method in the course of studies of time series of the alpha decay rate fluctuations. Despite different methods of the experimental data processing used in this work (spectral analysis based on Fourier transform and local fractal analysis by the all permutations method), as well as different raw experimental data (the temperature fluctuations and alpha-decay rate fluctuations), the same spectrum of periods was obtained. On this basis, we can consider the spectrum of periods as universal one. Keywords: starlings; rats; temperature fluctuations; universal spectrum, alfa-decay; local fractal analysis; all permutations method 1. Introduction temperature in birds. The birds were kept in the individual cages 35х40х30 cm at natural light. The papers [1-2] present the studies of the time series The second part of the study was performed with the in the alfa-decay rate fluctuations. The studies were mature Wistar males (n = 14) of 280-320 g body mass. The performed with the local fractal analysis by all animals were kept in the plastic cages (60х18,5х38 cm), 1- permutations method [3-4], and produced the following 2 animal per a cage at permanent artificial lighting from a results: 1) the authors have demonstrated the presence of a source with 4200 К color temperature and 1200-1500 lx stable spectrum of periods in the analyzed time series; 2) intensity. The animals were distributed into three the periods observed in the fluctuations of the alfa-decay experimental groups: I – intact animals (n = 5), II – rate coincided with the periods of the Earth natural gonadectomized (n = 6) and III - animals with the oscillations (ENOs);3) the authors have demonstrated that combined surgical gonadectomy and adrenalectomy the periods revealed in the time series of various nature (n = 3). During the surgeries, the animals were processes coincide with the periods in the spectrum of the anaesthesized with the intramuscular Zoletil («Virbac alfa-decay fluctuations. Basing on 3), a factor causing the Sante Animale», France), 10 mg/kg of body mass. periods in the fluctuations of the alfa-decay rate can be The body temperature of starlings and rats was considered as a universal underlying condition, its measured with the intraperitoneally implanted sensors biological “activity” being of special interest. DTN3-28 («EMBI RESEARCH», Novosibirsk) The biological periods coinciding with the periods programmed to measure temperature once a minute in the revealed in the spectrum of the radioactive decay rate starlings and every other minute in rats. fluctuations were found in the motion behavior of the The most probable hormones determining the ultradian experimental animals [5], in the time series of the rhythmical recurrence in mammals are fluctuations of the R–R-intervals [6], at the investigation glucocorticosteroids produced by the adrenals and, to a of the dynamic dielectric constant of biological object (Blattella germanica) [7], etc. lesser extent, by reproductive hormones. The ultradian Unfortunately, few studies of the biological systems variability of the secretion of the hypothalamic-pituitary- include thorough investigations of the periods that fall into adrenal axis hormones can be explained by the presence of the range from several minutes to tens of minutes. This an oscillator controlled by the central nervous system and may be explained by the fact that somewhat apparent the mechanisms of the primary feedback. In such a way, alterations in controlled biological parameters usually take the analysis of the alterations of the parameters of ultradian time from tens of minutes to hours, so a measurement rhythms in the rats with the extirpated adrenals and testes interval of a minute or less that provides a spectrum within can give a possibility to clarify the effect of the negative a range of minutes-tens-minutes is considered as a less feedback on the formation of these biorhythms. informative and hence used rarely. The aim of the present Fig. 1 shows an example of the experimental study is to fill this gap. registration: one time series of a gonadectomized rat 2. Raw experimental material temperature measurements with an intraperitoneally implanted sensor DTN3-28. Measurement interval is 2 Four starlings (Sturnus vulgaris) (two males and two min. females) were used to study the dynamics of the body Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) 39 38.5 38 37.5 Temperature 37 36.5 36 0 2000 4000 6000 8000 10000 12000 14000 16000 Time, Min Fig. 1. Time series of rat temperature fluctuations spectrum for the rats group III. A rectangular insert near 3. Results. Comparison of spectra each peak shows its period (Х-coordinate) in minutes. All We constructed the power spectra for the time series values of the periods shown at Fig.2 are recorded in an similar to that shown at Fig. 1, the values of the spectra appropriate line of Table 1. Fig. 3 shows an enlarged were summarized for the appropriate frequencies in each portion of the spectrum presented at Fig.2 for the period individual spectrum belonging to one of the groups: 1) range of up to 24 min. The spectrum is four times starlings, 2) I – intact rats, 3) II – gonadectomized rats and smoothed with a running average procedure with the use 4) III – rats with the surgical gonadectomy and of the Poisson triangular window. The values of the adrenalectomy. In such a way, we have obtained four periods shown at Fig.3 are included into Table 1 too. power spectra. Fig.2 presents an example of them: a power X: 113.8 Y: 13.13 12 10 X: 146.3 X: 73.14 Y: 9.003 Y: 9.09 8 PSD 6 X: 93.09 Y: 4.661 X: 56.89 Y: 3.878 4 X: 46.55 Y: 3.106 X: 40.96 Y: 1.96 2 X: 35.31 Y: 0.9668 0 20 40 60 80 100 120 140 160 Time, min Fig. 2. Power spectrum of the rats of group III temperature fluctuations sna summa, sgl: 4 X: 22.76 Y: 0.2412 0.2 X: 18.96 X: 16.79 Y: 0.179 Y: 0.176 0.15 X: 13.13 PSD Y: 0.1089 0.1 X: 14.63 Y: 0.07624 X: 11.25 Y: 0.05621 X: 7.42 Y: 0.04643 X: 8.258 0.05 Y: 0.03786 X: 12.05 Y: 0.05391 X: 10.04 Y: 0.02875 6 8 10 12 14 16 18 20 22 24 Time, min Fig. 3. Enlarged part of the power spectrum from Fig.2 in the period range of up to 24 min Table 1 [4-5] contains (a bracketed number the maximal period of the classical Earth natural corresponds to a line number): (1) – a number of a period; oscillations corresponds to the main mode of the (2) - averaged values of periods found in time series of the spheroidal oscillations 0S2 (the averaged value is 53.9 alfa-decay fluctuations; (3) – modes of the Earth natural min). For these reasons, lines (3) and (4) of the continued oscillations; (4) – numerical values of the appropriate Table 1 are replaced with a single line containing the so modes of the Earth natural oscillations; (5) – periods found called long-wave or seismogravitational natural in the averaged spectrum of the starling temperature oscillations of the Earth [8-9]. fluctuations; (6) – rats I; (7) - rats II; (8) - rats III. Note that Table 1. Average values of the periods in the power spectra of the temperature fluctuations and alpha-decay rate fluctuations № 1 2 3 4 5 6 7 8 Alpha-decay 3.3 9 12 13.8 21.3 25 27.5 32 8S5 1S7 MODES of the ENOs … … 0T 8 0T 6 0T4 0S4 0T3 0S3 15S2 5S2 4.0 10.1 Numerical values of the ENOs … … 12.3 15.5 21.7 25.8 28.4 35.6 3.0 8.0 7.3 6.3 11.01 STARLINGS 5.7 10.1 12.6 14.6 20.1 23.8 26.9 30.1 5.4 9.3 16.3 5 8.5 4 11.3 15.1 18 RATS-I 10 12.5 20.5 25.6 — 30.1 7.9 RATS-II 8.9 — 16.8 20.1 25 — 29.3 10.8 8.3 12 14.6 RATS-III 7.4 10 19 22.8 — 35.3 11.3 13.1 16.8 № 9 10 11 12 13 14 15 16 Alpha-decay 40 46 51 55.8 60.7 68.3 73 75.5 59,2 63.7 MODES of the ENOs 2S1 0T2 — 0S2 60,8 67.8 72 77 Numerical values of the ENOs 41.3 44.2 — 53.9 — 68.3 73.1 — STARLINGS 36.6 46.5 — 53.9 60.2 — — — I RATS — 44.5 — — — 64 — — II RATS 39.4 — — 53.9 60.7 68.3 73 75.5 59,2 63.7 III RATS 40.9 46.6 — 56.9 60,8 67.8 72 77 № 17 18 19 20 21 22 23 Alpha-decay 80 85.5 95 99.8 106.3 112.3 MODES of the ENOs 82 86.7 95.2 103 107 Numerical values of the ENOs — 85.3 93.1 — — 113.8 146.3 STARLINGS — 85.3 — 102.4 — — — I RATS — 85.3 — — — — 146.3 II RATS — — 93.1 — — 113.8 146.3 III RATS 80 85.5 95 99.8 106.3 112.3 frequency. Therefore, the columns number 1 and 2 contain A number of the modes of the Earth natural some multitude of the periods. For example, the periods oscillations grows exponentially with the growth of their included into the column №2 have 20 modes of natural oscillations (7.97 min … 10.1 min), while the periods [5] V. S. Martynyuk Ultradian (Intradiurnal) Geo- and included into the column №1 have 164 types of the Heliophysically Significant Periods in Integral oscillations (3 min … 4 min) [10]. Accuracy of the periods Rhythm of Animal Locomotive Activity // determination in the case of the radioactive decay, line (2), Biophysics, 1998, Vol. 43, No. 5, pp.747-753. is ± 1min, hence comparison of the periods from 1 and 2 [6] Т.А. Zenchenko, A.A. Medvedeva, N.I. Khorseva, in the terms of the present study is senseless, it needs some Т.К. Breus Synchronization of heart rate indices of following investigations with the improvement of the time human and geomagnetic field variations in the resolution as the main purpose. frequency range of 0.5–3.0 mHz // Geophysical The second distinctive feature of the ENOs is that Processes And Biosphere, 2013, Vol.12, No.4, pp.73- each mode of the natural oscillations is, in fact, a multiplet, 84 that is, some set of the periods. For example, several [7] Kopvillem U.Kh., Sharipov R.Z., Zapolsky A.M., periods - 51.5, 52.8, 53.8, 55.2, 56.3 and 58.2 min. - Aizdaycher N.A. Biological detector of weak cosmic correspond to the main mode of the spheroidal oscillations, fields // Biophysics, 1992, vol.37, No.4, pp.643-646. while Table 1 contains their averaged value, 53.9 min. [8] Buland R., Berger J., Gilbert F. Observations from the Therefore, in this case, coincidence of frequencies is rather IDA network of attenuation and splitting during a a crossing of the appropriate sets. recent earthquake. // Nature, 1979, 277, No.5695. pp. 358-362. 4. Conclusion [9] Petrova L.N. Seismogravitational oscillations of the Important to note that the spectrum, which found in this Earth and possible mechanism of their formation // work coincides with a previously revealed spectrum of the Biophysics, 1992, Vol. 37, No. 3, pp. 508-516. periods, obtained with the use of local fractal analysis by [10] T.G. Masters and R. Widmer, in Free oscillations: the all permutations method in the course of studies of time frequencies and attenuations, Ed. by T.J. Ahrens series of the alpha decay rate fluctuations. Despite (American Geophysical Union, 1995), pp. 104–125. different methods of the experimental data processing [11] Syngaevskaya A.A., Berberova M.A., Derevyankin used in this work and in work [3-4] (spectral analysis A.A. Studying the effect of stress on the probability based on Fourier transform and local fractal analysis by of errors by NPP personnel as part of personnel the all permutations method), as well as different raw reliability analysis // CPT-2018: proceedings of the experimental data (time series of the temperature International Scientific Conference. - Protvino- fluctuations in the starlings and rats and noise-like time Moscow: Publishing House. IFTI, p. 282-288. series of alpha-decay rate fluctuations), the same spectrum [12] M.A.Berberova, K.I.Chernyavskii, «Comparative of periods was obtained. assessment of the NPP risk (on the example of Rostov In our opinion, the results of the analysis of the time and Kalinin NPP). Development of risk indicators series in the starlings and rats temperature fluctuations atlas for Russian NPPs», GraphiCon 2019 Computer presented in Table 1 confirm the hypothesis of the Graphics and Vision. The 29th International universal character of the spectrum observed initially in Conference on Computer Graphics and Vision. the time series of the fluctuations of the radioactive decay Conference Proceedings (2019), Bryansk, Russia, rate. September 23-26, 2019, Vol-2485, urn:nbn:de:0074- The results of this work can have various practical 2485-1, ISSN 1613-0073, DOI: 10.30987/graphicon- applications [11-13]. 2019-2-290-294, http://ceur-ws.org/Vol- 2485/paper67.pdf, p. 290-294. References: [13] Zakharova A.A., Korostelyov D.A., Fedonin O.N. Visualization Algorithms for Multi-criteria [1] V.A. Panchelyuga, M.S. Panchelyuga Fractal Alternatives Filtering (2019). Scientific Visualization Dimension and Histogram Method: Algorithm and 11.4: 66 - 80, DOI: 10.26583/sv.11.4.06 Some Preliminary Results of Noise-Like Time Series Analysis // Biophysics, 2013, Vol.58, No.2, pp.283– About the authors 289. Diatroptov Mikhail Evgen’evich Dr.habil. (Biology), senior [2] V.A. Panchelyuga, M.S. Panchelyuga Local fractal research scientist in A.N. Severtsov Institute of Ecology and analysis of non-stationary time series by all Evolution, RAS, E-mail: diatrom@inbox.ru permutations method // Hypercomplex numbers in Panchelyuga Victor Anatolyevich, PhD (Physics and geometry and physics, 2014, Vol.11, No. 1(21), Mathematics), senior scientist in the Institute of Theoretical and pp.107-133. Experimental Biophysics, RAS E-mail: [3] Panchelyuga V.A., Panchelyuga M.S. Local Fractal victor.panchelyuga@gmail.com. Analysis of Noise-Like Time Series by the All- Panchelyuga Maria Sergeevna, scientist in the Institute of Permutations Method for 1–115 min Periods // Theoretical and Experimental Biophysics, RAS E-mail: Biophysics, 2015, Vol. 60, No. 2, pp. 317–330. victor.panchelyuga@gmail.com. [4] V.A. Panchelyuga, M.S. Panchelyuga Some Seraya Olga Yuzefovna, junior scientist in the Institute of preliminary results of local fractal analysis of noise- Theoretical and Experimental Biophysics, RAS E-mail: olgaseraya@gmail.com like time series by all permutations method for periods 1-120 min // Hypercomplex numbers in geometry and physics, 2014, Vol.11, No.1(21), pp. 134-156.