^{1}

^{*}

^{2}

The mathematical basis for the earlier reported spectrum of discrete electromagnetic field (EMF) frequencies that were shown to affect health and disease is substantiated and generalized in the present paper. The particular EMF pattern was revealed by a meta-analysis of, now, more than 500 biomedical publications that reported life-sustaining as well as life-decaying EMF frequencies. These discrete eigenfrequency values can be related to supposed bio-resonance of solitons or polaron quasi particles in life systems. Bio-solitons are conceived as self-reinforcing solitary waves that are constituting local fields, being involved in intracellular geometric ordering and patterning, as well as in intra- and inter-cellular signalling. Literature search, revealed very similar frequency patterns for wave resonances of nucleotides in aqueous solution, for a candidate RNA-catalyst, as well as for sound-induced vibrations evoked in thin vibrating membranes. This collective evidence points at a generalized biophysical algorithm underlying complexity in nature, evidently manifest in both animate and non-animate modalities. The detected EMF eigenfrequencies could be arithmetically scaled according to an adapted Pythagorean tuning. The mathematical analysis shows that the derived arithmetical scale exhibits a sequence of unique products of integer powers of 2, 3 and a factor . This generalized semi-harmonic frequency spectrum may reflect a discrete pilot-wave structure that can be interpreted as a, so called, hidden variable in Bohm’s causal interpretation of quantum field theory.

Why does mathematics exhibit such effectiveness in describing the physical world [

A bio-soliton model based upon patterns was earlier proposed by us on the basis of a spectrum of EM frequency bands that appeared to produce striking biological effects in living cells. Both endogenously measured and in particular exogenously applied electromagnetic fields indicate states of quantum coherence in living systems [

Arithmetic is part of mathematics that consists of the study of patterns of numbers, especially the properties of the traditional operations between them: addition, subtraction, multiplication and division. A number is a mathematical object used to count, measure, or label. The first historical finding of an arithmetically defined nature is a fragment on a clay tablet Plimpton (ca. 1800BCE) and contains a table of different numbers and “Pythagorean triples”. The Greek philosopher and scientist Philolaus (ca. 420BCE) studied numbers and argued that number one represents the generation of a first unity and that all objects in the universe basically result from a combination of limited and unlimited aspects, that are fitted together by harmony. Philolaus in his time conceived harmony as constructed according to a number ratio scale, as was considered by Pythagoreans, and later by Plato. In the following, we will discuss the knowledge of scales in relation to order and disorder in nature and stipulate that more detailed insight into the knowledge of scales is in principle ground breaking and can be scientifically included in current science. First of all a description is given of Philolaus’ and Plato’s work made by Huffman, McKay and McKirahan [

Philolaus presupposed a scale with an unlimited continuum of pitches (musical tones), that should be limited in some way, in order for a very scale to arise. In Philolaus' system the fitting together of “limiters and un-limiters” involves their combination, in accordance with a certain ratios of numbers. He choose a scale in which the ratio of the highest to the lowest pitch amounts 2:1, which produces the interval of a so-called octave. That octave can, in turn, be divided into a fifth and a fourth, which exhibit the ratios of 3:2 and 4:3 and if added, make a complete octave. The fifth can be further divided into three whole tones, each corresponding to the ratio of 9:8 and a remainder (small non-fitting rest value) with a ratio of 256:243; the fourth can be divided into two whole tones with the same remainder [

It is now generally known that living organisms are able to generate and receive electromagnetic pulses that are transferred and processed at a non-thermal level. According to Cifra, chemical and electrical interaction within and between cells is well established and the most probable candidate for a form of cellular interaction is the electromagnetic field [

Coherence is defined as the physical congruence of wave properties within a wave packet and it is a property of stationary waves (i.e. temporally and spatially constant) that enables a type of wave interference, known as constructive. The particular processes are called highly coherent when the variability of the phase differences between the signals is relatively small, whereas the wave processes are defined as incoherent, the phase difference has a high degree of variability. Constructive interference of wave patterns occurs in cellular domains of variable size, that is based on arithmetic rules [

In a similar vein, Müller proposed an arithmetic fractal scaling models of harmonic oscillators, in which natural numbers greater than one can be written as unique products of prime numbers. Resonant oscillations can be understood as a forming-mechanism of fractal structures and fractals show a spectral compression and decompression of high and low density structure areas inside a medium. Yet the author did not find a link or interaction between the elements of a particular oscillating system [

One of the fundamental questions in developmental biology is how the complex range of linked vibratory patterns in bio-molecular structures, that we observe in nature, emerges. It is postulate that coherent interactions and entanglement of waves are keys in the setting of a finite number of parameters, and can be described by corresponding arithmetic equations.

Coherence or non-randomness of quantum resonances has also been discussed by Einstein and Infield (1961) for the so-called “prequantum modes”. And it was Schrödinger who recognized that coherent interaction of waves is coupled to entanglement as “the characteristic aspect of quantum mechanics” and suggested that “eigenstates” are able to survive interaction with the environment. Einstein-Podolsky and Rosen (EPR) discovered nonlocal correlations in quantum phenomena in 1935. Two systems, which are in an entangled state, even if separated as far as you like from each other, retain correlations, which do not decrease with increasing separation. Bohm proposed that the particle positions are the “hidden variables” in a causal interpretation of the quantum mechanics. These particle positions are independent of the wavefunction and exhibit their own dynamical motion [

Research in the framework of electromagnetic pulses in and on living cells has been systematically undertaken the past eighty years. About 25.000 biological/physical reports are available, of which a part is dealing with non-thermal biological effects on cells. Influences of electromagnetic waves causing thermal effects on biological systems are relatively well understood, yet the knowledge about non-thermal effects of electromagnetic waves is rapidly increasing. The Polaron model of Fröhlich (1968) and the Soliton model of Davydov (1973) describe both the effects of coherent states of waves for inanimate as well as animate systems. Polarons are quasi-particles in which an electron is dressed with one or phonons and are also called solitons. Solitons, as self-reinforcing solitary waves, have been shown to interact with biological phenomena in the framework of cellular self-organisation [

The stability and life times of these waves depend upon the extent of thermal decoupling of the stable state(s) of cells from the heat bath. Yet, in order to maintain stability of bio-molecules in living systems, also external coherent information is at stake. Locations receiving resonance transfer in the case of living cells are the surrounding domains of ion water clathrates, nucleic acids and ion-protein complexes [

An earlier analysis of 254 articles from 1950 to 2015, dealing with effects of electromagnetic waves on in vitro and in vivo life systems has been reported before [

On the whole, a spectrum with a consistent pattern of frequency bands can be observed, with only some exceptions in the first and third elliptical bands from the left. Some clusters of frequency values of the separate bands seem to be very close to each other. This could be related to the choices made by the particular investigators in following earlier published frequency data, instead of performing a primary random screen to find optimal values. The ordered beneficial EM field values may induce Fröhlich condensate states in cells through resonant communication. The meta-analysis of more than 500 biomedical studies thus revealed an obvious 12-number frequency scale, that shows a marked predictive value for biological effects that either stabilize or de-stabilize living cells. It is striking that just in between the stabilizing frequency bands, 12-bands with destabilizing frequency bands could be identified that were experimentally shown to be detrimental for living cells.

Also a likely relation exists between quantum mechanics and the proposed 12-number scale. Quantum behaviour and coherence has been found not only for micro states, but also for macro processes such as photosynthesis, magneto-reception in birds, the human sense of smell as well as photon effects in vision, all showing a non-trivial role for quantum mechanisms throughout biology [

Bohm maybe at stake. The quantum potential, indicated as hidden variable, is an informational effect shared by the surroundings particles and waves that depends on its form and shape, that is derived from the ψ-field [

Conclusion: These observations provided clues for the existence of a specific pattern of electromagnetic frequencies and quantum resonances that affect the viability of life systems and may be involved in the functional structuring and self-organisation of bio-molecules within cells through organizing them at the lowest possible energy level. The combination of multiple discrete frequencies could tentatively even be considered as a potential algorithm of life.

Interestingly, there is also an analogy between the found coherent patterns of electromagnetic waves in living organisms and a so called Tonnetz (German: tone-network) in music theory. In the Tonnetz systematic the parameter pitch refers not only to the perceived frequency of sound, but in addition describes the distance between repeated elements in a musical structure possessing translational symmetry. Pitch/space relationships typically use distance parameters to model the degree of relatedness of closely related pitches, placed near one another, and less closely related pitches placed farther apart; for example: triangular lattices (major third, minor third and fifth ratio’s). Edge-adjacent triads that share two common pitches, are expressed as a motion on the Tonnetz, which wraps the planar graph into a torus at different helix angles [

Chew took the interior-point approach to model higher-level structures using spiral configurations of a harmonic network, see

On the basis of this research, some obvious questions arise: what are the mathematical principles behind these ordered data, and is it possible to calculate and predict the frequencies of the “macroscopic wave function” as proposed by Fröhlich. A further point of interest is the relation with number theory that is also based on knowledge of Philolaus, Pythagoras, Archytas and Plato.

The basic scale unit of ancient Greece was the tetrachord meaning four strings. The first and fourth music notes of the tetrachord were tuned to the interval of a fourth (3:4) but the tuning of the other strings depended on the genus and mode of the music. The diatonic genus comprised the tuning of intervals with three whole tones and a semitone. The chromatic genus comprised a minor third (three semitones) and two semitones. In this theory, the enharmonic mode comprised a major third (two tones) and two quarter tones. The Pythagoreans devised a musical system of tuning based solely upon the interval of a fifth (2:3), that was regarded as the next most consonant interval after unison (1:1) and the octave (1:2). They discovered that a musical scale can be constructed by continuing through the spiral of fifths (2:3), which means that all subsequent tones in

the serial scales obey mutual relations with ratios of 2:3 and 1:2. The Pythagorean arithmetical scales were not only used to design musical scales, but, interestingly, also used in studies to describe the ordering of the cosmos [

The twelve tones Pythagorean system was developed by medieval music theorists using the same method of tuning in perfect fifths and there is no evidence that Pythagoras himself went beyond the tetrachord [

The Pythagorean twelve tone scale shows two sizes of semitones: the diatonic and the chromatic semitone. By considering these semitones, it was known that the “circle of fifths” (ratios of 2:3) does not fit within an octave (ratios of 1:2), and an ongoing discussions raised how to divided 12 tones within a ratio of 1:2. Eventually in music, musicians settled on using just the twelve notes, and tuning them in many different ways. Major and minor thirds (4:5 and 5:6) became more important in music, but the thirds were never used as a harmony in medieval music, and later the extremely sharp third in Pythagorean tunings was unacceptable to musicians and different “well temperaments” were developed. Composers of the past (for example Bach, Mozart, Beethoven, and Brahms) favored different tunings other than this kind of Pythagorean tuning [

A mathematical eigenfrequency model is proposed after analysing the biophysical experiments in the framework of electromagnetic pulses in and on living cells related to discovered intervals that approach ratios of 2:3 [

1) Resonance vibrations that oscillate in a manner such that standing wave patterns can be formed at a semi-harmonic way are of interest, for example being present in a vibrating string or in a membrane. Philolaus and Plato studied preferably the harmonic scales [

A harmonic scale is defined as a “just” musical scale, allowing extended just intonation. In music, just intonation or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Pure intervals are important in music because they correspond to the vibrational patterns found in physical objects, that also correlate to processes involved in human sound perception [

Philolaus applied a harmonic scale derived from the concept of overtones, that show first, second, third and some higher harmonics: 1, 3/2, 4/3, 9/8, 16/9. It is proposed to apply these harmonics in a so called 12-number descending Pythagorean scale, that is based upon 2:3 ratios. A scale constructed through Pythagorean tuning uses only ratios of 3:2, and can be constructed “upwards” by wrapping a chain of perfect fifths around an octave, but it can also be constructed “downwards” by wrapping a chain of perfect fourths around the same octave. By juxtaposing of these two slightly different scales, it creates a so-called enharmonic scale that proceeds quarter tones. When ascending from an initial pitch for example the note C by a cycle of justly tuned perfect fifths (ratio 3:2), wrapping twelve times, one eventually reaches a pitch approximately seven whole octaves above the starting pitch. If this pitch is then lowered precisely

seven octaves, the resulting pitch is a very small amount higher than the initial pitch. This microtonal interval is called a Pythagorean comma and amounts a ratio of about 1.0136. The enharmonic scale is a scale that proceeds by quarter tones (Appendix 1) and the interval (or comma) existing between two enharmonically notes such as C and B♯, or D♭ and C♯ is equal to the Pythagorean comma.

2) A slight adaptation of the descending Pythagorean semi-harmonic scale is of interest. In this scale most ratios of numbers are 2:3 ratios, some are approaching closely 2:3, and contains harmonic ratios, discussed at as the first condition: 2:3, 3:4, 8:9, 16:9. Using this scale, a good fit with frequency patterns of the earlier mentioned 486 different published independent biological electromagnetic frequencies could be found [

3) Three different so-called mean structures are of interest in the proposed scale due to the fact that ratios of 1:2 are precise, but not all ratios of 2:3 are exact. The so-called Pythagorean mean structures are the arithmetic mean of 3:2, the harmonic mean of 4:3 and the geometric mean of 2 (see for the definitions

Based on these conditions a deterministic 12-number arithmetic scale can be derived making use of a combination of the following principles: Partially harmonic ratios, Pythagorean tuning, one is unity and fits in a 12-number scale, and the three mathematical means. The scale can be further extended from a single scale to 54 scales with overall ratios of 1:2, and contains 648 different numbers for ordered data and 648 different numbers for disordered data. The proposed 12-number scale shows harmonic intervals with ratios of 2:3, 3:4, 8:9, 16:9, shows whole tones distances in relation to six limma distances. The limma can be calculated as follows: an octave (1:2) has 12 semitones, and a perfect fifth (2:3) has 7 semitones, moving up three octaves equals 3 × 12 = 36 semitones, and moving down five fifth equals 5 × 7 = 35 semitones. Moving up three octaves and moving down five fifths equals 36 − 35 = 1 semitone, and can be expressed: 2^{3}/(3/2)^{5} = 2^{8}3^{−}^{5} = 256/243 = 1.0535. The proposed 12-number scale contains six Phytagorean limma’s and three means: the geometric, arithmetic, and harmonic mean (see

Name | Formula | Solution | Mean of octave (2/1) |
---|---|---|---|

Arithmetic | a − b = b − c | b = (a + c)/2 | B = 3/2 (perfect fifth) |

Geometric | a/b = b/c | b = ac | b = 2 (tritone) |

Harmonic | (a − b)/a = (b − c)/c | b = 2ac/(a + c) | b = 4/3 (perfect fourth) |

number. The scale is mainly composed of just fifths (3:2) and intervals between scale notes have ratios that can be expressed as 2^{a}3^{b}. The proposed tuning is partially a form of just intonation, and these tones are rational (a rational number is any number that can be expressed as the quotient p/q of two integers), such as the semitone 256/243. Based on these typical scale properties twelve frequencies of the scale can be calculated: 1.0, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 1.4142, 1.5000, 1.5803, 1.6875, 1.7778, 1.8984. The differences between the proposed coherent scale of 12 numbers, coined the GM-scale, a descending Pythagorean scale, an equal tempered scale and a harmonic scale are listed in

The 12-number-scale can be further extended to larger dimensions by multiplying with 2^{m} (m = < −4 till > 50), thereby producing a universal frequency scale, see

The numerical ratios, that are semi-harmonic (harmonic and non-harmonic) are further shown in Appendix 2; the calculation of the non-coherent-scale, of which the parameters are logarithmically located just in between the coherent parameters of the semi-harmonic scale are derived and shown in Appendix 4.

The present mathematical analysis shows that the derived arithmetical scale exhibits a sequence of unique products of 12 × > 54 integer powers of 2, 3 and a factor 2 . The proposed scale for life-sustaining frequencies is shown to contain a core of twelve eigenfrequency functions as expressed: 2^{0}3^{0}2^{m}, 2^{8}3^{−5}2^{m},

GM-scale | 1.0 | 1.0535 | 1.1250 | 1.1852 | 1.2656 | 1.3333 | 1.4142 | 1.5000 | 1.5803 | 1.6875 | 1.7778 | 1.8984 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Desc. Pyth. | 1.0 | 1.0535 | 1.1250 | 1.1852 | 1.2656 | 1.3333 | 1.4047 | 1.5000 | 1.5803 | 1.6875 | 1.7778 | 1.8984 |

Equal temp. | 1.0 | 1.0595 | 1.1225 | 1.1892 | 1.2599 | 1.3348 | 1.4142 | 1.4983 | 1.5874 | 1.6817 | 1.7818 | 1.8877 |

Harmonic | 1.0 | 1.0667 | 1.1250 | 1.2000 | 1.2500 | 1.3333 | 1.4000 | 1.5000 | 1.6000 | 1.6667 | 1.7778 | 1.8750 |

Harm. ratios | 1.0 | 16/15 | 9/8 | 6/5 | 5/4 | 4/3 | 7/5 | 3/2 | 8/5 | 5/3 | 16/9 | 15/8 |

F_{m}(coh.1) = 2^{0}3^{0}2^{m } | F_{m}(coh.7) = 2^{0.5}2^{m } |
---|---|

F_{m}(coh.2) = 2^{8}3^{−5}2^{m} | F_{m}(coh.8) = 2^{−1}3^{1}2^{m} |

F_{m}(coh.3) = 2^{−3}3^{2}2^{m} | F_{m}(coh.9) = 2^{7}3^{−4}2^{m} |

F_{m}(coh.4) = 2^{5}3^{−3}2^{m} | F_{m}(coh.10) = 2^{−4}3^{3}2^{m} |

F_{m}(coh.5) = 2^{−6}3^{4}2^{m} | F_{m}(coh.11)= 2^{4}3^{−2}2^{m} |

F_{m}(coh.6) = 2^{2}3^{−1}2^{m} | F_{m}(coh.12) = 2^{−7}3^{5}2^{m} |

2^{−3}3^{2}2^{m}, 2^{5}3^{−3}2^{m}, 2^{−6}3^{4}2^{m}, 2^{2}3^{−1}2^{m}, 2^{0.5}2^{m}, 2^{−1}3^{1}2^{m}, 2^{7}3^{−4}2^{m}, 2^{−4}3^{3}2^{m}, 2^{4}3^{−2}2^{m}, 2^{−7}3^{5}2^{m} being valid for a broad range of adjacent frequency spectra for the integer values of m = 0, 1, 2, 3, ・・・, up to overall >54 self-similar 12-number octave scales. The scale shows a small adaptation of the scale proposed in 2016 [

Thus it is proposed to apply: 1) A Pythagorean descending tuning with the adaptation of the 7th ratio as the geometric mean of 1 and 2: 2 in a 12-number scale, 2) to expand this 12-number scale from 1 to > 54 octaves/scales, that overall affords 648 numbers and 3) each scale contains five harmonics and six limma’s to unite ratios of 1:2 with 2:3.

Quite surprisingly we detected in literature, that next to living cells also the same principles are valid for inanimate materials such as optical parametric oscillators used to show Bell’s inequality, ordered water molecules and thin metal membranes, that all show typical frequencies that comply with the calculated 12-number scale expressed in Hertz frequencies. A typical characteristic frequency of this membrane is 96 Hz that can be expressed as 2^{5}3^{1} [^{−}^{1}, is 54 Hz (2^{1}3^{3}) according to Henry [

M ⋅ c 2 = h ⋅ f ⇒ f ( Hz ) = 2 . 981 ⋅ M ( g ⋅ mol − 1 )

(M is molecular weight of water molecule, c = 299,792,458 m/s, h = 6.62606959 × 10^{−}^{34} J・s, f is the frequency of a water molecule).

So ordered number scales are able to represent geometric measures and are able to describe biological as well as physical processes. Therefore it is proposed to apply a 12-number-reference-scale expressed in Hertz, and is as follows: 1, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 2 , 1.5000, 1.5803, 1.6875, 1.7778, 1.8984, 2 Hz. The reader is referred to the appendices 2 and 3, and for the mathematical definition of the coherence inducing scale, to appendix 4 for the non-coherence inducing scale, while Appendix 5 provides an example of calculation results with the given equations. As mentioned before, all typical frequencies of living cells, cell systems and bio-molecules, from sub Hertz till Peta Hertz, can be further derived by multiplying each parameter of the reference scale by 2^{m}, of which m is an integer (see examples in Appendix 5). Twelve coherent acoustic frequencies, twelve coherent colours (nm) and the different interval distances are respectively calculated in Appendices 6-8.

The earlier mentioned analysis of about 500 articles from 1950 to 2017, dealing with endogenously measured and exogenously applied EM field frequencies in tissues, cells and biomolecules, thus shows patterns of beneficial biological effects related to electromagnetic waves on in vitro and in vivo life systems, and can be positioned from sub Hertz till Peta Hertz into the GM-scale. Frequencies just between the beneficial frequencies are related to patterns of detrimental biological properties, (see

A total of about 315 independent endogenous and exogenous beneficial biological frequency data of electromagnetic waves ranging from tenth of Hz till PHz, were normalized to a 12-number scale frequency scale by multiplying or dividing by multiples of 2 and can be positioned in the coherent-scale together with the calculated discrete beneficial frequencies (see the green points in

Totally about 171 independent endogenous and exogenous detrimental biological frequency data of electromagnetic waves ranging from tenth of Hz till PHz were also normalized to a 12-number-scale by multiplying or dividing by multiples of 2 and can be positioned in the non-coherent-scale together with the calculated discrete detrimental frequencies (see the red squares in

It is of interest that very different examples of ordered coherent data reported in (bio)-physical literature can be positioned in the chosen scales:

1) biological electromagnetic data expressed in Hertz [

2) spectrum of terahertz frequency patterns of oligonucleotides in aqueous solutions (Appendix 13)

3) quantum resonances of a candidate RNA-catalyst expressed in Hertz [

4) vibrating patterns in membranes expressed in Hertz [

5) coherent colours expressed in nanometre wavelengths [

Disordered data can be accommodated too:

1) biological electromagnetic data expressed in Hertz [

2) distorted patterns in sound induced geometric patterns on flat membranes, expressed in Hertz [

Are there other examples of number systems that underlie natural processes? There is not yet a consensus about the construction of the genetic code and how to explain it has been the subject for a lot of studies during many decades. Wohlin [

Of note, a striking resemblance has also been found between the proposed coherent scale and a spectrum of measured terahertz frequency patterns of oligonucleotides and the protein albumin in aqueous solutions, see appendix 13 and [

Summarized: The proposed universal semi-harmonic code of nature shows frequency ratios and stabilizing frequencies of living cells from sub Hertz till PHz and is able to predict frequencies of nucleotides, frequencies of a candidate RNA-catalyst and there are some indications to describe the ordering of the genetic code.

In the present paper a set of 12-number scales and sequences thereof have been revealed that describe coherent as well as non-coherent (non-coherent) eigen frequency functions. The scales are able to predict where typical numbers are positioned that are coherent, non-coherent, or chaotic. The coherence promoting scale of frequencies has been mathematical calculated and biologically verified for 12 × 54 = 648 different frequency in Hertz detected in living cells, nucleotides, a candidate RNA-catalyst, a thin vibrating membrane and presumably also in the genetic code. The non-coherence inducing scale has also been calculated for 12 × 54 = 648 different frequency values detected in destabilized living cells and in a thin vibrating membrane. The power of the proposed 12 number-scales could be directly demonstrated by data presented in about 500 biological studies. The particular EM field pattern, in our opinion, may have a close relation with the study of solitons, that are self-reinforcing solitary waves, and are supposed to interact with complex biological phenomena such as cellular self-organisation. Solitons in the cells are able to constitute local fields that both can be involved in intracellular geometric ordering and patterning, as well as in intercellular communication. The presently proposed mathematical calculations therefore complement the earlier proposed “macroscopic wave function” of the soliton models of Davydov [

The theoretical background of the found regularities of standing wave patterns, not only in biological properties of living cells, but also in inanimate materials and in thin vibrating membranes systems, might be that nature organizes its components at a highly coherent semi-harmonic way. Therefore the 12-number scale might be tentatively called a universal scale. The underlying mechanism is evidently instrumental in the unification of first, second, and third harmonics, as described by a Pythagorean descending scale and octave hierarchy. Possibly nature make use of this scale at the lowest possible energy level operating within a broad range of coherence inducing frequencies from sub Hertz till PHz, as was biologically verified. Of note, even much lower and higher frequencies can be probably considered, starting from sub Hertz to frequencies of Higgs particles.

The present analysis of the frequencies can be regarded as Fröhlich condensate frequencies and may have a possible correlation with the quantum potential as described in the theory of Bohm. The proposed model has also been based upon the knowledge of Philolaus, who was probably the first person to write down Pythagoras’s ideas and teachings [

Inferred Postulates:

1) Nature organizes animate and inanimate components at a highly coherent way, able to unite first, second, third and higher harmonics of waves within a semi harmonic scale, described by a slightly adapted semi-harmonic Pythagorean scale using arithmetic, geometric and harmonic means. The arithmetical 12-number scale uses 12 sequences of unique products of integer powers of 2, 3 and a factor 2 and can be regarded as eigenfrequency functions. The biological verified scale acts at a frequency distance from about < 0.01 Hz till > PHz (10^{15} Hz).

2) The discovered frequency patterns can be interpreted as hidden variables in Bohm’s causal interpretation of quantum mechanics theory.

3) In preliminary work, we inferred that the here proposed eigenfrequency functions may also fit in the EPR (Einstein-Podolsky-Rosen) argument, considering the particular measurements reported with regards to the testing of Bell’s theorem (Geesink, 2018).

Future plans: A first approach has been made into analysing the involvement of toroidal geometric structures, while applications of the concept have been described recently in cancer research [

In this last section, we want to put our mathematically based hypothesis in a somewhat broader perspective of information and mathematics, since at least four of its aspects are quite striking: 1) the algorithm shows not only constructive frequencies but also, intermediate, deconstructive elements, 2) the revealed coherent number system seems to accommodate both animate and inanimate systems related to certain atomic cascade transitions, 3) the frequency pattern is compatible with ancient music theory and the apparent pattern suggests the influence of a pilot-wave steering mechanism that reminds us of the implicated order interpretation of quantum physics by Bohm, 4) the link between external fields and the ultra-structure of cells is provided by a dedicated resonating bio-photon/phonon/soliton system, picturing an interactive discrete field system that is probably energy and information dissipative.

1) Coherent (constructive) and non-coherent (destructive) EM frequencies

Constructive and destructive interference of light was first shown in 1801 by Thomas Young, who sent sunlight through two narrow slits and showed that an interference pattern could be seen on a screen placed behind the two slits. The interference pattern was a set of alternating bright and dark lines, corresponding to where the light from one slit was alternately constructively and destructively interfering with the light from the second slit (see

This also makes use of Huygen’s principle: the principle that each point on a wave can be considered to be a source of secondary waves. Applying this to the

two slits, each slit acts as a source of light of the same wavelength, with the light from the two slits interfering constructively or destructively to produce an interference pattern of bright and dark lines. The principle of superposition of waves states that when two or more propagating waves of same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves. If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes―this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes―this is known as destructive interference (see

Our meta-analysis of more than 500 biomedical studies shows sets of opposing frequency spectra that are constructive and deconstructive, and that can be related to be beneficial and detrimental for life conditions. Do these separate modalities have an implicit relation with a geometry? It has been proposed that 12 different interfering constructive states and octaves thereof (ratios of 1:2) fit in coherent wave patterns with typical geometrical structures and sub-structures on a torus of which these states have their “zeros” at a single point. The torus model we propose accommodates properties of various types of localized states, similar to the states of semi-harmonic oscillators, which are maximally localized in phase space. The states on this torus have many properties in common with coherent states on a string, on a plane, on a sphere, and on Platonic solids [

2) Number systems valid for animate and inanimate systems

It is proposed that Life Systems are resembling typical coherent resonances of atomic cascade transitions of materials used to show Einstein-Podolsky-Rosen’s argument, and Bell’s theorem that should be placed by a local realistic process in space-time. Potentially, these informational frequencies are linked with the zero point energy field, through resonances leading to phase-locked cellular information attractors, that are functionally separated by non-coherent wave activity [

“non-coherent” EM/quantum values and the presence of trajectories corresponding with initial vibrational energies of molecules and atoms equal to their measured vibrational zero-point energies. A morphogenetic aspect, that is observed in animate (life) systems (spectral properties of proteins and nucleotides) as well as in inanimate models may indicate that a generalized bio-physical principle is at stake that is involved in morphogenetic ordering and guided organization and replication. Scientists have also observed self-replication in non-living systems. According to research led by Marcus, vortices in turbulent fluids spontaneously replicate themselves by drawing energy from shear in the surrounding fluid [

3) Steering mechanism based on Bohm’s pilot theory

The concept of rational control of shape by soliton-waves and the proposed “coherent wave pattern” observed in physical and biological experiments, the GM-model, shows an analogy with Bohm’s quantum potential. Bohm’s interpretation of the quantum mechanics is nonlocal, and causal. He makes use of the term quantum potential that is an informational effect shared by the surroundings particles/waves that depends on its shape and is derived from the ψ-field [

4) Potential link between GM-scale and energy/heat

A further step in developing a morphogenetic mechanism has been achieved by also taking dissipation into account. Dissipation is possible when the interaction of a system with its environment is considered. Vitiello described how the system-environment interaction causes a doubling of the collective modes of the system in its environment [

The authors support these ideas, but stipulate that a potential electromagnetic energy source should be more differentiated with regard to its frequency spectrum. We argue that the overall complexity of cells requires a fine-tuned set of input energies including coherent and damping frequencies, and that only a concerted action of the combined frequencies can be instrumental in the mathematical construction of extremely complex animate and inanimate systems.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Geesink, H.J.H. and Meijer, D.K.F. (2018) Mathematical Structure for Electromagnetic Frequencies that May Reflect Pilot Waves of Bohm’s Implicate Order. Journal of Modern Physics, 9, 851-897. https://doi.org/10.4236/jmp.2018.95055

Note | Ratio | Note | Ratio |
---|---|---|---|

C | 1:1 | Fies | 729:512 |

Des | 256:243 | G | 3:2 |

Cies | 2187:2048 | As | 128:81 |

D | 9:8 | Gies | 6561:4096 |

Es | 32:27 | A | 27:16 |

Dies | 19,683: 16,384 | Bes | 16:9 |

E | 81:64 | As | 59,049:32,768 |

F | 4:3 | B | 243:128 |

Ges | 1024:729 | C | 2:1 |

The calculated different numerical ratios of the 12-number; F1 till F12 stand for the twelve numbers of the Coherent-scale, that show harmonic, non-harmonic and irrational parameters.

Harmonic part | Non-harmonic | Irrational |
---|---|---|

F1 = 1 | F2 = Λ F1 | F7 = 2 |

F3 = 2^{−}^{3}3^{2} F1 | F4 = Λ F3 | |

F6 = Λ F5 | F5 = 2^{−}^{6} 3^{4} F1 | |

F8 = 2^{−}^{1}3^{1} F1 | F9 = Λ F8 | |

F11 = Λ F10 | F10 = 2^{−}^{4} 3^{3} F1 | |

F12 = 2^{−}^{7} 3^{5} F1 |

Harmonic part | Non-harmonic | Non-harmonic |
---|---|---|

F1 = 1 | F2 = 2^{8}3^{−}^{5} | F7 = 2 |

F3 = 2^{−}^{3}3^{2} | F4 = 2^{5}3^{−}^{3} | |

F6 = 2^{2}3^{−}^{1} | F5 = 2^{−}^{6}3^{4} | |

F8 = 2^{−}^{1}3^{1} | F9 = 2^{7}3^{−}^{4} | |

F11 = 2^{4}3^{−}^{2} | F10 = 2^{−}^{4}3^{3} | |

F12 = 2^{−}^{7}3^{5} |

Harmonic part | Non-harmonic | Non-harmonic |
---|---|---|

F1 = 1 | F2 = 1.0535 | F7 = 1.4142 |

F3 = 1.1250 | F4 = 1.1852 | |

F6 = 1.3333 | F5 = 1.2656 | |

F8 = 1.5000 | F9 = 1.5803 | |

F11 = 1.7778 | F10 = 1.6875 | |

F12 = 1.8984 |

The GM-function can be written as twelve unique combinations of 2^{p}・3^{q}, multiplied by 2^{m}, where p = 0, −1, 2, −3, 4, −4, 5, −6, 7, −7, 8, 2 , q = 0, 1, 2, 3, 4, 5, −1, −2, −3, −4, −5, and m are integers from 0 till 54.

F_{m}(coh.1) = 2^{0}3^{0}2^{m } | F_{m}(coh.7) = 2^{0.5}2^{m } |
---|---|

F_{m}(coh.2) = 2^{8}3^{−5}2^{m } | F_{m}(coh.8) = 2^{−1}3^{1}2^{m } |

F_{m}(coh.3) = 2^{−3}3^{2}2^{m } | F_{m}(coh.9) = 2^{7}3^{−4}2^{m } |

F_{m}(coh.4) = 2^{5}3^{−3}2^{m } | F_{m}(coh.10) = 2^{−4}3^{3}2^{m} |

F_{m}(coh.5) = 2^{−6}3^{4}2^{m } | F_{m}(coh.11)= 2^{4}3^{−2}2^{m } |

F_{m}(coh.6) = 2^{2}3^{−1}2^{m } | F_{m}(coh.12) = 2^{−7}3^{5} 2^{m } |

A non-coherent-scale can be calculated based upon the finding that decoherent parameters are located logarithmically just in between the coherent parameters and can be calculated as follows (m = 0 till 54):

D_{m}(decoh.1) = 10^{(0.5logF1+0.5logF2)} | D_{m}(decoh.2) = 10^{(0.5logF2+0.5logF3)} |
---|---|

D_{m}(decoh.3) = 10^{(0.5logF3+0.5logF4)} | D_{m}(decoh.4) = 10^{(0.5logF4+0.5logF5) } |

D_{m}(decoh.5) = 10^{(0.5logF5+0.5logF6) } | D_{m}(decoh.6) = 10^{(0.5logF6+0.5logF7)} |

D_{m}(decoh.7) = 10^{(0.5logF7+0.5logF8)}^{ } | D_{m}(decoh.8) = 10^{(0.5logF8+0.5logF9)} |

D_{m}(decoh.9) = 10^{(0.5logF9+0.5logF10)} | D_{m}(decoh.10) = 10^{(0.5logF10+0.5logF11) } |

D_{m}(decoh.11) = 10^{(0.5logF11+0.5logF12)} | D_{m}(decoh.12) = 10^{(0.5logF12+0.5logF13) } |

Factor | F1, m | F2, m | F3, m | F4, m | F5, m | F6, m | F7, m | F8, m | F9, m | F10, m | F11, m | F12, m |
---|---|---|---|---|---|---|---|---|---|---|---|---|

m = 0 | 1.0000 | 1.0535 | 1.1250 | 1.1852 | 1.2656 | 1.3333 | 1.4142 | 1.5000 | 1.5803 | 1.6875 | 1.7778 | 1.8984 Hz |

m = 1 | 2.0000 | 2.1070 | 2.2500 | 2.3704 | 2.5312 | 2.6666 | 2.8284 | 3.0000 | 3.1606 | 3.3750 | 3.5556 | 3.7968 Hz |

m = 2 | 4.0000 | 4.2140 | 4.5000 | 4.7408 | 5.0624 | 5.3332 | 5.6568 | 6.0000 | 6.3212 | 6.7500 | 7.1112 | 7.5936 Hz |

m = 3 | 32.000 | 33.712 | 36.000 | 37.9264 | 40.4992 | 42.6656 | 45.2544 | 48.000 | 50.5696 | 54.000 | 56.8896 | 60.7488 Hz |

m = 8 | 256.00 | 269.70 | 288.00 | 303.41 | 324.00 | 341.33 | 362.04 | 384.00 | 404.54 | 432.00 | 455.12 | 486.00 Hz |

m = 12 | 4.0960 | 4.3151 | 4.6080 | 4.8546 | 5.1839 | 5.4613 | 5.7926 | 6.1440 | 6.4729 | 6.9120 | 7.2819 | 7.7759 KHz |

2^24 | 16.777 | 17.675 | 18.874 | 19.884 | 21.233 | 22.370 | 23.726 | 25.166 | 26.513 | 28.312 | 29.827 | 31.850 Hz |

2^32 | 4.2950 | 4.5248 | 4.8318 | 5.0904 | 5.4357 | 5.7266 | 6.0739 | 6.4425 | 6.7873 | 7.2478 | 7.6356 | 8.1536 Hz |

2^40 | 1.0995 | 1.1583 | 1.2370 | 1.3031 | 1.3915 | 1.4660 | 1.5549 | 1.6493 | 1.7376 | 1.8554 | 1.9547 | 2.0873 Hz |

2^48 | 281.47 | 296.53 | 316.66 | 333.60 | 356.23 | 375.29 | 398.06 | 422.21 | 444.81 | 474.99 | 500.41 | 534.35 Thz |

532.5 | 505.6 | 473.4 | 449.3 | 420.8 | 399.5 | 376.6 | 710.1 | 674.0 | 631.3 | 599.1 | 561.0 nm |

An acoustic coherent scale at m = 8: 256, 269.70, 288, 303.41, 324, 341.33, 362.04, 384, 404.54, 432, 455.12, 486 Hz.

The 12-number GC-scale is positioned between a ratio of 1:2 and contains five whole “tone” distances of 9/8 and twelve half “tone” distances of three different types of half tones: six Limma’s (2^{8}3^{−}^{5} = 1.0535), four Apotomes (3^{7}2^{−}^{11} = 1.0679) and two means of a Limma and an Apotome (1.0607); 1, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 2 , 1.5000, 1.5803, 1.6875, 1.7778, 1.8984, 2.

The calculated mean of all fifth’s (ratios of 2:3) is:

2 7 12

Typical fifths are distributed as follows, see

8^{th}/1^{th} = 1.5000 | 14^{th}/7^{th} = 1.4899^{ } |
---|---|

9^{th}/2^{th} = 1.5000 | 15^{th}/8^{th} = 1.5000^{ } |

10^{th}/3^{th} = 1.5000^{ } | 16^{th}/9^{th} = 1.5000^{ } |

11^{th}/4^{th} = 1.5000 | 17^{th}/10^{th} = 1.5000^{ } |

12^{th}/5^{th} = 1.5000 | 18^{th}/11^{th} = 1.5000^{ } |

13^{th}/6^{th} = 1.5000 | 19^{th}/12^{th} = 1.4899^{ } |

The 12-number scale has a closed circle of fifth’s, which means that the defined fifth’s fit in a ratio of 1:2. The brokenness of the circle (the fact that pure fifth’s do not fit in a ratio of 1:2), as defined by the Pythagorean comma ((3/2)^{12}/27 = 1.0136), has been redistributed over two fifth’s. The means of all fifths over a total of 54 scales amounts:

∑ m = 0 54 ∑ n = 1 12 F ( 12 m + n + 7 ) F ( 12 m + n ) = 12 ( m + 1 ) 2 7 12 (A1)

Formulae (A1): The mean of all fifth’s in all scales from n = 1 till 12, m = 1 till 54.

Typical mutual ratios of the numbers in the scale are, see Formulae (A2):

F ( 12 m + n ) F ( 12 m + n − 12 ) = 2 (A2)

F ( 12 m + 8 ) ⋅ F ( 12 m + 6 ) = F ( 12 m + 7 ) 2

F ( 12 m + 7 ) F ( 12 m + 1 ) = 2

F ( 12 m + 6 ) F ( 12 m + 1 ) = 4 3

F ( 12 m + 8 ) F ( 12 m + 1 ) = 3 2

F ( 12 m + 3 ) F ( 12 m + 1 ) = 9 8

Formulae (A2): Typical mutual relations of numbers for n = 1 till 12, m = 1 till 54.

The mutual distances of the subsequent 12 numbers are: 1.0535, 1.0678, 1.0535, 1.0678, 1.0535, 1.0607, 1.0607, 1.0535, 1.0678, 1.0535, 1.0678, 1.0535, whereas all mutual distances of an equal tempered scale are 1.0595. And all individual sequences of quint ratios of the scales in the frequency range from sub Hertz till PHz approach 1.498 at 0.00% - 0.07%, with the exception of the quint’s related to a so-called Wolf-interval (the Wolf interval is in music theory a particularly dissonant musical interval spanning seven semitones). Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament).

When the numerical differences of the frequencies of all intervals of quarts and major thirds are calculated, than the mean of this differences approximates ф (1.618) at 0.38%:

∑ m = 0 54 ∑ n = 1 12 F ( 12 m + n + 9 ) − F ( 12 m + n + 4 ) F ( 12 m + n + 4 ) − F ( 12 m + n ) = ~ 12 m ф (A3)

Formulae (A3): Arithmetical sequences that approach phi from n = 1 till 12, m = 1 till 54.

The different biological studies related to endogenous and exogenous frequencies of electromagnetic oscillations are listed in alphabetical order below:

Activation of the extracellular signal-regulated kinase signal pathway

Anti-proliferative effects on tumour cells

Biological membranes

Brain activity

Brain stimulation, spinal cord stimulation

Changes in gene expression in neural stem cells and mesenchymal stem cells

Chromatin remodelling and pro-neuronal gene expression

Decrease of inflammatory cells

Depressive disorders and neurological defects

Entorhinal-hippocampal interactions

Improve of cognitive function

Improvement of attention

Increase of bone growth

Increase of fibroblast proliferation

Influence on fibroblast morphology

Influence on memory tasks

Influence on transcriptome and genetic networks

Inhibition of tumour growth

Foci in differentiated cells

Genetic expressions

Genome-wide methylation

Ion-channel proteins

Light-harvesting complexes from bacteria, and bioluminescence

Microtubular proteins

Muscle regeneration

Neurogenesis

Neuro-regeneration

Neuro-stimulation, restore of neurological disorders

Neutrophil calcium homeostasis

Neuronal communication

Oligonucleotides

Osteogenic differentiation of human bone marrow-derived mesenchymal

stem cells

Pigment-protein complexes

Prefrontal and parietal human cortex

Promotion of proliferation of human mesenchymal stem cells

Protein synthesis by cells, increase of endothelial cells

Protein folding

Receptors in human neutrophils endogenous electric fields

Reduced and repression of tumour growth, improvement of memory

Reduction of diabetic peripheral neuropathy

Reduction of Parkinson

Regeneration of cells

Restore of spectrum of disorders such as traumatic brain injury

Rhythmic neuronal synchronization

Self-assembly of microtubulins

Skin healing

Stimulation of angiogenesis, granulation of tissue formation

Synthesis of collagen

Transcranial magnetic stimulation

Tubulin protein molecules

Wound healing

The experiments in these studies were described in the areas of:

Alteration of protein conformation

Angiogenesis, inhibition of cell growth

Antigen-antibody interaction

Cancer

Cardiovascular effects

Cardiovascular responses

Chromosomal instability

Cognitive impairment

DNA single-strand breaks

Effects on blood pressure

Gene expression

Genotoxicity

Induction of spermatogenic germ cell apoptosis

Influence on alkaline phosphatase activity

Influence on behaviour

Influence on sleeping

Influence on specific brain rhythms

Influence on teratogenic potential

Influence on the permeability of the blood-brain barrier

Influences on sperm parameters

Learning and memory alterations

Maculopathy

Phototoxic effects on human eye health

Phototoxic effects on human eye health, and on the retina

Skin healing

Tumour growth

Aaron RK, Ciombor DM, Jolly G (1987).

Aaron RK, Ciombor DM, Jolly G (1989).

Adamskaya N, Dungel P, Mittermayr R, Hartinger J, Feichtinger G, Wassermann K (2011).

Adey et al (1999).

Ahmed I, Istivan T, Cosic I, Pirogova E (2013).

Albert EN (1977).

Algvere PV, Marshall J, Seregard S (2006).

Almeida-Lopes L, Rigau J, Zângaro RA, Guidugli-Neto J, Jaeger MM (2001).

Amaral AC, Parizotto NA, Salvini TF (2001).

Ando, T, Xuan W, Xu T, Dai T, Sharma SK, Kharkwal GB, Huang YY, Wu Q, Whalen MJ, Sato S, Obara M, Hamblin MR (2011).

Araújo CEN, Ribeiro MS, Favaro R, Zezell DM, Zorn TMT (2007).

Arendash G, Mori T, Dorsey M, Gonzalez R, Tajiri N, Borlongan C (2012).

Arns, M (2011).

Assis L, Moretti AI, Abrahão TB, de Souza HP, Hamblin MR, Parizotto NA (2012).

Astoreca, R, Rousseau, V, Ruddick K, Van Mol, B, Parent JY, and Lancelot C (2005).

Aydogan F et al. (2015).

Bastos, AM, Vezoli J, and Fries P (2015).

Battini R, Monti MG, Moruzzi MS, Ferrari S, Zaniol P, Barbiroli B (1991).

Bawin SM, Gavalas-Medici RJ, Adey WR (1973).

Belloni F, Alifano P, Doria D, Lorusso C, Monaco V, Nassisi, Talk A, Tredici M (2005).

Belyaev IY, Alipobv YeD, Matronchik AY (1998).

Belyaev IY, Alipov ED (2001).

Beneduci A, Chidichimo G, De Rose R, Filippelli L, Straface SV, Venuta S. (2008).

Beneduci A, Chidichimo G, De Rose R, Filippelli L, Straface SV, Venuta S. (2005).

Bin Lv, Zhiye Chen, Tongning Wu, Qing Shao, Duo Yan, Lin Ma, Ke Lu, Yi Xie, 2014.

Bin Lv, Zhiye Chen, Tongning Wu, Qing Shao, Duo Yan, Lin Ma, Ke Lu, Yi Xie, 2013.

Blackinton D, LeFebvre, Cherlin D, et al. (1992).

Blackman CF, Elder, JH, Weil, CM, Benane, SG. (1979).

Blackman CF, Benane, SG, Rabinowitz, JR, House DE, Joines WT (1985).

Blumenfeld Z, Velisar A, Miller Koop M, Hill BC, Shreve LA, Quinn EJ, Kilbane C, Yu H, Henderson JM, Brontë-Stewart H (2015).

Bogomazova AN, Vassina EM, Goryachkovskaya TN, Popik VM, Sokolov AS, Kolchanov NA, Lagarkova MA, Kiselev SL, Peltek SE (2015).

Bowmaker JK, Dartnall H.J.A. (1980).

Braun KA, Lemons JE. (1982).

Brown-Woodman PDC, Hadley JA (1988).

Buhl, DL et al. (2003).

Buzsaki G, Horvath Z, Urioste R, Hetke J, Wise K (1992).

Byrnes KR, Barna L, Chenault VM, Waynant RW, Ilev IK, Longo L (2004).

Cameron IL, Sun LZ, Short N, Hardman WE, Williams CD (2005).

Cane V, Botti P, Soana S (1993).

Carvalho PT, Mazzer N, Dos Reis FA, Belchior AC, Silva IS. (2006).

Cassano P, Petrie SR, Hamblin MR, Henderson TA, Iosifescuh DV (2016).

Ceccarelli G, Bloise N, Mantelli M, Gastaldi G, Fassina L, Cusella De Angelis MG, Ferrari D, Imbriani M, Visai L (2013).

Cecconi S, Gualtieri G, Di Bartolomeo A, Troiani G, Cifone MG, Canipari R (2000).

Cherry NJ (2003).

Cheing GL, Li X, Huang L, Kwan RL, Cheung KK (2014).

Chen CC, Litvak V, Gilbertson T, Kuhn A, Lu CS, Lee ST, Tsai CH, Tisch S, Limousin P, Hariz M, and Brown P (2007).

Chen CH, Chen TH, Wu MY, Chou TC, Chen JR, Wei MJ, Lee SL, Hong LY, Zheng CM, Chiu IJ, Lin YF, Hsu M, Hsu (2017).

Chen X, Zhuang J, Kolb JF, Schoenbach KH, Beebe SJ (2012).

Cheng-Hsien Chen, Tso-Hsiao Chen, Mei-Yi Wu, Tz-Chong Chou, Jia-Rung Chen, Meng-Jun Wei, San-Liang Lee, Li-Yu Hong, Cai-Mei Zheng, I-Jen Chiu, Yuh-Feng Lin, Ching-Min Hsu & Yung-Ho Hsu (2017).

Cheon MW, Kim TG, Lee YS, Kim SH (2013).

Cheron G, Gall D, Servais L, Dan, B, Maex, R, Schiffmann, SN (2004).

Lin CC, Liu XM, Peyton K, Wang H, Yang WC, Lin SJ, Durante W (2008).

Huang PH, Chen JW, Lin CP et al. (2012).

Choi YK, Cho H, Seo YK, Yoon HH, Park JK (2012).

Choi DH, Lee KH, Kim JH, Kim MY, Lim JH. Lee J (2012).

Chou CK, Guy AW (1978).

Chrobak JJ, Lorincz A, Buzsaki G (2000).

Chung TY, Peplow PV, Baxter GD (2010).

Ciombor DM, Aaron RK (1993).

Collini E, Wong KY, Wilk KE, Curmi PMC, Brumer P, Scholes GD (2010).

Correa F, Lopes Martins RA, Correa JC, Iversen VV, Joenson J, Bjordal JM (2007).

Cressoni MD, Dib Giusti HH, Casarotto RA, Anaruma CA (2008).

Conner-Kerr, PT, Howlett A. et al. (2015).

Copty AB, Neve-Oz Y, Barak I, Golosovsky M, Davidov D (2006).

Cressoni MD, Dib Giusti HH, Casarotto RA, Anaruma CA. (2008).

Curley SA, Palalon F, Lu X, Koshkina NV (2014).

Dai J, Wu S, Kong Y, Chi Z, Si L, Sheng X, Cui C, Fang J, Zhang J, Guo J (2016).

Daniells et al. (1998).

D’Andrea JA, Thomas A, Hatcher DJ (1994).

Delle Monache S, Alessandro R, Iorio R, Gualtieri G, Colonna R (2008).

De Sousa AP, Paraguassú GM, Silveira NT, de Souza J, Cangussú MC, dos Santos JN, et al. (2013).

De Sousa AP, Santos JN, Dos Reis JA Jr, Ramos TA, de Souza J, Cangussú MC (2010).

De Mattei M, Varani K, Masieri FF, Pellati A. Ongaro A, Fini M, Cadossi R, Vincenzi F, Borea PA, Caruso A (2009).

De Taboada L et al. (2011).

De Pomerai (2000).

De Pomerai DI, Smith B, Dawe A, North K, Smith T, Archer DB, Duce IR, Jones D, Candido EP. 2003.

Deshmukh P.S. et al. (2015).

Desmedt JD, Tomberg C. (1994).

Donnellan M et al. (1997).

Elliott JP, Smith RL, Block CA (1988).

Eris AH, Kiziltan HS, Meral I, Genc H, Trabzon M, Seyithanoglu H, Yagci B, Uysal O (2015).

Esmekaya MA, Aytekin E, Ozgur E, Güler G, Ergun MA, Omeroğlu S, et al. (2011).

Eusebio A, Cagnan H, and Brown P (2012).

Fadel MA (1998).

Fadel MA, (2002).

Fadel MA, El-Gebaly RE, Amany A, Aly AA, Ibrahim FF (2005).

Fahimipour F, Mahdian M, Houshmand B, Asnaashari M, Sadrabadi AN, Farashah SE (2013).

Fedorov VI (2011).

Finkel RW (2013).

Foffani G, Priori A, Egidi M, Rampini P, Tamma F, Caputo E, Moxon K A, Cerutti, S, and Barbieri S (2003).

Frei MR (1989).

Fröhlich F (2014).

Fröhlich H (1968).

Fukuzaki Y, Ang FY, Yamanoha B, Kogure S (2014).

Fukuzaki Y, Shin H, Kawai HD, Yamanoha B, Kogure S (2015).

Furia JP (2012).

Fushimi T, Inui S, Nakajima T, Ogasawara M, Hosokawa K, Itami S (2012).

Gandhi CR, Ross DH (1989).

Ganesan K, Gengadharan AC, Balachandran C, Manohar BM, Puvanakrishnan R (2009).

Gao X, Luo R, Ma B, Wang H, Liu T, Zhang J, Lian Z, Cui X (2014).

Gapeyev AB, Chemeris NK (1999).

Gerner C, Haudek V, Schandl U, Bayer E, Gundacker N, Hutter HP, Mosgoeller W (2010).

Ghannam MM, El-Gebaly RH, Gaber MH, Ali FM (2002).

Ghione S., Del Seppia C, Mezzasalma L, Emdin M, Luschi P (2004).

Glazer-Hockstein and al. (2006).

Goldstein L, Sisko Z (1974).

Golgher L (2007).

Gomes Henriques, ÁC, Ginani F, Oliveira RM et al. (2014).

Gonçalves RV, Novaes RD, Matta SL, Benevides GP, Faria FR, Pinto MV (2010).

Gordon ZV (1970).

Gouras P (2007).

Gray CM, Singer W (1989).

Gray CM, Konig P, Engel AK, Singer W (1989).

Griffiths MJ, Garcin C, van Hille RP, Harrison ST (2011).

Grin AN (1974).

Gruenau SP, Oscar KJ, Folker, MT, Rapoport SI (1982).

Grundler W, Kaiser F (1992).

Gungormus M, Akyol UK (2009).

Gupta A, Avci P, Dai T, Huang Y, Hamblin MR (2013).

Gye MC, Park CJ (2012).

Ham, W T, Mueller HA, Ruffolo JJ, Guerry D (1980).

Dongmei H, Yang L, Chen S, Tian Y, Wu S (2012).

Havas M, Marrongelle J (2013).

Hawkins D, Abrahamse H (2007).

Helmholtz von H (1867).

Hernández-Bule ML, Paíno CL, Trillo MÁ, Úbeda A (2014).

Hirakawa, M, Tanaka M, Tanaka Y, Okubo A, Koriyama C, Tsuji M, Akiba S, Miyamoto K, Hillebrand G, Yamashita T, Sakamoto T (2008).

Hisamitsu (1997).

Homenko A, et al. (2009).

Hood DA, Zak R, Pette D (1989).

Hopper RA, VerHalen JP, Tepper O, Mehrara BJ, Detch R, Chang EI, Baharestani S, Simon BJ, Gurtner GC (2009).

Hormuzdi, SG et al. (2001).

Houreld NN, Abrahamse H (2008).

Hoshiyama M, Kakigi R, Watanabe S, Miki K, Takeshima Y (2003).

Hsu YH, Chen YC, Chen TH, Sue YM, Cheng TH, Chen JR, Chen CH (2012).

Huang PJ, Huang YC, Su MF, Yang TY, Huang JR, Jiang CP (2007).

Huang YY et al. (2013).

Hussein AJ, Alfars AA, Falih MA, Hassan AN (2011).

Ichimura S (1960).

Imai N, Kawabe M, Hikage T, Nojima T, Takahashi S, Shirai T (2011).

Iorio R, Delle Monache S, Bennato F, Di Bartolomeo C, Scrimaglio R, Cinque B, Colonna RC (2011).

Jain S, Vojisavljevic V, Pirogova E (2015).

Jauchem JR (1997).

Jauchem F et al. (2000).

Jelínek F, Saroch J, Kucera O, Hasek J, Pokorný J, Jaffrezic-Renault, Ponsonnet N (2007).

Jensh RP (1984).

Wen JS, Lai CH, Sung JM (2012).

Johnson CC, Guy AW (1972).

Johnson RB, Hamilton J, Chou CK, Guy AW (1980).

Johnson EH, Chima SC, Muirhead DE (1999).

Joliot M. et al. (1994).

Iyama T, Ebara H, Tarusawa Y, Uebayashi S, Sekijima M, Nojima T, Miyakoshi J (2004).

Kalantaryan VP (2010).

Kang KS, Hong JM, Kang MS, Rhie JW, Cho DW (2013).

Karu TI. , Ludmila V. Pyatibrat and Natalia I. Afanasyeva, A (2004).

Kereıche S, Bourinet L, Keegstra W, Arteni AA, Verbavatz JM, Boekema EJ, Robert B, Gallb A (2008).

Kesari KK, Behari J (2009).

Kesari KK, Behari J, Kumar S (2010).

Kim HS, B. J. Park, H. J. Jang et al. (2014).

Kim J. Yoon Y, Yun S, Soo Park G, June Lee H, Song K (2012).

Kim, M, Jung H, Kim S, Park JK, Seo YK (2015).

Kim YW, Kim Hs, Lee JS et al. (2009).

Kirichuck, V (2008).

Kirichuk VF, Ivanov AN (2013).

Kitchel E (2000).

Ko WS, Chen TH, Chen CH, Chen TW, Chen YC (2012).

Komine N, Ikeda K, Tada K, Hashimoto N, Sugimoto N, Tomita K (2010).

Kuchimaru T, Iwano S, Kiyama M, Mitsumata S, Kadonosono T, Niwa H, Maki S, Kizaka-Kondoh S (2016).

Khuman J, Zhang J, Park J, Carroll JD, Donahue C, et al. (2012).

Kwan (2015).

Lacjaková K, Bobrov N, Poláková M, Slezák M, Vidová M, Vasilenko T et al. (2010).

Lai and Pittelkow (2015).

Lanzafame RJ, Stadler I, Kurtz AF, Connelly R, Peter TA Sr, Brondon P, et al. (2007).

Lapchak PA, Boitano PD, Butte PV, Fisher DJ, Hölscher T, Ley EJ, Nuño M, Voie AH, Rajput PS (2015).

Lai H, Horita A, Chou CK, Guy AW (1987).

Lai H, Horita A, Chou CK, Guy AW (1988).

Lai H, Singh NP (1995).

Lee S, Johnson D, Dunbar K, Dong H, Ge X, Kim YC, Wing C, Jayathilaka N, Emmanuel N, Zhou CQ, Gerber HL, Tseng CC, Wang SM (2005).

Lee, SK, Park S, Gimm YM, Yoon-Won (2014).

Lee JS, Ahn SS, Jung KC, Kim YW, Lee SK (2004).

Lai, H, Carino MA, Horita A, Guy AW (1992).

Lass J, Tuulik, V, Ferenets, R, Riisalo, R, Hinrikus, H (2002).

Lee S, Johnson D, Dunbar K, Dong H, Ge X, Kim YC, Wing C, Jayathilaka N, Emmanuel N, Zhou CQ, Gerber HL, Tseng CC, Wang SM (2005).

Lee, SK, Park, S, Gimm, YM, Yoon-Won (2014).

Lee MW (2003).

Lei T, Jing D, Xie K, Jiang M, Li F, Cai J, Wu X, Tang C, Xu Q, Liu J, Guo W, Shen G, Luo E (2013).

Leoci R, Aiudi, G, Silvestre F., Lissner E, Lacalandra GM (2014).

Lestard NdR, Valente RC, Lopes AG, Capella MAM (2013).

Li Y, Qu X, Wang X, Liu M, Wang C, Lv Z, Li W, Tao T, Song D, Liu X (2014).

Lim WB, Kim JS, Ko YJ, Kwon H, Kim SW, Min HK, et al. (2011).

Lin CC, Liu XM, Peyton K, Wang H, Yang WC, Lin SJ, Durante W (2008).

Lin TC, Lin CS, Tsai TN, Cheng SM, Lin WS, Cheng CC, Wu CH, Hsu CH (2015).

Llinas R, Ribary U (1993).

Lisi A, Foletti A, Ledda M, Rosola E, Giuliani L, D’Emilia E, Grimaldi S (2006).

Lisi A, Foletti A, Ledda, M De Carlo, F Giuliani, L D’Emilia, E Grimaldi, S (2008).

Llinas R, Ribary U (1993).

Lobo TM, Pol DG (2015).

Loschinger M, Thumm S, Hammerle H, Rodemann HP (1999).

Lu ST, Brown DO, Johnson CE, Mathur SP, Elson E (1992).

Luben RA, Ross Adey et al. (1982).

Luukkonen J, Hakulinen P, Maki-Paakkanen J, et al. (2009).

Maes A, Collier M, Van Gorp U, Vandoninck S, Verschaeve L (1997).

Maiya GA, Kumar P, Rao L (2005).

Maiya G, Sagar M, Fernandes D (2006).

Marchionni I, Paffi A, Pellegrino M, Liberti M, Apollonio F, Abeti R, Fontana F, D’Inzeo G, Mazzanti M (2006).

Marino A, Becker R (19770.

Markov MS, Ryaby JT, Kaufman JJ, Pilla AA (1992).

Maskey D, Kim HG, Suh MW, Roh GS, Kim MJ (2014).

Mashevich M, Folkman D, Kesar A, Barbul A, Korenstein R, Jerby E, Avivi L (2003).

Maskey D, Kim HG, Suh MW, Roh GS, Kim MJ (2014).

Matic M, Lazetic B, Poljacki M, Djuran V, Matic A, Gajinov Z (2009).

Mayrovitz HN (2004).

Menteş B, Taşcilar O, Tatlicioglu E, Bor MV, Işman F, Türközkan N, Çelebi M (1996).

Meyer PF, Araújo HG, Carvalho MGF, Tatum BIS, Fernandes ICAG, Ronzio OA et al. (2010).

Millenbaugh NJ, Roth C, Sypniewska R, Chan V, Eggers JS, Kiel JL, Blystone RV, Mason PA (2008).

Mirzaei M, Bayat M, Mosafa N, Mohsenifar Z, Piryaei A, Farokhi B et al. (2007).

Moore RL (1979).

Moore P, Ridgway TD, Higbee RG, Howard EW, Lucroy MD (2005).

Murray JC, Farndale RW (1985).

Myers MR, Hardy JT, Mazel CH, Dustan P (1999).

Naeser MA, Saltmarche A, Krengel MH, Hamblin MR, Knight JA (2011).

Naeser MA, Michael R. Hamblin (2011).

Nardecchia I, Torres J, Lechelon M, Giliberti V, Ortolani M, Nouvel P, Gori M, Donato I, Preto J, Varani L, Sturgis J, Pettini M (2017).

Nascimento PM, Pinheiro AL, Salgado MA, Ramalho LM (2004).

Nazar AZMI, Dutta SK (1994).

Nemova EF, Fedorov VI (2010).

Nittby H, Brun A, Eberhardt J, Malmgren L, Persson BR, Salford LG (2009).

Nuccitelli R, Pliquett U, Chen X, Ford W, Swanson RJ, Beebe SJ, Kolb JF, Schoenbach KH (2006).

Nylund R, Leszcynski D (2006).

Oron A, Oron U, Streeter J, De Taboada L, Alexandrovich A, et al. (2007).

Oron A, Oron U, Streeter J, De Taboada L, Alexandrovich A et al. (2012).

Oscar KJ, Hawkins TD (1977).

Pasche B, Erman M, Mitler M: Diagnosis and Management of Insomnia (1990).

Pasche B, Erman M, Hayduk R, Mitler M, Reite M, Higgs L, Dafni U, Rossel C, Kuster N, Barbault A, Lebet J-P (1996).

Pasche B, Barbault (2003).

Paksy K, Thuróczy G, Forgács Z, Lázár P, Gaáti I (2000).

Palacios AG, Srivastava R, Goldsmith TH (1998).

Patruno A et al. (2009).

Paulraj R, Behari J 2012.

Pavicic I, Trosic I (2008).

Pelling AE, Sehati S, Gralla EB, Valentine JS, Gimzewski JK (2004).

Pelling AE, Sehati S, Gralla EB, Valentine JS, Gimzewski JK (2005).

Pereira AN, Eduardo CP, Matson E, Marques MM (2002).

Persinger MA (2013).

Persinger MA, Murugan NJ, Karbowski LM (2015).

Pfluger DH, Minder CE (1996).

Pikov V, Arakaki X, Harrington M, Fraser SE, Siegel PH (2010).

Pitt WG, Ross SA (2003).

Pokorny, Jelínek F, Cifra M, Pokorný J, Vanis J, Simsa J, Hasek J, Frýdlová I (2009).

Porcelli PG, Cacciapuotia S, Fuscoa R, Massab G, d'Ambrosiob C, Bertoldoa et al. (1997).

Pu et al. (1997).

Puharich A, Memories of a maverick (1974).

Pugliese LS, Medrado AP, Reis SR, Andrade ZdA (2003).

Quirk BJ, Torbey M, Buchmann E, Verma S, Whelan HT (2012).

Rabelo SB, Villaverde AB, Nicolau R, Salgado MC, Melo Mda S, Pacheco MT (2006).

Radzievsky A.A. et al. (2004).

Rahnama M. Tuszynski JA, Bókkon I, Cifra M, Sardar P, Salari V (2010).

Rannug A, Holmberg B, Ekstrom T, Mild KH (1993).

Reale M, Kamal MA, Patruno A, Costantini E, D’Angelo C, Pesce M, Greig NH (2014).

Reddy GK (2003).

Reed DD, Jones EA, Mroz GD, Liechty HO, Cattelino PJ, Jürgensen MF (1993).

Reis SR, Medrado AP, Marchionni AM, Figueira C, Fracassi LD, Knop LA (2008).

Reite M, Higgs L, Lebet JP, Barbault A, Rossel C, Kuster N, Dafni U, Amato D, Pasche B (1994).

Ren Z, Chen X, Cui G, Yin S, Chen L, Jiang J, Hu Z, Xie H, Zheng S, Zhou L (2015).

Rezende SB, Ribeiro MS, Nunez SC, Garcia VG, Maldonado EP (2007).

Ribary U. Ioannides AA, Singh KD, Hasson R, Bolton JPR, Lado F, Mogilner A, Llinas R (1991).

Riccicardi LM, Umezawa (1947).

Ricci E, Afaragan M (2010).

Ritz T, Thalau P, Phillips JB, Wiltschko R, Wiltschko W (2004).

Ritz T, Wiltschko R, Hore PJ, Rodgers CT, Stapput K, Thalau P, Timmel CR, Wiltschko W (2009).

Ross CL, Siriwardane M, Almeida-Porada G, Porada CD, Brink P, Christa GJ, Harrison BS (2015).

Rouleau N, and Dotta BT (2014).

Russell BA, Kellett N, Reilly LR (2005).

Saikin SK, Khin Y, Huh J, Hannout M, Wang Y, Zare F, Aspuru-Guzik A, Tang JKH (2014).

Salford LG, Brun A, Sturesson K, Eberhardt JL, Persson BR (1994).

Sanders AP, Schaefer DJ, Joines WT (1980).

Sannino A, Sarti M, Reddy SB, Prihoda TJ, Vijayalaxmi, Scarfì MR (2009).

Sarkar, S., Ali, S. and Bahari, J (1994).

Saygin M, Caliskan S, Karahan N, Koyu A, Gumral N, Uguz A (2011).

Sergeeva SE, Demidova O, Sinitsyna T, Goryachkovskaya A, Bryanskaya A, Semenov I, Meshcheryakova G, Popik DV, Peltek S (2016).

Shokri S, Soltani A, Kazemi M, Sardari MD, Mofrad FB (2015).

Sanchez-Vives MV, McCormick DA (2000).

Sahu S, Ghosh S, Fujita D, Bandyopadhyay A (2014).

Sancristóbal B, Vicente R, Garcia-Ojalvo J (2014).

Santoro N, Lisi A, Pozzi D, Pasquali E, Serafino A, Grimaldi S (1997).

Sausbier M, Hu H, Arntz C, Feil S, Kamm S, Adelsberger H, Sausbier U, Sailer CA, Feil R, Hofmann F, Korth M, Shipston MJ, Knaus HG, Wolfer DP, Pedroarena CM, Storm JF, Ruth P (2004).

Schindl A, Schindl M, Pernerstorfer-Schön H, Mossbacher U, Schindl L (2000).

Schirmacher A, Bahr A, Kullnick U, Stoegbauer F (1999).

Schmitz D. et al. (2001).

Shandala MG, Dumanski UD, Rudnev MI, Ershova LK, Los IP (1979).

Sharma A, Sisodia R, Bhatnaga D (2014).

Siekierzynski (1972).

Shipston, Knaus HG, Wolfer DP, Pedroarena CM, Storm JF, Ruth P (2004).

Singh N, Rudra N, Bansa P, Mathur R, Behari J, Nayar U (1994).

Sinha (2008).

Sırav B, Seyhan N (2015).

Sırav (2016).

Seeliger C, Falldorf K, Sachtleben J, Griensven M van (2014).

Segatore B, Setacci D, Bennato F, Cardigno R, Amicosante G, Iorio R (2012).

Senavirathna, MDHJ, Asaeda T, Thilakarathne BLS, Kadonoa H (2014).

Selvam R, Ganesan K, Narayana Raju KV, Gangadharan A, Manohar BM, Puvanakrishnan R (2007).

Setlow, Woodhead et al. (1993).

Sheer DE (1989).

Singh N, Rudra N, Bansal P, Mathur R, Behari J, Nayar U, Poly ADP (1994).

Shock (1995).

Shokri S, Soltani A, Kazemi M, Sardari MD, Mofrad FB (2015).

Shrivastava S, Schneider MF (2014).

Silveira PC, Silva LA, Freitas TP, Latini A, Pinho RA (2011).

Singer W (1998).

Singer W (1999).

Smick K et al. (2013).

Steriade M. et al. (1991).

Stolfa S, Skorvánek M, Stolfa P, Rosocha J, Vasko G, Sabo J (2007).

Streeter J, De Taboada L, Oron U (2004).

Suhova SV, Ivanov AN, Corableva TS et al. (2007).

Switzer WG, Mitchell DS, (1977).

Sypniewska RK, Millenbaugh NJ, Kiel JL, Blystone RV, Ringham HN, Mason PA, Witzmann FA (2010).

Tada K, Ikeda K, Tomita K (2009).

Tabrah F, Hoffmeier M, Gilbert F Jr, Batkin S, Bassett CA (1990).

Takebe H, Nakanishi Y, Hirose Y, Ochi M (2014).

Tang J, Zhang Y, Yang L, Chen Q1, Tan L, Zuo S, Feng H, Chen Z, Zhu G (2015).

Tang M, Huang Q, Wei D, Zhao G, Chang T, Kou K, Wang M, Du C, Fu W, Cui H (2015).

Taylor EM Ashleman BT (1975).

Thomas JR, Burch LS, Yeandle SC (1979).

Thomas JR, Schrot J, Banvard RA (1982).

Tice RR, Hook GG, Donner M, McRee DI, Guy AW (2002).

Tomany S.C. et al. (2004).

Tomany SC. (2008).

Tofani S, Agnesod G, Ossola P, Ferrini S, Bussi R (1986).

Tolgskaya MS, Gordon (1973).

Ueda T, Nakanishi-Ueda T, Yasuhara H, Koide R, Dawson WW (2011).

Ursache M, Mindru G, Creanga DE, Tufescu, FM, Goiceanu C (2009).

Usselman RJ, Chavarriaga C, Castello PR, Procopio M, Ritz T, Dratz EA, Singel DJ, Martino CF (2016).

Varani K, Gessi S, Merighi S, Iannotta V, Cattabriga E, Spisani S, Cadossi R, Borea AP (2002).

Vatansever F, Hamblin MR (2012).

Ventura C, Maioli M, Asara Y, Santoni D, Mesirca P, Remondini D, Bersani F (2005).

Veronesi FP, Torricelli G, Giavaresi M, Sartori F, Cavani S, Setti M, Cadossi A, Fini OM (2014).

Viegas VN, Abreu ME, Viezzer C, Machado DC, Filho MS, Silva DN, et al. (2007).

Vincenzi F, Targa M, Corciulo C, Gessi S, Merighi S, Setti S, Cadossi R, Borea PA, Varani K (2012).

Vianale G, Reale M, Amerio P, Stefanachi M, Di Luzio S, Muraro R (2008).

Viegas VN, Abreu ME, Viezzer C, Machado DC, Filho MS, Silva DN, et al. (2007).

Vojisavljevic V, Cosic I. et al. (2007).

Wake K, Mukoyama A, Watanabe S, Yamanaka Y, Uno T, Taki M (2007).

Wang LF, Li X, Gao YB, Wang SM, Zhao L, Dong J, Yao BW, Xu XP, Chang GM, Zhou HM, Hu XJ, Peng RY (2015).

Wang W, Li W, Song M, Wei S, Liu C, Yang Y, Wu H (2016).

Webb SJ, Dodds DD (1968).

Whelan HT, Smits RL Jr, Buchman EV, Whelan NT, Turner SG, Margolis DA, et al. (2001).

Wei Y, Xiaolin H, Tao S (2008).

Weiss RA, McDaniel DH, Geronemus RG, Weiss MA (2005).

Wen J, Jiang S, Chen B (2011).

Weng Y, Dang Y, Ye X, Liu N, Zhang Z, Ren Q (2011).

Whitman JC, Ward LM, Woodward TS (2013).

Williams CD, Markov MS, Hardman WE, Cameron IL (2001).

Wilmink GJ, Grundt JE (2011).

Wright WD (1946).

Wu HP, Persinger MA (2011).

Wu S (2013).

Xuan W, Hamblin MR. et al. (2013).

Xuan W, Vatansever F, Huang L, Hamblin MR (2014).

Yang YQ, Tan YY, Wong R, Wenden A, Zhang LK, Rabie AB (2012).

Yasukawa A, Hrui H, Koyama Y, Nagai M, Takakuda K (2007).

Ylinen A, Bragin A, Nadasdy Z, Jando G, Szabo I, Sik A, Buzsaki G (1995).

Yoon YJ, Li G, Kim GC, Lee HJ, Song K (2015).

Yu HS, K. L. Chang, C. L. Yu, J.W. Chen, and G. S. Chen (1996).

Yu HS, Wu CS, Yu CL, Kao YH, Chiou MH (2003).

Yu L, Dyer JW, Scherlag BJ, Stavrakis S, Sha Y, Sheng X, Garabelli P, Jacobson J, Po SS (2015).

Yu W, Naim JO, Lanzafame RJ (1997).

Yu SY, Chiu JH, Yang SD, Hsu YC, Lui WY, Wu CW (2006).

Zahanich I, Sirenko SG, Maltseva LA, et al. (2011).

Zhang Y, Li Z, Gao Y, Zhang C (2014).

Zhang Y, Li Z, Gao Y, Zhang C (2015).

Zhang X, Zhang H, Zheng C, Li C, Zhang X, Xiong W (2002).

Zmyslony M, Politanski P, Rajkowska E, et al. (2004).

Zong C, Ji Y, He Q, Zhu S, Qin F, Tong J, Cao Y (2015).

Zou H, Mellon S, Syms RR, Tanner KE (2006).

Coherent frequencies that stabilize living cells and calculated acoustic reference frequency.