scholarly journals ON THE DNA OF ELEVEN MAMMALS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250074 ◽  
Author(s):  
J. TENREIRO MACHADO ◽  
ANTÓNIO C. COSTA ◽  
MARIA DULCE QUELHAS
Keyword(s):  
Fourier Transform ◽  
Long Range ◽  
Power Law ◽  
Fractional Dynamics ◽  
Categorical Representation ◽  
Memory Characteristics

This paper studies the DNA code of eleven mammals from the perspective of fractional dynamics. The application of Fourier transform and power law trendlines leads to a categorical representation of species and chromosomes. The DNA information reveals long range memory characteristics.

scholarly journals And I say to myself: “What a fractional world!”

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
J. Tenreiro Machado
Keyword(s):  
Global Warming ◽  
Fourier Transform ◽  
Fractional Calculus ◽  
Complex Systems ◽  
Power Law ◽  
Deoxyribonucleic Acid ◽  
Warming Trend ◽  
Fractional Dynamics ◽  
The Fourier Transform ◽  
Musical Rhythms

AbstractThis paper discusses several complex systems in the perspective of fractional dynamics. For prototype systems are considered the cases of deoxyribonucleic acid decoding, financial evolution, earthquakes events, global warming trend, and musical rhythms. The application of the Fourier transform and of the power law trendlines leads to an assertive representation of the dynamics and to a simple comparison of their characteristics. Moreover, the gallery of different systems, both natural and man made, demonstrates the richness of phenomena that can be described and studied with the tools of fractional calculus.

scholarly journals Power-law bounds for critical long-range percolation below the upper-critical dimension

2021 ◽  
Author(s):  
Tom Hutchcroft
Keyword(s):  
Long Range ◽  
Power Law ◽  
Upper Bound ◽  
Mean Field ◽  
Maximum Size ◽  
Finite Graph ◽  
Critical Dimension ◽  
Point Function ◽  
Upper Critical Dimension ◽  
Infinite Cluster

AbstractWe study long-range Bernoulli percolation on $${\mathbb {Z}}^d$$ Z d in which each two vertices x and y are connected by an edge with probability $$1-\exp (-\beta \Vert x-y\Vert ^{-d-\alpha })$$ 1 - exp ( - β ‖ x - y ‖ - d - α ) . It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if $$0<\alpha <d$$ 0 < α < d then there is no infinite cluster at the critical parameter $$\beta _c$$ β c . We give a new, quantitative proof of this theorem establishing the power-law upper bound $$\begin{aligned} {\mathbf {P}}_{\beta _c}\bigl (|K|\ge n\bigr ) \le C n^{-(d-\alpha )/(2d+\alpha )} \end{aligned}$$ P β c ( | K | ≥ n ) ≤ C n - ( d - α ) / ( 2 d + α ) for every $$n\ge 1$$ n ≥ 1 , where K is the cluster of the origin. We believe that this is the first rigorous power-law upper bound for a Bernoulli percolation model that is neither planar nor expected to exhibit mean-field critical behaviour. As part of the proof, we establish a universal inequality implying that the maximum size of a cluster in percolation on any finite graph is of the same order as its mean with high probability. We apply this inequality to derive a new rigorous hyperscaling inequality $$(2-\eta )(\delta +1)\le d(\delta -1)$$ ( 2 - η ) ( δ + 1 ) ≤ d ( δ - 1 ) relating the cluster-volume exponent $$\delta $$ δ and two-point function exponent $$\eta $$ η .

Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (04) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob. 34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

scholarly journals Mirror and Circular Symmetry of Autofocusing Beams

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1794
Author(s):  
Svetlana N. Khonina
Keyword(s):  
Fourier Transform ◽  
Gaussian Beam ◽  
Field Distribution ◽  
Power Law ◽  
Fractional Fourier Transform ◽  
Crucial Importance ◽  
Fraunhofer Diffraction ◽  
Circular Symmetry ◽  
Symmetrization Method

This article demonstrates the crucial importance of the symmetrization method for the formation of autofocusing beams. It is possible to impart autofocusing properties to rather arbitrary distributions, for example, truncated and inverted classical modes (such as Hermite–Gaussian, Laguerre–Gaussian, and Bessel modes) or shift the fundamental Gaussian beam by inserting mirror or circular symmetry. The most convenient for controlling autofocusing characteristics is the truncated sinus function with a power-law argument dependence. In this case, superlinear chirp beams (with power q > 2) exhibit sudden and more abrupt autofocusing than sublinear chirp beams (with power 1 < q < 2). Comparison of the different beams’ propagation is performed using fractional Fourier transform, which allows obtaining the field distribution in any paraxial region (both in the Fresnel and Fraunhofer diffraction regions). The obtained results expand the capabilities of structured beams in various applications in optics and photonics.

scholarly journals RESTRICTIONS ON THE HYPOTHETICAL LONG RANGE INTERACTIONS FROM THE CASIMIR-TYPE NULL EXPERIMENT WITH THREE TEST BODIES

1994 ◽  
Vol 09 (29) ◽  
pp. 2671-2680 ◽  
Author(s):  
M. BORDAG ◽  
V. M. MOSTEPANENKO ◽  
I. YU. SOKOLOV
Keyword(s):  
Long Range ◽  
Power Law ◽  
Casimir Force ◽  
Power Laws ◽  
Gravitational Attraction ◽  
Spherical Lens ◽  
Plane Plate ◽  
Wide Range ◽  
Long Range Interactions

A realistic null experiment is suggested in which the Casimir force between a plane plate and a spherical lens is compensated by the force of gravitational attraction. This configuration is shown to be very sensitive to the existence of additional hypothetical forces of Yukawa-type or power laws. From the suggested null experiment the restrictions on the Yukawa constant α can be strengthened by a factor up to 1000 in a wide range 10−8 m < λ < 10−4 m and by a factor of 10 for λ from several centimeters to several meters. For power law interactions the strengthening of restrictions by a factor of 20 is possible for the force decreasing as r−5.

scholarly journals Finite-size effects in disordered λφ4 model

2016 ◽  
Vol 30 (30) ◽  
pp. 1650207 ◽  
Author(s):  
R. Acosta Diaz ◽  
N. F. Svaiter
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Power Law ◽  
Order Phase Transition ◽  
Size Effects ◽  
Finite Size ◽  
Second Order ◽  
Finite Size Effects ◽  
Power Law Decay ◽  
Second Order Phase Transition

We discuss finite-size effects in one disordered [Formula: see text] model defined in a [Formula: see text]-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a quenched random field. In order to obtain the average value of the free energy of the system, we use the replica method. We first discuss finite-size effects in the one-loop approximation in [Formula: see text] and [Formula: see text]. We show that in both cases, there is a critical length where the system develop a second-order phase transition, when the system presents long-range correlations with power-law decay. Next, we improve the above result studying the gap equation for the size-dependent squared mass, using the composite field operator method. We obtain again that the system present a second-order phase transition with long-range correlation with power-law decay.

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