Discrete mean square approximation applied to error calculation in biomolecules and brownian motion

2021 ◽  
Author(s):  
Branislav Randjelovic ◽  
Bojana Markovic ◽  
Vojislav V. Mitic ◽  
Sanja Aleksic ◽  
Dusan Milosevic ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Condensed Matter ◽  
Research Data ◽  
Mean Square ◽  
Fractal Nature ◽  
External Energy ◽  
The Earth ◽  
Whole Space ◽  
Get Complex ◽  
Research Frontiers

Advanced research frontiers are extended from biophysics relations on the Earth upto the discovering any type of alive matter within the whole space. Microorganisms’ motion within the molecular biology processes integrates variety of microorgnisms functions. In continuation of our Brownian motion phenomena research, we consistently build molecular-microorganisms structures hierarchy. We recognize everywhere biomimetic similarities between the particles in alive and nonalive matter. The research data are based on real experiments, without external energy impulses. So, we develop the analysis, inspired by fractal nature Brownian motion, as recognized joint parameter between particles in alive and nonalive biophysical systems. This is also in line with advance trends in hybrid submicroelectronic integrations. The important innovation in this paper is that we introduced approximation of trajectory and error calculations, using discrete mean square approximation, what cumulatively provide much more precise biophysical systems parameters. By this paper, we continue to generate new knowledge in direction to get complex relations between the particles clusters in biophysical systems condensed matter.

Interpolation Methods Applied on Biomolecules and Condensed Matter Brownian Motion

2021 ◽  
Author(s):  
Sanja Aleksic ◽  
Bojana Markovic ◽  
Vojislav V. Mitic ◽  
Dusan Milosevic ◽  
Mimica Milosevic ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Condensed Matter ◽  
Particle Systems ◽  
Fractal Nature ◽  
New Approach ◽  
Motion Data ◽  
Joint Properties ◽  
Physical Particle ◽  
High Level ◽  
Advanced Development

Biophysical and condensed matter systems connection is of great importance nowadays due to the need for a new approach in microelectronic biodevices, biocomputers or biochips advanced development. Considering that the living and nonliving systems’ submicroparticles are identical, we can establish the biunivocally correspondent relation between these two particle systems, as a biomimetic correlation based on Brownian motion fractal nature similarities, as the integrative property. In our research, we used the experimental results of bacterial motion under the influence of energetic impulses, like music, and also some biomolecule motion data. Our goal is to define the relation between biophysical and physical particle systems, by introducing mathematical analytical forms and applying Brownian motion fractal nature characterization and fractal interpolation. This work is an advanced research in the field of new solutions for high-level microelectronic integrations, which include submicrobiosystems like part of even organic microelectronic considerations, together with some physical systems of particles in solid-state solutions as a nonorganic part. Our research is based on Brownian motion minimal joint properties within the integrated biophysical systems in the wholeness of nature.

scholarly journals Processes and Procedures for Data Publication: A Case Study in the Geosciences

2013 ◽  
Vol 8 (1) ◽  
pp. 193-203 ◽  
Author(s):  
Sarah Callaghan ◽  
Fiona Murphy ◽  
Jonathan Tedds ◽  
Rob Allan ◽  
John Kunze ◽  
...  
Keyword(s):  
Earth Sciences ◽  
Research Data ◽  
Academic Publishing ◽  
Data Repository ◽  
Data Publication ◽  
The Earth ◽  
Policies And Procedures ◽  
Wide Range ◽  
Key Issues ◽  
Work Done

The Peer REview for Publication and Accreditation of Research Data in the Earth sciences (PREPARDE) project is a JISC and NERC funded project which aims to investigate the policies and procedures required for the formal publication of research data, ranging from ingestion into a data repository, through to formal publication in a data journal. It also addresses key issues arising in the data publication paradigm, including, but not limited to, issues related to how one peer reviews a dataset, what criteria are needed for a repository to be considered objectively trustworthy, and how datasets and journal publications can be effectively cross-linked for the benefit of the wider research community. PREPARDE brings together a wide range of experts in the research, academic publishing and data management fields both within the Earth Sciences and in the broader life sciences with the aim of producing general guidelines applicable to a wide range of scientific disciplines and data publication types. This paper provides details of the work done in the first half of the project; the project itself will be completed in June 2013.

scholarly journals Geometric Brownian motion with delay: mean square characterisation

2008 ◽  
Vol 137 (01) ◽  
pp. 339-348 ◽  
Author(s):  
John A. D. Appleby ◽  
Xuerong Mao ◽  
Markus Riedle
Keyword(s):  
Brownian Motion ◽  
Geometric Brownian Motion ◽  
Mean Square

scholarly journals Evaluation of Gravity Data Derived from Global Gravity Field Models Using Terrestrial Gravity Data in Enugu State, Nigeria

2018 ◽  
Vol 8 (1) ◽  
pp. 145-153 ◽  
Author(s):  
O.I. Apeh ◽  
E.C. Moka ◽  
V.N. Uzodinma
Keyword(s):  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Mean Square ◽  
Bouguer Gravity ◽  
Bouguer Anomalies ◽  
The Earth ◽  
Global Gravity ◽  
Enugu State ◽  
Gravity Field Models

Abstract Spherical harmonic expansion is a commonly applied mathematical representation of the earth’s gravity field. This representation is implied by the potential coeffcients determined by using elements/parameters of the field observed on the surface of the earth and/or in space outside the earth in the spherical harmonic expansion of the field. International Centre for Gravity Earth Models (ICGEM) publishes, from time to time, Global Gravity Field Models (GGMs) that have been developed. These GGMs need evaluation with terrestrial data of different locations to ascertain their accuracy for application in those locations. In this study, Bouguer gravity anomalies derived from a total of eleven (11) recent GGMs, using sixty sample points, were evaluated by means of Root-Mean-Square difference and correlation coeficient. The Root-Mean-Square differences of the computed Bouguer anomalies from ICGEMwebsite compared to their positionally corresponding terrestrial Bouguer anomalies range from 9.530mgal to 37.113mgal. Additionally, the correlation coe_cients of the structure of the signal of the terrestrial and GGM-derived Bouguer anomalies range from 0.480 to 0.879. It was observed that GECO derived Bouguer gravity anomalies have the best signal structure relationship with the terrestrial data than the other ten GGMs. We also discovered that EIGEN-6C4 and GECO derived Bouguer anomalies have enormous potential to be used as supplements to the terrestrial Bouguer anomalies for Enugu State, Nigeria.

scholarly journals Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Longjin Lv ◽  
Luna Wang
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Dispersion Equation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
European Option ◽  
Stochastic Representation ◽  
Pricing Models ◽  
Advection Dispersion ◽  
Black Scholes

In this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. Then, applying the subordinated Brownian motion into the option pricing problem, we obtain the closed-form pricing formula for the European option, when the underlying of the option contract is supposed to be driven by the subordinated geometric Brownian motion. At last, we compare the obtained option pricing models with the classical Black–Scholes ones.

Brownian Motion on Cantor Sets

2020 ◽  
Vol 21 (3-4) ◽  
pp. 275-281
Author(s):  
Ali Khalili Golmankhaneh ◽  
Saleh Ashrafi ◽  
Dumitru Baleanu ◽  
Arran Fernandez
Keyword(s):  
Brownian Motion ◽  
Classical Method ◽  
Mean Square Displacement ◽  
Planck Equation ◽  
Cantor Sets ◽  
Mean Square ◽  
Fokker Planck Equation ◽  
Fractal Time ◽  
The Mean ◽  
Fokker Planck

AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

scholarly journals Emergent Structure: the First Two Centuries of the First Two Eons

2005 ◽  
Vol 216 ◽  
pp. 161-169
Author(s):  
Virginia Trimble
Keyword(s):  
Large Scale ◽  
Vantage Point ◽  
Fractal Nature ◽  
Linear Fashion ◽  
Voronoi Tesselation ◽  
The Earth ◽  
External Galaxies ◽  
Emergent Structure ◽  
The Universe ◽  
Early Maps

“Early” maps of the cosmos included the 26th dynasty air god Shu supporting the sky goddess Nut above the earth god Geb, Descartes' Voronoi tesselation, William Herschel's star gauging, and Carl Charlier's 1922 plot of the nebulae in NGC, which he intended as observational support for the fractal nature of large scale cosmic structure (about which he was probably wrong, though right about there being more than one level of clustering). Because Shapley, van Maanen, and others were still denying the very existence of external galaxies at the same time that Lundmark and Opik were measuring their distances and masses and Charlier plotting hierarchies, the story of the discovery of very large scale structure (and streaming) in the universe cannot be told in perfectly linear fashion. There are, however, half a dozen or so discrete phases that can be recognized and three underlying themes, (1) expanding horizons, (2) additional levels of structure, and (3) increasing mediocrity of our vantage point.

scholarly journals Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Long Shi ◽  
Aiguo Xiao
Keyword(s):  
Brownian Motion ◽  
Continuous Time ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Weak Ergodicity ◽  
Normal Diffusion ◽  
Weak Ergodicity Breaking ◽  
The Mean ◽  
Ergodicity Breaking

We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<1. The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered.

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