Ioannis Gkigkitzis

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

Mathematical representations of brain networks in neuroscience through the use of graph theory may be very useful for the understanding of neurological diseases and disorders and such an explanatory power is currently under intense investigation. Graph metrics are expected to vary across subjects and are likely to reflect behavioural and cognitive performances. The challenge is to set up a framework that can explain how behaviour, cognition, memory, and other brain properties can emerge through the combined interactions of neurons, ensembles of neurons, and larger-scale brain regions that make information transfer possible. "Hidden" graph theoretic properties in the construction of brain networks may limit or enhance brain functionality and may be representative of aspects of human psychology. As theorems emerge from simple mathematical properties of graphs, similarly, cognition and behaviour may emerge from the molecular, cellular and brain region substrate interactions. In this review report, we identify some studies in the current literature that have used graph theoretical metrics to extract neurobiological conclusions, we briefly discuss the link with the human connectome project as an effort to integrate human data that may aid the study of emergent patterns and we suggest a way to start categorizing diseases according to their brain network pathologies as these are measured by graph theory.

Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human brain and cognition.

We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on the orbiting body. More specifically, two equations are derived to approximate the perigee/perihelion/periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the quantum as well as post- Newtonian accelerations. Numerical results have been obtained for the artificial Earth satellite Molnya, Mercury, and, finally, the for the HW Vir c, planetary companion.

The aim of this report is to propose a new methodology to treat prostate cancer with macro-rod-shaped gold seeds irradiated with ultrasound and develop a new computational method for temperature and thermal dose control of hyperthermia therapy induced by the proposed procedure. A computer code representation, based on the bio-heat diffusion equation, was developed to calculate the heat deposition and temperature elevation patterns in a gold rod and in the tissue surrounding it as a result of different therapy durations and ultrasound power simulations. The numerical results computed provide quantitative information on the interaction between high-energy ultrasound, gold seeds and biological tissues and can replicate the pattern observed in experimental studies. The effect of differences in shapes and sizes of gold rod targets irradiated with ultrasound is calculated and the heat enhancement and the bio-heat transfer in tissue are analyzed.

In this chapter, we study Sedimentation…?>the effects of the acceleration gravity on the sedimentation deposition probability, as well as the aerosol deposition rate on the surface of the Earth and Mars, but also aboard a spacecraft in orbit around Earth and Mars as well for particles with density ρ _p = 1,300 kg/m³, diameters d _p = 1, 3, 5 μm, and residence times t = 0.0272, 0.2 s, respectively. For particles of diameter 1 μm we find that, on the surface of Earth and Mars the deposition probabilities are higher at the poles when compared to the ones at the equator. Similarly, on the surface of the Earth we find that the deposition probabilities exhibit 0.5 and 0.4 % higher percentage difference at the poles when compared to that of the equator, for the corresponding residence times. Moreover in orbit equatorial orbits result to higher deposition probabilities when compared to polar ones. For both residence times particles with the diameters considered above in circular and elliptical orbits around Mars, the deposition probabilities appear to be the same for all orbital inclinations. Sedimentation probability increases drastically with particle diameter and orbital eccentricity of the orbiting spacecraft. Finally, as an alternative framework for the study of interaction and the effect of gravity in biology, and in particular gravity and the respiratory system we introduce is the term information in a way Shannon has introduced it, considering the sedimentation probability as a random variable. This can be thought as a way in which gravity enters the cognitive processes of the system (processing of information) in the cybernetic sense.

This study contains a discussion on the connection between current mathematical and biological modeling systems in response to the main research need for the development of a new mathematical theory for study of cell survival after medical treatment and cell biological behavior in general. This is a discussion of suggested future research directions and relations with interdisciplinary science. In an effort to establish the foundations for a possible framework that may be adopted to study and analyze the process of cell survival during treatment, we investigate the organic connection among an axiomatic system foundation, a predator–prey rate equation, and information theoretic signal processing. A new set theoretic approach is also introduced through the definition of cell survival units or cell survival units indicating the use of “proper classes” according to the Zermelo–Fraenkel set theory and the axiom of choice, as the mathematics appropriate for the development of biological theory of cell survival.