A brief history of cosmology and cosmological models of our universe

Cosmology is the study of the origin, structure, evolution  and changes in the Universe.  In this talk, I will present a brief history of cosmology and the cosmological models of our Universe from  Babylonians' cosmology  to recent ones.

Prof. Bang-yen Chen is a University Distinguished Professor of  Michigan State University. In 2008 he was the first recipient of the Simon Stevin Prize for Geometry.

Exploring the Willmore-Chen inequality for n-dimensional compact spacelike submanifolds in (n+2)-dimensional Lorentz-Minkowski spacetime

For any (oriented) compact surface M2 in 3-dimensional Euclidean space E3, T.J. Willmore  proved that any n2-dimensional compact submanifold Mn in m-dimensional Euclidean space Em,  where H is the mean curvature vector field of the submanifold and Sn the n-dimensional unit round sphere. Moreover, the equality holds if and only if Mn is embedded as a totally umbilical round sphere in an (n + 1)-dimensional affine subspace of Em, [1]. 

In this talk, we will show that this Willmore-Chen inequality does not hold for any n-dimensional compact spacelike submanifold in (n + p)-dimensional Lorentz-Minkowski spacetime Ln+p, p   Even more, that the equality in Willmore-Chen inequality does not characterize the extrinsic geometry of the spacelike submanifold. Moreover, we will explain an extension of the Willmore-Chen inequality to certain codimension two compact spacelike submanifolds in L6 in such way that the equality characterizes the extrinsic geometry of the spacelike submanifold.

Alfonso Romero is Professor of Mathematics, University of Granada in Spain.

General Relativity and the Physics of Neutron Stars

Imagine the universe's most extreme environments: Neutron stars, born in the fiery deaths of massive stars, pose a compelling challenge to general relativity. This talk explores how Einstein's theory helps us understand these fascinating remnants. In the last one-two decades, pulsars like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SAX J1808.4-3658, and Her X-1 have significantly advanced our understanding of these supermassive objects, both observationally and theoretically. The recent discovery of PSR J0952-0607 by the Fermi Gamma-ray Space Telescope further fuels this investigation. 

By combining theoretical models based on Einstein's field equations with meticulous observations, we can gain more profound insights into the physics of these compact objects and potentially uncover new information about the extremities that dwell in the universe. This work has far-reaching implications for our understanding of general relativity and the behaviour of matter under extreme pressure and density.

Dishant Pandya is at the Departement of Mathematics at Pandit Deendayal Energy University, India

Finsler Spacetimes, Observers and Applications

In classical relativity theory, different observers measure space and time and their measurements are coherent in a precise way (related by Lorentz transformations). However, in trying to unify relativity with quantum theory, small anisotropies may be introduced on spacetime, and their effects may add up to break the classical Lorentz symmetry. This gives rise to Finsler spacetimes.

After covering their geometric foundations, we will discuss their surprisingly large array of applications. First, we will comment on anisotropic propagation of signals and, particularly, the refined modelling of wildfires. Then, we will focus on recently studied new phenomena in cosmology. These have the potential to explain measurements such as the accelerated expansion of the universe as purely geometrical effects, without the need of introducing dark energy or dark matter.

Fidel Fernández Villaseñor is at the University of Granada, Joint work with, Miguel Sánchez (Univ. of Granada) and Miguel Ángel Javaloyes (University of Murcia)

Genetic Boolean-logical coding, cyclicity in the living organisms, and cyclic Gray codes. Collective algebraic-logical consciousness.

 When dealing with the problem of consciousness and artificial intelligence, we must remember the following well-known position: without mathematical logic, discussions about whether a machine can think lose all ground, and the urgent problem of creating artificial intelligence becomes meaningless. 

Living organisms are endowed with an innate ability for conscious actions in search of food, escape from predators, construction of structures, etc. Even organisms lacking nerve cells are endowed with a similar ability. It is characteristic that the physiology of active tissues is based on the fundamental binary law of "all or nothing": a nerve cell and a muscle unit give only "yes" or "no" answers to the actions of various stimuli. They do not respond to subthreshold stimuli, but they respond to suprathreshold stimuli with full amplitude. This is associated with the work of computer triggers (hypotheses about living bodies as computers have long been known).

Crocodiles and turtles, having hatched from an egg, immediately crawl to the water with quite coordinated movements based on the logically coordinated activity of millions of their binary-working nerve and muscle cells. Such facts about genetically inherited bodies suggest a possible connection between the genetic coding system and the Boolean algebra of logic.

The objectives of the report: 1) to show the connection between the genetic coding system and the Boolean algebra of logic and Gray's cyclic codes; 2) to argue the author's statement on the existence - in addition to the well-known genetic 3-plet code of amino acid sequences of proteins - of a more general genetic n-plet code of Boolean functions, which is important for understanding the inherited logic of interactions of body parts; 3) to present the concept of "collective algebraic consciousness" associated with the Boolean genetic code, as a subsection of the general topic of consciousness; 4) to present universal rules of stochastic organization of nucleotide sequences of genomic DNA.

Prof. Serge Petoukhov is Chief of Laboratory of Biomechanical Systems, and Mechanical Engineering at the Russian Academy of Sciences in Moscow.

Geometric changes in plants due to stress: a morphogenetic syndrome’

Plant stress is a theme usually considered from a very anthropocentric perspective: if there is any basic definition at all, stress is defined as any set of environmental conditions that causes suboptimal growth responses in plants (which are, even more so, usually crops). This reduction in growth is in turn usually measured in terms of growth deficits – plants form less biomass (read – there is less to be harvested). Moreover, plant stress physiology traditionally investigates the biochemical, metabolic and transcriptional changes exhibited by the subject of the stress. 

Analysis of distinctly scarce morphological data has demonstrated that plants may acclimatize to stress conditions by changing the rate and directions of growth, however, adding a geometric dimension to the plant stress response. This acclimation strategy, termed “stress-induced morphogenesis response” (SIMR) has been observed in plants exposed to heavy metals, salt, phosphate deficiency, UV light, mechanical touch, and even biotic factors (such as fungi and bacteria). The syndrome manifests itself through an inhibition of root and shoot elongation, and the formation of additional lateral meristems, giving the plant a bush-like appearance. Regulation of the onset of this phenotype seems linked to the plant stress hormone auxin. Ecologically, SIMR may be a plant’s interpretation of the animal adage “fight or flight”. 

Lastly, SIMR may point towards a more plant-centric interpretation of the concept of stress. Following a more thermodynamic point of view as presented by Lichtenthaler or Tsimilli-Michael, plants may simply be trying to live in harmony with their biotic and abiotic environments, maximizing survival, instead of maximizing productivity. 

Geert Potters is professor biology at the Maritime Academy, Antwerp, Belgium

Deterministic Constrained Synthesis Technique for Conformal Aperiodic Linear Antenna Arrays

Abstract: A deterministic approach to the synthesis of a general aperiodic arc or ring antenna array is presented and thoroughly detailed in this paper. The proposed technique, which is based on the auxiliary array pattern concept, is aimed at the semianalytical determination of the optimal excitation tapering and array element angular distribution for mimicking a given radiation pattern mask without resorting to any optimization procedure. This, in turn, enables a dramatic reduction in design times. The developed technique is validated by application to the synthesis of antenna arrays adopted in satellite communications and radar applications.

Diego Caratelli is an associate professor at TU/e Eindhoven, and co-founder and CTO of The Antenna Company (www.antennacompany.com)

Deep Learning Architectures for Classification and Regression. A Mathematical Point of View

Among the many variants of Deep learning architectures, Recurrent Neural Networks are particularly effective in managing sequential and temporal data, thanks to their ability to maintain internal memory.  They can be used for classification and regression tasks in a wide range of scenarios, such as electrical signal recognition, energy production or consumption profiles prediction, time series analysis or, in the biological field, the recognition of geometric shapes in Nature. In this context, hybrid forms of neural networks for multivariate data analysis will also be presented. The analysis of the underlying mathematical models will show how different sets of hyperparameters can significantly affect the final performance, in terms of accuracy, error and computational costs.

Silvia Licciardi is associate professor of mathematics at the University of Palermo

Mass-Energy-Information Equivalence, Gielis Transformation, and Circular Tai-Chi Motions of Mind

In 1961, Rolf Landauer formulated a principle stating that logical irreversibility implies physical irreversibility and demonstrated that information is physical. Based on Landauer’s principle, Melvin Vopson proposed mass-energy-information equivalence principle (M/E/I principle) in 1996. It states that a bit of information is not just physical, but it has a finite and quantifiable mass while it stores information. Information itself can be considered as a form of energy, and therefore, can be linked to mass, meaning that the storage and processing of information within the brain requires energy expenditure and is physically manifested within the brain's structure. In this talk we review Tai-Chi motions.  Mathematically each set in Tai -Chi practice is a circle, and alternating sides start or completes cycles. Tai-Chi motion involves focusing on each motion and becoming aware of the processes in the body, energy, and mind. The goal of Tai-Chi is to create geometric harmony between the mind and body by cultivating the flow of inner life energy (qi). We show that Tai-Chi motion is a geometric circular motion of body mass movement, breathing energy exchanges, and mind information intention, and demonstrate that circular Tai-Chi motions support the M/E/I principle. We also demonstrate that Tai-Chi motion can be viewed as a type of Gielis Transformation.

Matthew He is professor mathematics of the Halmos College of Arts and Sciences of Nova Southeastern University, Florida, USA.  Notable is the long-term collaboration with Sergey Petoukhov on DNA and Information.