It is known that linearization of the Einstein equations for a nearly-flat spacetime metric (weak gravitational field) leads to a set of equations that resembles Maxwell's formalism.
From an experimental point of view, it has been shown that generalized electric-type fields can be induced in (super)conductors by the presence of the Earth’s weak gravitational field. These observations led to the formal introduction of a fundamental, modified electric-type field, characterized by an electrical component and a gravitational one, determining detectable corrections to the free fall of charged particles.
The above remarkable experimental results can be now combined to the theoretical weak-field gravity formulation, leading to a more general definition of new generalized electromagnetic fields. The latter feature a component defined in terms of the weak gravitational perturbations, and satisfy a specific set of equations that can be put in a form closely analogous to Maxwell's equations. This symmetry is then exploited to analyze a gravity/superconductivity interplay, the new generalized fields being involved in quantum effects originating from the interaction with the weak gravitational background (in analogy to what happens for gravity-induced electric fields in superconductors).
In particular, the emerging formal symmetry between the Maxwell and weak gravity equations allows to use the Ginzburg–Landau model for the description of the physics, resulting in a mean-field theory for the system's thermodynamics, including the effects of thermal fluctuations. We then analyse how the local gravitational field could couple to the superfluid condensate in the superconductor, making use of the time-dependent Ginzburg–Landau equations in the regime of fluctuations. Special symmetries of the system of differential equations will be also used to obtain analytic solutions, explicitly describing the effects of the proposed interplay.

The dependence relations have been recently introduced to better describe, from an algebraically point of view, the interdependencies between sets of elements that appear in nature in numerous models, as for example, environmental variables, pieces of secrets, characteristics of materials, etc. These relations are not viewed as n-ary relations and generally they are not symmetric or transitive, while the reflexivity property is without any significant meaning. In simple words, a dependence relations can be read as a formula expressing that the value of one variable (situated on the left hand side of the relation) depends on the values of other variables (written on the right hand side of the relation). Therefore we can say that one variable has an impact or an influence on other variables and we are interested in characterizing these two degrees of impact and influence. In an initial study on this argument, the thoey of algebraic hypercompositional structures has proved to be a useful tool to study the dependence relations. In this note we will continue in this direction, aiming to involve also some elements from fuzzy set theory.

We demonstrate in this talk that any non-Abelian gauge theory (with and without couplings to gauge-nonsinglet matter fields) can be expressed classically as an Abelian gauge theory with global non-Abelian symmetry with specific interactions derived by a recursive Noether coupling scheme. We clarify the role of spacetime transverse projections in this classical formulation, based on a publication co-authored by one of us (PM) in the journal Symmetry in 2019. We analyze how this classical equivalence translates into a possible quantum equivalence, using the functional integral formalism for the deconstructed gauge theory. In particular we explore whether the Abelian gauge theory with non-Abelian global symmetry can reproduce two key properties of any quantum non-Abelian gauge theory : asymptotic freedom (a perturbative consequence)and the existence of a mass gap in its non-perturbative spectrum following Feynman's classic work of 1981. The successes and pitfalls we encounter will be discussed. The programme, if successful, will provide an easier path to quantize fundamental theories of strong, weak and electromagnetic ineractions

The modified gravity models with higher derivatives with respect to scalar curvature can be transformed to GR with a few scalar fields using Lagrange multipliers and a conformal transformation from Jordan to Einstein frame. Such resulting models can be presented as Chiral Self-Gravitating Models with fixed functional dependence for a chiral (target) space and the potential energy.

In the present contribution, we study Killing symmetries for the chiral spaces corresponding to f(R, (\nabla R)^2), f(R, \Box R) and few versions of f(R, (\nabla R)^2, \Box R) gravity. Special investigation is devoted to the modified f(R) gravity with a kinetic scalar curvature of the form: f(R, (\nabla R)^2, \Box R)=f_1(R) +X(R) \nabla_\mu R \nabla^\mu R. We investigate connection of obtained Killing vectors of target space with Killing symmetry of Friedmann-Robertson-Walker and spherically symmetric spacetimes with the aim to find exact solutions of the models under consideration.

Error-control codes are used to detect and correct errors that occur when data are transmitted across some noisy channel or stored on some medium. The study of error-control codes is called coding theory and emerged in 1948 by Claud Shannon's paper which demonstrated that by proper encoding of the data, errors induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transmission. Some algebraic structures, includes the study and discovery of various coding schemes, are used to increase the number of errors that can be corrected during data transmission. One of the classes of logical algebra is ordered algebras which were introduced by Imai and Iseki in 1966. In this note, I study the codes generating by the ordered algebraic structures such as BCK-algebras and BL-algebras. For this goal, symmetric relations on these ordered structures facilitate us to design the correspondence codeword. Moreover, I show that the structure of ordered algebra and the code generated by it will be the same.

In this work, we present the study of thermal properties of a relativistic quantum system describing the oscillatory motion of DKP particle (spins 0 and 1) under the effect of an external magnetic field in non-commutative space.In the first step, which is in the case of spin 0, the motion equation is reduced to the Klein-Gordon problem with the same interaction, where the spectrum energy and wave functions are then deduced using the confluent hypergeometric method. In the second step, which dealing with the case of spin 1, we have subtracted that the problem is analogous to the behavior of the DKP equation of spin 1 describing the motion of a vector boson subjected to the action of a constant magnetic field in a commutative space, with additional correction depending on the parameter of non-commutatively,so that the problem refer to the non relativistic limit in order to obtain the spectrum. In the end, we analyze the system’s thermodynamic properties.

Tumor cell progression and metastasis are complex phenomena, which involve ongoing molecular and cellular changes. Despite the considerable progress that has been made in the fundamental understanding of the biological and genetic events governing both phenomena, there is still much to be elucidated with regard to the impact of the tumor microenvironment on tumor initiation and progression and the response to treatment. As such, the development of a theory correlating tumor cell progression and metastasis with biomechanical abnormalities in tumors and their microenvironment due to the continuous buildup of mechanical stresses may be viewed as a timely – and indeed urgent – need.

We present ongoing development of the rheological model capable to simulate for tumor cell progression and metastasis by focusing on epithelial to mesenchymal transition (EMT) in carcinomas. The model treats the carcinoma as visco-elastic fluid and aims to be able: (i) to account for the mechanical properties and the structural alterations caused by the EMT, (ii) to model the motility of both individual cells and cell colonies, and (iii) to take into account realistic variations in the sizes and shapes of cells in different regions of the cell colony.

The digital images of carcinomas obtained by employing of the developed model have been extensively validated by comparison with the data available in the literature in terms of the conservation of area after cell division, the cell area doubling time, the duration of the cytokinesis process, and the temporal evolution of the proliferation and the tumor area. Additionally, it was verified that the morphology of the digitally generated carcinoma satisfies the local minimum of the total mechanical energy.

The main goal of the presentation is to give a purely geometric view of the simulation of materials and their characteristics regardless of the specificity of the material. In particular, we consider how aspects of geometrization can be translated and implemented in materials theory. Modeling the crystallization of a multicomponent chemical system with interacting species, we assume that the generation of periodic structure occurs by breaking the spatial isotropy of the original (generic) configuration space. The idea is to effectively use the concept of structural sparsity, what may allow to reduce the symmetry group to crystallographic groups. Condensation is then seen as a consistent transition to a discrete point system characterized by the emergence of order, i.e. a certain structural organization. In the context of the closest approximation of sphere geometry, such a transition suggests an isoperimetric scheme. This scheme constructively considers atoms not as objects periodically ordered in discrete points of 3-dimensional space, but as a set of point elements with geometry that imposes octahedral symmetry constraints. To characterize the structural evolution, we focus on the corresponding manipulations of symmetry operations and on the effects caused by permutations. The symmetry change leads to discrete transformations of crystal symmetry described by the Bärnighausen tree of canonical group-subgroup relations. Discrete optimization using quantum-chemical modeling or density functional theory modeling can be performed to find the most stable and energetically favorable structural configurations among potentially possible candidate models.

In this paper, we propose the methods for quantitative analysis of protein helical and superhelical structure chirality. A necessary and sufficient condition is the mutual arrangement of α-carbons, which allows a reduction of the amount of processed information and is a clear advantage when processing large data arrays. The analysis of the chirality sign of the protein helical structures is based on determining the mixed product of every three consecutive vectors between neighboring reference points - α-carbon atoms. The skeleton of α-carbons and the helix axis are directed from the C-terminus to the N-terminus. Structures of α-helices, 3-10-helices, π-helices, and polyprolines are considered. The method for evaluating the chirality sign of coiled coil structures is based on determining the direction and value of the angle between the coiled coil axis and the α-helices axes. The chirality sign of the coiled coil is calculated by averaging the value of the cosine of the corresponding angle for all helices forming the superhelix. The estimate of the chirality sign of the superhelix is calculated by averaging the cosine value of the corresponding angle for all helices forming the superhelix. The calculation for collagens is performed similarly. Chirality maps of helical and superhelical protein structures are presented. Based on the methods, computer programs in Python 3.7 are implemented. The programs allow to load a model from a file, display a list of helical structures, determine the sign of their chirality, and display a three-dimensional image using the matplotlib library. Input data are files with .pdb or .txt extension. The results obtained adequately reflect the data presented in the scientific literature. These approaches, tested on protein helical structures, are planned to be further developed for the β-structures and irregular secondary structures analysis.

Discrete Asymmetries for Neutrino Oscillations are contaminated by Matter Effects. Their Physics is discussed in terms of a basis of 3 independent components in correspondence with invariance under CPT (genuine), Time Reversal T (matter) and Charge-Parity CP (interference). They have definite and different parities under the baseline L -theory independent-, the imaginary part of the flavor mixing, the matter potential and the hierarchy of the neutrino spectrum. In terms of the Standard Model of neutrino oscillations, these definite model-independent parities manifest in terms of definite parities in the standard parameters, which can be studied analytically thanks to the smallness of some of these quantities. The two fake components vanish at the same MAGIC ENERGY E, with the connection L/E = 1420 Km/GeV near the second oscillation maximum, where the genuine component is also maximal. The experimental CPV Asymmetry for the appearance nu_mu --> nu_e can separate the genuine (CPT-invariant) and the fake matter-induced (T-invariant) components by either L-dependence (HKK) or E-dependence (DUNE).