Proceedings, 2018, Symmetry 2017

Potassium channels are integral membrane proteins that selectively transport K⁺ ions across cell membranes. They function through a pair of gates, which work in tandem to allow the passage of the ions through the channel pore in a coupled system, to which I refer here as the “gate linker”. To closely examine the role of the gate linker in channel functioning, I mutated the amino acids in the cDNA of this region, either alone or together with amino acids of adjacent regions. The functional effects of these mutations suggest that the gate linker functions analogously to a triad of coiled springs arranged in series. Accordingly, I constructed a physical model of harmonic oscillators and analyzed it mechanically and mathematically. The operation of this model indeed corresponds to the phenomena observed in the mutations study. The harmonic oscillator model shows that the strength of the gate linker is crucial for gate coupling and may account for the velocity, direction, and efficiency of ion transfer through the channel. Such a physical perspective of the gating process suggests new lines of investigation regarding the coupling mode of potassium channels and may help to explain the importance of the gate linker to channel function. Full article

A plane wave reconstruction technique is presented for the solution of Helmholtz’s equation governing wave propagation in equilateral triangular electromagnetic waveguides in order to aid in the classification of symmetric and antisymmetric modes as well as to resolve the problem of excitation of triangular patch antennas. [...] Full article

Radio frequency interference has been considered a major common issue in wireless communication systems; among several other potential major issues, the emergence and massive development of Internet of things (IoT) is also considered a crucial issue as each device connected wirelessly causes enough of an increment to have destructive effects on radio-frequency interference (RFI). [...] Full article

We consider a class of discrete time two-dimensional dynamic systems that are symmetric, i.e., (x’,y’) = T(x,y) such that ToS = SoT, where S: (x,y)→(y,x) is the reflection through the diagonal. Symmetry implies some properties in terms of qualitative and quantitative dynamics, for instance there exist synchronized trajectories, while fixed points and other invariant sets are symmetric w.r.t. the main diagonal or they are invariant as well. Synchronization may also emerge. After showing some of the main features related to this kind of systems (such as attractors and their basins), some numerical examples obtained using software MatLab will be presented and the related algorithms will be discussed. Full article

In this paper, we prove a Nekhoroshev theorem for the Toda lattice with Dirichlet boundary conditions, i.e., fixed ends. The Toda lattice is a special case of a Fermi-Pasta-Ulam (FPU) lattice, and in view of the unexpected recurrence phenomena observed numerically in these chains, it has been conjectured that the theory of perturbed integrable systems could be applied to these lattices, especially since the Toda lattice has been shown to be a completely integrable system. Whereas various results have already been obtained for the periodic lattice, the Dirichlet lattice is more important from the point of view of applications, since the famous numerical experiments have been performed for this type of system. Mathematically, the Dirichlet lattice can be treated by exploiting symmetries of the periodic lattice. Precisely, by considering the phase space of the Dirichlet lattice as an invariant submanifold of the periodic lattice, namely the fixed point set of a certain symmetry of the periodic lattice, the results obtained for the periodic lattice can be used to obtain similar results for the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of other results such as those of the KAM theorem. Full article

In non-relativistic quantum mechanics, the dynamics of closed quantum systems is described by Hamiltonians which are self-adjoint in appropriately chosen Hilbert spaces. For PT-symmetric quantum systems, the Hamiltonians are, in general, no longer self-adjoint in standard Hilbert spaces, rather they are self-adjoint in Krein spaces—Hilbert spaces endowed with indefinite metric structures. Moreover, the spectra of PT-symmetric Hamiltonians are symmetric with regard to the real axis in the spectral plane. Apart from Hamiltonians with purely real spectra, this includes also Hamiltonians whose spectra may contain sectors of pairwise complex-conjugate eigenvalues. Considering families of parameter-dependent Hamiltonians, one can arrange parameter-induced passages from sectors of purely real spectra to sectors of complex-conjugate spectral branches. Corresponding passages can be regarded as PT-phase transitions from sectors of exact PT-symmetry to sectors of spontaneously broken PT-symmetry. Approaching a PT-phase transition point, the eigenvectors of the Hamiltonian tend toward their isotropic limit—an, in general, infinite-dimensional (Krein-space) generalization of the light-cone limit in Minkowski space. At a phase transition, the Hamiltonian is no longer diagonalizable, but similar to an arrangement of nontrivial Jordan-blocks. The interplay of these structures is briefly reviewed with special emphasis on the related Lie-algebraic and Lie-group aspects. With the help of Cartan-decompositions, associated hyperbolic structures and Lie-triple-systems are discussed for finite-dimensional setups as well as for their infinite-dimensional generalizations (Hilbert-Schmidt (HS) Lie groups, HS Lie algebras, HS Grassmannians). The interconnection of Krein-space structures and PT-phase transitions is demonstrated on two exactly solvable models: PT-symmetric Bose-Hubbard models and PT-symmetric plaquette arrangements. Full article

In order to combine internal symmetries and spacetime that has Poincaré symmetry, it is necesary to introduce supersymmetry, Supersymmetry of Connes is based on involution, and that of Cartan is based on triality. Cartan’s supersymmetry allows violation of Lorentz symmetry and time reversal violation can occur. Full article

Firstly, a short reminder of the Kaluza-Klein programme and a review of the Coset Space Dimensional Reduction of higher dimensional gauge theories will be given. Then, the “fuzzy sphere” will be presented, as a representative example of a non-commutative coset as well as the construction of gauge theories on such spaces. Eventually, examples will be presented of (a) a higher dimensional Unified Theory with fuzzy coset spaces as extra dimensions, (b) gravity as a gauge theory on non-commutative spaces. Full article

We discuss various theories of modified gravity which aim to describe the whole evolution of the universe, from early-time inflation via radiation/matter dominance and finally to the dark energy era. Such unified evolution may be described in frames of the same modified gravity. Special attention is paid to F(R) gravity where R is scalar curvature and modified Gauss- Bonnet gravity. The modified gravity solves the problem of universe acceleration without the need to introduce inflation or unknown dark fluid. The explicit models of such F(R) gravity are presented where quantum gravity effects may also be taken into account. The possible generalizations of modified gravity to non-local gravity, string-inspired gravity, and teleparallel gravity are briefly discussed. A number of applications such as the qualitative change of mass-radius relation in neutron stars or the anti-evaporation effect in multiple-horizon black holes are mentioned. Full article

It is well known that the field equations of f(T) gravity break local Lorentz invariance if one a priori assumes a vanishing spin connection, except in the teleparallel equivalent of general relativity (TEGR) case f(T) = T + Λ. One consequence is the existence of “bad” tetrads, i.e., tetrads which force a constraint on the field equations, which can be satisfied only in the TEGR case, hence prohibiting any modification of the gravitational dynamics. In order to overcome this difficulty, one may either restrict oneself to “good” tetrads, from which no such constraint arises, or introduce a suitable spin connection, which cancels the constraint. However, there is no simple procedure or general formula for these good tetrads or suitable spin connections, and only particular examples have been constructed. I will show how spacetime symmetries act on good and bad tetrads, and can be used to distinguish them, hence giving a simpler criterion for good tetrads. I will also show how a sufficiently high amount of symmetry can be used to determine either the good tetrads or the required spin connection. Full article

We consider the most general form of the Noether theorem which is suitable for the treatment of global symmetries, described by symmetry-groups, and local symmetries, described by symmetry-algebras, which may not be integrable to symmetry groups. The principle new notion is specific dynamical functionals which solve the problem by replacing the standard action functionals. We also discuss the compatibility of the boundary conditions and the corresponding variational principles. Many illustrative examples are shown. Full article

The relationship between morphological symmetry and mating success in animals varies dramatically across species and populations. The reasons for this heterogeneity in effect size are poorly understood, which has lead to intense debate among evolutionary biologists. I will evaluate the general hypothesis that differences in the level of developmental instability (DI) across populations accounts for heterogeneity in the effect of symmetry on sexual selection. According to this hypothesis, most populations have levels of DI insufficient to propel adaptive processes such as mate selection; only when DI levels surpass a critical threshold will selection operate and be detectable. I will test this hypothesis using results of our work with Drosophila bipectinata Duda (Diptera: Drosophilidae), focusing on fluctuating asymmetry (FA) and size of the male sex comb, a model secondary sexual trait for animal studies. The following key predictions will be tested: (1) Intensity of sexual selection depends on the level of DI in the population. Data from nine distinct populations sampled throughout Australasia and the South Pacific will be evaluated for this test; (2) the level of DI in a population, in turn, is the result of the particular history of directional selection for trait size experienced by that population. This prediction will be evaluated using comparative data as well as the results of artificial selection for increasing trait size under laboratory conditions. This study will provide a framework for understanding the dramatic variation in effect size across FA-sexual selection studies. Full article

Humans tend to judge and sort parts of their social and non-social environment permanently into a few basic categories: those parts they like and those parts they do not. Indeed, we have developed aesthetic preferences for those things and people we are exposed to. Furthermore, needless to say, these preferences shape our behavioural choices—our tendency to seek out or avoid what the world has to offer to us. Humans and other animals have evolved preferences for food and habitats, for naturally occurring sensations such as smells and sounds, as well as for the broad array of culturally created artefacts Full article

This paper discusses the new auspicious trends of internet of things (IoT) and its advanced developments in various sectors of today’s IT arena, including for industrial sectors. Each object acts as a communication node (or entity) that is able to communicate with other nodes, and corresponding information could be accessed and controlled, via several of today’s commonly used electronic devices such as laptops and cellular devices, etc., through an IoT-designed platform. Moreover, in industrial automation sectors, the employment of IoT is very advantageous, in terms of remote communication support; low-cost operations and maintenance; and autonomous collaborations among remote networked field devices, etc. The facility of autonomous collaborations provisioned by IoT, in the context of a supervisory control and data acquisition (SCADA) system as part of an industrial control system, somehow exists in a distributed network protocol (DNP3) during automation and controls. Therefore, the current study takes the step to model a new IoT framework for a SCADA system, which will be efficient at facilitating industrial automation through the collaborative DNP3-Modbus acquisitions and automation, called the SCADA-IoT system. An IoT gateway is employed and configured that supports for both SCADA protocols, such as DNP3 and Modbus and is efficient at communicating, from networked field devices, with inter-processing from both. In the overall SCADA-IoT design, the transmission is carried from an enormous amount of sensors and/or field devices, employing proprietary and nonproprietary protocols; further, sent information is analyzed via big data, stored in a cloud center, monitored and controlled over a SCADA-IoT supportive platform. At the same time, information security (IS) is a big associated challenge and one of the main contributions of this study. Thus, this study also analyzed the potential security mechanisms for securing SCADA-IoT and found cryptography to be a noteworthy security solution, based on the proposed system requirements and its communication demands. Full article

We analyze Symmetry, Entropy, and therefore, Uncertainty Measures, to obtain new ways to model adequate conditions, constructed from vague pieces of information. Over time, it was adapted by Shannon, thus creating the Information Theory. However, the Hungarian mathematician Rényi shows that there exist different and valid entropy measures, according to the need of applications. So, it will be very necessary to clarify the different types of measures, and their mutual relationships. Full article

We study a class of isoperimetric problems on R^N with respect to weights that are powers of the distance to the origin. We consider different weights in the volume and in the perimeter. We investigate cases in which, among all smooth sets Ω in R^N with fixed weighted measure, the ball centered at the origin has minimum weighted perimeter. The results also imply a weighted Pólya- Szegö principle. In turn, we establish radiality of optimizers in some Caffarelli-Kohn-Nirenberg inequalities, and we obtain sharp bounds for eigenvalues of some nonlinear problems. Full article

One of the core concepts essential to understanding natural phenomena and the dynamics of social systems is the concept of “relation”. Social and interconnection networks, traffic systems, chemical structures, etc. can be expressed as relational structures. Furthermore, scientists rely on relational structures with high levels of symmetry because of their optimal behavior and high performance. A mathematical model capturing the essence of this situation is a graph exhibiting a high level of symmetry. The underlying mathematical discipline is algebraic graph theory involving a wide range of methods from combinatorics, algebra, algorithms, geometry, topology, etc. While some symmetries are obvious, certain additional symmetries remain hidden or difficult to grasp. Knowing the full (or as near as possible) set of symmetries of an object is important because it provides the most complete description of that object's structure. This brings us to the crucial question: given a graph or more general a discrete mathematical object, are there any symmetries beyond the obvious ones, and, if yes, how can one determine the full set? In this talk I will present some recent developments with regards to this question together with some applications within mathematics as well as other scientific disciplines. Full article