Proteins are nature’s favorite building block as they can support numerous biological processes while exhibiting variable levels of complexities, and as such mimicking their properties has been the focus of extensive research. As a rule of thumb structural and functional complexities exhibited by protein constructs go hand in hand. However, creating elaborate structures from scratch is non-trivial and requires meticulous tailoring of the interacting interfaces. Symmetry is often nature’s preferable design strategy that facilitates the formation of macromolecular structures using only a handful of interacting interfaces. Protein cages are considered a lucrative target for the de novo design of proteinaceous structures as they are composed of multiple subunits that engage in several interfaces that are templated by various symmetry axes. As a design strategy for protein-protein interactions (PPIs) we employed the metal-directed protein self-assembly (MDPSA) method where metal-binding ligands are installed on the designated interfaces, leading to the formation of stable supramolecular assemblies in the presence of interacting metals. In this work, a robust cytochrome cb-562 was employed as a building block where two sets of orthogonal ligands were installed into the protein backbone based on the Pearson Hard-Soft Acid-Base (HSAB) classification, in order to differentiate between interfaces and to template the formation of appropriate symmetry axes. One set included native ligands that were used to coordinate Zn(II) ions and stabilize C2 symmetry axis, while a bioinspired hydroxamic acid set was used as a strategic handle to coordinate hard Fe(III) ions, leading to the formation tris-hydroxamate-Fe(III) complexes at the C3 nodes. This strategy proved both successful and flexible as it mediated the formation of two types of nanometer-size protein cages. Moreover, the interfacial metal sites imbued the cages with kinetic lability that manifested in a stimuli-responsive disassembly via various mechanisms.

The running path of automated guided vehicles（AGVs）in the automated terminal is affected by the storage location of containers, and the running time caused by congestion, deadlock and other problems during the driving process is uncertain. In this paper, considering the different AGVs congestion conditions along the path, a symmetric triangular fuzzy number is used to describe the AGVs operation time distribution, and a multi-objective scheduling optimization model is established to minimize the risk of quay cranes (QCs) delay and the shortest AGVs operation time. An improved genetic algorithm was designed to verify the effectiveness of the model and algorithm by comparing the results of the AGVs scheduling and container storage optimization model based on fixed congestion coefficient under different example sizes. The results show that considering the AGVs task allocation and container storage location allocation optimization scheme with uncertain running time can reduce the delay risk of QCs, reduce the maximum completion time, and have important significance for improving the loading and unloading efficiency of the automated terminal.

A symmetry assisted approach to multidimensional vibronic problem: theoretical background and some chemical applications

Boris Tsukerblat¹, Andrew Palii²

¹Ben-Gurion University of the Negev, Department of Chemistry, Beer-Sheva, Israel

² Institute of Problems of Chemical Physics (IPCP), Chernogolovka, Moscow Region, Russia

The classical treatment of the nuclear motion is invalid (despite the difference in masses of electrons and nuclei) in the region of crossover of the terms or, more commonly, when we are dealing with the orbitally degenerate or pseudo degenerate levels. To overcome significant limitations implied by the adiabatic approximation, we propose a symmetry-adapted approach aimed to the accurate solution of the quantum-mechanical (dynamic) vibronic problem in large scale molecular systems. The algorithm for the solution of the eigen-problem with a huge Hilbert space takes full advantage of the point symmetry arguments. Applying the successive coupling of the bosonic creation operators, we introduce complex irreducible tensors that can be referred to as multivibronic operators. The generated vibrational basis is coupled to the electronic one to get the symmetry adapted electron-vibrational basis within which the full matrix of the Hamiltonian is blocked to maximum extent according to the irreducible representations of the point group. The approach allows to treat optical and thermodynamic properties of the nanoscale multilevel vibronic system, such as mixed-valence molecules and impurity centers in crystals. The developed technique is applied to consideration of 2e-reduced mixed-valence dodecanuclear Keggin anion in which the electronic pair is delocalized over twelve sites, tetrameric systems in which two mobile electrons are employed to encode binary information in molecular quantum cellular automata, complex organic systems exhibiting unusual intervalence optical vibronically assisted absorption.

Acknowledgements: Support from Russian Science Foundation (No. 20-13-00374) and the Ministry of Science and Higher Education (creation of the Lab. of Molecular Magnetic Nanomaterials at IPCP, No. 14.W03.31.0001) is acknowledged.

Symmetry is a common geometric feature in human-made objects. Urban objects are no exception and are guided by bilateral or radial symmetry. Symmetry has been used as a feature for object detection in images, although in many cases, the objects are not acquired in their entirety, so the symmetry detection is greatly complicated or not applicable. The same problem occurs in point clouds, Mobile Laser Scanning (MLS) technology allows acquiring 3D urban environments in precise and fast way and allows mapping the elements of the urban scene. Urban objects, although symmetrical, are often acquired partially.

This work studies the occlusions of urban objects and the relationship with the symmetry and the MLS acquisition trajectory. In the case of vehicles, objects with bilateral symmetry, a new automatic method is presented to correct the occlusions in vehicles by reflecting the point cloud with respect to the symmetry axis of the vehicle. The proposed method consists of three phases: (1) a quasi-axis symmetry is generated in the partially acquired object, (2) the point cloud is reflected, and (3) the input point cloud and the reflected point cloud are registered using the ICP algorithm. The method has been tested on data acquired with Terrestrial Laser Scanning to quantify the registration error and MLS for evaluation the results on large urban scenes.

Molecules of carbon ideal nanotori can form columnar phases with symmetric parallel optical axes due to the large depth of potential wells in direction of tori axes. The formed columns are often called "liquid lines". They are the principal fragments constituting the liquid crystal. Along the axes of these structural formations, not only light quanta can propagate, but also atomic or molecular particles of some gas components. This fact is used in this report for membrane separation of gas mixtures under standard temperature conditions. The nanotor itself is a surface crystal. Many papers talk about the applications of nanotori and their physical properties. However, the collective effects of these objects, the states and properties of symmetric liquid crystals obtained on their basis, have been little studied. In this report, two approaches are used to study the permeability of liquid crystal films. The first is the atom-atom interaction approach. According to this approach, the nanotor is represented by a set of carbon atoms located in their middle positions. These atoms interact with free atoms (molecules) of the gas phase. The second approach is based on finding the integral action directly from the nanotorus or effective surface approximating such an action. For points located on axes of liquid lines, it is convenient to take the surface of ring as approximating surface, which has the same size as the central section of torus. A columnar carbon structure, built in one of the ways, is shot with beams of atoms or simple molecules of gas phase in the direction of the axes of liquid lines. The results of numerical experiments are used to determine the permeability of a liquid crystal film and the selectivity of separating a gas mixture using a layer of such films.

Acknowledgment: The reported study was funded by RFBR, project number 19-31-90087.

The dihedral group represents a group of symmetries of a regular polygon. Moreover, it is generated by rotation and axial symmetries. Due to this structure, in a recently published paper, we analyzed the HX-groups associated with them and we computed the commutativity degree of the associated HX-groups. Since there is an interesting connection between the HX-groups and the complete hypergroups- both of them can be constructed using the structure of a group, in this paper, we aim to determine the relationships between the lattice of the dihedral group and the lattice of the associated HX-groups, as well as that of the associated complete hypergroups. Furthermore, we will present some conditions to describe the modular and the distributive lattices, using elements from hypercompositional algebra. This has the advantage that the interaction called hyperproduct or hyperoperation between two elements of the considered set is not anymore just an element, as in the classical algebra, but a subset of the support set.

The Transcendental Psychology Approach (A.I. Mirakyan) to the study of perception (has been developed since 1990) assumes that in the perception there are so-called structurally-generative processes that are realized outside their mediation by conceptual data of cognitive categories. To study these transcendental processes, it is proposed to use an axiomatic methodology based on general natural principles that provide conditions and possibilities for form creation. Several general principles were developed including structure-process anisotropy, formation of symmetric relations, spatial-temporal discreteness, co-presentation, and some others. They are both explanatory for the generative process of perception and are the direct object of further specification. The conducted experiment was devoted to the verification of a theoretical model based on a possible hierarchy of center-symmetrical and temporal relations in human visual perception. It was shown that sequential formation of temporal relations between the results of center-symmetrical relations can predict a special phenomenon of perception of short-term displayed objects that vary in size at a fairly high speed. According to the Fröhlich effect, it is usually impossible for these stimuli with a speed of resizing up to 15 visual deg/s to see the start of the process, while the final position of the object can be observed regardless of the direction of resizing. The studied model indicated the possibility of the appearance for subjects of the reversed Fröhlich effect for stimuli decreasing in size at high speeds of 15-60 deg/s. The results of the experiments showed that for a speed of 15 deg/s, the percentage of such subjects was 8%, and for a speed of 30 deg/s - 22%, while for a speed of 60 deg/s this percentage exceeds 65 %. Thus, for the last speed, there was a significant number of tests with the reversed Fröhlich effect, which was predicted by the model.

$F(R)$ gravity cosmological models with an additional scalar field as well as two-field cosmological models with nonminimal coupling are actively studied.
These models can be transformed into the General Relativity models with two scalar fields by a conformal transformation of the metric. The key property of the obtained chiral cosmological models is a nonstandard kinetic part of the scalar fields Lagrangian. Exact analytical solutions of the evolution equations play an important role in the investigation of some important qualitative features of cosmological models. Most of the results of the exact integration of cosmological models with scalar fields are connected with one-field cosmological models and $F(R)$ gravity models without scalar fields. Usually, numerical methods, different approximation schemes and the search for particular solutions in the analytic form are applied for studying evolution equations of two-field cosmological models. We consider chiral cosmological models with two scalar fields (including the case of phantom scalar fields) and the cosmological constant. We analyze the obtained cosmological solutions both in the Einstein frame and in the initial Jordan frame.

One of the directions of Biophysics is studying the physical foundations of the organization and functioning of living systems, as well as the principles and mechanisms of performing "useful work" by biological machines. A molecular machine is a hierarchical device that cyclically conjugates the transformation of the energy form necessary to perform useful work and a series of symmetry transformations in its regular structural elements, realizing "selected (quasi)mechanical degrees of freedom" during self-assembly and functioning. Molecular machines are hierarchically organized dynamic chiral constructs.

The concept is proposed and substantiated according to which the chiral dualism of carbon compounds is the physical symmetry basis of structure formation and systemic interactions in molecular biology. In macromolecular systems, sign-alternating hierarchies of chiral structures in sequences from the “lower” asymmetric carbon atom in sp3-hybridization to helices, supercoils, and helical supramolecular structures of the cytoskeleton have been identified as chiral invariants.

The uniqueness of homochirality, evolutionarily selected by living systems, lies in the possibility of self-assembly of molecular machines - converters of energy, matter, and information. Spatial folding of a protein machine is considered as an autowave process of self-organization in an active medium, where the distributed resource of free energy is contained in the initial homochirality of the system as a whole. The chain of structural transformations forms the optimal trajectory of movement along the surface of the potential energies of the funnel. The revealed regularity makes it possible to predict the development of biotechnology for the self-assembly of molecular machines with desired properties.

The Kadomtsev-Petviashvili (KP) equation is a nonlinear partial differential equation in 2+1 dimensions that describes the complex web-like patterns of waves that can appear on the surface of shallow water. The KP equation is the simplest nontrivial equation in the KP hierarchy, a system of equations with diverse applications in mathematics and theoretical physics. Many important nonlinear partial differential equations in 1+1 dimensions, such as the Burgers', Korteweg-de Vries, nonlinear Schrodinger and Boussinesq equations, all arise as symmetry reductions of the KP hierarchy.

Among the numerous special properties of KP (both the equation and the hierarchy) is the existence of a Backlund transformation (BT), a way to construct a new solution from a given one by solution of a simpler system. Backlund transformations commute, and this allows the construction of an associated lattice, in which the vertices are solutions of KP (equation or hierarchy), connected by an edge if they are related by a BT. In this talk we show new reductions of KP arise by imposing translational invariances on this lattice. The reductions obtained in this way appear to be, at least in some cases, the so-called Schwarzian versions of the classical symmetry reductions.