Symmetry Problems for PDE

The results of this paper allow one to derive several results of general interest: to prove the Schiffer’s conjecture, to solve the Pompeiu problem, to prove two symmetry results in harmonic analysis and to give a new method for solving an old symmetry problem.

Novel dynamic residue network analysis approaches to study homodimeric allosteric modulation in SARS-CoV-2 Mpro and in its evolutionary mutations

The rational search for allosteric modulators and the allosteric mechanisms of these modulators in the presence of evolutionary mutations, including resistant ones, is a relatively unexplored field. Here, we established novel in silico approaches and applied to SARS-CoV-2 main protease (Mpro). First, we identified six potential allosteric modulators (SANC00302, SANC00303, SANC00467, SANC00468, SANC00469, SANC00630) from the South African Natural Compounds Database (SANCDB) bound to the allosteric pocket of Mpro that we determined in our previous work. We also checked the stability of these compounds against Mpro of laboratory strain HCoV-OC43 and identified differences due to residue changes between the two proteins. Next, we focused on understanding the allosteric effects of these modulators on each protomer of the reference Mpro protein, while incorporating the symmetry problem in the functional homodimer. In general, asymmetric behavior of multimeric proteins is not commonly considered in computational analysis. We introduced a novel combinatorial approach and dynamic residue network (DRN) analysis algorithms to examine patterns of change and conservation of critical nodes, according to five independent criteria of network centrality (betweenness centrality (BC), closeness centrality (CC), degree centrality (DC), eigencentrality (EC) and katz centrality (KC)). The relationships and effectiveness of each metric in characterizing allosteric behavior were also investigated. We observed highly conserved network hubs for each averaged DRN metric on the basis of their existence in both protomers in the absence and presence of all ligands, and we called them persistent hubs (residues 17, 111, 112 and 128 for averaged BC; 6, 7, 113, 114, 115, 124, 125, 126, 127 and 128 for averaged CC; 36, 91, 146, 150 and 206 for averaged DC; 7, 115 and 125 for EC; 36, 125 and 146 for KC). We also detected ligand specific signal changes some of which were in or around functional residues (i.e. chameleon switch PHE140). Using EC persistent hubs and ligand introduced hubs we identified a residue communication path between allosteric binding site and catalytic site. Finally, we examined the effects of the mutations on the behavior of the protein in the presence of selected potential allosteric modulators and investigated the ligand stability. The hit compounds showed various levels of stability in the presence of SARS-CoV-2 Mpro mutations, being most stable in A173V, N274D and R279C, and least stable in R60C, N151D V157I, C160S and A255V. SANC00468 was the most stable compound in the 43 mutant protein systems. We further used DRN metric analysis to define cold spots as being those regions that are least impacted, or not impacted, by mutations. One crucial outcome of this study was to show that EC centrality hubs form an allosteric communication path between the allosteric ligand binding site to the active site going through the interface residues of Domain I and II; and this path was either weakened or lost in the presence of some of the mutations. Overall, the results of this study revealed crucial aspects that need to be considered in drug discovery in COVID-19 specifically and in general for rational computational drug design purposes.

The Multipole Structure and Symmetry Classification of Even-Type Deviators Decomposed from the Material Tensor

The number of distinct components of a high-order material/physical tensor might be remarkably reduced if it has certain symmetry types due to the crystal structure of materials. An nth-order tensor could be decomposed into a direct sum of deviators where the order is not higher than n, then the symmetry classification of even-type deviators is the basis of the symmetry problem for arbitrary even-order physical tensors. Clearly, an nth-order deviator can be expressed as the traceless symmetric part of tensor product of n unit vectors multiplied by a positive scalar from Maxwell’s multipole representation. The set of these unit vectors shows the multipole structure of the deviator. Based on two steps of exclusion, the symmetry classifications of all even-type deviators are obtained by analyzing the geometric symmetry of the unit vector sets, and the general results are provided. Moreover, corresponding to each symmetry type of the even-type deviators up to sixth-order, the specific multipole structure of the unit vector set is given. This could help to identify the symmetry types of an unknown physical tensor and possible back-calculation of the involved physical coefficients.

The symmetry problem for testimonial conservatism

A prima facie plausible and widely held view in epistemology is that the epistemic standards governing the acquisition of testimonial knowledge are stronger than the epistemic standards governing the acquisition of perceptual knowledge. Conservatives about testimony hold that we need prior justification to take speakers to be reliable but recognise that the corresponding claim about perception is practically a non-starter. The problem for conservatives is how to establish theoretically significant differences between testimony and perception that would support asymmetrical epistemic standards. In this paper I defend theoretical symmetry of testimony and perception on the grounds that there are no good reasons for taking these two belief forming methods to have significant theoretical differences. I identify the four central arguments in defence of asymmetry and show that in each case either they fail to establish the difference that they purport to establish or they establish a difference that is not theoretically significant.

An Efficient Login Authentication System against Multiple Attacks in Mobile Devices

Access management of IoT devices is extremely important, and a secure login authentication scheme can effectively protect users’ privacy. However, traditional authentication schemes are threatened by shoulder-surfing attacks, and biometric-based schemes, such as fingerprint recognition and face recognition, that are commonly used today can also be cracked. Researchers have proposed some schemes for current attacks, but they are limited by usability. For example, the login authentication process requires additional device support. This method solves the problem of attacks, but it is unusable, which limits its application. At present, most authentication schemes for the Internet of Things and mobile platforms either focus on security, thus ignoring availability, or have excellent convenience but insufficient security. This is a symmetry problem worth exploring. Therefore, users need a new type of login authentication scheme that can balance security and usability to protect users’ private data or maintain device security. In this paper, we propose a login authentication scheme named PinWheel, which combines a textual password, a graphical password, and biometrics to prevent both shoulder-surfing attacks and smudge attacks and solves the current schemes’ lack of usability. We implemented PinWheel and evaluated it from the perspective of security and usability. The experiments required 262 days, and 573 subjects participated in our investigation. The evaluation results show that PinWheel can at least effectively resist both mainstream attacks and is superior to most existing schemes in terms of usability.

An overvew of nucleosynthesis and Cosmological parameters and observations using CMB and redshift

The Big Bang nucleosynthesis has some elements in it which are of utmost importance to understand how the Universe is as we know it. Our consideration in this paper will primarily be on TGUT, the temperature (and also therefore time period) when all the forces behaved under the laws of the same Unification theory. Next, we will consider the QCD transition phase, when the behaviour of matter (quarks, gluons) was quite important in the structure of the Big Bang model. Finally, we will consider the Baryon symmetry problem, where we will discuss the inequality of matter and anti-matter. We will also briefly discuss the synthesis of Baryons and leptons (labelled Baryonsynthesis and leptonsynthesis respectively), the Sakharov outlines and the Baryon number, and its conditions with the outline under Thermodynamic equilibrium departure and the C-CP symmetry violation conditions.

Design of Concentric Ring Antenna Arrays Based on Subarrays to Simplify the Feeding System

The global synthesis for antenna arrays that produce a desired radiation pattern is a scientific symmetry problem. This paper deals with the design of concentric ring antenna arrays to simplify the feeding system using a cophasal subarray configuration. This simplification in the feeding network is achieved by the reduction of phase shifters via a proper clustering of radiators applying one amplitude and one phase excitation by subarray in the array system. The array design for this geometry considers an optimization process based in differential evolution to reduce the side-lobe level, resulting in simplification of the feeding network. Simulation results based on CST Microwave Studio and HFSS are provided to verify the accuracy of the array model and to take mutual coupling into account. These simulations are provided using a circular patch as antenna element to generate a scannable array pattern over the elevation plane. Furthermore, an analysis of the manufacturing tolerances was made to verify the reliability of our design.

Implementation of ARINC 659 Bus Controller for Space-Borne Computers

As one of the key technologies of Honeywell, the aeronautical radio incorporated (ARINC) 659 bus is popular in current space-borne computers. However, Honeywell does not design ARINC 659 bus controller separately, and there are only a few papers about FPGA-based ARINC 659 bus controllers. Accordingly, to promote the extremely high performance needs of space-borne computers, this paper designs an ARINC 659 bus controller chip which integrates two independent bus interface units (BIUs), one 8-bit MCU, and several peripheral interfaces (i.e., UART, SPI, and I2C). Because the two BIUs are identical and mutually checked, the symmetry problem is emphatically dealt with in the design of this bus controller, and effective timing convergence is realized, which makes the bus controller work reliably and stably. In addition, due to the circuit’s large scale, design for testability (DFT) is also considered. Accordingly, on-chip clock (OCC) and scanning compression test technique are used to realize the at-speed test and shorten the test time, respectively.

Feature Input Symmetry Algorithm of Multi-Modal Natural Language Library Based on BP Neural Network

When using traditional knowledge retrieval algorithms to analyze whether the feature input of words in multi-modal natural language library is symmetrical, the symmetry of words cannot be analyzed, resulting in inaccurate analysis results. A feature input symmetric algorithm of multi-modal natural language library based on BP (back propagation) neural network is proposed in this paper. A Chinese abstract generation method based on multi-modal neural network is used to extract Chinese abstracts from images in multi-modal natural language library. The Word Sense Disambiguation (WSD) Model is constructed by the BP neural network. After the word or text disambiguation is performed on the Chinese abstract in the multi-modal natural language library, the feature input symmetry problem in the multi-modal natural language library is analyzed according to the sentence similarity. The experimental results show that the proposed algorithm can effectively analyze the eigenvalue symmetry problem of the multi-modal natural language library. The maximum error rate of the analysis algorithm is 7%, the growth rate of the analysis speed is up to 50%, and the average analysis time is 540.56 s. It has the advantages of small error and high efficiency.