radial symmetry
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We use a recently proposed fast test of copula radial symmetry based on multiplier bootstrap and obtain an equivalent randomization test. The literature shows the statistical superiority of the randomization approach in the bivariate case. We extend the comparison of statistical performance focusing on the high-dimensional regime in a simulation study. We document radial asymmetry in the joint distribution of the percentage changes of sectorial industrial production indices of the European Union.

AbstractWe consider Newton’s problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that certain conical parts contained in the boundary of a convex body inhibit the optimality in the classical Newton’s problem with finite height. This result is applied to certain bodies considered in the literature, which are conjectured to be optimal for the classical Newton’s problem, and we show that they are not.

Neuronal activity is the result of both the electrophysiology and chemophysiology. A neuron can be well represented for the purposes of electrophysiological simulation as a tree composed of connected cylinders. This representation is also apt for 1D simulations of their chemophysiology, provided the spatial scale is larger than the diameter of the cylinders and there is radial symmetry. Higher dimensional simulation is necessary to accurately capture the dynamics when these criteria are not met, such as with wave curvature, spines, or diffusion near the soma. We have developed a solution to enable efficient finite volume method simulation of reaction-diffusion kinetics in intracellular 3D regions in neuron and network models and provide an implementation within the NEURON simulator. An accelerated version of the CTNG 3D reconstruction algorithm transforms morphologies suitable for ion-channel based simulations into consistent 3D voxelized regions. Kinetics are then solved using a parallel algorithm based on Douglas-Gunn that handles the irregular 3D geometry of a neuron; these kinetics are coupled to NEURON's 1D mechanisms for ion channels, synapses, etc. The 3D domain may cover the entire cell or selected regions of interest. Simulations with dendritic spines and of the soma reveal details of dynamics that would be missed in a pure 1D simulation. We describe and validate the methods and discuss their performance.

The purpose of the study is to reveal methods of image creation in dynamic visual communications based on symmetry. Methodology. Research methodology is interdisciplinary. It is based on systems and synergistical approaches. They consider dynamic visual communications as an integral field of interaction between human and environment. We systematized design methods of the image creation of a visual message by using the system and functional, structural and dynamic, composition, artistic and image design-analyses according to the principles of symmetry. Results. We represent symmetry as a method of dynamic visual communications form and image creation. Symmetrical relations are formed at the object structure level (mirror symmetry and central symmetry), the process level (translational symmetry, multilevel central symmetry and radial symmetry) and environment level (scale invariance and recursion). Integrative basis strengthening allows forming the structure of the image content providing fusion with an environment. Rethinking of the design methods on the based on the principles of symmetry increases the efficiency of perception and visual communications dynamic in the context of changeable external conditions. Scientific novelty. In the research we rethought the role of symmetry in dynamic visual communications design based on the systems approach for the first time. It is well-proven that the symmetric transformations support increasing of aesthetic, functional and communicative qualities of dynamic visual information. Practical significance. Research materials can serve as basis for harmonization and optimization of the form and content of different visual communications types. Their image structurization according to the principles of symmetry provides new development strategies of the integrated visual communications. It is important to increase perception efficiency in the conditions of continuously growing information volumes. Researched design methods of visual communications symmetric structures can be used by specialists in order to arrange the modern space. We also use them as the basis for designers’ system thinking forming as an educational technology.

Abstract In this work we analyze the multi-elliptic rogue wave clusters as new solutions of the nonlinear Schr\"odinger equation (NLSE). Such structures are obtained on uniform backgrounds by using the Darboux transformation scheme of order $n$ with the first $m$ evolution shifts that are equal, nonzero, and eigenvalue-dependent, while the imaginary parts of all eigenvalues tend to one. We show that an Akhmediev breather of $n-2m$ order appears at the origin of the $(x,t)$ plane and can be considered as the central rogue wave of the cluster. We show that the high-intensity narrow peak, with characteristic intensity distribution in its vicinity, is enclosed by $m$ ellipses consisting of the first-order Akhmediev breathers. The number of maxima on each ellipse is determined by its index and the solution order. Since rogue waves in nature usually appear on a periodic background, we utilize the modified Darboux transformation scheme to build these solutions on a Jacobi elliptic dnoidal background. We analyze the minor semi-axis of all ellipses in a cluster as a function of an absolute evolution shift. We show that the cluster radial symmetry in the $(x,t)$ plane is violated when the shift values are increased above a threshold. We apply the same analysis on Hirota equation, to examine the influence of a free real parameter and Hirota operator on the cluster appearance. The same analysis can be extended to the infinite hierarchy of extended NLSEs.

Object localization is an important application of remote sensing images and the basis of information extraction. The acquired accuracy is the key factor to improve the accuracy of object structure information inversion. The floating roof oil tank is a typical cylindrical artificial object, and its top cover fluctuates up and down with the change in oil storage. Taking the oil tank as an example, this study explores the localization by combining the traditional feature parameter method and convolutional neural networks (CNNs). In this study, an improved fast radial symmetry transform (FRST) algorithm called fast gradient modulus radial symmetry transform (FGMRST) is proposed and an approach based on FGMRST combined with CNN is proposed. It effectively adds the priori of circle features to the calculation process. Compared with only using CNN, it achieves higher precision localization with fewer network layers. The experimental results based on SkySat data show that the method can effectively improve the calculation accuracy and efficiency of the same order of magnitude network, and by increasing the network depth, the accuracy still has a significant improvement.

AbstractA multiscale mathematical model is presented to describe de novo granulation, and the evolution of multispecies granular biofilms, in a continuously fed bioreactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation governing the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass as well as exchange fluxes with the bulk liquid. Starting from a vanishing initial value, the expansion of the free boundary is initiated by the attachment process, which depends on the microbial species concentrations within the bulk liquid and their specific attachment velocity. Nonlinear hyperbolic PDEs model the growth of the sessile microbial species, while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species within the granular biofilm. Nonlinear ODEs govern the evolution of soluble substrates and planktonic biomass within the bulk liquid. The model is applied to an anaerobic, granular-based bioreactor system, and solved numerically to test its qualitative behaviour and explore the main aspects of de novo anaerobic granulation: ecology, biomass distribution, relative abundance, dimensional evolution of the granules and soluble substrates, and planktonic biomass dynamics within the bioreactor. The numerical results confirm that the model accurately describes the ecology and the concentrically layered structure of anaerobic granules observed experimentally, and that it can predict the effects on the process of significant factors, such as influent wastewater composition; granulation properties of planktonic biomass; biomass density; detachment intensity; and number of granules.

Abstract In this paper a mathematical model describing the heat transport in a spherical nanoparticle subject to Newton heating at its surface is presented. The governing equations involve a phonon hydrodynamic equation for the heat flux and the classical energy equation that relates the heat flux and the temperature. Assuming radial symmetry the model is reduced to two partial differential equation, one for the radial component of the flux and one for the temperature. We solve the model numerically by means of finite differences. The resulting temperature profiles show characteristic wave-like behaviour consistent with the non Fourier components in the hydrodynamic equation.

The nematode Caenorhabditis elegans utilizes chemosensation to navigate an ever-changing environment for its survival. A class of secreted small-molecule pheromones, termed ascarosides, play an important role in olfactory perception by affecting a host of biological function ranging from development to behavior. The ascaroside ascr#8 mediates sex-specific behaviors, driving avoidance in hermaphrodites and attraction in males. Males sense ascr#8 via the ciliated male-specific cephalic sensory (CEM) neurons, which exhibit radial symmetry along dorsal-ventral and left-right axes. Calcium imaging studies suggest a complex neural coding mechanism that translates stochastic physiological responses in these neurons to reliable behavioral outputs. To test the hypothesis that the neurophysiological complexity arises from differential expression of genes within subsets of these neurons, we performed cell-specific transcriptomic profiling of these sensory neurons. Expression profiling revealed between 20 and 639 genes enriched at least two-fold per CEM neuron and identified multiple G protein coupled receptor (GPCR) candidates enriched in non-overlapping subsets of CEM neurons. GFP reporter analysis confirmed that RNA expression of two of the GPCR genes, srw-97 and dmsr-12, is enriched in specific subsets of the CEM neurons. Single CRISPR-Cas9 knockouts of either srw-97 or dmsr-12 resulted in partial defects, while a double knockout of both srw-97 and dmsr-12 completely abolished the attractive response to ascr#8, suggesting that each receptor acts in a non-redundant manner in discrete olfactory neurons. Together, our results suggest that the evolutionarily distinct GPCRs SRW-97 and DMSR-12 act to facilitate male-specific sensation of ascr#8 through discrete subsets of CEM neurons.