Symmetry2015, 7(4), 1788-1802; doi:10.3390/sym7041788 - published 1 October 2015 Show/Hide Abstract
Abstract: This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in traditional mechanical dynamic problems and current scientific disciplines. The conditions of being quasi-filiform and nilpotent are applied carefully and in several stages, and appropriate changes of the basis are achieved in an iterative and interactive process of simplification. This has been implemented by means of the development of more than thirty Maple modules. The process has led from the first family formulation, with 64 parameters and 215 constraints, to a family of 16 parameters and 17 constraints. This structure theorem permits the exhaustive classification of the quasi-filiform nilpotent Lie algebras of dimension nine with current computational methodologies.
Symmetry2015, 7(4), 1780-1787; doi:10.3390/sym7041780 - published 30 September 2015 Show/Hide Abstract
Abstract: Signalling proteins are key regulators of basic cell physiology and tissues morphogenesis. Whilst signalling proteins are paramount for the cell to function optimally, their down regulation or inhibition is also central to tune the cell and its environment. One process involved in this tuning mechanism is membrane budding, otherwise known as endocytosis. The origin of the physical force driving the budding process and endocytosis has been the subject of much controversy. After two decades the budding process is now well described and it is acknowledged that fundamental principles from soft matter physics are at play. This opens a new window for understanding gene regulations, pharmacokinetic and multi drug resistance in cancer. This review recalls the first steps that have led to a better understanding of cell biology through the use of physics and; how the use of physics has shed light in areas of cell biology, cancer and pharmacology. It is, therefore, not a review of the many enzymes involved in membrane vesiculation and membrane curvature; it is more of an historical account.
Symmetry2015, 7(4), 1768-1779; doi:10.3390/sym7041768 - published 29 September 2015 Show/Hide Abstract
Abstract: To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA) models under regular and random initial conditions corresponds to three Wolfram’s classes of CAs, identified as Classes II, III, and IV. Regular initial conditions occur in two groups. One group that makes a broken, regular pattern formation has four types of symmetry, whereas the other group that makes a higher hierarchy pattern formation has only two types. Additionally, both final pattern formations show an increased amount of symmetropy as time passes. Moreover, the final pattern formations are affected by iterations of base rules of CA models of chaos dynamical systems. The growth design formations limit possibilities: the ratio of developing final pattern formations under a regular initial condition decreases in the order of Classes III, II, and IV. This might be related to the difference in degree in reference to surrounding conditions. These findings suggest that calculations of symmetries of the structures of one-dimensional cellular automata models are useful for revealing rules of pattern generation for animal bodies.
Symmetry2015, 7(4), 1751-1767; doi:10.3390/sym7041751 - published 29 September 2015 Show/Hide Abstract
Abstract: Additional nonlocal symmetries of diffusion-convection equations and the Burgers equation are obtained. It is shown that these equations are connected via a generalized hodograph transformation and appropriate nonlocal symmetries arise from additional Lie symmetries of intermediate equations. Two entirely different techniques are used to search nonlocal symmetry of a given equation: the first is based on usage of the characteristic equations generated by additional operators, another technique assumes the reconstruction of a parametrical Lie group transformation from such operator. Some of them are based on the nonlocal transformations that contain new independent variable determined by an auxiliary differential equation and allow the interpretation as a nonlocal transformation with additional variables. The formulae derived for construction of exact solutions are used.
Symmetry2015, 7(4), 1734-1750; doi:10.3390/sym7041734 - published 28 September 2015 Show/Hide Abstract
Abstract: Aiming to effectively recognize train center plate bolt loss faults, this paper presents an improved fault detection method. A multi-scale local binary pattern operator containing the local texture information of different radii is designed to extract more efficient discrimination information. An improved teaching-learning-based optimization algorithm is established to optimize the classification results in the decision level. Two new phases including the worst recombination phase and the cuckoo search phase are incorporated to improve the diversity of the population and enhance the exploration. In the worst recombination phase, the worst solution is updated by a crossover recombination operation to prevent the premature convergence. The cuckoo search phase is adopted to escape the local optima. Experimental results indicate that the recognition accuracy is up to 98.9% which strongly demonstrates the effectiveness and reliability of the proposed detection method.
Symmetry2015, 7(4), 1721-1733; doi:10.3390/sym7041721 - published 28 September 2015 Show/Hide Abstract
Abstract: The mechanisms imposing the Dorsal/Ventral (DV) polarity of the early sea urchin embryo consist of a combination of inherited maternal information and inductive interactions among blastomeres. Old and recent studies suggest that a key molecular landmark of DV polarization is the expression of nodal on the future ventral side, in apparent contrast with other metazoan embryos, where nodal is expressed dorsally. A subtle maternally-inherited redox anisotropy, plus some maternal factors such as SoxB1, Univin, and p38-MAPK have been identified as inputs driving the spatially asymmetric transcription of nodal. However, all the mentioned factors are broadly distributed in the embryo as early as nodal transcription occurs, suggesting that repression of the gene in non-ventral territories depends upon negative regulators. Among these, the Hbox12 homeodomain-containing repressor is expressed by prospective dorsal cells, where it acts as a dorsal-specific negative modulator of the p38-MAPK activity. This review provides an overview of the molecular mechanisms governing the establishment of DV polarity in sea urchins, focusing on events taking place in the early embryo. Altogether, these findings provide a framework for future studies aimed to unravel the inceptive mechanisms involved in the DV symmetry breaking.