Tiling mechanisms of the compound eye through geometrical tessellation

Tilling patterns are observed in many biological structures. Hexagonal tilling, commonly observed in the compound eyes of wild-type Drosophila, is dominant in nature; this dominance can probably be attributed to physical restrictions such as structural robustness, minimal boundary length, and space filling efficiency. Surprisingly, tetragonal tiling patterns are also observed in some Drosophila small eye mutants and aquatic crustaceans. Herein, geometrical tessellation is shown to determine the ommatidial tiling patterns. In small eye mutants, the hexagonal pattern is transformed into a tetragonal pattern as the relative positions of neighboring ommatidia are stretched along the dorsal-ventral axis. Hence, the regular distribution of ommatidia and their uniform growth collectively play an essential role in the establishment of tetragonal and hexagonal tiling patterns in compound eyes.

Interplay of positive and negative feedback loops governs robustness in multistable biological networks

Biological networks are widely reported to be robust to both external and internal perturbations. However, the exact mechanisms and design principles that enable robustness are not yet fully understood. Here we investigated dynamic and structural robustness in biological networks with regards to phenotypic distribution and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yield similar phenotypic distributions. Using perturbations to network topology and by varying network parameters, we show that multistable biological networks are structurally and dynamically more robust as compared to their randomized counterparts. These features of robustness are governed by an interplay of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths and sign, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology based approach to quantify robustness in multistable biological networks.

Section Optimization Design of a Flexible Cable-Bar Tensile Structure Based on Robustness

As the current literature lacks effective nonlinear robustness evaluation method and optimal design theory of the structural robustness for flexible cable-bar tensile structure, this paper aimed to conduct further studies. Based on the theory, a fundamental robustness analysis method and a detailed calculation way through the combination of induction of performance criterion and random theory for nonlinear structural robustness quantitative evaluation method were proposed. Following this, a real Geiger cable dome structure was studied as its research object, and the influences of structural robustness of simultaneous changes of all elements section and changes of every kind of element section were analysed, respectively. Finally, the genetic algorithm was applied through MATLAB and ANSYS software to achieve optimal section layout, with the goal of minimizing structural quality on the condition that the structural robustness indicator keep less than that of the initial structure. The result revealed that the increase of the section of elements can effectively enhance structural robustness and the section changes of various elements showed different sensitivities to the influence of structural robustness. Meanwhile, structural quality can be effectively reduced by optimizing measures such as increasing the section of elements with significant effect on structural robustness and reducing the section of elements with minor effects on structural robustness, while the structural robustness indicator keeps less than that of the initial structure. The optimization reveals that quality was reduced by 42.5% in this paper.

Controlling the Structural Robustness of Zirconium-Based Metal Organic Frameworks for Efficient Adsorption on Tetracycline Antibiotics

Tetracyclines (TCs) are the most widely used antibiotics for the prevention and treatment of livestock diseases, but they are toxic to humans and have frequently been detected in water bodies. In this study, the physical and chemical properties of the zirconium-based metal organic framework (MOF) UiO-66 and its NH2-functionalized congener UiO-66-NH2 were investigated along with batch TC adsorption tests to determine the effect of functionalization on TC removal. TC removal was highest at pH 3 and decreased with increasing pH. Pseudo-1st and pseudo-2nd-order kinetic models were used to study the adsorption equilibrium times, and Langmuir isotherm model was found to be more suitable than Freundlich model. The maximum uptake for UiO-66 and UIO-66-NH2 was measured to be 93.6 and 76.5 mg/g, respectively. Unexpectedly, the TC adsorption capacity of UiO-66-NH2 was observed to be lower than that of UiO-66. Density functional theory calculations revealed that the pore structures are irrelevant to TC adsorption, and that the –NH2 functional group could weaken the structural robustness of UiO-66-NH2, causing a reduction in TC adsorption capacity. Accordingly, robust MOFs with zirconium-based metal clusters can be effectively applied for the treatment of antibiotics such as TC in water.

Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness

Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several dimensionless evaluation indexes have been defined for structural robustness so far, such as the structural reliability-based redundancy index. However, these different evaluation indexes are usually based on subjective definitions, and they are also difficult to put into engineering practice. The mathematical relational model between structural reliability and structural robustness has not been established yet. This paper is a quantitative study, focusing on the mathematical relation between structural reliability and structural robustness so as to further develop the theory of structural robustness. A strain energy evaluation index for structural robustness is introduced firstly by considering the energy principle. The mathematical relation model of structural reliability and structural robustness is then derived followed by a further comparative study on sensitivity, structural damage, and random variation factor. A cantilever beam and a truss beam are also presented as two case studies. In this study, a parabolic curve mathematical model between structural reliability and structural robustness is established. A significant variation trend for their sensitivities is also observed. The complex interaction mechanism of the joint effect of structural damage and random variation factor is also reflected. With consideration of the variation trend of the structural reliability index that is affected by different degrees of structural damage (mild impairment, moderate impairment, and severe impairment), a three-stage framework for structural life-cycle maintenance management is also proposed. This study can help us gain a better understanding of structural robustness and structural reliability. Some practical references are also provided for the better decision-making of maintenance and management departments.