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.

Spectroscopic study on peculiarities of fumed silica hydridesilylation with triethoxysilane under fluidized bed conditions

Fumed silica has found widespread application in industry due to variety of fascinating properties. Owing to its specific manufacturing process, it consists of finely dispersed particles and is featured with large specific surface area covered by profoundly reactive silanol groups which are available for chemical grafting. Spherical shape of fumed silica particles and lacking porosity provides a space-filling structure. These characteristics implement the fume silica’s utilization as high-surface-area carriers for various catalysts, i.e. metallic nanometer-sized particles, organic moieties, etc. Currently a great attention is called to on-surface grafting to improve the silica-based carrier. Most of research is carried out in area of liquid phase chemistry involving an abundance of expensive and often toxic solvents while the space-filling properties of silica are favoring reactions in fluidized bed conditions. In current research fumed silica (A-300) was a subject for hydridesilylation with triethoxysilane under fluidized bed conditions. In all synthesis reported in current research the insignificant amount of solvent (1.00 wt. % of the amount used in typical wet-chemical modifications method) was spent for the silica surface silylation. While the mass ratio of silica/TES was kept constant, other conditions, i.e. solvent/catalyst presence, surface pretreatment, additional treatment with water, and the fluidized bed heating mode have been varied. FTIR spectroscopy revealed the interaction between groups of triethoxysilane and silica surface silanol groups and demonstrated the effect of modification conditions on the density of the hydridesilyl groups coverage. The results of FTIR spectroscopic studies have confirmed the presence of grafted silicon hydride groups on the surface of modified silica, as well as the presence of ethoxy and/or silanol groups – either intact or formed due to hydrolysis of the ethoxy groups. Titrimetric and spectrophotometric analysis was performed to estimate the concentration of grafted SiH groups (in all samples prepared under fluidized bed conditions their concentration ranged within about 0.28–0.55 mmol/g as dependent on the reaction conditions). Other important aspects of fluidization such as the presence of solvent and/or hydrolyzing agent, bed heating mode and the effect of the silica sample thermal pre-treatment are also discussed.

PointSCNet: Point Cloud Structure and Correlation Learning Based on Space-Filling Curve-Guided Sampling

Geometrical structures and the internal local region relationship, such as symmetry, regular array, junction, etc., are essential for understanding a 3D shape. This paper proposes a point cloud feature extraction network named PointSCNet, to capture the geometrical structure information and local region correlation information of a point cloud. The PointSCNet consists of three main modules: the space-filling curve-guided sampling module, the information fusion module, and the channel-spatial attention module. The space-filling curve-guided sampling module uses Z-order curve coding to sample points that contain geometrical correlation. The information fusion module uses a correlation tensor and a set of skip connections to fuse the structure and correlation information. The channel-spatial attention module enhances the representation of key points and crucial feature channels to refine the network. The proposed PointSCNet is evaluated on shape classification and part segmentation tasks. The experimental results demonstrate that the PointSCNet outperforms or is on par with state-of-the-art methods by learning the structure and correlation of point clouds effectively.

Robustness of Maximin Space-filling Designs

In this report, we first have a review of the maximin space-filling design methods that is often applied and discussed in the literature (for example, Müller (2007)). Then we will discuss the robustness of the maximin space-filling design against model misspecification via numerical simulation. For this purpose, we will generate spatial data sets on a n x n grid and design points are selected from the n2 locations. The predictions at the unsampled locations are made based on the observations at these design points. Then the mean of the squared prediction errors are estimated as a measure of the robustness of the designs against possible model misspecification. Surprisingly, according to the simulation results, we find that the maximin space-filling designs may be robust against possible model misspecification in the sense that the mean of the squared prediction error does not increase significantly when the model is misspecified. Although the results were obtained based on simple models, this result is very inspiring. It will guide further numerical and theoretical studies which will be done as future work.

MP-CE Method for Space-Filling Design in Constrained Space with Multiple Types of Factors

Space-filling design selects points uniformly in the experimental space, bringing considerable flexibility to the complex-model-based and model-free data analysis. At present, space-filling designs mostly focus on regular spaces and continuous factors, with a lack of studies into the discrete factors and the constraints among factors. Most of the existing experimental design methods for qualitative factors are not applicable for discrete factors, since they ignore the potential order or spatial distance between discrete factors. This paper proposes a space-filling method, called maximum projection coordinate-exchange (MP-CE), taking into account both the diversity of factor types and the complexity of factor constraints. Specifically, the maximum projection criterion and distance criterion are introduced to capture the “bad” coordinates, and the coordinate-exchange and the optimization of experimental design are realized by solving one-dimensional constrained optimization problem. Meanwhile, by adding iterative perturbations to the traditional coordinate exchange process, the adjacent areas of the local optimal solution are explored and the optimum performances of the current optimal solution are retained, while the shortcomings of random restart are effectively avoided. Experiments in the regular space and constraint space, as well as experimental design for the terminal interception effectiveness of a missile defense system, show that the MP-CE method significantly outperforms existing popular space-filling design methods in terms of space-projection properties, while yielding comparable or superior space-filling properties.

Management of Uncertainty in Reservoir Modelling for an Onshore Carbonate Reservoir in the Middle East: A Case Study

As part of a reservoir modelling study for an onshore oil field in the Middle East, our study implemented a workflow with the objective to evaluate the impact of uncertainty on the long-term development scenario. The presence of several geological uncertainties characterized the field: many faults with uncertainty in juxtaposition and conductivity, lateral distribution of permeability in high permeability layers, and uncertainty on the rock typing. A deterministic geological model was available. There were also many dynamic uncertainties. The workflow started with an identification of uncertain variables, both from the static and the dynamic point of view, through an integrated team approach supported by a previous reservoir synthesis (Major Field Review). Subsequently, a screening analysis allowed identifying the relative impact of uncertain variables. After selecting the uncertainties with the largest impact on recovery, use of an experimental design methodology with a space-filling design resulted in alternative history matches. Statistical analysis of forecasts yielded probability density functions and low and high estimates of ultimate recovery. Forty-five uncertain variables, including both static and dynamic uncertainties, characterized the production profiles. Screening allowed reducing these to 11 main uncertain variables. A Wootton, Sergent, Phan-Tan-Luu (WSP) space-filling design yielded 162 simulation runs. Only five out of these corresponded to acceptable history matches. This number being statistically insignificant, a reexamination of the uncertainty ranges followed by a narrowing, allowed obtaining 45 history matches (out of 198 runs). The obtained spread in the cumulative oil production was narrow, with a slightly skewed distribution around the base case (closer to P90 than to P10). The study resulted in an estimation of final uncertainty in reserves that is smaller than the typical uncertainty found in post-mortem analysis of oil field development projects. Other reservoir studies in the company and in literature, employing a similar workflow, yielded outcomes with a similar bias. To tackle this issue, as a way forward we suggest history matching of multiple geological scenarios, either with multiple deterministic cases (min, base, max) or with an ensemble history matching loop including structural model generation, in-filling, and dynamic parameter uncertainty.

Endocytic Trafficking Promotes Vacuolar Enlargements for Fast Cell Expansion Rates in Plants

The vacuole has a space-filling function, allowing a particularly rapid plant cell expansion with very little increase in cytosolic content (Loefke et al., 2015; Scheuring et al., 2016; Duenser et al., 2019). Despite its importance for cell size determination in plants, very little is known about the mechanisms that define vacuolar size. Here we show that the cellular and vacuolar size expansions are coordinated. By developing a pharmacological tool, we enabled the investigation of membrane delivery to the vacuole during cellular expansion. Counterintuitively, our data reveal that endocytic trafficking from the plasma membrane to the vacuole is enhanced in the course of rapid root cell expansion. While this "compromise" mechanism may theoretically at first decelerate cell surface enlargements, it fuels vacuolar expansion and, thereby, ensures the coordinated augmentation of vacuolar occupancy in dynamically expanding plant cells.

On biological flow networks: Antagonism between hydrodynamic and metabolic stimuli as driver of topological transitions.

A plethora of computational models have been developed in recent decades to account for the morphogenesis of complex biological fluid networks, such as capillary beds. Contemporary adaptation models are based on optimization schemes where networks react and adapt toward given flow patterns. Doing so, a system reduces dissipation and network volume, thereby altering its final form. Yet, recent numeric studies on network morphogenesis, incorporating uptake of metabolites by the embedding tissue, have indicated the conventional approach to be insufficient. Here, we systematically study a hybrid-model which combines the network adaptation schemes intended to generate space-filling perfusion as well as optimal filtration of metabolites. As a result, we find hydrodynamic stimuli (wall-shear stress) and filtration based stimuli (uptake of metabolites) to be antagonistic as hydrodynamically optimized systems have suboptimal uptake qualities and vice versa. We show that a switch between different optimization regimes is typically accompanied with a complex transition between topologically redundant meshes and spanning trees. Depending on the metabolite demand and uptake capabilities of the adaptating networks, we are further able to demonstrate the existence of nullity re-entrant behavior and the development of compromised phenotypes such as dangling non-perfused vessels and bottlenecks.