Algorithm for the Conformal 3D Printing on Non-Planar Tessellated Surfaces: Applicability in Patterns and Lattices

In contrast to the traditional 3D printing process, where material is deposited layer-by-layer on horizontal flat surfaces, conformal 3D printing enables users to create structures on non-planar surfaces for different and innovative applications. Translating a 2D pattern to any arbitrary non-planar surface, such as a tessellated one, is challenging because the available software for printing is limited to planar slicing. The present research outlines an easy-to-use mathematical algorithm to project a printing trajectory as a sequence of points through a vector-defined direction on any triangle-tessellated non-planar surface. The algorithm processes the ordered points of the 2D version of the printing trajectory, the tessellated STL files of the target surface, and the projection direction. It then generates the new trajectory lying on the target surface with the G-code instructions for the printer. As a proof of concept, several examples are presented, including a Hilbert curve and lattices printed on curved surfaces, using a conventional fused filament fabrication machine. The algorithm’s effectiveness is further demonstrated by translating a printing trajectory to an analytical surface. The surface is tessellated and fed to the algorithm as an input to compare the results, demonstrating that the error depends on the resolution of the tessellated surface rather than on the algorithm itself.

BayesProject: Fast computation of a projection direction for multivariate changepoint detection

This article focuses on the challenging problem of efficiently detecting changes in mean within multivariate data sequences. Multivariate changepoints can be detected by projecting a multivariate series to a univariate one using a suitable projection direction that preserves a maximal proportion of signal information. However, for some existing approaches the computation of such a projection direction can scale unfavourably with the number of series and might rely on additional assumptions on the data sequences, thus limiting their generality. We introduce BayesProject, a computationally inexpensive Bayesian approach to compute a projection direction in such a setting. The proposed approach allows the incorporation of prior knowledge of the changepoint scenario, when such information is available, which can help to increase the accuracy of the method. A simulation study shows that BayesProject is robust, yields projections close to the oracle projection direction and, moreover, that its accuracy in detecting changepoints is comparable to, or better than, existing algorithms while scaling linearly with the number of series.

A device for exploring the full angular excitation space - Can more angular projections improve determination of a molecules 3D-orientation in the presence of noise?

In the past, different methods have been presented to determine the 3D orientation of single molecules in a microscopic set-up by excitation polarization modulation. Using linearly polarized illumination from different directions and thereby measuring different 2D projections enables reconstructing the full 3D orientation. Theoretically, two projections suffice for a full 3D orientation determination if the intensities are properly calibrated. If they are not, a third projection will enable unambiguous orientation measurements. The question arises if three projections already contain the maximum information on the 3D orientation when also considering the limited number of available photons and shot noise in an experiment, or if detecting more projections or even continuously changing the projection direction during a measurement provides more information with an identical number of available photons. To answer this principle question, we constructed a simple device allowing for exploring any projection direction available with a particular microscope objective and tested several different excitation modulation schemes using simulated as well as experimental single molecule data. We found that three different projections in fact already do provide the maximum information also for noisy data. Our results do not indicate a significant improvement in angular precision in comparison to three projections, both when increasing the number of projections and when modulating the projection direction and polarization simultaneously during the measurement.In fluorescence microscopy polarized illumination from different directions enables the determination of the 3D orientation of single molecules by combining the 2D information of different projection directions. Ambiguities that emerge when using only two projections can be eliminated using a third projection. In a systematic study we show that – also considering the limited number of available photons and shot noise in an experiment – three projection directions already contain the maximum information on the 3D orientation. Our results do not indicate a significant improvement in angular precision in comparison to three projections, both when increasing the number of projections and when modulating the projection direction and polarization simultaneously during the measurement.

Analysis and Comprehensive Evaluation of Water Use Efficiency in China

Proper water use requires its monitoring and evaluation. An indexes system of overall water use efficiency is constructed here that covers water consumption per 10,000 yuan GDP, the coefficient of effective utilization of irrigation water, the water consumption per 10,000 yuan of industrial value added, domestic water consumption per capita of residents, and the proportion of water function zone in key rivers and lakes complying with water-quality standards and is applied to 31 provinces in China. Efficiency is first evaluated by a projection pursuit cluster model. Multidimensional efficiency data are transformed into a low-dimensional subspace, and the accelerating genetic algorithm then optimizes the projection direction, which determines the overall efficiency index. The index reveals great variety in regional water use, with Tianjin, Beijing, Hebei, and Shandong showing highest efficiency. Shanxi, Liaoning, Shanghai, Zhejiang, Henan, Shanxi, and Gansu also use water with high efficiency. Medium efficiency occurs in Inner Mongolia, Jilin, Heilongjiang, Jiangsu, Hainan, Qinghai, Ningxia, and Low efficiency is found for Anhui, Fujian, Jiangxi, Hubei, Hunan, Guangdong, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, and Xinjiang. Tibet is the least efficient. The optimal projection direction is a* = (0.3533, 0.7014, 0.4538, 0.3315, 0.1217), and the degree of influence of agricultural irrigation efficiency, water consumption per industrial profit, water used per gross domestic product (GDP), domestic water consumption per capita of residents, and environmental water quality on the result has decreased in turn. This may aid decision making to improve overall water use efficiency across China.

A Powerful Global Test Statistic for Functional Statistical Inference

We consider the problem of performing an association test between functional data and scalar variables in a varying coefficient model setting. We propose a functional projection regression model and an associated global test statistic to aggregate relatively weak signals across the domain of functional data, while reducing the dimension. An optimal functional projection direction is selected to maximize signal-to-noise ratio with ridge penalty. Theoretically, we systematically study the asymptotic distribution of the global test statistic and provide a strategy to adaptively select the optimal tuning parameter. We use simulations to show that the proposed test outperforms all existing state-of-the-art methods in functional statistical inference. Finally, we apply the proposed testing method to the genome-wide association analysis of imaging genetic data in UK Biobank dataset.

Globality-Locality Preserving Maximum Variance Extreme Learning Machine

An extreme learning machine (ELM) is a useful technique for machine learning; however, the existing extreme learning machine methods cannot exploit the geometric structure information or discriminate information of the data space well. Therefore, we propose a globality-locality preserving maximum variance extreme learning machine (GLELM) based on manifold learning. Based on the characteristics of the traditional ELM method, GLELM introduces the basic principles of linear discriminant analysis (LDA) and local preservation projection (LPP) into ELM, fully taking account of the discriminant information contained in the sample. This method can preserve the global and local manifold structures of data to optimize the projection direction of the classifier. Experiments on several widely used image databases and UCI datasets validate the performance of GLELM. The experimental results show that the proposed model achieves promising results compared to several state-of-the-art ELM algorithms.

CONSTRUCTING PATHS TO AVOID MULTIPLE OBSTACLES

This article deals with the issues of modeling the trajectory of an object moving on a plane, on the path of which there may be obstacles. The authors propose an algorithm for changing the initial trajectory of the object taking into account the movement of obstacles. At the beginning, we describe how to divide the initial trajectory into sections. Then we describe how to modify the line on each segment in two cases, depending on the angle between the projection direction and the direction of movement of the center of the obstacle.

From space to time: Spatial inhomogeneities lead to the emergence of spatio-temporal activity sequences in spiking neuronal networks

Spatio-temporal sequences of neuronal activity are observed in many brain regions in a variety of tasks and are thought to form the basis of any meaningful behavior. Mechanisms by which a neuronal network can generate spatio-temporal activity sequences have remained obscure. Existing models are biologically untenable because they require manual embedding of a feedforward network within a random network or supervised learning to train the connectivity of a network to generate sequences. Here, we propose a biologically plausible, generative rule to create spatio-temporal activity sequences in a network model of spiking neurons with distance dependent connectivity. We show that the emergence of spatio-temporal activity sequences requires: (1) individual neurons preferentially project a small fraction of their axons in a specific direction, and (2) the preferential projection direction of neighboring neurons is similar. Thus, an anisotropic but correlated connectivity of neuron groups suffices to generate spatio-temporal activity sequences in an otherwise random neuronal network model.