Modeling piecewise helix curves from 2D sketches

We describe a method for a reconstructing piecewise helix curve from its 2D sketch. The system takes as input a hand-drawn polygonal curve and generates a piecewise helix curve such that its orthogonal projection matches the input curve. The first step is an algorithm to generate a set of helices such that their orthogonal projection approximates the input curve. This step is followed by a global optimization to minimize the tangent discontinuity of the junctions of the helices while keeping the fitting error small.     

3D medial axis point approximation using nearest neighbors and the normal field

We present a novel method to approximate medial axis points given a set of points sampled from a surface and the normal vectors to the surface at those points. For each sample point, we find its maximal tangent ball containing no other sample points, by iteratively reducing its radius using nearest neighbor queries. We prove that the center of the ball constructed by our algorithm converges to a true medial axis point as the sampling density increases to infinity. We also propose a simple heuristic to handle noisy samples. By simple extensions, our method is applied to medial axis point simplification, local feature size estimation and feature-sensitive point decimation. Our algorithm is simple, easy to implement, and suitable for parallel computation using GPU because the iteration process for each sample point runs independently. Experimental results show that our method is efficient both in time and in space.     

Warp-based helical implicit primitives

Implicit modeling with skeleton-based primitives has been limited up to now to planar skeleton elements, since no closed-form solution was found for convolution along more complex curves. We show that warping techniques can be adapted to efficiently generate convolution-like implicit primitives of varying radius along helices, a useful 3D skeleton found in a number of natural shapes. Depending on a single parameter of the helix, we warp it onto an arc of circle or onto a line segment. For those latter skeletons closed-form convolutions are known for entire families of kernels. The new warps introduced preserve the circular shape of the normal cross section to the primitive.     

Computation of lucid factors for Bezout identity

One approach to control system design is based on the Youla parameterization, and the application of this design approach requires one to solve for system coprime factors and the solution to the Bezout identity. A new and simple computational approach to acquire sets of factors that satisfy Bezout identity is developed; the algorithm along with the associated software in the MATLAB environment are presented. Previous work, required the solution to two pole-placement problems along with implementation of the Leverrier algorithm for inversion of four alphanumeric matrices. The presented software is by far less computationally intensive, and it only requires solution to a set of simultaneous linear algebraic equations.     

An algorithm for the medial axis transform of 3D polyhedral solids

The medial axis transform (MAT) is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning and tolerance specification. In this paper, an algorithm for determining the MAT is developed for general 3D polyhedral solids of arbitrary genus without cavities, with nonconvex vertices and edges. The algorithm is based on a classification scheme which relates different pieces of the medial axis (MA) to one another, even in the presence of degenerate MA points. Vertices of the MA are connected to one another by tracing along adjacent edges, and finally the faces of the axis are found by traversing closed loops of vertices and edges. Representation of the MA and its associated radius function is addressed, and pseudocode for the algorithm is given along with recommended optimizations. A connectivity theorem is proven to show the completeness of the algorithm. Complexity estimates and stability analysis for the algorithms are presented. Finally, examples illustrate the computational properties of the algorithm for convex and nonconvex 3D polyhedral solids with polyhedral holes     

Shape Smoothing Using Medial Axis Properties

A shape smoothing algorithm is presented which uses properties of the medial axis to define segments of the shape border and their prominence relative to the local radius of the shape. Prominence values are used to classify axes as either major or minor, and minor axes are then deleted. An augmented medial axis transform is also defined using an approximate Euclidean distance transform, and medial axis interpolation and linking.     

Global Structure Optimization of Quadrilateral Meshes

We introduce a fully automatic algorithm which optimizes the high‐level structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since state‐of‐the‐art quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element alignment, but usually they are still far away from the high‐level structure which is typical for carefully designed meshes manually created by specialists and used e.g. in animation or simulation. In this paper we show that the quality of the high‐level structure is negatively affected by helical configurations within the quadrilateral mesh. Consequently we present an algorithm which detects helices and is able to remove most of them by applying a novel grid preserving simplification operator (GP‐operator) which is guaranteed to maintain an all‐quadrilateral mesh. Additionally it preserves the given singularity distribution and in particular does not introduce new singularities. For each helix we construct a directed graph in which cycles through the start vertex encode operations to remove the corresponding helix. Therefore a simple graph search algorithm can be performed iteratively to remove as many helices as possible and thus improve the high‐level structure in a greedy fashion. We demonstrate the usefulness of our automatic structure optimization technique by showing several examples with varying complexity.     

Identification of the most significant amphipathic helix with application to HIV and MHV envelope proteins

Amphipathic helices, which play important roles in protein structure, occur in a wide variety of lengths. Yet existing methods employ fixed window lengths. We present a hierarchical procedure that identifies the Q most significant amphipathic helices regardless of length. Since the observed hydrophobicities are not normally distributed, test statistics usually employed for least-squares regression are inappropriate for assessing statistical significance of amphipathic helices. We show that an adjusted F statistic provides a good test. An application to the envelope protein of HIV finds an unexpected long amphipathic helix in gp41.     

Automatic RNA secondary structure prediction with a comparative approach

This paper presents an algorithm, DCFold, that automatically predicts the common secondary structure of a set of aligned homologous RNA sequences. It is based on the comparative approach. Helices are searched in one of the sequences, called the 'target sequence', and compared to the helices in the other sequences, called the 'test sequences'. Our algorithm searches in the target sequence for palindromes that have a high probability to define helices that are conserved in the test sequences. This selection of significant palindromes is based on criteria that take into account their length and their mutation rate. A recursive search of helices, starting from these likely ones, is implemented using the 'divide and conquer' approach. Indeed, as pseudo-knots are not searched by DCFold, a selected palindrome (p, p') makes possible to divide the initial sequence into two sequences, the internal one and the one resulting from the concatenation of the two external ones. New palindromes can be searched independently in these subsequences. This algorithm was run on ribosomal RNA sequences and recovered very efficiently their common secondary structures.     

Algorithms for finding the axis of a helix: Fast rotational and parametric least-squares methods

Several methods for finding the axis of a helix are presented and compared. The most accurate determines the helix axis as the axis of rotation necessary to map point i to point i + 1 of the helix. The fastest method calculates the helix axis as the best-fit line through the coordinates by a three-dimensional parametric linear least-squares algorithm, taking advantage of the sequential nature of the data.     

Binding and discerning interactions of PTP1B allosteric inhibitors: Novel insights from molecular dynamics simulations

The α7 helix is either disordered or missing in the three co-crystal structures of allosteric inhibitors with protein tyrosine phosphatase 1B (PTP1B). It was modeled in each complex using the open form of PTP1B structure and studied using molecular dynamics (MD) simulations for 25 ns. B-factor analysis of the residues sheds light on its disordered nature in the co-crystal structures. Further, the ability of inhibitors to act as allosteric inhibitor was studied and established using novel hydrogen bond criteria. The MD simulations were utilized to determine the relative importance of electrostatic and hydrophobic component in to the binding of inhibitors. It was revealed that the hydrophobic interactions predominantly drive the molecular recognition of these inhibitors. Per residue energy decomposition analysis attributed dissimilar affinities of three inhibitors to the several hydrogen bonds and non-bonded interactions. Among the secondary structure elements that surround the allosteric site, helices α6, α7 and loop α6–α7 were notorious in providing variable affinities to the inhibitors. A novel hydrophobic pocket lined by the α7 helix residues Val287, Asn289 and Trp291 was identified in the allosteric site. This study provides useful insights for the rational design of high affinity PTP1B allosteric inhibitors.     

运动物体位移及姿态参数的一种图像测量方法

利用散焦图像深度估计原理,给出了一种运动物体移动距离和姿态的测量方法,并对 图像特征点的获取和跟踪方法作了研究．该测量方法首先在物体上设置了四个明暗分明的圆 形特征点,然后根据物体运动过程中特征点图像边缘的模糊程度,测量计算物体沿摄像机光 轴的移动距离．当物体发生倾斜后,可由被测量的四个特征点沿光轴的移动距离值不同来计 算物体的倾斜角．该方法仅需一台摄像机,测量原理简单,计算量小,能满足实时性要求, 并具有一定的测量精度．     

Dynamic analysis of multibody systems using component modes

This paper is concerned with dynamic analysis of flexible multibody systems. The configuration of each elastic components is identified by three sets of modes; rigid-body, reference, and normal modes. Rigid body modes are introduced using a set of Lagrangian coordinates that describe rigid-body translation and large rotations of a body reference. Reference modes are defined using a set of reference conditions that are required to define a unique displacement field. These reference conditions, that define the nature of the body axes, have to be consistent with the system constraint equations. Their number should be equal or greater than the number of the rigid-body modes. Normal modes, however, define the deformation relative to the body reference. An automated scheme for imposing the boundary conditions of a constrained flexible component in a multibody system is presented. It is also shown that the mean axis and the body-fixed axis are the result of imposing a special set of reference conditions.     

Position of helical kinks in membrane protein crystal structures and the accuracy of computational prediction

The structural features of helical transmembrane (TM) proteins, such as helical kinks, tilts, and rotational orientations are important in modulation of their function and these structural features give rise to functional diversity in membrane proteins with similar topology. In particular, the helical kinks caused by breaking of the backbone hydrogen bonds lead to hinge bending flexibility in these helices. Therefore it is important to understand the nature of the helical kinks and to be able to reproduce these kinks in structural models of membrane proteins. We have analyzed the position and extent of helical kinks in the transmembrane helices of all the crystal structures of membrane proteins taken from the MPtopo database, which are about 405 individual helices of length between 19 and 35 residues. 44% of the crystal structures of TM helices showed a significant helical kink, and 35% of these kinks are caused by prolines. Many of the non-proline helical kinks are caused by other residues like Ser and Gly that are located at the center of helical kinks. The side chain of Ser makes a hydrogen bond with the main chain carbonyl of the i − 4th or i + 4th residue thus making a kink. We have also studied how well molecular dynamics (MD) simulations on isolated helices can reproduce the position of the helical kinks in TM helices. Such a method is useful for structure prediction of membrane proteins. We performed MD simulations, starting from a canonical helix for the 405 TM helices. 1 ns of MD simulation results show that we can reproduce about 79% of the proline kinks, only 59% of the vestigial proline kinks and 18% of the non-proline helical kinks. We found that similar results can be obtained from choosing the lowest potential energy structure from the MD simulation. 4–14% more of the vestigial prolines were reproduced by replacing them with prolines before performing MD simulations, and changing the amino acid back to proline after the MD simulations. From these results we conclude that the position of the helical kinks is dependent on the TM sequence. However the extent of helical kinking may depend on the packing of the rest of the protein and the lipid bilayer.     

Position of helical kinks in membrane protein crystal structures and the accuracy of computational prediction

The structural features of helical transmembrane (TM) proteins, such as helical kinks, tilts, and rotational orientations are important in modulation of their function and these structural features give rise to functional diversity in membrane proteins with similar topology. In particular, the helical kinks caused by breaking of the backbone hydrogen bonds lead to hinge bending flexibility in these helices. Therefore it is important to understand the nature of the helical kinks and to be able to reproduce these kinks in structural models of membrane proteins. We have analyzed the position and extent of helical kinks in the transmembrane helices of all the crystal structures of membrane proteins taken from the MPtopo database, which are about 405 individual helices of length between 19 and 35 residues. 44% of the crystal structures of TM helices showed a significant helical kink, and 35% of these kinks are caused by prolines. Many of the non-proline helical kinks are caused by other residues like Ser and Gly that are located at the center of helical kinks. The side chain of Ser makes a hydrogen bond with the main chain carbonyl of the i − 4th or i + 4th residue thus making a kink. We have also studied how well molecular dynamics (MD) simulations on isolated helices can reproduce the position of the helical kinks in TM helices. Such a method is useful for structure prediction of membrane proteins. We performed MD simulations, starting from a canonical helix for the 405 TM helices. 1 ns of MD simulation results show that we can reproduce about 79% of the proline kinks, only 59% of the vestigial proline kinks and 18% of the non-proline helical kinks. We found that similar results can be obtained from choosing the lowest potential energy structure from the MD simulation. 4–14% more of the vestigial prolines were reproduced by replacing them with prolines before performing MD simulations, and changing the amino acid back to proline after the MD simulations. From these results we conclude that the position of the helical kinks is dependent on the TM sequence. However the extent of helical kinking may depend on the packing of the rest of the protein and the lipid bilayer.     

基于GhostNet残差结构的轻量化饮料识别网络

YOLOv4-Tiny目标检测网络算法存在参数多和计算量大等问题,无法部署在资源有限的平台上。提出一种基于GhostNet残差结构的主干轻量级目标检测网络算法YOLO-GhostNet。该算法采用GhostNet结构将普通卷积分成两步,即使用较少的卷积核生成一部分特征图,对生成的特征图通过简单计算获得另一部分特征图,并将两组特征图进行拼接,以减少计算所需资源与参数量。通过GhostNet构建残差结构的YOLO-GhostNet算法在经过批量归一化层优化后模型尺寸只有2.18 MB,较YOLOv4-Tiny算法模型尺寸减小90%。YOLO-GhostNet算法在GPU加速环境下平均处理图片速度比YOLOv4-Tiny算法提高24%,CPU处理速度比YOLOv4-Tiny加快56%。实验结果表明,该算法在饮料测试集中的平均精确度均值达到79.43%,相比YOLOv4-Tiny算法,其在精度无损失情况下能够大幅降低网络计算量和参数量,同时加快推理速度,更适合部署于资源算力不足的嵌入式设备。     

A Shape Metric for Blum Ribbons

A Blum ribbon is a figure whose boundary is the envelope of a family of circles the centers of which lie along a single unbranched curve called its medial axis. Define a Blum ribbon to be simple if its medial axis is the line segment joining points (0,0) and (1,0). Any Blum ribbon can be made simple by flexing the medial axis, rotating, then dilating, all of which are basic transformations in Blum's geometry of shape. The Lie group SL(2, R) acts on circles centered on the x-axis by linear fractional transformations. By means of this action it is possible to associate to any simple Blum ribbon a curve in SL(2, R). A distance between corresponding points lying on such curves is defined using the bi-invariant metric on SL(2, R). Resulting scale-invariant metrics on the set of figures defined as Blum ribbons are described and it is shown that these metrics can provide effective measures of shape difference.     

A parallel residue-to-binary conversion algorithm without trial division

In recent years, the conversion of residue numbers to a binary integer has been intensively studied. The Chinese Remainder Theorem (CRT) is a solution to this conversion problem of a number to the Residue Number System with a general moduli set. This paper presents a new division-free conversion approach for the conversion of residue numbers to a binary integer. The algorithm differs from others employing a great number of division instructions by using shift instructions instead. These simple instructions keep the power consumption lower. This algorithm can also be implemented with a lookup table or upon a vector machine. Both make the conversion process efficient. This division-free algorithm employs the concept of Montgomery multiplication algorithm. There are two variations of Montgomery algorithm proposed, which are algorithms MMA and IMA. The algorithm MMA is to transform the input number into the output presentation of Montgomery algorithm. Algorithm IMA is therefore inverse the computation of Montgomery algorithm to obtain the multiplicand. These two algorithms are in the complexity of O(n), where n is log₂ q_i. q_i is a modulus. The proposed algorithm for converting the residues to a binary integer therefore runs on O(n × log m) times on O(m) processors. There are O(log m) iterations of O(n) complexity. Compared with the traditional conversion algorithm, the advantages of this proposed algorithm are not only in employing simpler operations but also in performing fewer iterations.