Minimum Distance Function Research Articles

Regularity index of the generalized minimum distance function

We show that the generalized minimum distance function is non-increasing as the degree varies for reduced standard graded algebras over a field. This allows us to define its regularity index and its stabilization value. The stabilization value is computed for every cases. We study how the regularity index varies as the number of polynomial increases, and use this to give bounds for it.

Study on Burning Surface Regression Algorithm under Erosive Burning Based on CT Images of Solid Rocket Motor Grain

The presence of the erosive burning effect during the operation of a solid rocket motor (SRM) is one of the most important factors affecting the proper operation of the motor. To solve the effects of the operating process of the motor under erosive burning, a synthesis algorithm based on the actual CT images is proposed to combine the Level-set (LS) method with the minimum distance function (MDF) method for the simulation of the burning surface regression of the grain under erosive burning. The Hamilton–Jacobi control equation can be solved exactly for the discrete form of LS. To improve the computational efficiency of the LS method, the minimum distance field is initialized and only the distortion grid is adjusted during the reinitialization. The third-order TVD Runge–Kutta method is used to solve the problem of numerical oscillation and improve the calculation accuracy. The experiments simulate the burning process of the NAWC No. 6 partial grain under erosive burning, which can provide the main basis for the performance design of solid propellant. The experimental results show that the method has good applicability to three-dimensional complex grains. It can realize the simulation of grains under erosive burning and its calculation accuracy is high.

Fast evaluation of smooth distance constraints on co-dimensional geometry

We present a new method for computing a smooth minimum distance function based on the LogSumExp function for point clouds, edge meshes, triangle meshes, and combinations of all three. We derive blending weights and a modified Barnes-Hut acceleration approach that ensure our method approximates the true distance, and is conservative (points outside the zero isosurface are guaranteed to be outside the surface) and efficient to evaluate for all the above data types. This, in combination with its ability to smooth sparsely sampled and noisy data, like point clouds, shortens the gap between data acquisition and simulation, and thereby enables new applications such as direct, co-dimensional rigid body simulation using unprocessed lidar data.

Layout optimization for safety evaluation on LNG-fueled ship under an accidental fuel release using mixed-integer nonlinear programming

The Liquefied Natural Gas (LNG)-fueled ship is an alternative solution to deal with the Emission Control Area (ECA) issued by the International Maritime Organization (IMO). LNG fuel has eco-green characteristics since sulfur oxide and particulate matter are eliminated. The equipment sitting on the Fuel Gas Supply System (FGSS) layout needs a good arrangement to prevent the domino effect. This study’s scopes are to establish the feasible FGSS layout based on the equipment position and conduct an accidental LNG release that adopts the Computational Fluid Dynamics (CFD). Mixed-Integer Nonlinear Programming (MINLP) is provided as an optimization tool. The MINLP framework is written in the Python programming language. The minimum separation distance, deck size, and non-overlapping functions of equipment are included as the MINLP constraint. The separation distances are provided based on the Center of Chemical Process Safety (CCPS) recommendation. Also, several options of the separation distance are added that consist of 5.0, 6.0, and 7.0 m to observe the congestion effect. The total pipe length is considered as the MINLP objective that can be used to estimate the pipe cost. The proposed MINLP framework is designated to generate a feasible layout that has an adequate separation distance and minimum cost of the pipe. CFD results show that the increase of separation distance can reduce the gas accumulation effectively which eventually reduces the severity of other consequences. Finally, the feasible layout is proposed based on a series of several consequences under an accidental LNG release, such as gas dispersion, fire, and vapor cloud explosion.

Three-Dimensional Distance Maps of Ankle and Syndesmotic Joints from Weightbearing CT in Progressive Collapsing Foot Deformity: A Retrospective Case-Control Study

Category:AnkleIntroduction/Purpose:Recently, weightbearing computed tomography (WBCT) has been utilized to provide more comprehensive and accurate assessment of complex foot and ankle deformities, notably to diagnose and stage Progressive Collapsing Foot Deformity (PCFD). The 3D data provided by WBCT has enabled the developed of novel tools like distance mapping (DM), coverage mapping (CM), and volume measurements. Over the past year, novel DM and CM have shown promise in providing sensitive automated measures of peritalar subluxation, a major component of PCFD. However, the early effects of PCFD on the tibiotalar joint have not yet been quantified. This study sought to use DM and CM to objectively characterize the effects of PCFD on the tibiotalar and tibiofibular joints. We hypothesized that changes seen in early PCFD will be identified.Methods:IRB approval for retrospective review of patient data from 2014-2020 was obtained to identify patients with clinical and radiographic diagnoses of PCFD. The first consecutive 20 patients with symptomatic flexible PCFD and high-resolution weightbearing CT examination without arthritis that had not undergone prior surgery were selected and compared with 20 controls. Fully automated volume measurements of the syndesmosis at 1cm, 3cm, and 5cm from the tibiotalar joint were performed as well as of the medial and lateral tibiotalar gutters based on models created in Disior Bonelogic. Distance Maps (DMs) were obtained for the tibiofibular incisura, tibiotalar joint, and gutters. Coverage maps (CMs) were created using the measured 3DDMs to identify joint interaction, subluxation, and impingement. Data were checked for normality using the Shapiro- Wilk W test. Two-tailed independent samples student t-tests or Wilcoxon Tests were used to assess differences between groups.Results:There were significant decreases in coverage of all 3 anterior regions of the tibiotalar joint in PCFD patients when compared to controls along with corresponding significant increases in coverage of all 3 posterior regions (Figure). There were no significant differences in mean or minimum distances in any region of the tibiotalar joint surface. Significant increases in average and minimum DMs of the anterior medial (36%, p<0.01, 19%, p<0.03) gutter were observed with significant decreases in coverage of both anterior medial and anterior lateral regions. Significant decreases in the average and minimum distances of the tibiofibular joint were found anteriorly in PCFD patients compared to controls (-26%, p<0.006). There were no significant differences in overall syndesmotic distance or volume at any level.Conclusion:The results of our study were able to identify that, compared to controls, patients with early stage PCFD demonstrated significant tibiotalar and tibiofibular joint changes ahead of developing the tibiotalar narrowing associated with arthritis and syndesmotic widening associated with instability. Decreases in anterior coverage with increases posteriorly support early plantarflexion of the talus in PCFD. When combined with plantarflexion of the talus and unchanged syndesmotic volume, decreases in anterior tibiofibular distances support the absence of syndesmotic joint instability in early PCFD. Novel tools may assist with clinical decision-making regarding restoration of normal tibiotalar and tibiofibular alignment during PCFD correction.

Bounds for the minimum distance function

Abstract Let I be a homogeneous ideal in a polynomial ring S. In this paper, we extend the study of the asymptotic behavior of the minimum distance function δI of I and give bounds for its stabilization point, rI , when I is an F -pure or a square-free monomial ideal. These bounds are related with the dimension and the Castelnuovo–Mumford regularity of I.

Energy Conservation for Internet of Things Tracking Applications Using Deep Reinforcement Learning.

The Internet of Things (IoT)-based target tracking system is required for applications such as smart farm, smart factory, and smart city where many sensor devices are jointly connected to collect the moving target positions. Each sensor device continuously runs on battery-operated power, consuming energy while perceiving target information in a particular environment. To reduce sensor device energy consumption in real-time IoT tracking applications, many traditional methods such as clustering, information-driven, and other approaches have previously been utilized to select the best sensor. However, applying machine learning methods, particularly deep reinforcement learning (Deep RL), to address the problem of sensor selection in tracking applications is quite demanding because of the limited sensor node battery lifetime. In this study, we proposed a long short-term memory deep Q-network (DQN)-based Deep RL target tracking model to overcome the problem of energy consumption in IoT target applications. The proposed method is utilized to select the energy-efficient best sensor while tracking the target. The best sensor is defined by the minimum distance function (i.e., derived as the state), which leads to lower energy consumption. The simulation results show favorable features in terms of the best sensor selection and energy consumption.

3D Hand Gestures Segmentation and Optimized Classification Using Deep Learning

Hand gestures recognition system has massive applications which are mainly utilized in robotics and computer vision specially to control Unmanned Aerial Vehicles (UAV). These methods bypass the presence of electronic control to UAVs and provide an ease to the operators. In this paper, we present a method for 3D hand gestures segmentation and classification by combining MASK-RCNN with Grass Hopper Optimization. We created a private 3D and RGB hand gestures dataset using Intel Kinetic and Intel Real sense d435i camera, then proposed a model for RGB hand gestures to estimate the key points using human kinematics, the key points later then utilize to get the best degree of freedom (DoF). The grass hopper optimization besides minimum distance function was applied to achieve the finest deep features from the 3D hand gestures dataset. The ResNet50 network is used as the backbone to calculate the Overlap Coefficient (OC) for segmentation and the ResNet50, ResNet101 networks to calculate the classification for 3D hand gestures. The classification accuracy achieved on the private dataset is 99.05% and 99.29% on public Microsoft Kinect and Leap Motion dataset where the OC are 88.16%. and 88.19% respectively.

Solid rocket motor propellant grain burnback simulation based on fast minimum distance function calculation and improved marching tetrahedron method

To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor, a unified framework of burning surface regression simulation has been developed based on minimum distance function. In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface, a fast distance querying method based on the equal size cube voxel structure was employed. An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements, achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously. The cases of star grain, finocyl grain, and non-uniform tube grain were studied to verify the proposed method. The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.

Facility location games with optional preference

In this paper, we study the optional preference model of the facility location game problem with two heterogeneous facilities on a line. The preference of each agent is one of the two facilities or both facilities, and the cost of each agent is a function of the distances to the facilities that the agent prefers. We consider two cost functions: Minimum Distance and Maximum Distance functions. Aiming at minimizing the maximum cost or the social cost of agents, we propose different strategyproof mechanisms without monetary transfers and derive both lower and upper bounds of the approximation ratios with respect to strategyproof mechanisms. In the variant of Minimum Distance, we propose a 2-approximation deterministic strategyproof mechanism for the maximum cost objective, and prove a lower bound of 4/3, while for the social cost objective we propose a (n/2+1)-approximation deterministic strategyproof mechanism and prove a lower bound of 2, also a lower bound of 3/2 for randomized mechanisms. In the variant of Maximum Distance, we propose an optimal deterministic strategyproof mechanism for the maximum cost objective and a 2-approximation deterministic strategyproof mechanism for the social cost objective.

Development of a hybrid method in a 3-D numerical burn-back analysis for solid propellant grains

This study was performed to analyze the performance of a solid propulsion system quickly and accurately. Systems that are currently in operation use a propellant with a complicated configuration to satisfy the performance requirements. Multi-dimensional internal ballistics analysis is essential in this case. The propellant's burning surfaces move in all directions, and the local burning velocity changes, so a 3-D analysis technique is necessary for the moving boundary. Previous research focused on improving the accuracy of the combustion configuration analysis using new methods, but it is difficult to apply them because user convenience was not considered. Therefore, the problems of the analysis methods were analyzed, and a hybrid burn-back analysis method was developed. The method's accuracy was improved by selectively using the minimum distance function (MDF) manipulation method, which has fast calculation speed, as well as a level set method for regions where the configuration of the propellant grains is complicated. The results verified that the accuracy was increased, and the calculation time was reduced.

Topology optimization for three-dimensional design of segmented permanent magnet arrays

This paper proposes a topology optimization formulation for the three-dimensional (3-D) design of segmented permanent magnet (PM) arrays. Specifically, the proposed formulation aims to find an optimal 3-D structural topology of PM segments and their discrete magnetization directions. To achieve this, a design variable is defined in the vector form of a Cartesian coordinate system. The magnitude of the design variable vector determines a PM density, and the directional cosines of the vector determine PM magnetization directions. To acquire a segmented PM design with discrete magnetization directions, a PM strength penalization scheme is proposed. In this scheme, a PM strength is controlled using a minimum distance function between a magnetization direction and target discrete directions. Here, the minimum distance function is approximated using the p-norm for sensitivity calculation. To validate the effectiveness of the proposed formulation, three design examples are provided. In the first example, a two-dimensional (2-D) dipole Halbach cylinder is designed to confirm that the proposed formulation can be applied for a 2-D design problem. The second example aims to design 3-D dipole PM arrays with a cuboid cavity. In the third example, a 3-D PM arrays are designed for maximizing the magnetic force acting on a soft ferromagnetic material.

Multiple-Mixing-Cell Model for Calculation of Minimum Miscibility Pressure Controlled by Tie-Line Length

A simple and robust algorithm has been developed to calculate the minimum miscibility pressure (MMP), which is considered one of the crucial and essential design parameters of miscible gas injection projects for enhanced oil recovery (EOR). This algorithm is to track all tie-line lengths through the cell-cell calculation by the minimum distance function for the prediction of MMP. The MMP is the pressure at which any one of all key tie-line lengths becomes zero. To verify the accuracy of the revised MMC algorithm for determining MMP, several examples taken from the published literature have been examined. The calculation results of our revised MMC algorithm show excellent agreement with those estimated by MOC, MMC, and slim-tube experiments, which are found to be reliable within acceptable accuracy (4.53%-0.50%).

Generalized minimum distance functions and algebraic invariants of Geramita ideals

Motivated by notions from coding theory, we study the generalized minimum distance (GMD) function δI(d,r) of a graded ideal I in a polynomial ring over an arbitrary field using commutative algebraic methods. It is shown that δI is non-decreasing as a function of r and non-increasing as a function of d. For vanishing ideals over finite fields, we show that δI is strictly decreasing as a function of d until it stabilizes. We also study algebraic invariants of Geramita ideals. Those ideals are graded, unmixed, 1-dimensional and their associated primes are generated by linear forms. We also examine GMD functions of complete intersections and show some special cases of two conjectures of Tohăneanu–Van Tuyl and Eisenbud-Green-Harris.

Optimization of planar mechanisms by using a minimum distance function

The paper examines the application of a general minimum distance error function to the dimensional kinematic synthesis of bidimensional mechanisms. The minimum distance approach makes it possible to solve the problem maintaining the same generality as that of the minimum deformation energy method while solving the problems that occasionally appear in the former method involving low stiffness mechanisms. It is a general method that can deal both with unprescribed and prescribed timing problems, and is applicable for path generation problems, function generation, solid guidance, and any combination of the aforementioned requirements as introduced in the usual precision point scheme. The method exhibits good convergence and computational efficiency. The minimum distance error function is solved with a sequential quadratic programming (SQP) approach. In the study, the synthesis problem is also optimized by using SQP, and the function can be easily adapted to other methods such as genetic algorithms.In the study, the minimum distance approach is initially presented. Subsequently, an efficient SQP method is developed by using analytic derivatives for solving. The next point addresses the application of the concept for the synthesis of mechanisms by using an SQP approach with approximate derivatives. This delivers a situation where the optimization is performed on an error function that itself consists of an inner optimization function. A few examples are presented and are also compared with the minimum deformation energy method. Finally, a few conclusions and future studies are discussed.

Solving geoinformatics parametric polynomial systems using the improved Dixon resultant

Improvements in computational and observational technologies in geoinformatics, e.g., the use of laser scanners that produce huge point cloud data sets, or the proliferation of global navigation satellite systems (GNSS) and unmanned aircraft vehicles (UAVs), have brought with them the challenges of handling and processing this “big data”. These call for improvement or development of better processing algorithms. One way to do that is integration of symbolically presolved sub-algorithms to speed up computations. Using examples of interest from real geoinformatic problems, we will discuss the Dixon-EDF resultant as an improved resultant method for the symbolic solution of parametric polynomial systems. We will briefly describe the method itself, then discuss geoinformatics problems arising in minimum distance mapping (MDM), parameter transformations, and pose estimation essential for resection. Dixon-EDF is then compared to older notions of “Dixon resultant”, and to several respected implementations of Grobner bases algorithms on several systems. The improved algorithm, Dixon-EDF, is found to be greatly superior, usually by orders of magnitude, in both CPU usage and RAM usage. It can solve geoinformatics problems on which the other methods fail, making symbolic solution of parametric systems feasible for many problems.

Minimum distance functions of complete intersections

We study the minimum distance function of a complete intersection graded ideal in a polynomial ring with coefficients in a field. For graded ideals of dimension one, whose initial ideal is a complete intersection, we use the footprint function to give a sharp lower bound for the minimum distance function. Then we show some applications to coding theory.

Generalized minimum distance functions

Using commutative algebra methods, we study the generalized minimum distance function (gmd function) and the corresponding generalized footprint function of a graded ideal in a polynomial ring over a field. The number of solutions that a system of homogeneous polynomials has in any given finite set of projective points is expressed as the degree of a graded ideal. If $${\mathbb {X}}$$ is a set of projective points over a finite field and I is its vanishing ideal, we show that the gmd function and the Vasconcelos function of I are equal to the rth generalized Hamming weight of the corresponding Reed–Muller-type code $$C_{\mathbb {X}}(d)$$ of degree d. We show that the generalized footprint function of I is a lower bound for the rth generalized Hamming weight of $$C_{\mathbb {X}}(d)$$ . Then, we present some applications to projective nested Cartesian codes. To give applications of our lower bound to algebraic coding theory, we show an interesting integer inequality. Then, we show an explicit formula and a combinatorial formula for the second generalized Hamming weight of an affine Cartesian code.

Implementing Speed and Separation Monitoring in Collaborative Robot Workcells.

We provide an overview and guidance for the Speed and Separation Monitoring methodology as presented in the International Organization of Standardization's technical specification 15066 on collaborative robot safety. Such functionality is provided by external, intelligent observer systems integrated into a robotic workcell. The SSM minimum protective distance function equation is discussed in detail, with consideration for the input values, implementation specifications, and performance expectations. We provide analytical analyses and test results of the current equation, discuss considerations for implementing SSM in human-occupied environments, and provide directions for technological advancements toward standardization.

Minimum distance functions of graded ideals and Reed–Muller-type codes

We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of projective Reed–Muller-type codes over finite fields. This gives an algebraic formulation of the minimum distance of a projective Reed–Muller-type code in terms of the algebraic invariants and structure of the underlying vanishing ideal. Then we give a method, based on Gröbner bases and Hilbert functions, to find lower bounds for the minimum distance of certain Reed–Muller-type codes. Finally we show explicit upper bounds for the number of zeros of polynomials in a projective nested cartesian set and give some support to a conjecture of Carvalho, Lopez-Neumann and López.