Polygonal Line Research Articles

On the Cauchy problem with an initial point lying on the boundary of ordinary differential equation’s domain of definition

In this paper we investigate the existence of solution of the initial-value problem with an initial point located at the boundary of the domain of definition for the first-order differential equation. This initial-value problem differs from the one accepted in classical theory, where the initial point is always internal for domain. Our aim is to find such conditions for the right-hand side of the equation and the boundary that would guarantee the existence or absence of this solution. In its previous article the authors used the standard Euler polygonal line method to solve this problem and described all cases when this method is used to get the desired answer. The polygonal line method, having certain advantages (constructibility, the ability to use a computer), requires for its implementation that both the equation and the domain of its definition meet certain restrictions, which inevitably narrows the class of acceptable equations. In this paper, we attempt to maximize the results obtained earlier, and for this purpose we use a completely different approach. The original equation is extended in such a way that the boundary initial-value problem becomes an ordinary internal initial-value problem, for which the standard Peano theorem is applied. To answer the question whether the solution of the modified initial-value problem is also the solution of the original boundary initial-value problem, so-called comparison theorems and differential inequalities are applied. This article is an independent study, not based on our previous work. For the sake of completeness, new proofs are given for previously obtained results, which are based on a new approach. As a result, we expanded the class of equations under consideration, removed the previous requirements for convexity and smoothness of boundary curves, and added cases that could not be considered using the polygonal line method. This work closes a certain gap that exists in the literature on the existence or absence of solutions to the boundary initial-value problem.

Accuracy, precision, and consistency of methods for pathogen-specific cerebrospinal fluid/serum Q-value calculation

For a CSF/serum samples pair the specific Q-value is the ratio of antibody concentrations and proportional to the pathogen-specific antibody index. It is usually extracted from optical density (OD) measurements by applying appropriate evaluation methods. Six different methods for Q-value determination, partly using parameter variation, were assessed with respect to accuracy, precision, and the methods' parameter consistency. The methods are based on the Four Parameters Logistic (4PL) equation or the α-method; one method is a polygonal line composed of calibration data. We tested on OD data of 51 CSF/serum sample pairs, measured with EUROIMMUN AG (Lübeck, Germany) ELISA tests for antibody determination in CSF, as part of INSTAND e.V. proficiency survey tests for the MRZH reaction (Measles, Rubella, Varicella zoster, Herpes simplex virus).Each method was tested with four ODs, standard curve methods additionally with only two ODs, identified by a selection rule. We found all methods to be of comparable accuracy and precision. With the standard curve methods, there were no differences between two ODs and four ODs evaluations.Consistency between method parameters and measured OD values is a key property of standard curve methods with a strong impact on accuracy and precision. We found a statistically significant difference with parameter consistency between a 4PL standard curve evaluation of this study and an α-method evaluation of data, measured with ELISAs of Siemens Healthcare GmbH (Marburg, Germany).General considerations show Q-values obtained by parameter variation to be more reliable than those resulting from selection rule application with standard curves.

Optimal Alignments for Designing Urban Transport Systems: Application to Seville

The achievement of some of the Sustainable Development Goals (SDGs) from the recent 2030 Agenda for Sustainable Development has drawn the attention of many countries towards urban transport networks. Mathematical modeling constitutes an analytical tool for the formal description of a transportation system whereby it facilitates the introduction of variables and the definition of objectives to be optimized. One of the stages of the methodology followed in the design of urban transit systems starts with the determination of corridors to optimize the population covered by the system whilst taking into account the mobility patterns of potential users and the time saved when the public network is used instead of private means of transport. Since the capture of users occurs at stations, it seems reasonable to consider an extensive and homogeneous set of candidate sites evaluated according to the parameters considered (such as pedestrian population captured and destination preferences) and to select subsets of stations so that alignments can take place. The application of optimization procedures that decide the sequence of nodes composing the alignment can produce zigzagging corridors, which are less appropriate for the design of a single line. The main aim of this work is to include a new criterion to avoid the zigzag effect when the alignment is about to be determined. For this purpose, a curvature concept for polygonal lines is introduced, and its performance is analyzed when criteria of maximizing coverage and minimizing curvature are combined in the same design algorithm. The results show the application of the mathematical model presented for a real case in the city of Seville in Spain.

Experimental and analytical investigation on the nonlinear behaviors of glulam moment-resisting joints composed of inclined self-tapping screws with steel side plates

Glulam moment-resisting joint composed of inclined self-tapping screws with steel side plates were designed and its nonlinear moment-rotational skeleton curve was predicted by taking nonlinear load ( P)–deformation ( u) relationships of all moment-resisting components into considerations within step-wise linear calculation process. P-u relationships of all moment-resisting components were estimated by the fundamental shear joint tests or appropriate empirical relationships, and they were approximated by the tetra polygonal line curves or bi-linear curves. The extended Normalized Characteristic Loop model, which was originally developed for reinforced concrete construction, was applied to describe the hysteresis loops. For predicting failure load, the design equations for a mechanical joint loaded with inclination to the grain direction were applied. Three replications of T-shaped beam-column joint specimens were fabricated using Canadian spruce glulam beam and column. Connections of steel plates to glulam members were all composed of full-threaded inclined self-tapping screws. Static push-pull cyclic loading tests were conducted and observed behaviors were compared with step-wise linear analytical results. Agreements between predicted nonlinear behaviors and observed ones were good on the whole.

Revisiting random polygonal lines iteratively generated on the plane

Revisiting random polygonal lines iteratively generated on the plane

Demarcation of Coastal Municipalities in Spain

Pina-Garcia, F.; de Luis-Ruiz, J.M.; Castillo-Lopez, E.; Pereda-Garcia, R., and Perez-Alvarez, R., 2019. Demarcation of coastal municipalities in Spain. Journal of Coastal Research, 35(2), 305–313. Coconut Creek (Florida), ISSN 0749-0208.The demarcation of municipalities is essential for an adequate functioning of local administrations and the exercise of other public functions, such as jurisdiction, spatial planning, and urbanism. This research emphasizes the definition of municipalities in coastal areas, understanding that the beaches and the maritime–terrestrial zones are part of them. The limits of the beaches and the maritime–terrestrial zones are hard to determine, and the hydrographic zero is defined as an abstract line that separates terrestrial from marine. This line is difficult to define and even worse to materialize as it is a fractal object (too irregular for a geometric definition) and, in some cases, undergoes great changes through time. By analogy with what is done with normal baselines, which allow straight lines, or with the demarcation of the inner limit of the maritime–terrestrial public domain, it is proposed to identify the border of the municipality as a polygonal line whose vertices are defined by coordinates. A strictly administrative demarcation is thus proposed, which should neither modify the maritime–terrestrial public domain nor affect the inner waters or the territorial sea. As a result of the application of this methodology, the boundaries of a municipality would be defined and, therefore, its area. The proposal is applied to a practical case: the municipality of Ribamontan al Mar (Cantabria, Spain). Both the ambiguity of data and the imprecisions among the several sources of information regarding its boundary with respect to the sea are analyzed. A polygonal line defined by coordinates is proposed. This procedure could be generalized for the boundaries of any coastal municipality.

Segmentation of Lung in Chest Radiographs Using Hull and Closed Polygonal Line Method

Accurate lung segmentation in chest radiographs is a challenging problem due to the presence of strong edges at the rib cage and clavicle, the varying appearance in the upper clavicle bone region, too small costophrenic angle and the lack of a consistent anatomical shape among different individuals. In this paper, we propose a hybrid semi-automatic method called Hull-Closed Polygonal Line Method (Hull-CPLM) to detect the boundaries of the lung Region of Interest (ROI). To the best of our knowledge, this is the first attempt at lung segmentation using the Hull-CPLM in chest radiographs. The proposed method has two main steps: 1) an image preprocessing method is constructed to implement the coarse segmentation by using as low as 15% of the manually delineated points as the initial points, 2) a refinement step is used to fine-tune the segmentation results based on the improved principal curve model and the machine learning model at the refinement step. To prove the performance of the proposed method, both the private and public databases were used. The private database is used to select the optimal parameters for the proposed method, where the result showed a good performance with the Dice Similarity Coefficient (DSC) as high as 97.08%. While on the public databases, our proposed algorithm not only surpassed the performance of different hybrid algorithms but also reached superior segmentation results by comparing with state-of-the-art methods.

Specific polygonal lines on the number of days of daily exercise and sports activities by cross-sectional and semi-longitudinal cohort analyses through National survey reports on physical fitness and motor abilities conducted by Ministry of Education, Science, Sports and Culture and Ministry of Education, Culture, Sports, Science and Technology indicated severe decrease of physical fitness and motor abilities on children and

Specific polygonal lines on the number of days of daily exercise and sports activities by cross-sectional and semi-longitudinal cohort analyses through National survey reports on physical fitness and motor abilities conducted by Ministry of Education, Science, Sports and Culture and Ministry of Education, Culture, Sports, Science and Technology indicated severe decrease of physical fitness and motor abilities on children and

Multi-granularity principal curves extraction based on improved spectral clustering of complex distribution data

In order to address the problem of instability of existing principal curve algorithms and their difficulties to deal with complex distribution data, in this study, invoking the ideas of information granulation, we propose a local-to-global multi-granularity principal curves extraction approach based on improved spectral clustering. Firstly, we propose an improved spectral clustering algorithm based on inflection point estimation to granulate complex distribution data into several granular data, and develop techniques of an automatic selection of a parameter, which determines the number of clusters (granular data). Secondly, PL (polygonal line) principal curves algorithm proposed by Kégl is utilized to extract the local principal curves of each granular data. Finally, with the use of the shortest Hamiltonian path algorithm and noise variance, the local principal curves are gradually connected together to form a global curve. A number of numeric studies completed for synthetic and publicly available data sets provide a useful quantifiable insight into the effectiveness of the proposed algorithm.

1-D cubic NLS with several Dirac masses as initial data and consequences

In this proceedings article we present a result on the 1-D cubic nonlinear Schrödinger equation with a sum of Dirac masses as initial data. We shall give a sketch of the proof. By using this result we show how to construct the evolution in time of a polygonal line through the binormal flow. This equation is a geometric flow for curves in ℝ 3 and it is used as a model for the evolution of a vortex filament in fluid mechanics. These results were obtained in collaboration with Luis Vega in [4].

Detection of Lung Contour with Closed Principal Curve and Machine Learning.

Radiation therapy plays an essential role in the treatment of cancer. In radiation therapy, the ideal radiation doses are delivered to the observed tumor while not affecting neighboring normal tissues. In three-dimensional computed tomography (3D-CT) scans, the contours of tumors and organs-at-risk (OARs) are often manually delineated by radiologists. The task is complicated and time-consuming, and the manually delineated results will be variable from different radiologists. We propose a semi-supervised contour detection algorithm, which firstly uses a few points of region of interest (ROI) as an approximate initialization. Then the data sequences are achieved by the closed polygonal line (CPL) algorithm, where the data sequences consist of the ordered projection indexes and the corresponding initial points. Finally, the smooth lung contour can be obtained, when the data sequences are trained by the backpropagation neural network model (BNNM). We use the private clinical dataset and the public Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) dataset to measure the accuracy of the presented method, respectively. To the private dataset, experimental results on the initial points which are as low as 15% of the manually delineated points show that the Dice coefficient reaches up to 0.95 and the global error is as low as 1.47 × 10-2. The performance of the proposed algorithm is also better than the cubic spline interpolation (CSI) algorithm. While on the public LIDC-IDRI dataset, our method achieves superior segmentation performance with average Dice of 0.83.

Computation of the area in the discrete plane: Green’s theorem revisited

The detection of the contour of a binary object is a common problem; however, the area of a region, and its moments, can be a significant parameter. In several metrology applications, the area of planar objects must be measured. The area is obtained by counting the pixels inside the contour or using a discrete version of Green’s formula. Unfortunately, we obtain the area enclosed by the polygonal line passing through the centers of the pixels along the contour. We present a modified version of Green’s theorem in the discrete plane, which allows for the computation of the exact area of a two-dimensional region in the class of polyominoes. Penalties are introduced and associated with each successive pair of Freeman displacements along the contour in an eight-connectivity system. The proposed equation is shown to be true and properties of the equation related to the topology of the regions are presented. The proposed approach is adapted for faster computation than the combinatorial approach proposed in the literature.

Asymptotics of convex lattice polygonal lines with a constrained number of vertices

A detailed combinatorial analysis of planar convex lattice polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained.

Weak invariance principle in some Besov spaces for stationary martingale differences

We extend the classical Donsker weak invariance principle to some Besov space framework. We consider polygonal line processes built from partial sums of stationary martingale differences and of independent and identically distributed random variables. The results obtained are shown to be optimal.

Bezier Curve Based Path Planning in a Dynamic Field using Modified Genetic Algorithm

Mobile robots have been used in different applications such as assembly, transportation, and manufacturing. Although, the great work to get the optimum robot's path, traditional path planning algorithms often assume that the environment is perfectly known and try to search for the optimal path that contains sharp turns and some polygonal lines. This paper proposes an efficient, Bezier curve based approach for the path planning in a dynamic field using a Modified Genetic Algorithm (MGA). The proposed MGA aims to boost the diversity of the generated solutions of the standard GA which increases the exploration capabilities of the MGA. In our proposed method, the robot's path is dynamically decided based on the obstacles’ locations. With the goal of optimizing the distance between the start point and the target point, the MGA is employed to search for the most suitable points as the control points of the Bezier curve. Using the chosen control points, the optimum smooth path that minimizes the total distance between the start and the end points is selected. Our model was tested on different environments with different scales, different numbers of obstacles, and six benchmark maps. As a result, the proposed method provides an efficient way to avoid robot's energy consumption in harsh environments.

Fast 3-D Analysis of Eddy Current in Litz Wire Using Integral Equation

Eddy current loss in a litz wire which has 3-D structure is analyzed using the integral equation method considering the proximity effect. In the present method, each wire is modeled as a polygonal line. 1-D integral equation is solved for the dipole magnetization generated by the anti-parallel eddy currents in the wire. The discretized integral equation can effectively be solved using an iterative method solver to compute the eddy current distribution in the wire due to the proximity effect.

Droplets on Microdecorated Surfaces: Evolution of the Polygonal Contact Line

Interaction of liquids with surfaces is ubiquitous in our physical environment as well as many engineering applications. Recent advances on this topic have not only provided us with valuable insight into nature's design, but also enabled improved fluidic manipulation for liquid-based printing applications such as biomicroarrays for protein and DNA sequencing, multicolor polymer-based LED displays, inkjet printing, and solder droplet printing, among others. For example, droplet contact lines, which are typically circular on a smooth and homogeneous surface, when deposited on a microdecorated surface may take various common polygonal shapes such as squares, rectangles, hexagons, octagons and dodecagons. These polygonal contact line shapes are highly stable due to the local energy barriers associated with the anisotropy in depinning contact angles. In addition to the knowledge of the eventual contact line shapes, liquid-based printing applications would require accurate prediction of temporal evolution of contact line on these surfaces. In this work, we model and validate the evolution of droplets on microdecorated surfaces with microgoniometry experiments reported in the literature. We show that various metastable contact line shapes are formed in-between the well-known stable polygonal contact line shapes usually observed in experiments. We elucidate that the movement of the contact line between adjacent micropillars can primarily be categorized as primary zipping and transition zipping. Primary zipping occurs when the contact line moves radially outward to the next row of pillars, often resulting in the formation of a metastable contact line shape. Conversely, metastable droplet attains stable polygonal contact line shape via transition zipping wherein the contact line advances sideways. We believe that the current simulation approach can be effectively utilized for designing optimized textured surfaces for applications where control over liquid supply via surface design is required.

Parameter optimization of the program trajectory of the cellular concrete autoclaving control system

Manufacturing of cellular-concrete products that are widely used in modern construction involves high energy consumption attributable mostly to the process of autoclaving. Insufficient elaboration of issues of mathematical description of autoclaving that would be usable in engineering practice and, consequently, the lack of adequate computational models aimed for practicing technologists, make it necessary to use heuristic approaches to parameter determination for the program trajectories of autoclave automatic control systems (ACS) in manufacturing. Therefore, design and development of autoclaving computational models aimed at parameter optimization of the program trajectory is a very relevant issue. The authors have developed mathematical models of cellular concrete autoclave curing and computational algorithms enabling determination of energy consumption under the variation in dynamic parameters of the automatic system's driver unit. Using the methods of conducting computational experiments under the discrete parameter change of the program trajectory, under the conditions of limitation on the temperature derivative of semi-finished concrete and autoclaving process duration, we have established that completion of the known program trajectory as a polygonal line with two variable slope sections of the third section forming unit with a variable slope, enables reduction of energy consumption up to 8%. The research conducted is specifically focused on the use of the obtained results for optimization of cellular concrete autoclaving ACSs.

Stress Corrosion Cracking of Progressively Cold-Drawn Pearlitic Steels: From Tintoretto to Picasso

Progressive cold drawing in eutectoid steels produces a preferential orientation of the pearlitic microstructure in the wire axis or drawing direction. This affects the posterior behaviour of the steels under conditions of stress corrosion cracking (SCC). The experimental results show that cold drawing induces strength anisotropy in the steel, and thus the resistance to SCC is a directional property that depends on the angle in relation to the drawing direction. Therefore, an initial transverse crack changes its propagation direction to approach that of the wire axis, thus producing mixed mode propagation, the deflection angle being an increasing function of the cold drawing degree. This experimental result may be explained by micro-mechanical considerations on the basis of the lamellar microstructure of the steels. A relationship is established between the microstructural angles and the deflection angles of the macroscopic SCC crack, thus providing a materials science type relationship between the microstructure and the macroscopic crack paths with regard to hydrogen assisted cracking (HAC) associated with the cathodic regime and in the matter of localised anodic dissolution (LAD) linked to the anodic regime. Whereas in hot rolled (not cold drawn at all) and slightly drawn steels the phenomenon of SCC develops in mode I, i.e., the SCC crack is a straight line linked with the classical linear perspective painting by Tintoretto, in the case of heavily drawn steels, the SCC deflected crack is a polygonal line associated with the multi-perspective cubist painting by Picasso, these conclusions being valid for both HAC and LAD.

О восстановлении функции по ее интегралам вдоль ломаных одного семейства на плоскости

О восстановлении функции по ее интегралам вдоль ломаных одного семейства на плоскости