Polygonal Line Research Articles

Video imaging of structural dynamics of amyloid β protofibrils.

Soluble aggregates including oligomers and protofibrils (PFs) of amyloid β (Aβ) have been reported to be more toxic than mature fibrils (MFs). Recently, clinical trials of antibodies targeting these aggregates are also in progress. Their structure is dynamic, which makes it difficult to extract and analyze them in a stable state. Therefore, the molecular process among the soluble Aβ aggregates has been unclear. Development of high-speed atomic force microscopy (HS-AFM) allows video-imaging of structural dynamics of individual amyloid aggregates in liquid. Here, we investigated structural dynamics and mechanical property of Aβ protofibrils and anti-Aβ antibody binding to PFs, using HS-AFM. Aβ1-42 PF and MF were prepared in vitro, which was deposited on the HS-AFM stage. Structural dynamics of the aggregates were observed by HS-AFM in phosphate buffered saline (PBS). Young's moduli of the individual aggregates were measured by force spectrometry mode of HS-AFM in PBS. The anti-Aβ antibody was added in the chamber, followed by HS-AFM observation of the antibody binding to PFs. Aβ1-42 PF showed diffusive 2D motion on bare mica and its typical structure was composed of several globular parts in a polygonal line. The angle between each segment of a PF was maintained during the diffusive motion. The length of PFs showed a single exponential distribution. Its mean length depended on PF concentration. The Young's modulus of PFs was higher than that of MFs in liquid. Lecanemab (BAN2401) bounded to PFs both most rapidly and abundantly, while 4G8 showed the weakest and least binding to PFs. Assembly and disassembly of the globular parts in PFs are dynamic, while their segment structure is stiffer than MFs and the bonds between the globular parts are rigid. These characteristics indicated the difference in internal structure between PFs and MFs, which supports that PFs may not be a direct precursor of MFs. Lecanemab binds to all various parts and length of PFs.

Basic Input–Output Gain Tuning System Based on Control Input Histogram Leveling for Human-Operated Machines

This article explores a scheme of tuning a basic input–output (I/O) gain (BIOG) depending on usage conditions for improving the work performance of human-operated machines. I/O gain tuning is effective for improving operability and workability, but continual and/or huge changes makes operators confuse the machine dynamics, and then degrade the operability. Thus, the proposed tuning system tunes the BIOG at long terms according to comprehensive characteristics of the work content and operator, collected from a control lever input histogram. The target value is specified by a Gaussian distribution, meaning that all ranges of the spring-type control lever are equally used. This approach was chosen because leveling the control lever histogram independently of the operator and work content provides a consistent operational experience, leading to comfortable operations. In this article, BIOG curves are specified as a polygonal line involving a break and saturation point. These points are adjusted by reciprocal conversion of differential areas between the Gaussian distribution and obtained histogram curves. Experimental results obtained with a robot arm indicated that the developed BIOG tuning system could improve time efficiency by decreasing the differential area and increase the subjective usability as compared to a conventional fixed BIOG system. Moreover, the relationship between the histogram and BIOG curve could reveal features of both the work content and the operator's skill level.

Urban perimeters issues in low-density areas

In the domain of spatial planning, there is a concern to preserve the territory whilst ensuring a proper expansion of urban perimeters. Cities, towns and villages should be contained within urban perimeters for building and urbanization purposes. The concept of urban perimeter is defined as the closed polygonal line demarcating the continuous territory of urban land-use. The spatial planning instruments should define the urban land-use referring to areas totally or partially urbanized or built. Regarding low-density territories with a greater propensity to urban sprawl and population ageing, the previously mentioned rules are not always met. Thus, this study focuses on the case of the Interior region of Portugal classified as low-density territory. Here the number of inhabitants is decreasing with low demand for urban spaces. However, the urban perimeters were mainly defined without being based on territorial features, topographic mapping or ecological sensitive areas. Thus, for a diversity of aspects, there are inappropriate areas to build that were wrongly included as part of urban areas, creating as a result urban void. One main reason for this problem are the topographic conditions that don’t fit with the urbanization and building requirements in urban perimeters. In this sense, this research aims to describe the articulation between the urbanization and building processes, under the rules of the Municipal Master Plans, regarding the topographic features of urban perimeters. The conclusion shows that the most sloped areas are those that were less sought after for urbanization, however these zones comprise a significant part of the urban perimeters. Finally, there is the need to stress that in low-density territories, many urban voids will never be urbanized.

The first-order phase transition of melting for molecular crystals by Frost–Kalkwarf vapor- and sublimation-pressure equations

Abstract Thermodynamic quantities in the coexistence of the liquid and the solid phases for Frost–Kalkwarf vapor- and sublimation-pressure equations are investigated at an isobaric process. Gibbs free energy changes in the gaseous and the liquid phases, ΔG GL, has been derived from the Frost–Kalkwarf vapor-pressure equation. Similarly, Gibbs free energy changes in the gaseous and the solid phases, ΔG GS, may be estimated by the Frost–Kalkwarf sublimation-pressure equations which are determined by data of sublimation pressures and temperatures for 24 substances. In coexistence between the liquid and the solid phases, Gibbs free energy changes in the liquid and the solid phases, ΔG LS, may be expressed as the difference of ΔG GL and ΔG GS. The melting temperatures and enthalpy changes of melting are evaluated by numerical calculations for 24 substances. The behaviors of H2O for the neighborhood at the melting and the boiling points are investigated. The Gibbs free energy indicates two polygonal lines. Entropy, volume and enthalpy jump from the solid to the liquid phase at the melting point and from the liquid to the gaseous phase at the boiling point. The heat capacity does not diverge to infinity but shows a finite discrepancy at the melting and the boiling points. This suggests that first-order phase transitions at the melting and the boiling points may occur.

Approximation of BSDEs with super-linearly growing generators by Euler’s polygonal line method: A simple proof of the existence

This paper develops the Euler’s polygonal line method for the backward stochastic differential equations (BSDEs) with super-linearly growing generators. The generators are allowed to be super-linearly growing in the first unknown variable y and sub-quadratic growing in the second unknown variable z when the monotonicity condition is satisfied. The convergence rate of the Euler approximation is derived, which also provides a simple proof for the existence of the solution to the monotone BSDEs. The proof is very simple and short, without involving the conventional techniques of truncating and smoothing on the generators.

Enforcing convergence of derivatives for L∞ approximation of a regular curve

Converging approximation of a regular curve by polygonal lines in the uniform norm does not imply the convergence of the discrete differentials to their smooth counterpart. In this paper, we provide a constructive approach that, given a converging polygon sequence and an approximation of its distance to the objective curve, provides another sequence of polygons for which convergence of discrete differentials occurs as well. This approach is based on the notion of local scale of a polygon and uses multi-resolution decomposition as well as a non linear smoothing process. We provide the proof of the convergence and some numerical evidence of it, with application to the evaluation of solid friction in a pipe.

Frechet Similarity Between Two Ambiguously Defined Polygonal Lines

The paper considers the problem of comparing two polygonal lines that are not strictly defined. Instead, two sets of polygonal lines are given assets of paths on two acyclic directed graphs. The problem is to determine whether there exists a pair of lines each from its respective set such that the Frechet distance between them is not greater than a given number. An algorithm is given that solves the problem in time, were and are the sets of edges in each graph respectively.

Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

Applicability of the Specimens with Holes Aligned to the Polygonal Line that Cause Acoustic Emission for Evaluating Acoustic Emission Measurement Systems

Applicability of the Specimens with Holes Aligned to the Polygonal Line that Cause Acoustic Emission for Evaluating Acoustic Emission Measurement Systems

Variational convergence of discrete elasticae

AbstractWe discuss a discretization of the Euler–Bernoulli bending energy and of Euler elasticae under clamped boundary conditions by polygonal lines. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to the set of smooth Euler elasticae under mesh refinement in (i) the $W^{1,\infty }$-topology for piecewise-linear interpolation; and in (ii) the $W^{2,p}$-topology, $p \in [2,\infty [$, using a suitable smoothing operator to create $W^{2,p}$-curves from polygons.

Deep Belief Network and Closed Polygonal Line for Lung Segmentation in Chest Radiographs

Abstract Due to the varying appearance in the upper clavicle bone region, sharp corner at the costophrenic angle, the presence of strong edges at the rib cage and clavicle and the lack of a consistent anatomical shape among different individuals, accurate segmentation of lung on chest radiographs remains challenging. In this work, we propose a novel segmentation method for lung segmentation, containing two subnetworks, where few manually delineated points are used as the approximate initialization. The first one is a preprocessing subnetwork based on a deep learning model (i.e. Deep Belief Network and K-Nearest Neighbor). The second one is a refinement subnetwork, designed to make the preprocessed result to be optimized by combining an improved principal curve method and a machine learning method. To prove the performance of the proposed method, several public datasets were evaluated with Dice Similarity Coefficient (DSC), overlap score (Ω), Sensitivity (Sen), Positive Predictive Value (PPV), global Error (E) and execution time (t). Compared with state-of-the-art methods, our method reaches superior segmentation performance.

Tracing Mental Models in Cartographic Datasets – The Case of OpenStreetMap

Abstract. Geographical features can be represented in different ways. Buildings, for instance, can be represented as areal features defined by polygonal lines or as point features in a map. While the type of representation chosen to represent a building strongly depends on the scale of the map, it seems common to represent points of interests (POIs) as point features. More complex examples exist. For example, the way buildings that are part of a mosque are conceptualized and thus labelled in a map strongly depends on how familiar we are with the Arabic culture. The same applies to the often perceived separation between public and private space in Arabic cultures, which can have an impact on geometrical aspects of map representations. Such coexisting representations of geographical features can, in particular, be observed in collaboratively created data sources (Mocnik et al., 2019), such as OpenStreetMap (OSM) data and maps generated from these.Competing representations of geographical features can reduce the readability of a map, but they can also open up opportunities to draw conclusions about the underlaying mental model (Mayer et al., 2020). When the people involved in the map creation process have different mental representations of a geographical feature, the representations they create often differ. This, in turn, impacts the readability, which refers to the process of transferring a map representation into a mental one, i.e., the process opposed to map creation, as there is often no clear and unambiguous correspondence between the symbols in the map and the represented geographical features (Scheider et al., 2009; Mocnik et al., 2018) Over time, these conceptualizations can mutually influence and lead to a convergence (Mocnik et al., 2017). Despite this, the coexistence of different cartographic representations makes possible to draw conclusions about the way a feature has been conceptualized. The symbols in the map encode, accordingly, besides the intended information about the geographical features, also information about the mental models involved (Mayer et al., 2020).The effect of mental models on the map representation often goes unnoticed because there is, in many cases, only very subtle variation between the map representations of one type of geographical features. If such variation would be much larger, it would even be impossible to interpret the symbols of a map. While the examples discussed above can be traced very well in individual cases, it is yet unclear how systematic the influence of mental models is. A systematic examination of such examples can investigate the influence statistically and at a larger scale. Further research might show the extent to which conclusions can practically be drawn about the conceptualization of geographical features and corresponding mental representations.The ability to trace mental models through maps is a suitable tool for exploring the conceptualization of geographies. For instance, future research might investigate in detail the impact culture has on the way we conceptualize. Likewise, it might investigate how people experience urban landscapes in different ways. By using maps and the data behind them as a source of information for mental models, maps gain a new purpose while the original one is put into the background. While such thinking is common for sketch maps, it also also applies, to a lesser degree, to Volunteered Geographic Information (VGI), which can become a valuable data source for ethnologists, human geographers, psychologists, and cognitive scientists.In a similar way, a better understanding of how mental models relate to cartographic representations can help to improve the latter. The cartographic representation of idiosyncratically experienced geographies, for instance, still poses challenges. Also, stories are, in many cases, hard to convey through classical maps (Mocnik and Fairbairn, 2018). The same applies to places and corresponding cartographic representations, which often are characterized by subjective and idiosyncratic aspects (Westerholt et al., 2018; Westerholt et al., 2020). The empirical investigation of the effect mental models have on cartographic representations can be expected to also provide insights into the reverse process, thus leading to cartographic techniques that make it possible to convey idiosyncratic experience and, eventually, also emotions.

Extensions of dynamic programming for multi-stage combinatorial optimization

We propose a dynamic programming framework for an exact multi-stage (lexicographic) combinatorial optimization. Unlike conventional algorithms of dynamic programming that return one optimal solution, two dynamic programming algorithms proposed in this paper are coping with the whole set of optimal solutions or with its essential part. We describe the set of elements for optimization by a labeled directed acyclic graph, which in some sense, is similar to the structure of subproblems of the considered problem. For a given cost function (objective), the first algorithm constructs a subgraph of this graph that describes the whole set of optimal elements or its essential part. This algorithm can be used for multi-stage optimization of elements relative to a sequence of cost functions. The second algorithm counts elements before the optimization and after each optimization step. The considered labeled directed acyclic graph is a kind of circuit. This circuit builds the set of elements for optimization from one-element sets attached to input nodes. It uses the operation of union of sets attached to unifying nodes and functional operations attached to functional nodes. The algorithms for optimization and counting elements are defined for an arbitrary circuit without repetitions in which each element is generated exactly one time. For a considered problem with a known conventional dynamic programming solution algorithm, usually, it is easy to construct a corresponding circuit without repetitions. Once the circuit and cost functions are defined, our framework provides the correctness proofs and detailed time complexity analysis for the proposed algorithms. To make this approach more intuitive, we consider an illustrative example related to the maximum subarray problem. We tested our approach on the following nine combinatorial optimization problems: matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, optimal bitonic tour, segmented least squares, convex polygon triangulation, one-dimensional clustering, and line breaking (text justification). We consider the last three problems in detail: construct a circuit without repetitions, describe at least two cost functions, evaluate a number of operations and time required by the algorithms, discuss an example, and consider the results of computer experiments with randomly generated instances of the problem.

Evolution of Polygonal Lines by the Binormal Flow

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on $$\mathbb {R}$$ in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. We also construct solutions of the binormal flow that present an intermittency phenomena. Finally, the solution we construct for the binormal flow is continued for negative times, yielding a geometric way to approach the continuation after blow-up for the 1-D cubic nonlinear Schrödinger equation.

Empirical formulae of wave loads on quasi-ellipsoid-type foundations surrounded by cylindrical perforated breakwaters

This study provides empirical formulae of wave loads on quasi-ellipsoid-type foundations coaxially surrounded by perforated breakwaters. The variation of the wave load on each structure versus wave number is characterized as a polygonal line by four key points. The coordinates of these points can be directly obtained from the empirical formulae, which are developed by using mathematical models in the framework of potential theory. The empirical formulae can consider not only the geometric parameters and porous parameters but also the wave exposures and wave numbers. Comparison with the experimental results indicates that the empirical formulae can effectively determine the wave loads on the models under different wave scenarios. Further investigation is conducted on circular foundations, which are the most distinct case of quasi-ellipsoid-type foundations. The wave load magnitudes and phase differences are investigated by experimental and theoretical methods with the consideration of porous parameters and geometric parameters. The experimental results also validate the occurrence of the “phase jump” when the wave loads on the breakwater are minimum. Empirical formulae for the distribution of the “phase jump” points are also presented.

Feedback Control to a Static Target Angle in the Middle Finger Metacarpophalangeal Joint Using Functional Electrical Stimulation

ABSTRACT In this study, we proposed a feedback control method for a finger joint angle, which has been considered difficult, via functional electrical stimulation using the surface electrode method. If detailed finger movement can be realized by functional electrical stimulation using the surface electrode method, this can be applied in various situations such as musical instrument performance, daily movements, and so on. The control method was designed based on the following three proposals. First, the non-linear relationship between the electrical stimulation intensity and joint angle change was absorbed by constructing polygonal line regression models of the relationship between the electrical stimulation intensity reaching each muscle and the flexion and extension force of the middle finger’s metacarpophalangeal joint. Second, the concepts of the muscle antagonist ratio and muscle antagonist sum were adopted to translate the input/output relationship to a single-input/single-output system while maintaining joint stiffness. Finally, the proportional–integral–derivative control parameters were determined using the Ziegler–Nichols ultimate sensitivity method. Using the control method based on the aforementioned three proposals, we conducted feedback control experiments for three static target angles in the middle finger’s metacarpophalangeal joint. Results show that at all target angles, greater than 80% of the participants were able to control the joint with nearly no error. Therefore, the control method proposed in this study can be used to control an arbitrary static target joint angle with high accuracy via functional electrical stimulation.

On optimal polyline simplification using the Hausdorff and Fréchet distance

We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Frechet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given e > 0, choose a minimum size subsequence of the vertices of the input such that the Hausdorff or Frechet distance between the input and output polylines is at most e.We analyze how the well-known Douglas-Peucker and Imai-Iri simplification algorithms perform compared to the optimum possible, also in the situation where the algorithms are given a considerably larger error threshold than we require for the optimum solution. Furthermore, we show that computing an optimal simplification using the undirected Hausdorff distance is NP-hard. The same holds when using the directed Hausdorff distance from the input to the output polyline, whereas the reverse can be computed in polynomial time. Finally, to compute the optimal simplification from a polygonal line consisting of n vertices under the (continuous) Frechet distance, we give an $O(kn^5)$ time algorithm that requires $O(kn^2)$ space, where $k$ is the output complexity of the simplification.

The shape of planar smooth gestures and the convergence of a gesture recognizer

In this work we provide the mathematical framework of !FTL, a new gesture recognition algorithm. This allows us to algebraically quantify the notion of shape for a smooth planar curve, inspired by the notion of shape of a triangle given previously by Lester in this same journal. In particular, we approximate every gesture, considered as a smooth planar curve, by a polygonal path inscribed on that curve. Then, we consider each triple of consecutive points on that polygonal path as the vertices of a triangle having a shape. We show that, as the polygonal line pointwise converges to the original gesture, the corresponding sequence of shapes pointwise converges to a limiting curve of shapes, that we consider to be the shape of that gesture. We use the Euclidean metric and the Riemann integral to measure the distance between the shapes of two gestures. The position, scale and rotation invariances of the shape of a triangle still hold for the shape of a gesture, and this provides one of the main achievements of !FTL. Finally, we mention, for further research, that the two dimensional Euclidean notion of shape can be extended to higher dimensional settings and more general metrics using Clifford numbers.

Numerical investigation of the cavitation performance of annular jet pumps with different profiles of suction chamber and throat inlet

To find the influence of the suction chamber and throat inlet profiles on the cavitation performance of an annular jet pump (AJP), a numerical method using a combination of the realizable k–ϵ turbulence model and the Schnerr–Sauer cavitation model was applied. This paper comprehensively studied the cavitation performance of AJPs with a polygonal line profile (POL) and a streamlined profile (STR). The results showed that the pump efficiency (η) can be increasedby using the STR and the largest increase was 1.4%. Since the throat is smoothly connected with the suction chamber in the AJP with STR, flow separation and local low pressure did not appear. The critical flow rate ratio (qc ) of the AJP with STR was higher than that of the AJP with POL, implying that the former had a wider normal working range. During critical working, the cavitation region in the AJP with STR was narrower than that of the AJP with POL. Importantly, the region of cavitation inception and development in the AJP with STR was closer to the downstream. Hence, it was concluded that the cavitation in the AJP with STR had less influence on the inner flow field.

On Bernstein–Kantorovich invariance principle in Hölder spaces and weighted scan statistics

Let ξn be the polygonal line partial sums process built on i.i.d. centered random variables Xi, i ≥ 1. The Bernstein-Kantorovich theorem states the equivalence between the finiteness of E|X1|max(2,r) and the joint weak convergence in C[0, 1] of n−1∕2ξn to a Brownian motion W with the moments convergence of E∥n−1/2ξn∥∞r to E∥W∥∞r. For 0 < α < 1∕2 and p (α) = (1 ∕ 2 - α) -1, we prove that the joint convergence in the separable Hölder space Hαo of n−1∕2ξn to W jointly with the one of E∥n−1∕2ξn∥αr to E∥W∥αr holds if and only if P(|X1| > t) = o(t−p(α)) when r < p(α) or E|X1|r < ∞ when r ≥ p(α). As an application we show that for every α < 1∕2, all the α-Hölderian moments of the polygonal uniform quantile process converge to the corresponding ones of a Brownian bridge. We also obtain the asymptotic behavior of the rth moments of some α-Hölderian weighted scan statistics where the natural border for α is 1∕2 − 1∕p when E|X1|p < ∞. In the case where the Xi’s are p regularly varying, we can complete these results for α > 1∕2 − 1∕p with an appropriate normalization.