Intersection Problem Research Articles

Geometric-Based Method for Regional-Target Coverage Analysis

This study proposes a geometric-based method of providing regional target visibility from a satellite considering the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_2$</tex-math></inline-formula> perturbation. First, the basic mathematical model is introduced followed by the field-element equations for ground-point visibility analysis and envelope equations of a family of curves. Then, the concept of a regional-field-mapping envelope and its subset baseline field-mapping envelope are presented for calculating visible intervals. The envelopes transform the complex problem of calculating a visible interval into a simple intersection problem for a group of parallel lines representing a satellite's trajectory and the regional-field-mapping envelope. Based on the analytical partial differential of the field-element equations, the baseline-field-mapping envelope for smooth and non-smooth field of views can be rapidly calculated where the regional-field-mapping envelope can be obtained by splicing the baseline-field-mapping envelopes. The simulation results show that the proposed method is rapid, accurate, and intuitive, demonstrating its wide applications for regional-target coverage analysis.

Implicit-implicit and parametric-implicit surface intersections in Euclidean n-space

In this paper, we study the intersection problem of two surfaces in which at least one surface is given by its implicit equation in Euclidean n-space. We first obtain the curvatures of the transversal intersection curve of two implicit surfaces. Later, the intersection problem is studied for a parametric surface and an implicit surface in n-dimensional Euclidean space. Finally, we present examples as applications of the given methods.

CMSTR: A Constrained Minimum Spanning Tree Based Routing Protocol for Wireless Sensor Networks

How to extend the network lifetime with given limited energy budget is always one of the main concerns in Wireless Sensor Networks (WSNs). However, imbalanced energy consumption and overlong intra-cluster communication paths are prevalent in the hierarchical routing protocols, which shortens the network lifetime inevitably. To this end, an energy-efficient routing Protocol based on Constrained Minimum Spanning Tree (CMSTR) is proposed in this paper. To be specific, a new multichain routing scheme to balance the energy consumption for intra-cluster communications is presented. Based on the multichain routing scheme, the problem of establishing intra-cluster routing is transformed into a shortest Hamiltonian path problem on the basis of a graph-theoretic analysis model, which is solved through a Constrained Minimum Spanning Tree (CMST) algorithm proposed in this paper, with the aim to obtain the initial path for intra-cluster communications. In order to shorten the initial path length to obtain higher energy-efficient chain routes, a Neighbor Node Replacement (NNR) algorithm and a Link Intersection Detection and Elimination (LIDE) algorithm are proposed, in which the problem of potential long links and intersections is to be effectively alleviated. With shorter chain routes, unnecessary intra-cluster communication energy depletion can be reduced accordingly. In order to evaluate the performance of CMSTR, extensive simulation experiments are conducted. The results show that CMSTR can greatly prolong the network lifetime with regard to the metrics of FND and HND. To be specific, compared with LEACH, R-LEACH, and DCMSTR, the value of FND increased by 800%, 540% and 57%, that of HND increased by 322%, 286% and 22%, and overall network lifetime (AND) increased by 29%, 10% and 5%, respectively. Besides, CMSTR has a stable and lowest packet loss percentage (0.4%). In summary, CMSTR has excellent performance in terms of energy efficiency and network stability.

Визуализация геометрических моделей гранных тел в точечном исчислении

The paper considers the case of faceted solids and discusses visualisation of geometric solids in the form of a three-parameter set of points which belongs to a three-dimensional space. To visualize geometric solids, taking advantage of the modern GPU hardware acceleration, the Ray marching method is used. The implementation considers the definition of a signed distance function, which is reduced to the task of determining the set of intersection points of the projection rays with the rendered geometric solid. After that, for each pixel of the screen, its color is determined in accordance with whether the ray passes through the geometric solid or not. The analytical description of geometric solids and the solution of their intersection problem with projecting rays are solved within the framework of the point calculus mathematical apparatus. As a result, it was concluded that the proposed approach justifies itself, providing high rendering performance and the complete absence of visual artifacts when rendering faceted solids.

Unlikely intersection problems for restricted lifts of a p-th power

We applied the theory of perfectoid spaces to prove dynamical versions of the Manin-Mumford conjecture, Mordell-Lang conjecture, and Tate-Voloch conjecture for lifts of a p-th power, generalizing the work of Xie in [39] for lifts of Frobenius.

GIS-Based Optimal Route Selection of Submarine Cables Considering Potential Seismic Fault Zones

Submarine lifelines (pipelines and cables) often cross areas characterized by earthquake-related geohazards (tectonic faulting, landslides and seabed liquefaction). Avoiding geologically hazardous areas increases the length (i.e., cost), whereas a potential crossing may detrimentally affect the structural performance of the infrastructure, requiring more sophisticated design approaches and/or more costly and probably impractical deep sea condition-mitigation measures. Under such adverse conditions, a cost-effective and resilient lifeline route is deemed necessary. The current paper presents a smart decision-support tool for the optimal route selection of submarine cables, assessing whether the proposed routing could effectively cross a (seismically) geologically hazardous area. The GIS-based tool is based on an efficient methodology that combines a least-cost path analysis with a multi-criteria decision method. Accordingly, several routes can be derived for user-defined scenarios, by assigning different weight factors in the adopted design criteria and hazards. When crossing fault zones, the problem of fault-cable intersection is quantitatively assessed in a realistic manner via advanced numerical models. The optimal route can be selected by considering the potential cable distress (i.e., exceedance of allowable cable strains). This tool can be efficiently implemented for deriving the optimal route of energy and telecommunication offshore cables, as it is described in the examined real case studies.

A Generalized RSK for Enumerating Linear Series on n-pointed Curves

We give a combinatorial proof of a recent geometric result of Farkas and Lian on linear series on curves with prescribed incidence conditions. The result states that the expected number of degree-d morphisms from a general genus g, n-marked curve C to ℙ r , sending the marked points on C to specified general points in ℙ r , is equal to (r+1) g for sufficiently large d. This computation may be rephrased as an intersection problem on Grassmannians, which has a natural combinatorial interpretation in terms of Young tableaux by the classical Littlewood-Richardson rule. We give a bijection, generalizing the well-known RSK correspondence, between the tableaux in question and the (r+1)-ary sequences of length g, and we explore our bijection’s combinatorial properties.

Estimasi Nilai Ekuivalensi Mobil Penumpang untuk Simpang Tak Bersinyal di Yogyakarta

Passenger Car Equivalent (PCE) is expected to be very accurate because it is very important in determining the capacity, degree of saturation, and handling of unsignalized intersections. Several methods have been used to estimate the PCE value, but based on the literature review, it is stated that the occupancy time method and the speed method are the most applicable for the unsignalized intersection conditions. This study aims to determine the most appropriate PCE value by comparing the occupancy time method and the speed method. To determine the most appropriate method in calculating the PCE of the unsignalized intersection, the calculation of the value of capacity and degree of saturation based on the method of speed and occupancy time is compared with the PCE value of MKJI. The result shows that the most suitable PCE value for unsigned intersections is the speed method. The recommended changes in the value of PCE are unmotorized vehicle PCE = 0.45, motorcycle PCE = 0.17, and large vehicle PCE = 2.2. Determining the correct PCE value is expected to provide accurate intersection performance results and determination of intersection problems.

The intersection problem for kite-GDDs

In this paper the intersection problem for a pair of kite-GDDs of type 4u is investigated. The intersection problem for kite-GDDs is the determination of all pairs (T, s) such that there exists a pair of kite-GDDs (X,H,B1) and (X,H,B2) of the same type T and |B1?B2| = s. Let J(u) = {s : ? a pair of kite-GDDs of type 4u intersecting in s blocks}; I(u) = {0, 1,..., bu ? 2, bu}, where bu = 2u(u ? 1) is the number of blocks of a kite-GDD of type 4u. We show that for any positive integer u ? 3, J(u) = I(u).

A Methodology for the Analysis of Tunnel Intersections Using Two-dimensional Numerical Modeling

Intersections of tunnels are an integral component of most underground applications. The design and construction of tunnel intersections can be the most technically challenging element of a tunnel project. Yet, there are relatively few publications and methods regarding tunnel intersection design. Tunnel intersections are essentially a three-dimensional problem. However, 3D models require significantly longer time for solving and interpreting, greater computer resources, and higher user expertise. Hence, there is a great incentive to develop simpler and quicker analysis methods for tunnel intersections. In this paper, a methodology is developed so that a 3D tunnel intersection problem can be modelled using an equivalent 2D numerical model. For this purpose, it is proposed that the main tunnel cross section is modelled with an additional horizontal expansion component that represents the cross tunnel. Multiple 3D and 2D models were computed for the purpose of finding the expansion distances in the 2D models that yield similar deformations to the 3D models. Based on the results, regression analysis was employed to derive a formula relating the ratio of equivalent diameters of the main to cross tunnel to the proper expansion distance. This formula provides a useful and practical tool for preliminary tunnel intersection design. The current work relies on a number of assumptions, mainly that the rock mass is elastic. More work can be carried out to extend and modify the proposed method for more complex conditions.

Analysis of early rutting disease at urban road intersection

Because of the special stress characteristics and location of Urban Road intersection, the proportion of early rutting disease is larger than that of ordinary road section. In order to solve the early rutting problem of intersection, this paper analyzes the causes of rutting road conditions based on the actual project, through the verification of raw materials and mix proportion.

Assessment Performance at Al- Thawra Signalized Intersection in Babil City

Hilla cities center of province Babil is one of the most important cities in Iraq 100 km (62 mi) south of Baghdad .its relate the Governorate Baghdad with Governorates south Al-Thawra signalized intersection is one of the most important intersections in AL-Hilla city Being a major crossing point to the governorates of holy Karbala and Baghdad.The excessive traffic volumes, during the peak periods (at morning and evening), of vehicles that entering the intersection increase traffic density, reduce travel speed, increase travel time, and increase the delay values This paper aims to assess the traffic performance of Al-thawra signalized intersection in Babil city that is consistent with the existing conditions and intersection's geometric properties. For all approaches, video recording has been used to collect traffic volume data. These data are taken out of videos from Babil police cameras (department of communications and information systems)..The intersection was evaluated and analyzed using the SYNCHRO 10.0 software, and the best option was selected. The outcome of the evaluation process indicated that the intersection is operated at the level of service (LOS F) and with a control delay of 162.5 seconds.by recommending a variety of strategies, ranging from signal optimization to geometric enhancements. The suggestion of widening the pavement in the north-south direction was found to be the best solution. resulting in a decrease in vehicle delays from 162.2 seconds to 95.4 seconds and the level of service remains constant (LOS F) considered an acceptable and cost-effective solution to the intersection's problems.

Gapped Indexing for Consecutive Occurrences

The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting queries (return all positions where the pattern occurs), and counting queries (return the number of occurrences of the pattern). In this paper we consider a variant of string indexing, where the goal is to compactly represent the string such that given two patterns \(P_1\) and \(P_2\) and a gap range \({[}\alpha , \beta ]\) we can quickly find the consecutive occurrences of \(P_1\) and \(P_2\) with distance in \({[}\alpha , \beta ]\), i.e., pairs of subsequent occurrences with distance within the range. We present data structures that use linear space and query time \({\widetilde{O}}(|P_1|+|P_2|+n^{2/3})\) for existence and counting and \({\widetilde{O}}(|P_1|+|P_2|+n^{2/3}\hbox {occ}^{1/3})\) for reporting. We complement this with a conditional lower bound based on the set intersection problem showing that any solution using \({\widetilde{O}}(n)\) space must use \({\widetilde{\Omega }}(|P_1| + |P_2| + \sqrt{n})\) query time. To obtain our results we develop new techniques and ideas of independent interest including a new suffix tree decomposition and hardness of a variant of the set intersection problem.

A General Framework for Decentralized Safe Optimal Control of Connected and Automated Vehicles in Multi-Lane Signal-Free Intersections

We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from four multi-lane roads at a signal-free intersection where they conflict in terms of safely crossing (including turns) with no collision. The objective is to jointly minimize the travel time and energy consumption of each CAV while ensuring safety. This problem was solved in prior work for single-lane roads. A direct extension to multiple lanes on each road is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that first converts a multi-lane intersection problem into a decentralized optimal control problem for each CAV with less conservative safety constraints than prior work. We then employ a method combining optimal control and control barrier functions, which has been shown to efficiently track tractable unconstrained optimal CAV trajectories while also guaranteeing the satisfaction of all constraints. Simulation examples are included to show the effectiveness of the proposed framework under symmetric and asymmetric intersection geometries and different CAV sequencing policies.

Semiclassical gravity from averaged boundaries in two-dimensional boundary conformal field theories

The interpretation of semiclassical gravity as an ensemble-average of CFTs has provided much progress in understanding the factorization problem and the information paradox. In this article, we consider an averaging over boundary conditions in two-dimensional boundary conformal field theories (BCFTs). We show that the boundary averaging plays an important role not only in producing wormhole contributions but also in resolving the following problem. In general setups in AdS/BCFT, one can find unphysical solutions where branes have (self-)intersections. We show that the averaging nicely resolves this intersection problem. This provides another piece of evidence that averaging plays an important role in reproducing Einstein gravity. We also propose that the averaging provides a BCFT dual of the island model.

PMRQ: Achieving Efficient and Privacy-Preserving Multidimensional Range Query in eHealthcare

Healthcare data explosion and cloud computing booming have motivated healthcare centers to outsource their healthcare data and data-driven services to a powerful cloud. Nevertheless, due to privacy concerns, the data are usually encrypted before being outsourced, which will degrade the data utility and make it challenging to implement data-driven services. Although the multidimensional range query over encrypted data, as one of the most popular outsourced services in eHealthcare, has been extensively studied, existing solutions still have some limitations in efficiency, privacy, and practicality. Aiming at this challenge, in this article, we design an efficient and privacy-preserving multidimensional range query (PMRQ) scheme. We first build an R-tree to index the data set and reduce the R-tree-based range queries to the multidimensional range intersection problem. Then, by delicately designing a data comparison algorithm and a homomorphic encoding technique, we present an encoding-based range intersection algorithm. After that, by employing matrix encryption to protect the privacy of the encoding-based range intersection algorithm, we design a multidimensional range intersection predicate encryption (MRIPE) scheme. Based on the MRIPE scheme, we then propose our PMRQ scheme. A detailed security analysis illustrates that our PMRQ scheme is privacy preserving, and experimental results demonstrate that it is computationally efficient.

Pfaffian Pairs and Parities: Counting on Linear Matroid Intersection and Parity Problems

Spanning trees are a representative example of linear matroid bases that are efficiently countable. Perfect matchings of Pfaffian bipartite graphs are a countable example of common bases of two matrices. Generalizing these two, Webb Counting Bases, Ph.D. thesis, University of Waterloo, 2004 introduced the notion of Pfaffian pairs as a pair of matrices for which counting of their common bases is tractable via the Cauchy--Binet formula. This paper studies counting on linear matroid problems extending Webb's work. We first introduce “Pfaffian parities” as an extension of Pfaffian pairs to the linear matroid parity problem, which is a common generalization of the linear matroid intersection problem and the matching problem. We show that a large number of efficiently countable discrete structures are interpretable as special cases of Pfaffian pairs and parities. Our study then turns to algorithmic aspects. We observe that the fastest randomized algorithms for the linear matroid intersection and parity problems by Harvey SIAM J. Comput., 39 (2009), pp. 679--702 and Cheung, Lau, and Leung ACM Trans. Algorithms, 10 (2014), pp. 1--26 can be derandomized for Pfaffian pairs and parities. We further present polynomial-time algorithms to count the number of minimum-weight solutions on weighted Pfaffian pairs and parities. Our algorithms make use of Frank's weight-splitting lemma for the weighted matroid intersection problem and the algebraic optimality criterion of the weighted linear matroid parity problem given by Iwata and Kobayashi SIAM J. Comput., 51 (2002) pp. STOC17-238--STOC17-280.

Towards Practical and Privacy-Preserving Multi-Dimensional Range Query Over Cloud

It is undeniable that Internet of Things (IoT) in big data era can provide us with huge volumes of multi-dimensional data, transforming our society into a much more intelligent one. In order to fit for the multi-dimensional data processing in big data era, multi-dimensional range queries, especially over cloud platform, have received considerable attention in recent years. However, as the cloud server is not fully trustable, designing multi-dimensional range queries over encrypted data becomes a research trend, and many solutions have been proposed in the literature. Nevertheless, most existing solutions suffer from the leakage of the single-dimensional privacy, and such leakage would severely put the data at risk. Although a few existing works have addressed the problem of single-dimensional privacy, they are impractical in some real scenarios due to the issues of inefficiency, inaccuracy, and two-cloud-server requirement. Aiming at solving these issues, in this article, we propose a practical and privacy-preserving multi-dimensional range query (PRQ) scheme. Specifically, in our proposed PRQ scheme, we first index the multi-dimensional dataset with an R-tree and reduce R-tree based range queries to the problem of point intersection and range intersection. Then, by employing the lightweight matrix encryption technique, we design two novel algorithms for PRQ, i.e., multi-dimensional point intersection predicate encryption (PIPE) and multi-dimensional range intersection predicate encryption (RIPE), which can preserve the privacy of the proposed point intersection algorithm and range intersection algorithm, and further preserve the single-dimensional privacy of the proposed PRQ scheme. Detailed security analysis shows that our proposed PRQ scheme is indeed privacy-preserving. In addition, extensive simulations are conducted, and the results also demonstrate its efficiency.

Kinerja Persimpangan Jalan Emmy Saelan – Jalan Maluku, Jalan Wolter Monginsidi – Jalan Tj. Karang dan Jalan Emmy Saelan – Jalan Tj. Manimbaya

The purpose of this study is to determine the performance of intersections and provide solutions to problems that occur at the intersection of Emmy Saelan – Maluku street, and Wolter Monginsidi street – Tj. Karang street and Emmy Saelan street – Tj. Manimbaya street. The analysis included road performance, existing conditions and predictions over the next 5 years by calculating the average crossing delay based on the Indonesian Road Capacity Manual (MKJI)1997. From the results of research on the existing conditions DS = 1.24 crossing delay of Emmy Saelan street – Maluku street 55,89 det/smp that is in LOS E, intrection of Wolter Monginsidi – Tj. Karang street value of DS = 1.09 and corssing delay = 24.32 det/smp that is in LOS C and intersection of Emmy Saelan street – Tj. Manimbaya value of DS = 1.06 and crossing delay = 22.60 det/smp that is in LOS C. So it requires handling of the problem of intersections in the future, the first solution is to make the road median from intrection service levelof W. Monginsidi street – Tj. Karang street up to intrection of Emmy Saelan street – Anoa II street, with a median opening at the point before the bridge. Value of DS = 0.57 dan crossing delay of Emmy Saelan street – Maluku street = 10,16 det/smp that is in LOS B, intrection of Wolter Monginsidi street – Tj. Karang street value of DS = 0.76 dan crossing delay = 12.29 det/smp that is in LOS B and intrection of Emmy Saelan – Tj. Manimbaya street value of DS = 0.41 and crossing delay = 8.12 det/smp that is in LOS B.

Disjointness through the Lens of Vapnik–Chervonenkis Dimension: Sparsity and Beyond

The disjointness problem—where Alice and Bob are given twosubsets of {1, dots, n} and they have to check if their setsintersect—is a central problem in the world of communicationcomplexity. While both deterministic and randomized communicationcomplexities for this problem are known to be Theta(n), it isalso known that if the sets are assumed to be drawn from somerestricted set systems then the communication complexity can be muchlower. In this work, we explore how communication complexitymeasures change with respect to the complexity of the underlying setsystem. The complexity measure for the set system that we use inthis work is the Vapnik—Chervonenkis (VC) dimension. Moreprecisely, on any set system with VC dimension bounded by d, weanalyze how large can the deterministic and randomized communicationcomplexities be, as a function of d and n. The d-sparse setdisjointness problem, where the sets have size at most d, is onesuch set system with VC dimension d. The deterministic and therandomized communication complexities of the d-sparse setdisjointness problem have been well studied and are known to beTheta left( d log left({n}/{d}right)right) and Theta(d),respectively, in the multi-round communication setting. In thispaper, we address the question of whether the randomizedcommunication complexity of the disjointness problem is always upperbounded by a function of the VC dimension of the set system, anddoes there always exist a gap between the deterministic andrandomized communication complexities of the disjointness problemfor set systems with small VC dimension.We construct two natural set systems of VC dimension d, motivated from geometry. Using these set systems, we show that the deterministic and randomized communication complexity can be widetilde{Theta}left(dlog left( n/d right)right) for set systems of VC dimension d and this matches the deterministic upper bound for all set systems of VC dimension d. We also study the deterministic and randomized communication complexities of the set intersection problem when sets belong to a set system of bounded VC dimension. We show that there exist set systems of VC dimension d such that both deterministic and randomized (one-way and multi-round) complexities for the set intersection problem can be as high as Thetaleft( dlog left( n/d right) right).