Point Location Problem Research Articles

On the Acceleration of the Young Solar Wind from Different Source Regions

The acceleration of the young solar wind is studied using the first 17 encounters of the Parker Solar Probe. We identify wind intervals from different source regions: coronal hole (CH) interiors, streamers, and low-Mach-number boundary layers (LMBLs), i.e., the inner boundaries of coronal holes. We present their statistical trends in the acceleration process. Most of the observations can be reproduced by a two-fluid hydrodynamic model with realistic corona temperatures. In such a model, the solar wind is accelerated by the combined thermal pressures of protons and electrons, but it is mainly the difference in the proton pressure that leads to the difference in the solar wind speed. The proton pressure is the highest in the fastest CH wind, with a high initial proton temperature that decreases slowly. It is lower in the relatively slow LMBL wind and the lowest in the slowest streamer wind. The proton temperature is quadratically correlated with the wind speed when scaled to the same distance. In contrast, the electron temperature shows no significant differences for different wind types or wind speeds, indicating more similar contributions from the electron pressure. The model gives reasonable locations for the sonic critical point, which is on average at 3.6–7.3 Rs and can also extend to large distances when the proton temperature is extremely low, as in the LMBL wind. In addition to the thermal pressure, we raise the possibility that Alfvén waves may contribute to the solar wind acceleration, especially for the fast CH wind.

Analytical Solution for the Problem of Point Location in Arbitrary Planar Domains

This paper presents a general analytical solution for the problem of locating points in planar regions with an arbitrary geometry at the boundary. The proposed methodology overcomes the traditional solutions used for polygonal regions. The method originated from the explicit evaluation of the contour integral using the Residue and Cauchy theorems, which then evolved toward a technique very similar to the winding number and, finally, simplified into a variant of ray-crossing approach slightly more informed and more universal than the classic approach, which had been used for decades. The very close relation of both techniques also emerges during the derivation of the solution. The resulting algorithm becomes simpler and potentially faster than the current state of the art for point locations in arbitrary polygons because it uses fewer operations. For polygonal regions, it is also applicable without further processing for special cases of degeneracy, and it is possible to use in fully integer arithmetic; it can also be vectorized for parallel computation. The major novelty, however, is the extension of the technique to virtually any shape or segment delimiting a planar domain, be it linear, a circular arc, or a higher order curve.

Revisiting reachability-driven explicit MPC for embedded control

The real-time implementation of the explicit MPC suffers from the evaluation of the, potentially large, lookup table. The paper revisits the original approach and presents an efficient reachability-sets-driven-based explicit MPC method addressing this issue by splitting the look-up table into the set of the “relevant” subsets. Simultaneously, effective binary encoding is introduced to minimize the runtimes and the memory footprint. Further acceleration is achieved by introducing the “smart” order of the considered critical regions. Then, the significant real-time complexity reduction is ensured by online pruning and traversing the sorted lookup table associated with the optimal control law evaluation. Technically, the number of critical regions to be explored is reduced and the order is redefined to accelerate the point location problem and minimize the computational effort. While the optimality of the control law is still preserved, the cost that we need to pay for the accelerated point location problem lies in an additional offline computation effort and a minor increase in memory requirements of the underlying controller. The benefits of the proposed method are demonstrated using an extensive case study. The complexity reduction strategy was investigated on two fast-dynamic benchmark systems and the computational burden was analyzed by implementing the designed controllers on an embedded hardware.

A novel mathematical model for emergency transfer point and facility location

The significance of emergency transfer point and facility location lies in its potential to save lives, optimize resource allocation, and enhance the efficiency of healthcare services during emergencies. It ensures timely patient access and cost-effective care. So, this study introduces a novel Mixed Integer Programming Model (MIP) for addressing the Multi-Facility and Multi-Transfer Point Location Problem (MFMTPLP). The problem involves determining the optimal locations for q facilities and p transfer points to facilitate direct customer access to facilities or through transfer points. The objective is to minimize the maximum expected weight distance for all the required points via transfer points. The study focuses on identifying the required points that carry weight and proposes a viable solution for solving the associated mathematical problems. An important contribution of this study, which has been overlooked in previous research, is the exploration of relevant costs associated with not transferring patients from demand points and hospitalizing them at transfer points. Additionally, the study emphasizes the significance of prioritizing different points and considering the costs associated with not transferring injured individuals from demand points and admitting them to transfer points. Previous models for locating facility and transfer points did not account for these factors. The study concludes by presenting the computed results, which validate the feasibility and effectiveness of the proposed model.

Almost Optimal Exact Distance Oracles for Planar Graphs

We consider the problem of preprocessing a weighted directed planar graph in order to quickly answer exact distance queries. The main tension in this problem is between space S and query time Q , and since the mid-1990s all results had polynomial time-space tradeoffs, e.g., Q = ~ Θ( n/√ S ) or Q = ~Θ( n 5/2 /S 3/2 ). In this article we show that there is no polynomial tradeoff between time and space and that it is possible to simultaneously achieve almost optimal space n 1+ o (1) and almost optimal query time n o (1) . More precisely, we achieve the following space-time tradeoffs: n 1+ o (1) space and log 2+ o (1) n query time, n log 2+ o (1) n space and n o (1) query time, n 4/3+ o (1) space and log 1+ o (1) n query time. We reduce a distance query to a variety of point location problems in additively weighted Voronoi diagrams and develop new algorithms for the point location problem itself using several partially persistent dynamic tree data structures.

A Bi-Level Vaccination Points Location Problem That Aims at Social Distancing and Equity for the Inhabitants

Designing efficient vaccination programs that consider the needs of the population is very relevant to prevent reoccurrence of the COVID-19 pandemic. The government needs to provide vaccination points to give out vaccine doses to the population. In this paper, the authors analyze the location of vaccination points whilst addressing the inhabitants’ preferences. Two objectives that prevent crowding of inhabitants are considered. The government aims for the minimum distance between located vaccination points is maximized, and for the number of inhabitants that attend the different vaccination points to be equitable. One of the key aspects of this problem is the assumption that inhabitants freely choose the located vaccination point to go. That decision affects the objectives of the government, since crowding at vaccination points may appear due to the inhabitants’ decisions. This problem is modeled as a bi-objective, bi-level program, in which the upper level is associated to the government and the lower level to the inhabitants. To approximate the Pareto front of this problem, a cross-entropy metaheuristic is proposed. The algorithm incorporates criteria to handle two objective functions in a simultaneous manner, and optimally solve the lower-level problem for each government decision. The proposed algorithm is tested over an adapted set of benchmark instances and pertinent analysis of the results is included. An important managerial insight is that locating far vaccination points does not lead us to a more equitable allocation of inhabitants.

Simulation optimization for stochastic casualty collection point location and resource allocation problem in a mass casualty incident

After a severe disaster strikes, a large number of casualties in need of urgent treatment, known as a mass casualty incident (MCI) event, arise from multiple disaster areas in a very short period of time and overwhelm available resources of the local healthcare system. This paper focuses on the effective design of casualty collection point (CCP) locations and the efficient allocation of limited emergency medical service (EMS) resources to transport casualties quickly to appropriate hospitals and increase the survival rate of casualties. A hybrid simulation–optimization approach to optimize the CCP location and EMS resource allocation problem over mixed binary and integer feasible domains for the minimization of expected complete delivery time of all casualties from disaster region to hospitals is presented in this work due to the stochastic and dynamic nature of the MCI logistics environment. A high-resolution stochastic discrete event simulation model considering time-varying stochastic casualty arrivals, random triage service times, and stochastic travel times caused by road network vulnerability is first constructed to describe a more detailed modeling of comprehensive MCI humanitarian logistics from the disaster regions to the hospitals. Then, a novel two-stage sequential algorithm, namely a combination of optimal computing budget allocation-based rapid-screening algorithm and adaptive particle global and hyperbox local search (ORSA-APGHLS), is developed to speed up convergence to near-optimal solutions compared to three common existing algorithms (Genetic Algorithm, Tabu Search and Stochastic Nelder-Mead Algorithm) under a limited simulation budget. We collaborate with the National Science and Technology Center for Disaster Reduction (NCDR) in Taiwan to conduct computational experiments to demonstrate the efficiency and efficacy of the proposed two-stage ORSA-APGHLS algorithm according to a potential earthquake scenario occurring in Tainan City, Taiwan. Through sensitivity analysis, the influence of different levels of scarce emergency medical resources and degrees of road damage on the expected complete delivery time of all casualties and the location-allocation decisions are investigated.

A multi-Markovian switching-based strategy for solving the stochastic point location problem

A multi-Markovian switching-based strategy for solving the stochastic point location problem

Explicit Model Predictive Control for a Highly Interacting System

Explicit Model Predictive Control (MPC) of highly interacting systems using multiparametric programming is challenging as the offline solution to the Optimal Control Problem (OCP) typically entails calculation of a large number of regions of the uncertainty space. This can result in the case in which the point location problem is computationally more expensive than solving the OCP online. Hence, in this paper, with an aim to reduce computational costs of explicit MPC, we reformulate the OCP and study the computational and control performance of the reformulated explicit MPC compared to the conventional explicit MPC. As a case study, we consider a highly interacting quadruple tank process. The closed-loop simulation results show that between conventional MPC and reformulated MPC, in the online case, the total computational times are comparable, whereas in the explicit MPC case, the reformulation results in significant reduction in the total computational time by 44%.

Special point "trains" in the M-R diagram of hybrid stars

We present a systematic investigation of the possible locations for the special point (SP), a unique feature of hybrid neutron stars in the massradius diagram. The study is performed within the two-phase approach where the high-density (quark matter) phase is described by the covariant nonlocal Nambu–Jona-Lasinio (nlNJL) model equation of state (EOS) which is shown to be equivalent to a constant-sound-speed (CSS) EOS. For the nuclear matter phase around saturation density different relativistic density functional EOSs are used: DD2p00, its excluded-volume modification DD2p40 and the hypernuclear EOS DD2Y-T. In the present contribution we apply the Maxwell construction scheme for the deconfinement transition and demonstrate that a simultaneous variation of the vector and diquark coupling constants results in the occurrence of SP "trains" which are invariant against changing the nuclear matter EOS. We propose that the SP train corresponding to a variation of the diquark coupling at constant vector coupling is special since it serves as a lower bound for the line of maximum masses and accessible radii of massive hybrid stars.

Dynamic Distribution-Sensitive Point Location

We propose a dynamic data structure for the distribution-sensitive point location problem in the plane. Suppose that there is a fixed query distribution within a convex subdivision S , and we are given an oracle that can return in O (1) time the probability of a query point falling into a polygonal region of constant complexity. We can maintain S such that each query is answered in O opt (S) ) expected time, where opt ( S ) is the expected time of the best linear decision tree for answering point location queries in S . The space and construction time are O(n log 2 n ), where n is the number of vertices of S . An update of S as a mixed sequence of k edge insertions and deletions takes O(k log 4 n) amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of n sites can be performed in O(n log 4 n ) expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.

Developing a transfer point location problem considering normal demands distribution

In the scope of center location problem, transfer point location problems (TPLP) are the ones which have been studied more recently to make models more applicable in real world. The contribution of this work is to develop a model in which demand points are weighted and have a normal distribution. As an assumption, there is no transformation directly from a demand point to the service facility location. This means that the transfer point is always engaged. The contribution of work is summarized in two models. In the first model, all the points are considered in an area while in the second one the points are considered in several areas. The problem is to find out the best location for the transfer point so that the maximum expected weighted distance to all demand points through the transfer point is minimized. A mathematical solution is employed when demand points follow normal distribution, with some points of demands being in regions. Then, this model was solved by replacing real number in a real condition. We used Maple software to solve this objective function as well as MATLAB software to solve this model numerically.

МЕТОД РОЗВ’ЯЗАННЯ ДВОВИМІРНОЇ ЗАДАЧІ РОЗТАШУВАННЯ ТОЧОК НА РЕГУЛЯРНИХ СІТКАХ

Point location problems often arise in areas such as object visibility analysis, sensor location, human flow simulation, urban planning, mobile control, and paint and film application. In many such problems, it is often necessary to define a set of points that cover given positions, such as viewpoints on the observed surface. This problem can be considered in terms of finding the set of sensor positions, which provides maximum coverage of the points of the set by some criterion of reachability, which is formulated in the paper on the basis of the Euclidean metric. Usually, the object location problem does not have an exact solution, so in practice, optimization methods are used to solve it, which do not guarantee finding a global optimum solution. This makes it necessary to find more effective methods for solving point location problems. The paper presents a method of solving the problem of location of a set of points, which provides a given coverage of the input point set by the criterion of reachability based on drawing circles on a regular (pixel) grid, and determining the grid points that belong to such circles. The presented method allows to solve such problems in a linear time from the number of points of the input set. The main iterations of the algorithm for finding a set of points covering a given set are presented, an experimental study on test point sets on a plane is performed, and examples of the obtained solutions are given. The presented approach consists of the following steps: formation of the criterion of mutual reach of points; determining the dimensions of the pixel grid and the battery array; drawing circles of a given radius on the grid; determination of points belonging to the applied circles; increment of values in the accumulator.Keywords: placement problem, point set, mutual reachability of points, pixel grid, coverage of point set.

Hybrid neutron stars in the mass‐radius diagram

AbstractWe present a systematic investigation of the possible locations for the special point (SP), a unique feature of hybrid neutron stars in the mass‐radius diagram. The study is performed within the two‐phase approach where the high‐density (quark matter) phase is described by the constant‐sound‐speed (CSS) equation of state (EoS) and the nuclear matter phase around saturation density is varied from very soft (APR) to stiff (DD2 with excluded nucleon volume). Different construction schemes for the deconfinement transition are applied: Maxwell construction, mixed phase construction, and parabolic interpolation. We demonstrate for the first time that the SP is invariant not only against changing the nuclear matter EoS, but also against variation of the construction schemes for the phase transition. Since the SP serves as a proxy for the maximum mass and accessible radii of massive hybrid stars, we draw conclusions for the limiting masses and radii of hybrid neutron stars.

Well-testing based turbidite lobes modeling using the ensemble smoother with multiple data assimilation

The representation of geological bodies is a difficult task, which involves a large number of parameters and assumptions that are commonly simplified in object-based modeling. A famous method that has been extensively applied for modeling geological bodies is the use of non-uniform rational B-Spline curves (NURBS) to delimit the boundaries of an object. Although NURBS provides highly detailed models, it only considers geological observations and assumptions. Moreover, the use of NURBS neglects information obtained from well-testing. This method also requires the complex and time-consuming process of determining the interior of the object in the parametric space. This is a classic problem in computational geometry, known as point location. To address these problems, this study proposes a well-testing-based object-based model of turbidite lobes using the ensemble smoother with multiple data assimilation. To escape the point location problem, we use single-valued B-Spline curves (SVBS) to build the turbidite system model. These curves are planar type B-Spline curves but they are defined as functions. The use of SVBS avoids the use of all complex algorithms and structures for solving the point location problem in the parametric space, if it is straightforward to decide if a point is in or out of the object. Consequently, it is possible to use the ensemble smoother with multiple data assimilation method to estimate the geometric parameters of the object, where a large number of realizations is required.

Omnipolar Electrograms in Creation of High-Density Voltage Maps in Patients Undergoing Atrial Fibrillation Catheter Ablation

Introduction: Current strategies for mapping the atrial substrate in patients with a history of atrial fibrillation rely on bipolar peak-to-peak voltage mapping of the atria. This is limited by its reliance on the direction of conduction at the time of recording which may lead to inaccuracies in demarcating low voltage areas and produce false-positive results when assessing for PV isolation at the end of a procedure. We have developed a novel approach, termed omnipolar (OTmax) mapping which provides signals devoid of catheter-orientation dependence but generates the greatest possible voltage. Our hypothesis is that OT mapping may result in a more accurate visualization of the atrial substrate and that this may also help to accurately assess for possible regions of intact conduction across ablation lesions delivered around pulmonary vein antra. Methods: Electroanatomical maps created using the EnSite PrecisionTM cardiac mapping system from data acquired using the AdvisorTM HD Grid Sensor EnabledTM Mapping Catheter were extracted from the system and processed using the Matlab programming environment (R2020b, The MathWorks, Inc) using custom written Matlab functions. OT Vmax, bipolar along ,across, and the maximum peak voltages and surface locations for each mapping point were exported from Velocity and imported into Matlab for analysis and a comparison was made between all of these parameters. Results: OTmax was superior to bipolar mapping in all configurations in the quantification of the mean voltage recorded. OTmax was also found to result in the quantification of signals which would otherwise have been classified as regions of fibrosis. OTmax resulted in higher density physiologically relevant voltage map when compared with all bipolar modalities. OT mapping was superior to bipolar along, across and all bipoles in the detection of electrical points within the ablation zone which revealed regions of conduction not evident on bipolar mapping. Conclusion: OT mapping was superior to bipolar mapping modalities in the visualization of atrial substrate amongst patients undergoing catheter for atrial fibrillation. OT mapping was also shown to be superior to bipolar mapping for the identification of regions of conduction across ablation lesions, which may in part explain recurrences of atrial tachyarrhythmias.

Accelerating Unstructured Mesh Point Location With RT Cores.

We present a technique that leverages ray tracing hardware available in recent Nvidia RTX GPUs to solve a problem other than classical ray tracing. Specifically, we demonstrate how to use these units to accelerate the point location of general unstructured elements consisting of both planar and bilinear faces. This unstructured mesh point location problem has previously been challenging to accelerate on GPU architectures; yet, the performance of these queries is crucial to many unstructured volume rendering and compute applications. Starting with a CUDA reference method, we describe and evaluate three approaches that reformulate these point queries to incrementally map algorithmic complexity to these new hardware ray tracing units. Each variant replaces the simpler problem of point queries with a more complex one of ray queries. Initial variants exploit ray tracing cores for accelerated BVH traversal, and subsequent variants use ray-triangle intersections and per-face metadata to detect point-in-element intersections. Although these later variants are more algorithmically complex, they are significantly faster than the reference method thanks to hardware acceleration. Using our approach, we improve the performance of an unstructured volume renderer by up to 4× for tetrahedral meshes and up to 15× for general bilinear element meshes, matching, or out-performing state-of-the-art solutions while simultaneously improving on robustness and ease-of-implementation.

P-V-Tmeasurements of Fe3C to 117 GPa and 2100 K: Implications for stability of Fe3C phase at core conditions

AbstractWe report the thermal Equation of State (EoS) of the non-magnetic Fe3C phase based on in situ X-ray diffraction (XRD) experiments to 117 GPa and 2100 K. High-pressure and temperature unit-cell volume measurements of Fe3C were conducted in a laser-heated diamond-anvil cell. Our pressure-volume-temperature (P-V-T) data together with existing data were fit to the Vinet equation of state with the Mie-Grüneisen-Debye thermal pressure model, yielding V0 = 151.6(12) Å3, K0 = 232(24) GPa, K0′= 5.09(46), γ0 = 2.3(3), and q = 3.4 (9) with θ0 = 407 K (fixed). The high-T data were also fit to the thermal pressure model with a constant αKT term, PTh = αKT(ΔT), and there is no observable pressure or temperature dependence, which implies minor contributions from the anharmonic and electronic terms. Using the established EoS for Fe3C, we made thermodynamic calculations on the P-T locations of the breakdown reaction of Fe3C into Fe7C3 and Fe. The reaction is located at 87 GPa and 300 K and 251 GPa and 3000 K. An invariant point occurs where Fe, Fe3C, Fe7C3, and liquid are stable, which places constraints on the liquidus temperature of the outer core, namely inner core crystallization temperature, as the inner core would be comprised by the liquidus phase. Two possible P-T locations for the invariant point were predicted from existing experimental data and the reaction calculated in this study. The two models result in different liquidus “phases” at the outer core-inner core boundary pressure: Fe3C at 5300 K and Fe7C3 at 3700 K. The Fe7C3 inner core can account for the density, as observed by seismology, while the Fe3C inner core cannot. The relevance of the system Fe-C to Earth’s core can be resolved by constructing a thermodynamic model for melting relations under core conditions as the two models predict very different liquidus temperatures.

Standardization of Dolphin Cardiac Auscultation and Characterization of Heart Murmurs in Managed and Free-Ranging Bottlenose Dolphins (Tursiops truncatus).

Cardiac auscultation is an important, albeit underutilized tool in aquatic animal medicine due to the many challenges associated with in-water examinations. The aims of this prospective study were to (1) establish an efficient and repeatable in-water cardiac auscultation technique in bottlenose dolphins (Tursiops truncatus), (2) describe the presence and characterization of heart murmurs detected in free-ranging and managed dolphins, and (3) characterize heart murmur etiology through echocardiography in free-ranging dolphins. For technique development, 65 dolphins cared for by the Navy Marine Mammal Program (Navy) were auscultated. The techniques were then applied to two free-ranging dolphin populations during capture-release health assessments: Sarasota Bay, Florida (SB), a reference population, and Barataria Bay, LA (BB), a well-studied population of dolphins impacted by the Deepwater Horizon oil spill. Systolic heart murmurs were detected at a frequent and similar prevalence in all dolphin populations examined (Navy 92%, SB 89%, and BB 88%), and characterized as fixed or dynamic. In all three populations, sternal cranial and left cranial were the most common locations for murmur point of maximal intensity (PMI). An in-water transthoracic echocardiogram technique was refined on a subset of Navy dolphins, and full echocardiographic exams were performed on 17 SB dolphins and 29 BB dolphins, of which, 40 had murmurs. Spectral Doppler was used to measure flow velocities across the outflow tracts, and almost all dolphins with audible murmurs had peak outflow velocities ≥1.6 m/s (95%, 38/40); three dolphins also had medium mitral regurgitation which could be the source of their murmurs. The presence of audible murmurs in most of the free-ranging dolphins (88%) was attributed to high velocity blood flow as seen on echocardiography, similar to a phenomenon described in other athletic species. These innocent murmurs were generally characterized as Grade I-III systolic murmurs with PMI in the left or sternal cranial region. This study is the first to describe an efficient technique for in-water dolphin cardiac auscultation, and to present evidence that heart murmurs are common in bottlenose dolphins.

Fixed gate point location problems

Given a metric space with a set of given facilities, location theory asks to place a new facility which minimizes the distances to the given ones. Many results for a variety of problems with norms or metrics as distances are known in the space $${\mathbb {R}}^n$$ . This paper handles specific location problems in $${\mathbb {R}}^n$$ that have been induced from location problems in the so called phylogenetic tree space coming from an application in biology. Some of the location problems in this space may be transformed to $${\mathbb {R}}^n$$ and carry interesting properties. In this paper, we only focus on the resulting problems in $${\mathbb {R}}^n$$ and we call them fixed gate point problems. The twist is that one is only allowed to traverse between two orthants by going through a fixed gate point, which induces interesting distances. In this paper, these problems are investigated for three different objective functions and solution methods in form of closed formulas and algorithms are given.