Minimum Path Length Research Articles

A New Approach to Determine the Specular Point of Forward Reflected GNSS Signals

Accurate determination of the specular point is important for simulating and processing reflected global navigation satellite system signals for remote sensing applications. Existing methods for determining the specular point are based on both spherical and ellipsoidal approximations of the Earth and employ either Snell's law or Fermat's principle to formulate the problem. By analysis and simulation, it is shown that these methods produce significant errors at intermediate latitudes. In this paper, a novel formulation for the solution of the specular point is proposed that satisfies Snell's Law on the WGS84 ellipsoid. The proposed method is compared with the existing methods for various receiver orbit configurations and algorithm augmentations. It is shown that the proposed method is more accurate than the existing methods and more computationally efficient than the minimum path length (MPL) method. Additionally, the resultant grazing angles, MPL method errors, and specular point locations as a function of the receiver orbit are investigated, leading to the finding that the likelihood of an error is significant for geometries favored by reflectometry applications.

Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions

In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute molecules and the structure and dynamics of water.

A novel formation scheme for IEEE 802.15.4 WSN

This paper proposes a novel formation scheme for an IEEE 802.15.4 wireless sensor network which is organised into a tree topology. This scheme consists of the network formation initialisation algorithm and the network formation maintenance algorithm. In the initialisation algorithm, each node first calculate the lengths of routing paths reaching all other nodes in the network, and then the node with the minimum path length is elected as a root. In this way, the average length of the routing paths is reduced and accordingly the routing delay is also shortened. After the initialisation algorithm is executed, the maintenance algorithm is performed to maintain the tree topology. When the tree topology changes, the maintenance algorithm can dynamically adjust the root in order to reduce the average length of the routing paths and shorten the routing delay. This scheme employs beacons to achieve the initialisation algorithm and the maintenance algorithm, so the extra costs and delays are avoided. This scheme is analysed and evaluated, and the data results show that this scheme effectively reduces the average length of the routing paths and shortens the routing delay.

Interpolating clothoid splines with curvature continuity

An efficient algorithm for the computation of a C2 interpolating clothoid spline is herein presented. The spline is obtained following an optimisation process, subject to continuity constraints. Among the 9 various targets/problems considered, there are boundary conditions, minimum length path, minimum jerk, and minimum curvature (energy). Some of these problems are solved with just a couple of Newton iterations, whereas the more complex minimisations are solved with few iterations of a nonlinear solver. The solvers are warmly started with a suitable initial guess, which is extensively discussed, making the algorithm fast. Applications of the algorithm are shown relating to fonts, path planning for human walkers, and as a tool for the time‐optimal lap on a Formula 1 circuit track.

A mixed probabilistic–geometric strategy for UAV optimum flight path identification based on bit-coded basic manoeuvres

This paper presents a novel algorithm identifying optimal flight trajectories for Unmanned Aerial Vehicles compliant with environmental constraints. Such constraints are defined in terms of obstacles, fixed way-points and selected destination points. Optimality is evaluated taking the minimum path length as the specific objective function. The proposed path planning strategy is based on an original trajectory modelling coupled with a Particle Swarm optimizer (PSO). Flight paths starting from a specified point and ending at a selected destination point are divided into a finite number of segments made up of circular arcs and straight lines. In the proposed approach such a geometrical sequence is replaced with a finite sequence of binary-coded basic manoeuvres. This novel formulation allows to easily handle the manoeuvres sequence with a fixed number of integer variables taking advantage of PSO capability in handling discrete variables; moreover the use of mixed-type variables provides the optimization procedure a useful flexibility in the “decision making” modelling and operational scenarios definition as well. Specific geometric-based linear obstacle avoidance models have been implemented in addition to suitable penalty functions. The use of these models forces each path to be consistent with the environmental constraints favouring the identification of feasible trajectories with a reduced number of iterations and particles. The path planning model has been developed with particular care devoted to reduce computational effort as well as to improve algorithm capability in handling general-shaped obstacles both in 2-D and 3-D environments. Various applications have been performed in order to test the effectiveness of the proposed flight path generator. Applicability of the proposed optimization model also to vehicles with VTOL and hovering capabilities has been preliminarily assessed.

Magnetic Resonance Imaging of Optic Nerve Traction During Adduction in Primary Open-Angle Glaucoma With Normal Intraocular Pressure.

PurposeWe used magnetic resonance imaging (MRI) to ascertain effects of optic nerve (ON) traction in adduction, a phenomenon proposed as neuropathic in primary open-angle glaucoma (POAG).MethodsSeventeen patients with POAG and maximal IOP ≤ 20 mm Hg, and 31 controls underwent MRI in central gaze and 20° to 30° abduction and adduction. Optic nerve and sheath area centroids permitted computation of midorbital lengths versus minimum paths.ResultsAverage mean deviation (±SEM) was −8.2 ± 1.2 dB in the 15 patients with POAG having interpretable perimetry. In central gaze, ON path length in POAG was significantly more redundant (104.5 ± 0.4% of geometric minimum) than in controls (102.9 ± 0.4%, P = 2.96 × 10−4). In both groups the ON became significantly straighter in adduction (28.6 ± 0.8° in POAG, 26.8 ± 1.1° in controls) than central gaze and abduction. In adduction, the ON in POAG straightened to 102.0% ± 0.2% of minimum path length versus 104.5% ± 0.4% in central gaze (P = 5.7 × 10−7), compared with controls who straightened to 101.6% ± 0.1% from 102.9% ± 0.3% in central gaze (P = 8.7 × 10−6); and globes retracted 0.73 ± 0.09 mm in POAG, but only 0.07 ± 0.08 mm in controls (P = 8.8 × 10−7). Both effects were confirmed in age-matched controls, and remained significant after correction for significant effects of age and axial globe length (P = 0.005).ConclusionsAlthough tethering and elongation of ON and sheath are normal in adduction, adduction is associated with abnormally great globe retraction in POAG without elevated IOP. Traction in adduction may cause mechanical overloading of the ON head and peripapillary sclera, thus contributing to or resulting from the optic neuropathy of glaucoma independent of IOP.

A recommender system for train routing: When concatenating two minimum length paths is not the minimum length path

In this paper, we propose a method for finding the optimal route for a specific train from a station to another one in the Spanish railway network (or any railway network involving different incompatible features like gauges, electrification and signaling systems). The complexity of the Spanish railway infrastructure makes it difficult to give an estimation of the fastest route of a train from a given station to another. Indeed, very unintuitive situations may happen. The problem of finding fastest routes is typically modeled by a graph where nodes represent stations and edges represent railway sections. However, this approach is not suitable for the Spanish railway network. In order to solve the problem of calculating the fastest routes, we will propose here a novel approach based on modeling the railway network through a different graph whose nodes represent railway sections.

Improved dynamic routing algorithms in elastic optical networks

The considered Routing, Modulation Level and Spectrum Allocation (RMLSA) problem covers path length minimization while still meeting the spectrum continuity constraints, non-overlapping spectra constraints, spectrum contiguity constraints, and choice of modulation level. In this problem, the relationship between spectrum connection and bit rate of the incoming request has been taken into account. In this paper, two algorithms have been proposed. The first one is based on a set of shortest paths whose lengths are determined by the number of links in the network. The second one is a modified version of Dijkstra’s algorithm. Modification of this algorithm is based on introduction of weights of the network links depending on the utilization of the links and the introduction of a aggregated spectrum of the path that is being selected. Extensive research has shown that algorithms reject the lower traffic volume as compared to well-known algorithms proposed in literature.

Determining the Semantic Orientation of opinion words using typed dependencies for opinion word senses and Sentiwordnet scores from online product reviews

Opinion words express the information regarding the like and dislike of a user on the target entities such as products and product aspects present in the online reviews. The polarised information collected from the reviews is analysed by calculating the orientation of the adjectives. The synonymy relation graph is a way to determine the orientation of the adjectives present in the product reviews dataset. It considers the minimum path length between the adjectives under analysis using WordNet synsets. The synonymy relation graph cannot determine the orientations of all the opinion words present in the dataset. In order to evaluate opinion orientation of all the adjectives from the dataset, the synonymy relation graph of WordNet is to be replaced with the SentiWordNet scores of the opinion words. These scores are provided to the opinion words by finding the contextual clues surrounding the opinion words to disambiguate their sense. The contextual clues are finalised based on the typed dependencies grammatical relations. The distance between the opinion word and the context insensitive seed term (good/bad) is computed by calculating the difference between these scores. This paper addresses advantages of using SentiWordNet scores. This improves the accuracy of the determined opinion word orientations.

Optimal automated path planning for infinitesimal and real-sized particle assemblies

The present article introduces an algorithm for path planning and assembly of infinitesimal and real-sized particles by using a distance and path based permutation algorithm. The main objective is to define non-overlapping particle paths subject to minimal total path length during particles positioning and assembly. Thus, a local minimum is sought with a low computational cost. For this reason, an assignment problem, to be specific Euclidean bipartite matching problem, is presented, where the particles in the initial (random selection) and final (particle assembly) configurations are in one-to-one correspondence. The cost function for particle paths is defined through Euclidean distance of each particle between the initial and final configurations. Principally, a cost flow problem is formed and solved by determining an optimal permutation subject to the total Euclidean distance of the particles and their non-overlapping paths. Monte Carlo simulations are carried out for non-overlapping paths; thus, non-colliding particles, and then total path distances of the obtained sets are minimized, resulting in an optimal solution which may not be necessarily the global optimum. Case studies on basic and complex shaped infinitesimal and real-sized particle assemblies are shown with their total costs, i.e., path lengths. It is believed that the present study contributes to the current efforts in optical trapping automation for particle assemblies with possible applications, e.g., in the areas of micro-manufacturing, microfluidics, regenerative medicine and biotechnology.

Geometric Path Problems with Violations

In this paper, we study variants of the classical geometric shortest path problem inside a simple polygon, where we allow a part of the path to go outside the polygon. Let P be a simple polygon consisting of n vertices and let s, t be a pair of points in P. Let $$\text{ int }(P)$$ represent the interior of P and let $$\overline{P}$$ represent the exterior of P, i.e. $$\text{ int }(P)=P{\setminus }\partial (P)$$ and $$\overline{P}=\mathbb {R}^2{\setminus }\text{ int }(P)$$ . For an integer $$k\ge 0$$ , we define a k-violation path from s to t to be a path connecting s and t such that its intersection with $$\overline{P}$$ consists of at most k segments. There is no restriction in terms of the number of segments of the path within P. The objective is to compute a path of minimum Euclidean length among all possible $$({\le } k)$$ -violation paths from s to t. In this paper, we study this problem for $$k=1$$ and propose an algorithm that computes the shortest one-violation path in $$O(n^3)$$ time. We show that for rectilinear polygons, the minimum length rectilinear one-violation path can be computed in $$O(n\log n)$$ time. We extend the concept of one-violation path to a one-stretch violation path. In this case, the path between s and t is composed of (a) a path in P from s to a vertex u of P, (b) a path in $$\overline{P}$$ between u and a vertex v of P, and (c) a path in P between v and t. We show that a minimum length one-stretch violation path can be computed in $$O(n\log n\log \log n)$$ time. Next, we introduce one- and two-violation monotone rectilinear path problems among a set of n disjoint axis-parallel rectangular objects. Let s, t be two points in $$\mathbb {R}^2$$ that are not in the interior of any of the objects. In the case of one-violation monotone path problem, the desired rectilinear path from s to t consists of horizontal edges that are directed towards the right and vertical edges that are directed upwards, except for at most one edge. Similarly, in the case of a two-violation monotone path problem, all horizontal edges are directed towards the right except at most one and all vertical edges are directed upwards except at most one. Our algorithms for both of these problems run in $$O(n\log n)$$ time.

Mathematical model for path selection by ants between nest and food source

Several models have been proposed to describe the behavior of ants when moving from nest to food sources. Most of these studies where based on numerical simulations with no mathematical justification. In this paper, we propose a mechanism for the formation of paths of minimal length between two points by a collection of individuals undergoing reinforced random walks taking into account not only the lengths of the paths but also the angles (connected to the preference of ants to move along straight lines). Our model involves reinforcement (pheromone accumulation), persistence (tendency to preferably follow straight directions in absence of any external effect) and takes into account the bifurcation angles of each edge (represented by a probability of willingness of choosing the path with the smallest angle). We describe analytically the results for 2 ants and different path lengths and numerical simulations for several ants.

Functional brain networks in healthy subjects under acupuncture stimulation: An EEG study based on nonlinear synchronization likelihood analysis

Electroencephalogram (EEG) signal evoked by acupuncture stimulation at ”Zusanli” acupoint is analyzed to investigate the modulatory effect of manual acupuncture on the functional brain activity. Power spectral density of EEG signal is first calculated based on the autoregressive Burg method. It is shown that the EEG power is significantly increased during and after acupuncture in delta and theta bands, but decreased in alpha band. Furthermore, synchronization likelihood is used to estimate the nonlinear correlation between each pairwise EEG signals. By applying a threshold to resulting synchronization matrices, functional networks for each band are reconstructed and further quantitatively analyzed to study the impact of acupuncture on network structure. Graph theoretical analysis demonstrates that the functional connectivity of the brain undergoes obvious change under different conditions: pre-acupuncture, acupuncture, and post-acupuncture. The minimum path length is largely decreased and the clustering coefficient keeps increasing during and after acupuncture in delta and theta bands. It is indicated that acupuncture can significantly modulate the functional activity of the brain, and facilitate the information transmission within different brain areas. The obtained results may facilitate our understanding of the long-lasting effect of acupuncture on the brain function.

Using Individualized Brain Network for Analyzing Structural Covariance of the Cerebral Cortex in Alzheimer's Patients.

Cortical thinning patterns in Alzheimer's disease (AD) have been widely reported through conventional regional analysis. In addition, the coordinated variance of cortical thickness in different brain regions has been investigated both at the individual and group network levels. In this study, we aim to investigate network architectural characteristics of a structural covariance network (SCN) in AD, and further to show that the structural covariance connectivity becomes disorganized across the brain regions in AD, while the normal control (NC) subjects maintain more clustered and consistent coordination in cortical atrophy variations. We generated SCNs directly from T1-weighted MR images of individual patients using surface-based cortical thickness data, with structural connectivity defined as similarity in cortical thickness within different brain regions. Individual SCNs were constructed using morphometric data from the Samsung Medical Center (SMC) dataset. The structural covariance connectivity showed higher clustering than randomly generated networks, as well as similar minimum path lengths, indicating that the SCNs are “small world.” There were significant difference between NC and AD group in characteristic path lengths (z = −2.97, p < 0.01) and small-worldness values (z = 4.05, p < 0.01). Clustering coefficients in AD was smaller than that of NC but there was no significant difference (z = 1.81, not significant). We further observed that the AD patients had significantly disrupted structural connectivity. We also show that the coordinated variance of cortical thickness is distributed more randomly from one region to other regions in AD patients when compared to NC subjects. Our proposed SCN may provide surface-based measures for understanding interaction between two brain regions with co-atrophy of the cerebral cortex due to normal aging or AD. We applied our method to the AD Neuroimaging Initiative (ADNI) data to show consistency in results with the SMC dataset.

An Improved Integrality Gap for Asymmetric TSP Paths

The asymmetric traveling salesperson path problem (ATSPP) is one where, given an asymmetric metric space (V, d) with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V. This problem is closely related to the asymmetric TSP (ATSP), which seeks to find a tour (instead of an s-t path) visiting all the nodes: for ATSP, a ρ-approximation guarantee implies an O(ρ)-approximation for ATSPP. However, no such connection is known for the integrality gaps of the linear programming (LP) relaxations for these problems: the current-best approximation algorithm for ATSPP is O(ln n/ln ln n), whereas the best bound on the integrality gap of the natural LP relaxation (the subtour elimination LP) for ATSPP is O(ln n). In this paper, we close this gap, and improve the current best bound on the integrality gap from O(ln n) to O(ln n/ln ln n). The resulting algorithm uses the structure of narrow s-t cuts in the LP solution to construct a (random) tree spanning tree that can be cheaply augmented to contain an Eulerian s-t walk. We also build on a result of Oveis Gharan and Saberi and show a strong form of Goddyn’s conjecture about thin spanning trees implies the integrality gap of the subtour elimination LP relaxation for ATSPP is bounded by a constant. Finally, we give a simpler family of instances showing the integrality gap of this LP is at least 2.

Protecting core networks with dual-homing: A study on enhanced network availability, resource efficiency, and energy-savings

Core network survivability affects the reliability performance of telecommunication networks and remains one of the most important network design considerations. This paper critically examines the benefits arising from utilizing dual-homing in the optical access networks to provide resource-efficient protection against link and node failures in the optical core segment. Four novel, heuristic-based RWA algorithms that provide dedicated path protection in networks with dual-homing are proposed and studied. These algorithms protect against different failure scenarios (i.e. single link or node failures) and are implemented with different optimization objectives (i.e., minimization of wavelength usage and path length). Results obtained through simulations and comparison with baseline architectures indicate that exploiting dual-homed architecture in the access segment can bring significant improvements in terms of core network resource usage, connection availability, and power consumption.

Path planning algorithms for mobile anchors towards range-free localization

The objective of path planning for a mobile anchor is to find the path of minimum length that the anchor traverses to localize all sensors. The challenge is to design a movement strategy which reduces path length while meeting the requirements of a good range-free localization technique. A novel deterministic movement strategy is proposed in this paper that reduces path length and uses an existing range-free localization scheme which yields good positional accuracy. The mobile anchor moves in a hexagonal pattern to localize all the sensors which form a connected network. We compare performance of our algorithm with an existing path planning algorithm in terms of both path length and localization accuracy. Simulation results show that even in presence of irregular radio propagation, our algorithm achieves full localization. We have proposed another movement strategy for a mobile anchor using same hexagonal pattern to localize all the sensors lying in a rectangular region. Improvement in path length is shown theoretically compared to existing path planning schemes.

Asymmetries arising from the space-filling nature of vascular networks.

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the tradeoffs faced by biological networks and yields predictions that better match our empirical data.

An optimal path planning problem for heterogeneous multi-vehicle systems

Abstract A path planning problem for a heterogeneous vehicle is considered. Such a vehicle consists of two parts which have the ability to move individually, but one of them has a shorter range and is therefore required to keep in a close distance to the main vehicle. The objective is to devise an optimal path of minimal length under the condition that at least one part of the heterogeneous system visits all desired waypoints exactly once. Two versions of the problem are considered. One assumes that the order in which the waypoints are visited is known a priori. In such a case we show that the optimal path can be found by solving a mixed-integer second-order cone problem. The second version assumes that the order in which the waypoints are visited is not known a priori, but can be optimized so as to shorten the length of the path. Two approaches to solve this problem are presented and evaluated with respect to computational complexity.

Ion aggregation in high salt solutions. V. Graph entropy analyses of ion aggregate structure and water hydrogen bonding network.

Dissolved ions in water tend to form polydisperse ion aggregates such as ion pairs, relatively compact ion clusters, and even spatially extended ion networks with increasing salt concentration. Combining molecular dynamics simulation and graph theoretical analysis methods, we recently studied morphological structures of ion aggregates with distinctively different characteristics. They can be distinguished from each other by calculating various spectral graph theoretical properties such as eigenvalues and eigenvectors of adjacency matrices of ion aggregates and water hydrogen-bonding networks, minimum path lengths, clustering coefficients, and degree distributions. Here, we focus on percolation and graph entropic properties of ion aggregates and water hydrogen-bonding networks in high salt solutions. Ion network-forming K(+) and SCN(-) ions at high concentrations show a percolating behavior in their aqueous solutions, but ion cluster-forming ions in NaCl solutions do not show such a transition from isolated ion aggregates to percolating ion-water mixture morphology. Despite that the ion aggregate structures are strikingly different for either cluster- or network-forming ions in high salt solutions, it is interesting that the water structures remain insensitive to the electrostatic properties, such as charge densities and polydentate properties, of dissolved ions, and morphological structures of water H-bonding networks appear to be highly robust regardless of the nature and concentration of salt. We anticipate that the present graph entropy analysis results would be of use in understanding a variety of anomalous behaviors of interfacial water around biomolecules as well as electric conductivities of high electrolyte solutions.