Path Length Distance Research Articles

Optimal Trajectory Planning Method for the Navigation of WIP Vehicles in Unknown Environments: Theory and Experiment.

Navigation of underactuated wheeled inverted pendulum (WIP) vehicles in unknown environments is still facing great difficulties, especially when the optimal motion is required. This article proposes an optimal trajectory planning method for the navigation of WIP vehicles in unknown environments, where various performance demands, such as security, smoothness, efficiency, etc., are all considered. First, a map-building algorithm based on the improved Rao-Blackwellized particle filter is applied for the WIP vehicle to construct the environmental map. Then, a multiobjective optimization using the genetic algorithm is performed to find an optimized path between the given start and target point with path length, path curvature, and safe distance being taken into consideration simultaneously. Moreover, on the basis of kinematical and dynamical analysis, velocity, and acceleration constraints are parameterized with a path parameter, and the minimum-time trajectory along the optimized path is further planned with a sequence of maximum acceleration and deceleration trajectories. Finally, a WIP vehicle platform based on the robot operating system is designed, and related experiments in a real obstacle environment are conducted to validate the feasibility of the proposed method.

Analysis of Sound Field Distribution in Architecturally Diverse Temples

The results of the research, which aimed to analyze the acoustic properties of selected sacred buildings located in the city of Czestochowa, Poland are presented in the paper. Three architecturally unusual and completely different from each other churches were selected for the study. The churches differed in shape of their buildings, cubic volume, years of construction, interior furnishings, etc. Nine different objective parameters were used to describe the physical properties of acoustical field in the studied churches. Various factors characterizing the acoustic properties of each building were determined, such as the distribution of sound pressure level (SPL), reverberation time T30, definition D50. Next, they were thoroughly analyzed, so as to ultimately obtain distributions of individual acoustic parameters in the space of the tested building. It allowed to evaluate the quality of the received verbal or musical message depending on the place where the listener was. Further research on speech intelligibility and the musical quality of churches was performed by determining the averaged values of next four objective acoustic parameters: centre time Ts, speech clarity C50, music clarity C80, and speech transmission index (STI). A new approach to analyzing the objective physical parameters describing the sound field was presented in Sec. 4. Mean free path length and critical distance were determined for the investigated acoustic fields in each church and they were associated with a general geometric factor characterizing the complexity of the room shape. The final part of the work presents a comparative analysis of the obtained results of acoustic quality tests of the temples, and thus their usefulness in terms achieving a maximum intelligibility of speech and music. The interesting similarities were found in the spatial distribution of individual acoustic parameters characterizing the distribution of the acoustic field in temples with completely different architecture.

Average path length and Fermat distance in fractal networks composed of high-dimensional Sierpiński pyramids

Complex networks created by fractals have been associated with various applications such as social networks, modern communication, and fractal antennas. In this paper, we consider a series of scale-free networks based on the construction of high dimensional Sierpiński pyramids. Using self-similarity and elementary renewal theorem, we derive the asymptotic formulas of the average path length (APL) and the average Fermat distance (AFD) on our network sequence in turn. Our approaches are suitable for various networks modeled on self-similar fractals.It is known that the ratio of AFD to APL is between 3/2 and 2, which implies that AFD is also a key property to characterize small-world effect. Through an elaborate investigation of our networks, the limit of this ratio for our evolving networks is 3/2 and we analyze the result in the light of our interpretation. In fact, in some scale-free networks, the nodes with high degrees have more influence on the choice of Fermat points and thus Fermat distance. Our conclusions may lead to some interesting relations concerning the hyperbolicity, Laplacian spectrum and some multiparameter indices of networks.

Characterizing graphs with fully positive semidefinite Q-matrices

For q∈R, the Q-matrixQ=Qq of a connected simple graph G=(V,E) is Qq=(q∂(x,y))x,y∈V, where ∂ denotes the path-length distance. Describing the set π(G) consisting of those q∈R for which Qq is positive semidefinite is fundamental in asymptotic spectral analysis of graphs from the viewpoint of quantum probability theory. Assume that G has at least two vertices. Then π(G) is easily seen to be a nonempty closed subset of the interval [−1,1]. In this note, we show that π(G)=[−1,1] if and only if G is isometrically embeddable into a hypercube (infinite-dimensional if G is infinite) if and only if G is bipartite and does not possess certain five-vertex configurations, an example of which is an induced K2,3.

ACO+PSO+A*: A bi-layer hybrid algorithm for multi-task path planning of an AUV

Autonomous underwater vehicle (AUV) plays a great role in the ocean engineering, and path planning is one of its key technologies. For such scenarios as oil spill detection, AUV should execute multiple tasks, which become more challenging due to the 3D ocean environment with obstacles. To solve the multi-task path planning problem of AUV, this paper first proposes a bi-level multi-objective path planning model aimed at minimizing the path length and dangerous distance. Then, a bi-layer hybrid algorithm is developed to solve the above model. In this algorithm, ant colony optimization algorithm (ACO) is adopted to generate a task sequence of the upper level model in the outer layer; particle swarm optimization algorithm (PSO) is employed to produce some waypoints between two adjacent tasks, and A* algorithm is used to generate a collision-free path of the lower level model based on waypoints in the inner layer. After that, the collision-free path in the inner layer is feedback to the ACO in the out layer to update its pheromone, and ACO yield a better task sequence in the next iteration, thus obtaining the shortest collision-free path traversing all tasks. Finally, PSO+A* and A* algorithms, together with the proposed bi-layer hybrid algorithm and some two-stage optimization algorithms are compared, respectively. Empirical results show that the proposed algorithm can produce an optimal collision-free path with shorter length and higher security.

D-magic labelings of the halved n-cube

Let G=(V,E) be a graph with path-length distance function ∂ and diameter d. Let D⊆{0,1,…,d} be a set of distances in G and let ND(x)={y|∂(x,y)∈D} for a fixed vertex x∈V. A bijection φ:V→{1,2,…,|V|} is called a D-magic labeling of G if there exists a constant k such that ∑y∈ND(x)f(y)=k for any x∈V. In this paper, we will study D-magic labelings of the halved n-cube (n≥2) that is on all binary strings of length n with even number of 1s as vertices and edges between any two strings of Hamming distance 2. We prove that the halved n-cube is {1}-magic if and only if n=m2 where m≥2 and m≢0(mod4), and is {0,1}-magic if and only if n=m2+2 where m≥0 and m≢2(mod4).

Evaluation and Performance of Path Profile Characteristics in Communication System

This study presents the evaluation and performance of path profile characteristics in communication system, to determine the path profile characteristics such as margin fade (dB), receiver power (dBm), 2-ray propagation model (dB), free space propagation model (dB), LOSMAX (km) and critical distance (km). Data were obtained from Network ‘A’, using three different links within a geographical location in Edo State. Receiver power is mathematic model, the sensitivity of the receiver, which depends on the bandwidth (data rate) (dBm) of antennas were considered in this analysis. All the path profile characteristics were determined, it was observed, that increase in path length distance of microwave line of sight, will necessitate the increase in transmitter power in decibel. The Path length distance and margin fade of the three basic mobile propagation links were determined. It was observed that path length distance characteristic as such the length of distance, obstacle, reflection, diffraction from ground, water bodies and atmosphere resulted to the pattern of radio margin fade signal obtained in receiver antenna. The margin fade determined are 28.83 dB, 12.95 dB and 21.24 dB for the three different links considered from Network ‘A’ in Auchi, Nigeria.

Abnormal glutamatergic neurotransmission and cognitive impairment in male APPNL-F/NL-F mice.

It is well established that glutamatergic neurotransmission plays an essential role in learning and memory. In Alzheimer's disease (AD), previous studies indicate that glutamate dynamics shift with disease progression, inciting cognitive impairment and further perpetuating disease pathology. Here, we build upon previous work by utilizing a novel knock-in mouse model of AD (APPNL-F/NL-F ) to characterize hippocampal glutamate signaling and cognition during late stage AD. At 18-24 months old, male APPNL-F/NL-F and genetic background control (C57BL/6) mice underwent cognitive assessment through a Morris water maze (MWM) task. Following MWM, basal and 70 mM KCl stimulus-evoked glutamate release was measured in the CA1 region of the hippocampus using a glutamate-selective microelectrode in isoflurane anesthetized mice. Briefly, microelectrodes were coated with L-glutamate oxidase for the detection of glutamate at the electrode surface. A layer of 1,3-phenylenediamine was applied to prevent detection of electroactive compounds at the recording potential (+0.7 volts). A micropipette (diameter = ∼20 µm) was attached 50-100 µm from the recording surface for local application of KCl). Calibration and recordings are taken using the FAST-16 recording software. Preliminary MWM data indicates no significant differences in spatial learning performance (corrected integrated path length and cumulative distance from the platform) between C57BL/6 and APPNL-F/NL-F mice. We observed a trend of decreased platform entries during the probe trial, supporting long-term spatial memory impairment in APPNL-F/NL-F mice. Preliminary in vivo CA1 data support a trend of decreased basal and stimulus-evoked glutamate levels in APPNL-F/NL-F mice compared to control mice. Preliminary findings support impaired long-term spatial memory and hypoactive glutamatergic neurotransmission in aged male APPNL-F/NL-F mice compared to age-matched C57BL/6 mice. Lack of glutamate activity in late-stage AD may underlie cognitive decline in APPNL-F/NL-F mice. Our laboratory previously observed similar findings in a transgenic AD model. However, unlike APPNL-F/NL-F mice, those mice also displayed increased basal glutamate levels. This divergence could be attributed to possible differences in glutamate transporter expression or activity with disease progression. Together, these data support loss of glutamate excitation with amyloid accumulation. Studies are ongoing.

Plant ontogenetic changes in vein and stomatal traits and their relationship with economic traits in leaves of three Mediterranean oaks

Abstract Aims We compared vein and stomatal traits of seedlings and adults of three Mediterranean Quercus species. Previous work suggests that gas-exchange rates tend to be higher at the seedling stage than in adults. Our objective was to determine whether vein and stomatal traits vary throughout whole-plant ontogeny in parallel with the changes in gas-exchange rates. We addressed the following alternative hypotheses: hypothesis 1—seedlings show higher vein and stomatal densities than adults; and hypothesis 2—seedlings have lower investments in vascular tissues to reduce construction costs. Methods Ten specimens from each growth stage were randomly sampled for each species in a location in central-western Spain. We measured mean stomatal and vein traits (size and number of stomata per unit of leaf area, vein density, vein volume, vein to epidermis distance), leaf mass per area and lamina thickness. Important Findings Minor vein density and vein volume per area increased with tree age, which seems inconsistent with the ontogenetic trends in gas-exchange rates. This discrepancy is in support of our hypothesis 2, and it suggests that, at the seedling stage, reducing investments in vascular tissues in benefit of maximizing growth rates is a priority. Larger interveinal distances in seedlings were compensated by smaller vein to epidermis distances. The thin leaves of the seedlings may thus constitute as a necessary trait for achieving shorter path length distances for the transport of water to evaporation sites without the need for a strong investment in costly vascular tissues.

Visual avoidance of faces in socially anxious individuals: The moderating effect of type of social situation

Patients with social anxiety disorder appear to display aberrant gaze behavior across a variety of social situations. In contrast, the gaze behavior of high socially anxious (HSA) individuals from the community seems to depend on the type of situation and the aberration might be limited to gaze avoidance. This study investigated the differential effect of social situation—a face-viewing task and a public speaking task—on gaze behavior in HSA participants from a community sample. Participants’ eye movements were tracked using a wearable eye tracker. Two aspects of gaze behavior were measured: (1) gaze avoidance was assessed by total fixation time, fixation counts, and mean fixation time on faces; (2) hypervigilance was assessed by scan path length and mean distance between fixations. The results confirmed a moderating effect of task on total (though not mean) fixation time on faces and fixation counts. Compared to low socially anxious participants, HSA participants looked less frequently (hence shorter) at the audience during the speech only. This indicates that visual avoidance in HSA individuals does not occur by default, but only when risks of (negative) social consequences are perceived. High and low socially anxious participants showed no difference in hypervigilance in either situation.

Neural Network Based Control System for Robots Group Operating in 2-d Uncertain Environment

This study is devoted to development of a neural network based control system of robots group. The control system performs estimation of an environment state, searching the optimal path planning method, path planning, and changing the trajectories on via the robots interaction. The deep learning neural networks implements the optimal path planning method, and path planning of the robots. The first neural network classifies the environment into two types. For the first type a method of the shortest path planning is used. For the second type a method of the most safety path planning is used. Estimation of the path planning algorithm is based on the multi-objective criteria. The criterion includes the time of movement to the target point, path length, and minimal distance from the robot to obstacles. A new hybrid learning algorithm of the neural network is proposed. The algorithm includes elements of both a supervised learning as well as an unsupervised learning. The second neural network plans the shortest path. The third neural network plans the most safety path. To train the second and third networks a supervised algorithm is developed. The second and third networks do not plan a whole path of the robot. The outputs of these neural networks are the direction of the robot’s movement in the step k. Thus the recalculation of the whole path of the robot is not performed every step in a dynamical environment. Likewise in this paper algorithm of the robots formation for unmapped obstructed environment is developed. The results of simulation and experiments are presented.

Definition of work: unsolved problem in classical mechanics

The critical analysis of the foundations of classical mechanics is proposed. Methodological basis of the analysis is the unity of formal logic and rational dialectics. The main results of the analysis of concepts “force”, “work” and “work of force” are the following statements: (1) the standard concept “work of force” contradicts to dialectics (practice) and formal logic because the concept “force” is a general abstract concept. The concept “force of interaction of material objects” is a general concrete concept because this concept expresses the property (feature, sign, quality) of the interaction of material objects. But the property does not perform the work because the property is not a material object. Work is performed by a controllable (operated) material object. Consequently, the standard mathematical definition of work is an incorrect relationship; (2) the concept “force of interaction of material objects” can only be defined in a genetic way: one should measure the force of interaction with the help of a dynamometer. The dynamometer reading represents the value of the measured quantity (force). If the measured quantity (force) is a variable quantity, then a change of this quantity (force) is called the movement of this quantity (force). But if the force is a constant quantity, then the movement of the force does not exist. Consequently, the standard mathematical definition of work is an incorrect relationship; (3) the position of the force in the coordinate system cannot be determined because a force is not a material object, and the quantity of the force does not have the dimension (measure) “meter”. This signifies that: (a) a force does not exist in the material coordinate system; (b) a force does not exist on the material path; the path length (distance) for force does not exist. Consequently, force cannot move over a distance that has the dimension “meter”. This signifies that the standard mathematical definition of work is an incorrect relationship; (4) in point of view of dialectics, work and energy are nonidentity concepts. Work is the activity of man, a robot, a controllable machine created by man. Work represents a rational, reasonable, well-directed, purposeful, purposive activity which manifested in the informational and material change of reality. This activity is the impossible if intellectual, informational, energy, and material resources do not exist. Thus, the standard mathematical definition of the work of force is a formal-logical, dialectical (practical), and physical errors.

From Sensor-Space to Eigenspace – A Novel Real-Time Obstacle Avoidance Method for Mobile Robots

This paper presents a novel real-time obstacle avoidance and navigation technique called as “Free-configuration Eigenspace” (FCE). The FCE enables an autonomous robot to detect unknown obstacles and avoid collisions while simultaneously steering the robot towards the target. The methodology utilizes a two-dimensional (2D) Cartesian Eigenspace as a world model. 2D way points (in world model) are extracted by computing (through FCE model) stacked Eigenvectors of laser data at discrete time scans which manifest desired robotic trajectory. The world model is updated continuously upon obtaining discrete time laser scans sampled by on-board Light Detection and Ranging (LiDAR) sensors. The FCE technique has been implemented on Robotic Operating System and real-time robotics simulator Gazebo. Encouraging results are obtained and shown in this paper. The FCE has also been tested in real-time with laser scans obtained from VL6180X LiDAR sensor mounted on a custom autonomous robot. The results obtained are further compared with the state-of-the-art obstacle avoidance and path planning method called as vector field histogram (VFH). The FCE results (shown in the paper) are comparable, encouraging, and outperform VFH in path length and safe distance maintenance.

An $$O(n \log n)$$ Time Algorithm for Computing the Path-Length Distance Between Trees

Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in tree shape as well as differences between branch lengths. The distance equals the sum, over all pairs of taxa, of the squared differences between the lengths of the unique path connecting them in each tree. We describe an O(nlog n) time for computing this distance, making extensive use of tree decomposition techniques introduced by Brodal et al. [2].

Potential of carnosine, a histamine precursor in rat model of bilateral common carotid artery occlusion-induced vascular dementia.

The present study investigates the potential of Carnosine, a histamine precursor in rat model of bilateral common carotid artery occlusion (BCCAo)-induced vascular dementia (VaD). Wistar rats were subjected to BCCAo procedure under anaesthesia to induce VaD. The rats were subjected to Morris water maze (MWM) test (6th day onwards post-surgery). MWM test was employed to assess learning and memory of the animals whereby escape latency time, time spent in target quadrant and Path length (distance travelled) taken as important parameters. Serum nitrite level; Brain thiobarbituric acid reactive substances (TBARS) and reduced glutathione (GSH) levels; Brain acetylcholinesterase (AChE) activity; brain Myeloperoxidase activity (MPO) and neutrophil count were estimated as per standard procedures. BCCAo in rats produced a significant vascular endothelial dysfunction, as reflected by decrease in serum nitrite levels. Further, these animals showed poor performance on MWM, depicting impairment of learning and memory. There was a significant rise in brain oxidative stress level as indicated by increase in TBARS and decrease in GSH levels. An increase in brain AChE activity was also observed. Moreover, these rats also exhibited an increase in MPO activity and neutrophil infiltration in brain (as marker of inflammation). Treatment of Carnosine (200 and 400 mg/kg, i.p.)/Donepezil (0.3 mg/kg, i.p.) ameliorated BCCAo-induced memory deficits; endothelial dysfunction; biochemical and histopathological changes. It is concluded that Carnosine has shown efficacy in rat model of BCCAo-induced VaD and can be considered as an important therapeutic agent for the treatment of VaD.

An A-invariant subspace for bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint 2, both thin

Let \(\Gamma \) denote a bipartite distance-regular graph with vertex set X, diameter \(D \ge 4\), and valency \(k \ge 3\). Let \({{\mathbb {C}}}^X\) denote the vector space over \({{\mathbb {C}}}\) consisting of column vectors with entries in \({{\mathbb {C}}}\) and rows indexed by X. For \(z \in X\), let \({{\widehat{z}}}\) denote the vector in \({{\mathbb {C}}}^X\) with a 1 in the z-coordinate, and 0 in all other coordinates. Fix a vertex x of \(\Gamma \) and let \(T = T(x)\) denote the corresponding Terwilliger algebra. Assume that up to isomorphism there exist exactly two irreducible T-modules with endpoint 2, and they both are thin. Fix \(y \in X\) such that \(\partial (x,y)=2\), where \(\partial \) denotes path-length distance. For \(0 \le i,j \le D\) define \(w_{ij}=\sum {{\widehat{z}}}\), where the sum is over all \(z \in X\) such that \(\partial (x,z)=i\) and \(\partial (y,z)=j\). We define \(W=\mathrm{span}\{w_{ij} \mid 0 \le i,j \le D\}\). In this paper we consider the space \(MW=\mathrm{span}\{mw \mid m \in M, w \in W\}\), where M is the Bose–Mesner algebra of \(\Gamma \). We observe that MW is the minimal A-invariant subspace of \({{\mathbb {C}}}^X\) which contains W, where A is the adjacency matrix of \(\Gamma \). We show that \(4D-6 \le \mathrm{dim}(MW) \le 4D-2\). We display a basis for MW for each of these five cases, and we give the action of A on these bases.

Constructing Tree-Child Networks from Distance Matrices

A tree-child network is a phylogenetic network with the property that each non-leaf vertex is the parent of a tree vertex or a leaf. In this paper, we show that a tree-child network on taxa (leaf) set X with an outgroup and a positive real-valued weighting of its edges is essentially determined by the multi-set of all path-length distances between elements in X provided, for each reticulation, the edges directed into it have equal weight. Furthermore, we give a polynomial-time algorithm for reconstructing such a network from this inter-taxa distance information. Such constructions are of central importance in evolutionary biology where phylogenetic networks represent the ancestral history of a collection of present-day taxa.

Cluster of Optimal Chains of All-Pairs Shortest Paths to Deduce Minimum Cost Tour

This paper aims at analyzing all-pairs shortest paths algorithm by Floyd to extract optimal path between any pair of vertices of various path length. To form least cost round tour, vertices of an optimal chain are grouped into cluster. These optimal chains are combined by taking an account of both path length as well as magnitude of the path. The chain which has largest path length and optimal distance will be considered first. Tour is constructed by adding up vertices to optimal chains in suitable positions based on nearness. This approach is a mix of both dynamic and greedy strategies. Illustrations of different variations are focus of the study. Keywords:Cost Adjacency Matrix, Optimal Chain, Round tour, Path length matrix, predecessor matrix and all-pairs shortest paths

Nonsymmetric Askey–Wilson polynomials and Q-polynomial distance-regular graphs

In his famous theorem (1982), Douglas Leonard characterized the q-Racah polynomials and their relatives in the Askey scheme from the duality property of Q-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the q-Racah polynomials in the above situation. Let Γ denote a Q-polynomial distance-regular graph that contains a Delsarte clique C. Assume that Γ has q-Racah type. Fix a vertex x∈C. We partition the vertex set of Γ according to the path-length distance to both x and C. The linear span of the characteristic vectors corresponding to the cells in this partition has an irreducible module structure for the universal double affine Hecke algebra Hˆq of type (C1∨,C1). From this module, we naturally obtain a finite sequence of orthogonal Laurent polynomials. We prove the orthogonality relations for these polynomials, using the Hˆq-module and the theory of Leonard systems. Changing Hˆq by Hˆq−1 we show how our Laurent polynomials are related to the nonsymmetric Askey–Wilson polynomials, and therefore how our Laurent polynomials can be viewed as nonsymmetric q-Racah polynomials.

Ranging Behaviour of Verreaux's Eagles during the Pre-Breeding Period Determined through the Use of High Temporal Resolution Tracking.

Information on movement ecology is key in understanding the drivers and limitations of life history traits and has a potential role in indicating environmental change. Currently we have a limited understanding of the parameters of movement of territory-bound raptors, which are sensitive to environmental change. In this study we used GPS tracking technology to obtain spatially (within 3 m) and temporally (c. 3 mins) high-resolution movement data on a small sample of Verreaux’s eagle Aquila verreauxii during the pre-laying period (n = 4) with one additional example during the chick rearing period. We present GPS-derived home range estimates for this species and we examine temporal (timing, duration, frequency and speed) and spatial (total path length and maximum distance from nest) patterns of trips away from the nest. For eagles tagged in the agriculturally developed Sandveld region (n = 3), which is made up of a mosaic of land use types, we also undertook a habitat selection analysis. Home ranges were small and largely mutually exclusive. Trip activity was centred around midday, which is likely to be related to lift availability. Our habitat selection analysis found that eagles selected for near-natural and degraded habitat over natural or completely modified areas, suggesting that these eagles may have benefitted from some of the agricultural development in this region. Although our sample sizes are small, the resolution of our tracking data was essential in deriving this data over a relatively short time period and paves the way for future research.