Path Length Variance Research Articles

UAV Path Planning Based on an Improved Ant Colony Algorithm

Reviews and experimental verification have found that existing solution methods can be used to solve UAV path planning problems, but each approximate solution has its own advantages and disadvantages. For example, ant colony algorithm easily falls into the local optimum in the process of realizing path planning. In order to prevent too low pheromones on the longer path and too high pheromones in the shorter path, the upper and lower limits of pheromones as well as their volatile factors are set to avoid falling into the local optimum. Secondly, multi-heuristic factors are introduced, and the overall length of the path serves as an adaptive heuristic function factor that determines the probability of state transition, which affects the probability of ants choosing the corresponding path. The experimental results show that the path length planned by the improved algorithm is 93.6% of the original algorithm, and the optimal path length variance is only 14.22% of the original algorithm. The improved ant colony algorithm shortens the optimal path length and solves the UAV path planning problem in terms of local optima. At the same time, multiple enlightening factors are introduced to increase the suitability of UAV for complex environments and improve the performance of UAV.

Role of links on the structural properties of different network topologies

Complex networks are of major importance in many areas of science. The network property analysis of such networks can help researchers to understand many real-world systems. Different collective phenomena emerge in complex networks, synchronization is one of the most interesting states. The number of links plays a major role in synchronizability. In this paper, the specific properties of the different well-known network topologies are studied, and their synchronizability is compared. Networks with different structures, such as the regular, star, random, small-world, and scale-free networks, are investigated. For each topology, the clustering coefficient, average and variance of the path length, and the eigenvalues of the Laplacian matrix of connections are obtained by varying the number of links. The results show some relations between the network's properties and synchronizability. One of the obtained results is that the type-one networks in a small number of links show better synchronization in the lowest average and variance of path length. However, for a greater number of links, the best synchronizability belongs to the topologies with lower clustering coefficient.

Brain functional connectivity during the first day of coma reflects long-term outcome

ObjectiveIn patients with disorders of consciousness (DOC), properties of functional brain networks at rest are informative of the degree of consciousness impairment and of long-term outcome. Here we investigate whether connectivity differences between patients with favorable and unfavorable outcome are already present within 24 h of coma onset. MethodsWe prospectively recorded 63-channel electroencephalography (EEG) at rest during the first day of coma after cardiac arrest. We analyzed 98 adults, of whom 57 survived beyond unresponsive wakefulness. Functional connectivity was estimated by computing the ‘debiased weighted phase lag index’ over epochs of five seconds duration. We evaluated the network’s topological features, including clustering coefficient, path length, modularity and participation coefficient and computed their variance over time. Finally, we estimated the predictive value of these topological features for patients’ outcomes by splitting the patient sample in training and test datasets. ResultsGroup-level analysis revealed lower clustering coefficient, higher modularity and path length variance in patients with favorable compared to those with unfavorable outcomes (p < 0.01). Within all features, the path length variance in the network provided the best positive predictive value (PPV) for favorable outcome and specificity for unfavorable outcome in the test dataset (PPV: 0.83, p < 0.01; specificity: 0.86, p < 0.01) with above-chance negative predictive value and accuracy. Of note, the exclusion of patients with epileptiform activity (20 in total) eliminates all false positive predictions (n = 6) for path length variance. InterpretationTopological features of functional connectivity differ as a function of long-term outcome in patients on the first day of coma. These differences are not interpretable in terms of consciousness levels as all patients were in a deep unconscious state. The time variance of path length is informative of comatose patients’ outcome, as patients with favorable outcome exhibit a richer repertoire of path length than those with unfavorable outcomes.

Dynamic Compensation of Path Length Difference in Optical Coherence Tomography by an Automatic Temperature Control System of Optical Fiber

Optical fiber is widely used in optical coherence tomography (OCT) to propagate light precisely with low attenuation and low dispersion. However, the total optical path length within the optical fiber varies in accordance with changes of the temperature. This leads changes in the total optical travel path of the interfering signals and results in shifting of OCT image position to an unintended depth pixel value. In this paper, we presented the temperature-based automatic path length compensating method in OCT to limit the external temperature effect and control the image position in micro-scale without manual movement of optical components. By utilizing developed hardware and software of automatic temperature control system, the external temperature of optical fiber is precisely regulated that evokes thermal expansion and finally changes the physical length of fiber, which is main mechanism of temperature-based path length compensating method. The effectiveness of the presented method was verified by two-dimensional OCT images of mirror and in vivo retina. The obtained results confirmed the path length variance due to temperature change is computable and can be regulated in real-time for whole pixel range of OCT image. Therefore, the proposed temperature-based path length compensating method can be used as an alternative method to precisely control the position of OCT image, while eliminating the effect of external temperature and apply to effectively configuring compact optical systems.

Local-global nested graph kernels using nested complexity traces

In this paper, we propose two novel local-global nested graph kernels, namely the nested aligned kernel and the nested reproducing kernel, drawing on depth-based complexity traces. Both of the nested kernels gauge the nested depth complexity trace through a family of K-layer expansion subgraphs rooted at the centroid vertex, i.e., the vertex with minimum shortest path length variance to the remaining vertices. Specifically, for a pair of graphs, we commence by computing the centroid depth-based complexity traces rooted at the centroid vertices. The first nested kernel is defined by measuring the global alignment kernel, which is based on the dynamic time warping framework, between the complexity traces. Since the required global alignment kernel incorporates the whole spectrum of alignment costs between the complexity traces, this nested kernel can provide rich statistic measures. The second nested kernel, on the other hand, is defined by measuring the basic reproducing kernel between the complexity traces. Since the associated reproducing kernel only requires time complexity O(1), this nested kernel has very low computational complexity. We theoretically show that both of the proposed nested kernels can simultaneously reflect the local and global graph characteristics in terms of the nested complexity traces. Experiments on standard graph datasets abstracted from bioinformatics and computer vision databases demonstrate the effectiveness and efficiency of the proposed graph kernels.

Fast depth-based subgraph kernels for unattributed graphs

In this paper, we investigate two fast subgraph kernels based on a depth-based representation of graph-structure. Both methods gauge depth information through a family of K-layer expansion subgraphs rooted at a vertex [1]. The first method commences by computing a centroid-based complexity trace for each graph, using a depth-based representation rooted at the centroid vertex that has minimum shortest path length variance to the remaining vertices [2]. This subgraph kernel is computed by measuring the Jensen–Shannon divergence between centroid-based complexity entropy traces. The second method, on the other hand, computes a depth-based representation around each vertex in turn. The corresponding subgraph kernel is computed using isomorphisms tests to compare the depth-based representation rooted at each vertex in turn. For graphs with n vertices, the time complexities for the two new kernels are O(n2) and O(n3), in contrast to O(n6) for the classic Gärtner graph kernel [3]. Key to achieving this efficiency is that we compute the required Shannon entropy of the random walk for our kernels with O(n2) operations. This computational strategy enables our subgraph kernels to easily scale up to graphs of reasonably large sizes and thus overcome the size limits arising in state-of-the-art graph kernels. Experiments on standard bioinformatics and computer vision graph datasets demonstrate the effectiveness and efficiency of our new subgraph kernels.

Depth-based complexity traces of graphs

In this paper we aim to characterize graphs in terms of a structural measure of complexity. Our idea is to decompose a graph into layered substructures of increasing size, and then to measure the information content of these substructures. To locate dominant substructures within a graph, we commence by identifying a centroid vertex which has the minimum shortest path length variance to the remaining vertices. For each graph a family of centroid expansion subgraphs is derived from the centroid vertex in order to capture dominant structural characteristics of the graph. Since the centroid vertex is identified through a global analysis of the shortest path length distribution, the expansion subgraphs provide a fine representation of a graph structure. We then show how to characterize graphs using depth-based complexity traces. Here we explore two different strategies. The first strategy is to measure how the entropies on the centroid expansion subgraphs vary with the increasing size of the subgraphs. The second strategy is to measure how the entropy differences vary with the increasing size of the subgraphs. We perform graph classification in the principal component space of the complexity trace vectors. Experiments on graph datasets abstracted from some bioinformatics and computer vision databases demonstrate the effectiveness and efficiency of the proposed graph complexity traces. Our methods are competitive to state of the art methods.

A simplified method to estimate the free path length variance

Kutruff derived an analytical solution for the prediction of reverberation time in spaces with arbitrary shape. It is the most popular analytical equation that contains shape factors. However, in this equation the free path length variance remains as unknown parameter. Kutruff suggested the implementation of Monte-Carlo simulation to determine this value for each unique shape. In practice this method is not significantly simpler than a full ray tracing simulation. Fortunately, using methods from the probability field, the free path length variance does have an analytical solution, but this takes such a complicated form that it is not convenient to use. This article treats the development of a simplified method to estimate the free path length variance without losing accuracy when applied to concert halls. A simplified regression model is developed for rectangular shapes based on the analytical solution. This simple model explains 99.8% variance for any rectangular shape up to 1:10:10. Secondly, for arbitrary shapes, a simplified model is proposed by including several additional simple variables. This model is validated against simulation results. It will be shown that this simplified method not only can be used in Kutruff’s equation, but also reveals the significant shape-related parameters that influence the reverberation time.