Weighted Path Length Research Articles

Graph theory-based analysis reveals neural anatomical network alterations in chronic post-traumatic stress disorder

Abstract Multimodal imaging using network connectivity techniques shows promise for investigating neuropathology influencing Post-Traumatic Stress Disorder (PTSD) symptom maintenance and course. We recruited World Trade Center (WTC) responders who continued to suffer from chronic PTSD into a diffusion tensor neuroimaging protocol (n=100), along with nine unexposed controls without PTSD from other sources. Using a graph theory approach to probe network alterations in brain diffusion images, we calculated weighted characteristics path length as a surrogate marker for the effective neuroanatomical distance between anatomical nodes. The sample (N=109; 47 with chronic PTSD) was in their mid-fifties, and the majority were male. Responders were matched in terms of cognitive performance, occupation, and demographics. The anatomical connectivity graph was constructed for each participant using deterministic diffusion tractography. We identified a significant difference in weighted Characteristic Path Length (wCPL) between trauma-exposed WTC responders (Cohen’s d = 0.42, P<0.001) that was highest in people with PTSD, and not explained by WTC exposure severity or duration. We also found that wCPL was associated with PTSD symptom severity in responders with PTSD. In the largest study to date to examine the relationship between chronic PTSD and anatomy, we examined the anatomical topography of neural connections and found that wCPL differed between the PTSD+ and PTSD- diagnostic categories.

Connectomic insights into the impact of 1p/19q co-deletion in dominant hemisphere insular glioma patients.

This study aimed to elucidate the influences of 1p/19q co-deletion on structural connectivity alterations in patients with dominant hemisphere insular diffuse gliomas. We incorporated 32 cases of left insular gliomas and 20 healthy controls for this study. Using diffusion MRI, we applied correlational tractography, differential tractography, and graph theoretical analysis to explore the potential connectivity associated with 1p/19q co-deletion. The study revealed that the quantitative anisotropy (QA) of key deep medial fiber tracts, including the anterior thalamic radiation, superior thalamic radiation, fornix, and cingulum, had significant negative associations with 1p/19q co-deletion (FDR = 4.72 × 10-5). These tracts are crucial in maintaining the integrity of brain networks. Differential analysis further supported these findings (FWER-corrected p < 0.05). The 1p/19q non-co-deletion group exhibited significantly higher clustering coefficients (FDR-corrected p < 0.05) and reduced betweenness centrality (FDR-corrected p < 0.05) in regions around the tumor compared to HC group. Graph theoretical analysis indicated that non-co-deletion patients had increased local clustering and decreased betweenness centrality in peritumoral brain regions compared to co-deletion patients and healthy controls (FDR-corrected p < 0.05). Additionally, despite not being significant through correction, patients with 1p/19q co-deletion exhibited lower trends in weighted average clustering coefficient, transitivity, small worldness, and global efficiency, while showing higher tendencies in weighted path length compared to patients without the co-deletion. The findings of this study underline the significant role of 1p/19q co-deletion in altering structural connectivity in insular glioma patients. These alterations in brain networks could have profound implications for the neural functionality in patients with dominant hemisphere insular gliomas.

Multivariate joint order recurrence networks for characterization of multi-lead ECG time series from healthy and pathological heartbeat dynamics.

Analysis of nonlinear dynamic characteristics of cardiac systems has been a hot topic of clinical research, and the recurrence plots have earned much attention as an effective tool for it. In this paper, we propose a novel method of multivariate joint order recurrence networks (MJORNs) to evaluate the multi-lead electrocardiography (ECG) time series with healthy and psychological heart states. The similarity between time series is studied by quantifying the structure in a joint order pattern recurrence plot. We take the time series that corresponds to each of the 12-lead ECG signals as a node in the network and use the entropy of diagonal line length that describes the complex structure of joint order pattern recurrence plot as the weight to construct MJORN. The analysis of network topology reveals differences in nonlinear complexity for healthy and heart diseased heartbeat systems. Experimental outcomes show that the values of average weighted path length are reduced in MJORN constructed from crowds with heart diseases, compared to those from healthy individuals, and the results of the average weighted clustering coefficient are the opposite. Due to the impaired cardiac fractal-like structures, the similarity between different leads of ECG is reduced, leading to a decrease in the nonlinear complexity of the cardiac system. The topological changes of MJORN reflect, to some extent, modifications in the nonlinear dynamics of the cardiac system from healthy to diseased conditions. Compared to multivariate cross recurrence networks and multivariate joint recurrence networks, our results suggest that MJORN performs better in discriminating healthy and pathological heartbeat dynamics.

Detection of healthy and pathological heartbeat dynamics in ECG signals using multivariate recurrence networks with multiple scale factors

The electrocardiogram (ECG) is one of the physiological signals applied in medical clinics to determine health status. The physiological complexity of the cardiac system is related to age, disease, etc. For the investigation of the effects of age and cardiovascular disease on the cardiac system, we then construct multivariate recurrence networks with multiple scale factors from multivariate time series. We propose a new concept of cross-clustering coefficient entropy to construct a weighted network, and calculate the average weighted path length and the graph energy of the weighted network to quantitatively probe the topological properties. The obtained results suggest that these two network measures show distinct changes between different subjects. This is because, with aging or cardiovascular disease, a reduction in the conductivity or structural changes in the myocardium of the heart contributes to a reduction in the complexity of the cardiac system. Consequently, the complexity of the cardiac system is reduced. After that, the support vector machine (SVM) classifier is adopted to evaluate the performance of the proposed approach. Accuracy of 94.1% and 95.58% between healthy and myocardial infarction is achieved on two datasets. Therefore, this method can be adopted for the development of a noninvasive and low-cost clinical prognostic system to identify heart-related diseases and detect hidden state changes in the cardiac system.

WPL-Based Constraint for 3D Human Pose Estimation from a Single Depth Image

Three-dimensional human pose estimation from depth maps is a fast-growing research area in computer vision. The distal joints of the human body are more flexible than the proximal joints, making it more difficult to estimate the distal joints. However, most existing methods ignore the difference between the distal joints and proximal joints. Moreover, the distal joint can be constrained by the proximal joint on the same kinematic chain. In our work, we model the human skeleton as the tree structure called the human-tree. Then, motivated by the WPL (weighted path length) in the data structure, we propose a WPL-based loss function to constrain the distal joints with the proximal joints in a global-to-local manner. Extensive experiments on benchmarks demonstrate that our method can effectively improve the performance of the distal joints.

N-ary Huffman Encoding using High-Degree Trees - A Performance Comparison

In this paper we implement an n-ary Huffman Encoding and Decoding application using different degrees of tree structures. Our goal is to compare the performance of the algorithm in terms of compression ratio, decompression speed and weighted path length when using higher degree trees, compared to the 2-ary Huffman Code. The Huffman tree degrees that we compare are 2-ary, 3-ary, 4-ary, 5-ary, 6-ary, 7-ary, 8-ary and 16-mal. We also present the impact that branch prediction has on the performance of the n-ary Huffman Decoding.

The asymptotic formula on average weighted path length for scale-free modular network

In this paper, we discuss the average path length for a class of scale-free modular networks with deterministic growth. To facilitate the analysis, we define the sum of distances from all nodes to the nearest hub nodes and the nearest peripheral nodes. For the unweighted network, we find that whether the scale-free modular network is single-hub or multiple-hub, the average path length grows logarithmically with the increase of nodes number. For the weighted network, we deduce that when the network iteration [Formula: see text] tends to infinity, the average weighted shortest path length is bounded, and the result is independent of the connection method of network.

THE AVERAGE WEIGHTED PATH LENGTH FOR A CLASS OF HIERARCHICAL NETWORKS

In this paper, in order to calculate the average path length for unweighted and weighted hierarchical networks, we define the sum of the distances from each node to the vertex and the bottom nodes. For the unweighted network, we show that the average path length grows with the size of [Formula: see text] as [Formula: see text]. For the weighted network, we prove its weighted path length approaches a constant related to the weighting factor [Formula: see text] and parameter [Formula: see text]. In particular, for [Formula: see text], the average weighted path length of the network tends to a specific value [Formula: see text].

Knowledge transfer efficiency measurement with application for open innovation networks

Knowledge transfer efficiency is an important indicator to evaluate the performance of open innovation (OI). However, there are few researches on the measurement of knowledge transfer efficiency in the context of OI networks. To make up this gap, this study explores the measurement of knowledge transfer efficiency based on the weighted OI network. Firstly, this paper builds the weighted OI network model with node and edge weights. On the basis of the weighted OI network model, the weighted path length and clustering coefficient are introduced and analysed. Moreover, the efficiency of knowledge transfer is further proposed as the main measure of knowledge transfer efficiency by comprehensively embodying the above factors, and then an extended application of the proposed main measure is developed to identify and locate the important members with great impact on knowledge transfer. Finally, a real case of several OI networks is provided to illustrate the applicability of the weighted OI network model and the knowledge transfer efficiency measurement method.

Common network characteristics of four bus transport networks in Northeast China based on a perfect space P

The space P and space L representation models are often adopted together in the empirical analysis of bus transport networks (BTNs). In this paper, we develop a new representation model for BTNs using double edge weights and node weights, namely perfect space P. The model incorporates the number and lengths of directed routes between the two stations and the number of routes that connect to each station. Based on the model, we develop an empirical study on four large BTNs in Northeast China. Some common network characteristics of the BTNs are revealed and discussed in detail. The results show that several empirical distributions follow an exponential law. Moreover, the unweighted path length distributions can be fitted by a Gaussian function, while the weighted path length distributions can be fitted by a composite Gaussian function. Specifically, we introduce the weighted-degree distribution with different lengths and the special edge weight distribution, given the new evidence for the random behavior during the expansion of BTNs, including new stations and routes.

An RFID Indoor Positioning Algorithm Based on Support Vector Regression.

Nowadays, location-based services, which include services to identify the location of a person or an object, have many uses in social life. Though traditional GPS positioning can provide high quality positioning services in outdoor environments, due to the shielding of buildings and the interference of indoor environments, researchers and enterprises have paid more attention to how to perform high precision indoor positioning. There are many indoor positioning technologies, such as WiFi, Bluetooth, UWB and RFID. RFID positioning technology is favored by researchers because of its lower cost and higher accuracy. One of the methods that is applied to indoor positioning is the LANDMARC algorithm, which uses RFID tags and readers to implement an Indoor Positioning System (IPS). However, the accuracy of the LANDMARC positioning algorithm relies on the density of reference tags and the performance of RFID readers. In this paper, we introduce the weighted path length and support vector regression algorithm to improve the positioning precision of LANDMARC. The results show that the proposed algorithm is effective.

Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE

The neighbourhood of the largest eigenvalue λmax in the Gaussian unitary ensemble (GUE) and Laguerre unitary ensemble (LUE) is referred to as the soft edge. It is known that there exists a particular centring and scaling such that the distribution of λmax tends to a universal form, with an error term bounded by 1/N2/3. We take up the problem of computing the exact functional form of the leading error term in a large N asymptotic expansion for both the GUE and LUE—two versions of the LUE are considered, one with the parameter a fixed and the other with a proportional to N. Both settings in the LUE case allow for an interpretation in terms of the distribution of a particular weighted path length in a model involving exponential variables on a rectangular grid, as the grid size gets large. We give operator theoretic forms of the corrections, which are corollaries of knowledge of the first two terms in the large N expansion of the scaled kernel and are readily computed using a method due to Bornemann. We also give expressions in terms of the solutions of particular systems of coupled differential equations, which provide an alternative method of computation. Both characterisations are well suited to a thinned generalisation of the original ensemble, whereby each eigenvalue is deleted independently with probability (1 − ξ). In Sec. V, we investigate using simulation the question of whether upon an appropriate centring and scaling a wider class of complex Hermitian random matrix ensembles have their leading correction to the distribution of λmax proportional to 1/N2/3.

On Weighted Depths in Random Binary Search Trees

Following the model introduced by Aguech et al. (Probab Eng Inf Sci 21:133–141, 2007), the weighted depth of a node in a labelled rooted tree is the sum of all labels on the path connecting the node to the root. We analyse weighted depths of nodes with given labels, the last inserted node, nodes ordered as visited by the depth first search process, the weighted path length and the weighted Wiener index in a random binary search tree. We establish three regimes of nodes depending on whether the second-order behaviour of their weighted depths follows from fluctuations of the keys on the path, the depth of the nodes or both. Finally, we investigate a random distribution function on the unit interval arising as scaling limit for weighted depths of nodes with at most one child.

Self-organizing maps whose topologies can be learned with adaptive binary search trees using conditional rotations

Numerous variants of Self-Organizing Maps (SOMs) have been proposed in the literature, including those which also possess an underlying structure, and in some cases, this structure itself can be defined by the user. Although the concepts of growing the SOM and updating it have been studied, the whole issue of using a self-organizing Adaptive Data Structure (ADS) to further enhance the properties of the underlying SOM, has been unexplored. In an earlier work, we impose an arbitrary, user-defined, tree-like topology onto the codebooks, which consequently enforced a neighborhood phenomenon and the so-called tree-based Bubble of Activity (BoA). In this paper, we consider how the underlying tree itself can be rendered dynamic and adaptively transformed. To do this, we present methods by which a SOM with an underlying Binary Search Tree (BST) structure can be adaptively re-structured using Conditional Rotations (CONROT). These rotations on the nodes of the tree are local, can be done in constant time, and performed so as to decrease the Weighted Path Length (WPL) of the entire tree. In doing this, we introduce the pioneering concept referred to as Neural Promotion, where neurons gain prominence in the Neural Network (NN) as their significance increases. We are not aware of any research which deals with the issue of Neural Promotion. The advantage of such a scheme is that the user need not be aware of any of the topological peculiarities of the stochastic data distribution. Rather, the algorithm, referred to as the TTOSOM with Conditional Rotations (TTOCONROT), converges in such a manner that the neurons are ultimately placed in the input space so as to represent its stochastic distribution, and additionally, the neighborhood properties of the neurons suit the best BST that represents the data. These properties have been confirmed by our experimental results on a variety of data sets. We submit that all these concepts are both novel and of a pioneering sort.

온톨로지 기반 학습 콘텐츠의 난이도 계산 방법

이러닝 시스템에서 난이도를 이용한 학습추천 시스템 설계에 관한 연구가 활발히 진행 중이다. 난이도는 학습자의 수준에 맞는 후행학습을 추천하는데 매우 중요한 요소임에도 불구하고 현행 난이도 기반 학습 추천시스템은 각 학습 콘텐츠의 제작자가 주관적으로 정한 난이도를 적용함으로써 정확한 후행 학습 콘텐츠를 추천하기가 어렵다. 본 논문에서는 객관적인 난이도 지표를 제공하기 위하여 온톨로지에 기반한 새로운 학습콘텐츠 난이도 계산 방법을 제안한다. 기존 온톨로지나 지식맵을 이용한 난이도 계산 방법들은 선행학습과 후행학습 또는 주제간의 선후 관계를 표현하고 이를 이용하여 난이도를 계산하였으나, 이 방법들도 콘텐츠 작성자의 주관적인 판단에 의해 후행학습이 결정된다는 문제점이있다. 본 논문에서는 이를 해결하기 위하여 콘텐츠를 구성하는 단어들의 상하위 관계 및 심화도를 나타내는 온톨로지를 이용하여 단어들 간 온토로지의 경로상의 거리로 난이도를 계산한다. 이를 통하여 학습자에게 보다 객관적인 난이도 정보를 제공하고 학습자 수준에 가장 적합한 후행학습 콘텐츠를 추천할 수 있다. Much research has been conducted on the e-learning systems for recommending a learning content to a student based on the difficulty of it. The difficulty is one of the most important factors for selecting a learning content. In the existing learning content recommendation systems, the difficulty of a learning content is determined by the creator. Therefore, it is not easy to apply a standard rule to the difficulty as it is determined by a subjective method. In this paper, we propose an ontology-based method for determining the difficulty of a learning content in order to provide an objective measurement. Previously, ontologies and knowledge maps have been used to recommend a learning content. However, their methods have the same problem because the difficulty is also determined by the creator. In this research, we use an ontology representing the IS-A relationships between words. The difficulty of a learning content is the sum of the weighted path lengths of the words in the learning content. By using this kind of difficulty, we can provide an objective measurement and recommend the proper learning content most suitable for the student's current level.

Insulin Modulation of Magnetoencephalographic Resting State Dynamics in Lean and Obese Subjects

Lean and obese subjects can exhibit differences in neuronal activity during resting state and tasks. Changes in hormonal status and their action related to increased body weight may be the determining factor for these differences. One prime candidate is insulin, which until recently was mainly related to its metabolic function for the transport and regulation of glucose in the periphery. However insulin also acts as an anorexic signal in the central nervous system contributing to the termination of food intake in the postprandial state. In our study, we examined with whole-head magnetoencephalography the effect of intranasal insulin on the dynamics of the resting state network in a placebo controlled study. Weighted clustering coefficient C, which describes local interconnectedness, and weighted path length L, a measure of global interconnectedness, were computed. These parameters showed high intraindividual reliability. However, no difference for the network dynamics was found between lean and obese subjects in the basal state. The application of insulin led to subject specific changes and we found a statistically significant positive correlation between the insulin induced change in path length in the theta band (4–8 Hz) and body mass index. The change in pathway length after insulin administration indicates a strong insulin modulation on global communication efficiency, which is probably related to the signaling between different regions involved in satiation and homeostatic control.

Proof Pearl: Mechanizing the Textbook Proof of Huffman’s Algorithm

Huffman's algorithm is a procedure for constructing a binary tree with minimum weighted path length. Our Isabelle/HOL proof closely follows the sketches found in standard algorithms textbooks, uncovering a few snags in the process. Another distinguishing feature of our formalization is the use of custom induction rules to help Isabelle's automatic tactics, leading to very short proofs for most of the lemmas.

ON WEIGHTED PATH LENGTHS AND DISTANCES IN INCREASING TREES

We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process (e.g., recursive trees, plane-oriented recursive trees, and binary increasing trees), we can determine the limiting distribution that can be characterized as a generalized Dickman's infinitely divisible distribution.

EXTREMAL WEIGHTED PATH LENGTHS IN RANDOM BINARY SEARCH TREES

We consider weighted path lengths to the extremal leaves in a random binary search tree. When linearly scaled, the weighted path length to the minimal label has Dickman's infinitely divisible distribution as a limit. By contrast, the weighted path length to the maximal label needs to be centered and scaled to converge to a standard normal variate in distribution. The exercise shows that path lengths associated with different ranks exhibit different behaviors depending on the rank. However, the majority of the ranks have a weighted path length with average behavior similar to that of the weighted path to the maximal node.

Simulating the Gas Diffusion Coefficient in Macropore Network Images: Influence of Soil Pore Morphology

Knowledge of the diffusion coefficient is necessary for modeling gas transport in soils and other porous media. This study was conducted to determine the relationship between the diffusion coefficient and pore structure parameters, such as the fractal dimension of pores (Dmp), the shortest path length through the medium (lmin), and the fractal dimension of the shortest path (Dmin). The finite element method (FEM) was used to simulate the gaseous diffusion process in an idealized soil system with a highly connected macropore network. The analysis was performed on binary images of soil thin sections. We show that the ratio ξ of the diffusion coefficient in soil (Deff) to that in free air (D0) is a function of not only the air‐filled porosity ε, but also of other parameters, and hence no universal relationship exists between ξ and Dmp and Dmin Furthermore, ξ is shown to be strongly related to the pore‐space structure and the direction of the concentration gradient. The tortuosity (T) furthermore was found to be related to the weighted path length along the main diffusion direction.