Max Degree Research Articles

Sustainability of personal social networks of people with Down syndrome.

Research continues to demonstrate that the characteristics of one's social network could have an impact on the development of Alzheimer's disease. Given the predisposition of people with Down syndrome to develop Alzheimer's disease, analysis of their social networks has become an emerging focus. Previous pilot research demonstrated that the personal networks of people with DS could be quantitatively analyzed, with no difference between self-report and parent-proxy report. This manuscript focuses on a 12-month follow-up period with the same original participants (24 adults with Down syndrome). Their social networks demonstrated sustainability, but not improvement, as reported by people with DS (mean network size: 8.88; mean density: 0.73; mean constraint: 0.44; mean effective size: 3.58; mean max degree: 6.04; mean degree: 4.78) and their proxies (mean network size: 7.90; mean density: 0.82; mean constraint: 53.13; mean effective size: 2.87; mean max degree: 5.19; mean degree: 4.30). Intentional and continued efforts are likely needed in order to improve the social network measures of people with Down syndrome.

Active pairwise distance learning for efficient labeling of large datasets by human experts

AbstractIn many machine learning applications, the labeling of datasets is done by human experts, which is usually time-consuming in cases of large data sets. This raises the need for methods to make optimal use of the human expert by selecting model instances for which the expert opinion is of most added value. This paper introduces the problem of active pairwise distance learning (APDL), where the goal is to actively learn the pairwise distances between all instances. Any distance function can be used, which means that APDL techniques can e.g., be used to determine likeness between faces or similarities between users for recommender systems. Starting with an unlabeled dataset, each round an expert determines the distance between one pair of instances. Thus, there is an important choice to make each round: ‘Which combination of instances is presented to the expert?’ The objective is to accurately predict all pairwise distances, while minimizing the usage of the expert. In this research, we establish upper and lower bound approximations (including an update rule) for the pairwise distances and evaluate many domain-independent query strategies. The observations from the experiments are therefore general, and the selection strategies are ideal candidates to function as baseline in future research. We show that using the criterion max degree consistently ranks amongst the best strategies. By using this criterion, the pairwise distances of a new dataset can be labeled much more efficiently.

P-ResUnet: Segmentation of brain tissue with Purified Residual Unet

Brain tissue of Magnetic Resonance Imaging is precisely segmented and quantified, which aids in the diagnosis of neurological diseases such as epilepsy, Alzheimer’s, and multiple sclerosis. Recently, UNet-like architectures are widely used for medical image segmentation, which achieved promising performance by using the skip connection to fuse the low-level and high-level information. However, In the process of integrating the low-level and high-level information, the non-object information (noise) will be added, which reduces the accuracy of medical image segmentation. Likewise, the same problem also exists in the residual unit. Since the output and input of the residual unit are fused, the non-object information (noise) of the input of the residual unit will be in the integration. To address this challenging problem, in this paper we propose a Purified Residual U-net for the segmentation of brain tissue. This model encodes the image to obtain deep semantic information and purifies the information of low-level features and the residual unit from the image, and acquires the result through a decoder at last. We use the Dilated Pyramid Separate Block (DPSB) as the first block to purify the features for each layer in the encoder without the first layer, which expands the receptive field of the convolution kernel with only a few parameters added. In the first layer, we have explored the best performance achieved with DPB. We find the most non-object information (noise) in the initial image, so it is good for the accuracy to exchange the information to the max degree. We have conducted experiments with the widely used IBSR-18 dataset composed of T-1 weighted MRI volumes from 18 subjects. The results show that compared with some of the cutting-edge methods, our method enhances segmentation performance with the mean dice score reaching 91.093% and the mean Hausdorff distance decreasing to 3.2606.

The Power of D-hops in Matching Power-Law Graphs

This paper studies seeded graph matching for power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of high-degree seeds in $1$-hop neighborhoods, we develop an efficient algorithm that exploits the low-degree seeds in suitably-defined D-hop neighborhoods. Specifically, we first match a set of vertex-pairs with appropriate degrees (which we refer to as the first slice) based on the number of low-degree seeds in their D-hop neighborhoods. This approach significantly reduces the number of initial seeds needed to trigger a cascading process to match the rest of graphs. Under the Chung-Lu random graph model with n vertices, max degree Θ(√n), and the power-law exponent 2<β<3, we show that as soon as D>4-β/3-β, by optimally choosing the first slice, with high probability our algorithm can correctly match a constant fraction of the true pairs without any error, provided with only Ω((log n)4-β) initial seeds. Our result achieves an exponential reduction in the seed size requirement, as the best previously known result requires n1/2+ε seeds (for any small constant ε^>0). Performance evaluation with synthetic and real data further corroborates the improved performance of our algorithm.

The Power of D-hops in Matching Power-Law Graphs

This paper studies seeded graph matching for power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of high-degree seeds in $1$-hop neighborhoods, we develop an efficient algorithm that exploits the low-degree seeds in suitably-defined D-hop neighborhoods. Specifically, we first match a set of vertex-pairs with appropriate degrees (which we refer to as the first slice) based on the number of low-degree seeds in their D-hop neighborhoods. This approach significantly reduces the number of initial seeds needed to trigger a cascading process to match the rest of graphs. Under the Chung-Lu random graph model with n vertices, max degree Θ(√n), and the power-law exponent 2<β<3, we show that as soon as D> 4-β/3-β, by optimally choosing the first slice, with high probability our algorithm can correctly match a constant fraction of the true pairs without any error, provided with only Ω((log n)4-β) initial seeds. Our result achieves an exponential reduction in the seed size requirement, as the best previously known result requires n1/2+ε seeds (for any small constant ε>0). Performance evaluation with synthetic and real data further corroborates the improved performance of our algorithm.

On the approximability of Time Disjoint Walks

We introduce the combinatorial optimization problem Time Disjoint Walks (TDW), which has applications in collision-free routing of discrete objects (e.g., autonomous vehicles) over a network. This problem takes as input a digraph $G$ with positive integer arc lengths, and $k$ pairs of vertices that each represent a trip demand from a source to a destination. The goal is to find a walk and delay for each demand so that no two trips occupy the same vertex at the same time, and so that a min-max or min-sum objective over the trip durations is realized. We focus here on the min-sum variant of Time Disjoint Walks, although most of our results carry over to the min-max case. We restrict our study to various subclasses of DAGs, and observe that there is a sharp complexity boundary between Time Disjoint Walks on oriented stars and on oriented stars with the central vertex replaced by a path. In particular, we present a poly-time algorithm for min-sum and min-max TDW on the former, but show that min-sum TDW on the latter is NP-hard. Our main hardness result is that for DAGs with max degree $\Delta\leq3$, min-sum Time Disjoint Walks is APX-hard. We present a natural approximation algorithm for the same class, and provide a tight analysis. In particular, we prove that it achieves an approximation ratio of $\Theta(k/\log k)$ on bounded-degree DAGs, and $\Theta(k)$ on DAGs and bounded-degree digraphs.

Random topology organization and decreased visual processing of internet addiction: Evidence from a minimum spanning tree analysis.

ObjectivesInternet addiction (IA) has been associated with widespread brain alterations. Functional connectivity (FC) and network analysis results related to IA are inconsistent between studies, and how network hubs change is not known. The aim of this study was to evaluate functional and topological networks using an unbiased minimum spanning tree (MST) analysis on electroencephalography (EEG) data in IA and healthy control (HC) college students.MethodsIn this study, Young's internet addiction test was used as an IA severity measure. EEG recordings were obtained in IA (n = 30) and HC participants (n = 30), matched for age and sex, during rest. The phase lag index (PLI) and MST were applied to analyze FC and network topology. We expected to obtain evidence of underlying alterations in functional and topological networks related to IA.ResultsIA participants showed higher delta FC between left‐side frontal and parieto‐occipital areas compared to the HC group (p < 0.001), global MST measures revealed a more star‐like network in IA participants in the upper alpha and beta bands, and the occipital brain region was relatively less important in the IA relative to the HC group in the lower band. The correlation results were consistent with the MST results: higher IA severity correlated with higher Max degree and kappa, and lower eccentricity and diameter.ConclusionsFunctional networks of the IA group were characterized by increased FC, a more random organization, and a decrease of relative functional importance of the visual processing area. Taken together, these alterations can help us understand the influence of IA to brain mechanism.

The Odyssey's mythological network.

In this work, we study the mythological network of Odyssey of Homer. We use ordinary statistical quantifiers in order to classify the network as real or fictional. We also introduce an analysis of communities which allows us to see how network properties shall emerge. We found that Odyssey can be classified both as real and fictional network. This statement is supported as far as mythological characters are removed, which results in a network with real properties. The community analysis indicated to us that there is a power-law relationship based on the max degree of each community. These results allow us to conclude that Odyssey might be an amalgam of myth and of historical facts, with communities playing a central role.

Overlapping community detection based on discrete biogeography optimization

Community detection can be used to help mine the potential information in social networks, and uncovering community structures in social networks can be regarded as clustering optimization problems. In this paper, an overlapping community detection algorithm based on biogeography optimization is proposed. Firstly, the algorithm takes the method of label propagation based on local max degree and neighborhood overlap for initial network partitioning. The preliminary partition result used to construct initial population by cloning and mutating to accelerate the algorithm’s convergence. Next, to make biogeography optimization algorithm suitable for community detection, we design problem-specific migration rules and mutation operators based on a novel affinity degree to improve the effectiveness of the algorithm. Experiments on benchmark test data, including two synthetic networks and four real-world networks, show that the proposed algorithm can achieve results with better accuracy and stability than the compared evolutionary algorithms.

Vulnerability of complex networks under three-level-tree attacks

Abstract We investigate vulnerability of complex networks including model networks and real world networks subject to three-level-tree attack. Specifically, we remove three different three-level-tree structures: RRN (Random Root Node), MaxDRN (Max Degree Root Node) and MinDRN (Min Degree Root Node) from a network iteratively until there is no three-level-tree left. Results demonstrate that random network is more robust than scale-free network against three tree attacks, and the robustness of random network decreases as the 〈 k 〉 increases. And scale-free network shows different characteristics in different tree attack modes. The robustness of scale-free is not affected by the 〈 k 〉 parameters for RRN, but increases as the 〈 k 〉 increases for MinDRN. The important thing is that MaxDRN is the most effective in the three tree attack modes, especially for scale-free network. These findings supplement and extend the previous attack results on nodes and edges, and can thus help us better explain the vulnerability of different networks, and provide an insight into more tolerant real complex systems design.

Revisiting a randomized algorithm for the minimum rainbow subgraph problem

The minimum rainbow subgraph problem arises in bioinformatics. The graph is given as an edge-colored undirected graph. Our goal is to find a subgraph with minimum number of vertices such that there is exactly one edge from each color class. The currently best approximation ratio achieved by a deterministic approximation algorithm is O(Δ). (Here Δ is the max degree of a graph.) In [4] he proposes a randomized algorithm which achieves an approximation ratio of O(Δln⁡Δ). However, we find that there is a flaw in his probability analysis which renders this approximation ratio invalid. We present a simple example to show why his analysis does not work. Instead, we propose an alternative analysis for his randomized algorithm. Our estimate shows that this randomized algorithm may achieve approximation ratio of O(Δ) in general. However, if the number of colors is Θ(nΔr) for some positive r≤1, his randomized algorithm can beat the bound of O(Δ). Moreover, through our analysis, we also find that if we impose an extra constraint on the color function, the bound O(Δln⁡Δ) still holds.

On the robustness to multiple agent losses in 2D and 3D formations

Summary Multi-agent formations have been recently the subject of many studies. An important operational challenge, largely unaddressed in the literature, is to ensure that functionality of the formation is retained should agents be lost through misadventure, mission reassignment, and so on. In the context of sensor networks, it is also important to allow for the loss of multiple sensors as the low quality of sensor hardware, common unattended implementations, and so on makes it a common issue. In this paper, we address these issues by proposing information structures that are tolerant to the loss of multiple agents. Using graph theory (and more specifically rigidity theory), we characterize several properties of such formations/networks in a unified framework: We characterize the k-vertex rigidity property of the underling graph of such formations. This is performed by deriving a set of useful conditions that can form a guideline for designing agent-loss-tolerant formations. We elaborate the study by characterizing robust formations with the optimal number of control links. We also propose a set of operations preserving the tolerance to multiple agent losses in such formations. These operations provide flexibility in designing the formations in terms of several designing parameters (e.g., geometry, diameter, and max degree). Especially in the case of formations, the ability to handle controller adjustments in a distributed way is important, and the paper addresses this issue for a number of the robustness problems considered. Copyright © 2014 John Wiley & Sons, Ltd.

Performance of MAX Test and Degree of Dominance Index in Predicting the Mode of Inheritance

We evaluate power performance to detect the correct mode of inheritance in gene-disease associations of two different approaches: the MAX test and the degree of dominance index or h-index. The MAX test is a special case of the conditional independence tests that simultaneously test for association and select the most likely genetic model based on a three-dimensional normal distribution. The h-index is based on the philosophy of using orthogonal contrasts to infer the mode of inheritance quantitatively. A population genetic model is developed where the real mode of inheritance is known a priori and power performance can be accurately determined. The simulations showed that none of the two approaches generally outperforms the other, nor each of them provides a panacea to estimate efficiently the mode of inheritance in all parameter space. However, the simultaneous application of both approaches can provide insights in determining the underlying mode of inheritance.

Greedy Routing on Complex Networks

This paper proposes a new routing strategy on complex networks. Based on the idea of greedy algorithm, our routing strategy chooses the node that has the highest probability to reach destination with the studies of max degree search strategy. In the meantime, the dynamic information like queue length will affect influence our strategy in order to increase the capacity of network. The result of simulation shows our strategy has a better performance compare to other local routing strategy. This strategy can be used on different kinds of complex networks.

A TDMA scheduling scheme for many-to-one communications in wireless sensor networks

In wireless sensor networks, time division multiple access (TDMA)-based MAC can potentially reduce the delay and provide real-time guarantees as well as save power by eliminating collisions. In this kind of MAC, a common energy-saving strategy is to allow the sensors to turn their radio off when not engaged. However, too much state transitions between the active and sleep modes would also waste energy. In order to save this part of energy and further improve the time performance, a multi-objective TDMA scheduling problem for many-to-one sensor networks is presented. An effective optimization framework is then proposed, where genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are hybridized to enhance the searching ability. Simulation results with different network sizes are given. Three algorithms are used for comparisons, which are PSO algorithm, max degree first coloring algorithm and node based scheduling algorithm. It is shown that the proposed hybrid algorithm is superior over these three algorithms on a specified objective, which can be the total time or the total energy for data collection. In addition, the results reveal that the proposed optimization framework can flexibly deal with a multi-objective optimization problem.