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Recent developments on identifying the community structures in real-world networks have established that the community structure may be either disjoint community set (DCS) or overlapping community set (OCS), showing high resemblance with each other. Still, given a network, researchers mostly followed distinct approaches to achieve optimal solutions, either for DCS or for OCS. Moreover, prior knowledge of community structure is needed to select the appropriate class of algorithms, since one cannot produce the optimal solution for the other. In this article, a comprehensive two-phase approach based on genetic algorithm (GA) is proposed that can be applied to any small-world network to generate the DCS and the OCS very fast without any prior knowledge of the community structure. In the first phase, an upper bound on the mean path length of a community is applied, relative to the equivalent Erdős-Renyi (E-R) random graph that expedites the convergence significantly. In the second phase, the search space is reduced considerably, by selecting a smaller subset of boundary nodes of the DCS generated in the first phase, to be manipulated probabilistically. To the best of our knowledge, we are the first to consider the mean path length of the community as a key parameter for finding the good quality communities at the earliest. Experimental study on six synthetic networks and five real-world networks shows that the proposed approach not only outperforms the state-of-the-art algorithms in terms of quality and scalability, but its parallel implementation also improves the speedup significantly.

Reachability queries ask whether a vertex can reach another vertex on large directed graphs. It is one of the most fundamental graph operators and has attracted researchers in both academics and industry to study it. The main technical challenge is to support fast reachability queries by efficient managing the three main costs: the index construction time, the index size and the query processing time on large/small and sparse/dense graphs. As real world graphs grow bigger in size, these problems remain open challenges that demand high performance solutions. In this paper, we propose a Multi-Dimensional Graph Labeling approach (called MGTag) to supporting fast reachability queries. MGTag is novel in three aspects. First, it recursively partitions a graph into multiple subgraphs with disjoint vertex sets, called non-shared graphs, and several inter-partition edges, called cross-edges. Second, we build a four-dimensional label - one dimension of layer, one dimension of non-shared graph and two dimensions of interval for each vertex in non-shared graphs. Finally, with the four-dimensional labeling scheme, we design algorithms to answer reachability queries efficiently. The extensive experiments on 28 large/small and dense/sparse graphs show that building the high dimensional index is quickly and the index size is also competitive compared with most of the state-of-the-art approaches. The results also show that our approach is more scalable and efficient than the state-of-the-art approaches in answering reachability queries on large/small and sparse/dense graphs.

Joint pilot and data power control (JPDPC) is known to have a large impact on both the overall spectral/energy efficiency and fairness of cell-based systems. However, the impact of JPDPC on the inherent spectral/energy efficiency and fairness trade-off in cell-free (CF) systems is much less understood. In this paper, considering pilot contamination, user-centric clustering and multi-antenna access points, we formulate novel JPDPC problems in CF systems as distinct optimization tasks, whose objectives are maximizing the minimum spectral efficiency (SE), maximizing the total SE and maximizing the product of the individual signal-to-interference-plus-noise ratios. Since these problems are non-convex, we solve them by combining successive convex approximation and geometric programming. To the best of our knowledge, this is the first paper analyzing and optimizing JPDPC in user-centric CF systems. Our results indicate that JPDPC allows users to save more energy than the disjoint optimization of pilot and data powers when maximizing the minimum SE, while showing that JPDPC plays a crucial role in balancing between SE and fairness also in CF systems.

Occupancy grids encode for hot spots on a map that is represented by a two dimensional grid of disjoint cells. The problem is to recursively update the probability that each cell in the grid is occupied, based on a sequence of sensor measurements from a moving platform. In this paper, we provide a new Bayesian framework for generating these probabilities that does not assume statistical independence between the occupancy state of grid cells. This approach is made analytically tractable through the use of binary asymmetric channel models that capture the errors associated with observing the occupancy state of a grid cell. Binary-valued measurement vectors are the thresholded output of a sensor in a radar, sonar, or other sensory system. We compare the performance of the proposed framework to that of the classical formulation for occupancy grids. The results show that the proposed framework identifies occupancy grids with lower false alarm and miss detection rates, and requires fewer observations of the surrounding area, to generate an accurate estimate of occupancy probabilities when compared to conventional formulations.

To aggregate useful information among diversified sources, a hotspot research topic called truth discovery has emerged in recent years. Existing truth discovery methods attempt to infer the true attribute values for the entities by identifying and trusting reliable data sources. However, all these methods neglect the relations among different entities, which play important roles in truth discovery task. When reliable data sources cannot provide sufficient information of entities, the true attribute values of these entities can still be inferred by propagating trustworthy information from related entities. Motivated by this, in this paper, we introduce the constrained truth discovery problem. We incorporate denial constraints, a universally quantified first-order logic formalism, into the process of truth discovery. We formulate it as a constrained optimization problem and analyze its hardness. To address the problem, we propose algorithms to partition the entities into disjoint groups, and generate arithmetic constraints for each disjoint group separately. Then, the true attribute values of the entities in each disjoint group are derived by minimizing the objective function under the corresponding arithmetic constraints. Experimental results on both real-world and synthetic datasets demonstrate that the proposed approach achieves good performance even with very few constraints and reliable sources.

The 3-D point cloud segmentation has played an important role in spatial structure analysis. Nowadays, segmentation methods either use a primitive-based strategy to fit points in predefined geometric shapes or group points based on their attributes (e.g., spatial distance). However, the required segmentation results, e.g., primitive level or object level, depend on the application. Therefore, this letter develops a semiautomatic method to extract contours for the users' desired segmentation. First, we initialize a 3-D closed curve for the target. Second, we calculate the internal and external force based on the proposed vector flow to deform the curve. The deformation equation is solved based on the Euler equation and calculated iteratively. Finally, the curve is converged as object contours. After one removes contours, those disjoint points are grouped as the users' desired instances. Experiments are conducted on various point clouds to demonstrate the effectiveness in terms of accuracy and consistency. Our quantitative evaluation outperformed selected primitive- and object-based methods, which presents a new viewpoint to the point cloud processing.

In the area of change detection, there were a rare number of optimization methods. Most of the optimization methods that are used by change detection are morphological transformation or median filtering, which cannot best optimize change detection algorithm. In this paper, a general post-processing algorithm for change detection is proposed. We believe that some problems cannot be avoided in the area of change detection such as 1) region of moving object generated by change detection is slightly larger than the ground-truth and 2) there are always some disjoint and small regions that are independent from the moving objects. To address the problem, our method can optimize the change detection algorithm bases on the idea of edge detection, which can remove the wrong edge or pixel. In the experiments, more than 20 change detection algorithms that include the best algorithm in ChangeDetection.net are selected. Most of these change detection algorithms are optimized by the proposed method on PWC, Precision, and FMeasure, where, our optimized algorithm named FgSegNet_v2 is better than all other algorithms in the CDnet. The best-optimized margin of PWC is 0.64, and the fast speed is 548FPS on CPU. Our approach can better resolve the afore-mentioned problems that cannot be avoided and is general and fast. The experiments can be reproduced with C++ on Github https://github.com/walty19950301/CDA-contour-optimizer.

Efficient tag identification is critically important for the application of radio frequency identification (RFID). The recently proposed orthogonal coset identification (OCSID) achieves orthogonal tag ID scanning without spectrum spreading so that the tag IDs can be recovered from collision. In the OCSID, the IDs are generated from binary vector set $\{-1, +1\}^{B}$ , which is only available for binary modulation. In this letter, we show that $B$ dimensional $M$ order vector set $\left\{{1, e^{\mathrm {i}\frac {2\pi }{M}}, {\dots }, e^{\mathrm {i}\frac {2\pi (M-1)}{M}}}\right\}^{B}$ can be decomposed to $\frac {M^{B}}{B}$ disjoint orthogonal subsets, where $M$ is the modulation order, $B$ is a positive integer power of 2. Based on this, we generalize the OCSID from binary to arbitrary order and propose $M$ -ary phase shift keying (MPSK) OCSID. We show a possible way to adopt the MPSK OCSID into EPC global C1 Gen2 standard, and with the consideration of the synchronization error, we also present a hybrid of the MPSK OCSID and the Aloha. Numerical results show that the MPSK OCSID based protocol can considerably improve the efficiency, even for the non-perfect synchronization cases.

Determining the correct number of clusters is essential for efficient clustering and cluster validity indices are widely used for the same. Generally, the effectiveness of a cluster validity index relies on two factors: first, separation, defined by the distance between a pair of cluster centroids or a pair of data points belonging to different clusters and second, compactness, which is determined in terms of the distance between a data point and a centroid or between a pair of data points belonging to the same cluster. However, the existing cluster validity indices for centroid-based clustering are unreliable when the clusters are too close, but corresponding centroids are distant. To mitigate this, a new cluster validity index, Saraswat-and-Mittal index, has been proposed in this article for hyperellipsoid or hyperspherical shape close clusters with distant centroids, generated by fuzzy c-means. The proposed index computes compactness in terms of the distance between data points and corresponding centroids, whereas the distance between data points of disjoint clusters defines separation. These parameters benefit the proposed index in the analysis of close clusters with distinct centroids efficiently. The performance of the proposed index is validated against ten state-of-the-art cluster validity indices on artificial, UCI, and image datasets, clustered by the fuzzy c-means.

In automotive manufacturing, production systems typically involve multiple robots and, today, are being individualized by utilizing the concept of digital twins. Therefore, the robot programs need to be verified for each individual product. A crucial aspect is to avoid collisions between robots by velocity tuning: This involves an efficient analysis of pairs of robot paths and determining if swept volumes of (sub) paths are disjoint. In general, velocity uncertain motions require disjoint sweep volumes to be safe. We optimize a clearance lower bounding function to provide new sample points for clearance computations. Due to the computational cost of each distance query, our sampling strategy aims to maximize the information gained at each query. The algorithm terminates when robot paths are verified to be disjoint or a collision is detected. Our approach for disjoint paths is inspired by the technique for continuous collision detection known as conservative advancement . Our tests indicate that the proposed sampling method is reliable and computationally much faster than creating and intersecting octrees representing the swept volumes.

Wireless Sensor Networks (WSNs) lend themselves to a wide variety of applications in our daily lives, such as environmental monitoring, safety, health-care, animal monitoring, etc. However, one of the key issues in WSN is energy constraints. This makes energy-conservation one of the major keys to the efficient functioning and lifetime of WSN. In this paper, given a network of nodes with heterogeneous energy, our goal is to determine energy-aware disjoint dominating sets (DSs) that work as data collection nodes in each round, to improve overall WSN lifetime. In order to accomplish this goal, we propose an intelligent data collection technique with two phases, the collector nodes selection, and the data gathering path formation and collection phases. In the collector nodes selection phase, an energy-aware algorithm based on swarm intelligence is proposed to construct disjoint dominating sets that work as collector nodes in each round. In the data gathering path formation and collection phase, data gathering path is determined for achieving maximal data collection efficiency and reduced energy consumption. The efficiency of our proposed technique is proved mathematically and through simulations.

The parameters of a $q$ -ary MDS Euclidean self-dual codes are completely determined by its length and the construction of MDS Euclidean self-dual codes with new length has been widely investigated in recent years. In this paper, we give a further study on the construction of MDS Euclidean self-dual codes via generalized Reed-Solomon (GRS) codes and their extended codes. The main idea of our construction is to choose suitable evaluation points such that the corresponding (extended) GRS codes are Euclidean self-dual. Firstly, we consider the evaluation set consists of two disjoint subsets, one of which is based on the trace function, the other one is a union of a subspace and its cosets. Then four new families of MDS Euclidean self-dual codes are constructed. Secondly, we give a simple but useful lemma to ensure that the symmetric difference of two intersecting subsets of finite fields can be taken as the desired evaluation set. Based on this lemma, we generalize our first construction and provide two new families of MDS Euclidean self-dual codes. Finally, by using two multiplicative subgroups and their cosets which have nonempty intersection, we present three generic constructions of MDS Euclidean self-dual codes with flexible parameters. Several new families of MDS Euclidean self-dual codes are explicitly constructed.

Codes with availability allow us to access any code symbol simultaneously $t$ times using $t$ disjoint recovery sets in distributed data storage. Codes with availability that are studied in the literature provide availability for individual code symbols in the codeword. In this letter, we consider a new class of codes with availability. These codes provide availability $t$ for subsets of code symbols called multi-symbol sets. For these codes, an upper-bound on the minimum Hamming distance is derived. A construction for optimal codes with information multi-symbol availability is given. The optimal codes with multi-symbol availability allow us to access more symbols locally with the same locality, when compared to optimal codes with individual code symbol availability.

The steady-state security region of the integrated energy system (IES) is a useful tool for rapid security assessment and security evaluation of the integrated energy system. A complete characterization of the IES steady-state security region is derived. The derivation is under the nonlinear and non-convex AC power flow model, the gas flow model, and the uncertainty of renewable energy without any linear simplification. Then a novel and robust computation scheme to compute the IES steady-state security region is proposed and shown to eliminate the estimation errors of the existing methods. It is shown that the IES steady-state security region is non-convex and composed of several disjoint components. Numerical studies are conducted to show that the IES steady-state security regions obtained from the existing methods can be inaccurate, while the proposed characterization gives an exact estimation of the IES steady-state security region that significantly improves the previously proposed methods.

Sink mobility is a significant technique to improve the performance of wireless sensor networks (WSNs). Generally a mobile sink visits several rendezvous points (RPs), forming a trip tour for data collection. However, the low movement speeds of mobile sinks tend to incur serious data delivery delays. In this article, we propose a quick convex hull-based rendezvous planning (QCHBRP) scheme, which aims to not only achieve full connectivity for disjoint WSNs but also construct a shorter trip tour and minimize the data delivery latency accordingly. The trajectory formation of the mobile sink is based on a path skeleton, i.e., a near-convex hull, which is created by the quick determination of several special locations as RPs. The benefits of QCHBRP are threefold. First, it is especially designed for disjoint WSNs where sensor nodes are deployed in multiple isolated segments and the network connectivity is lost in advance. Second, it is suitable for delay-harsh applications which require short paths of the mobile sink. Third, it is of much lower computational complexity compared with existing methods. The extensive analysis and experiments validate the effectiveness and advantages of this new scheme in terms of connectivity cost and data delivery delay.

In this letter, a new algorithm is presented for synthesizing large linear and planar arrays. To reduce the system cost and implementation complexity, the large array is partitioned into multiple disjoint subarrays and is only weighted at subarray level. By the approximation of the optimization objective, the pattern synthesis problem is first formulated as a weight matching problem. Subsequently, a clustering methodology named $K$ -means approach is adopted to solve this problem. The proposed algorithm can produce a good-shaped pattern, which has lower peak sidelobe level than that synthesized by the state-of-the-art method. Numerical results demonstrate the effectiveness of the proposed algorithm.

Soft robotic sensors have been limited in their applications due to their highly nonlinear time variant behavior. Current studies are either looking into techniques to improve the mechano-electrical properties of these sensors or into modelling algorithms that account for the history of each sensor. Here, we present a method for combining multi-material soft strain sensors to obtain equivalent higher quality sensors; better than each of the individual strain sensors. The core idea behind this work is to use a combination of redundant and disjoint strain sensors to compensate for the time-variant hidden states of a soft-bodied system, to finally obtain the true strain state in a static manner using a learning-based approach. We provide methods to develop these variable sensors and metrics to estimate their dissimilarity and efficacy of each sensor combinations, which can double down as a benchmarking tool for soft robotic sensors. The proposed approach is experimentally validated on a pneumatic actuator with embedded soft strain sensors. Our results show that static data from a combination of nonlinear time variant strain sensors is sufficient to accurately estimate the strain state of a system. © 2016 IEEE.

Non-orthogonal multiple access (NOMA) is regarded as a promising technology to provide high spectral efficiency and support massive connectivity in 5G systems. In most existing NOMA user grouping approaches, users are grouped into disjoint groups, which may lead to a waste of power resources within each NOMA group. Motivated by this, in this paper we propose a novel generalized user grouping (GuG) concept for NOMA from an overlapping perspective, which allows each user to participate in multiple groups but subject to individual maximum power constraint. In order to achieve effective GuG and maximize the system sum rate, we formulate a joint power control and GuG optimization problem. Then, we address this problem by exploiting the overlapping coalition formation (OCF) game framework, and we further propose an OCF-based algorithm in which each user can be self-organized into a desirable overlapping coalition structure. Simulation results verify the efficiency of GuG in NOMA systems and indicate that compared with traditional NOMA user grouping schemes, our proposed OCF-based GuG NOMA scheme achieves significant performance gains in terms of system sum rate.

The present article proposes two construction ways to study the general forms of ordinal sums of fuzzy implications with the intent of unifying the ordinal sums existing in the literature. The first ordinal sum construction way, which we call “Implication Complementing,” is to study how to complement a specific fuzzy implication to the linear transformations of given fuzzy implications defined on respective disjoint subsquares whose principal diagonals are segments of the principal diagonal of the unit square, in order that the resulting ordinal sum on the unit square is a fuzzy implication. The second way, which we call “Implication Reconstructing,” is to study how to reconstruct an initial fuzzy implication through replacing its some values on given rectangular regions of the unit square with the linear transformations of respective given fuzzy implications such that the redefined function is a new fuzzy implication. In both ways, necessary and sufficient conditions for the final reconstructed functions to be fuzzy implications are given and several new constructions of ordinal sums of fuzzy implications are obtained, which would generalize the existing ordinal sums from several aspects. In particular, by adopting the idea behind the second way, the generalized ordinal sums of fuzzy implications are proposed, in which the regions where the linear transformations of given fuzzy implications are defined are neither necessarily subsquares nor necessarily along the principal or minor diagonal of the unit square.

In radio-frequency identification (RFID)-based sensors networks, each sensor is integrated with a tag and sensors may co-exist in an area of interest. Before sending data packets, the sensors send their IDs for channel reservations. However, ID collisions happen frequently at the reservation stage which leads to significant time delays, especially for massive and dense networks. In this article, by employing group theory, we show that for $B=2^{k}$ , where $k$ is a positive integer, the set $\{-1,+1\}^{B}$ and the Hadamard product $\circ $ forms a group $\{\{-1,+1\}^{B}, \circ \}$ that can be divided into $(2^{B}/B)$ disjoint subsets, each of which has $B$ binary vectors that are mutually orthogonal. Based on this finding, we propose orthogonal coset identification (OCSID) and its generalization, query tree (QT)-OCSID, that can recover ID information from collisions, and thus considerably improve the efficiency at the reservation stage, particularly when the network is large and/or dense. In an ideal case, it can recover/decode $B$ tags for each query. The fundamental difference between the proposed OCSID schemes and code-division multiple access-based schemes is that, OCSID achieves orthogonal design for ID information recovery by exploiting the inherent orthogonal structure of the binary vector set, instead of spreading the spectrum. Hence, it requires a narrower frequency band, lower circuit complexity, and lower synchronization precision, which are much more preferred by hardware limited devices.

In genetic regulatory networks (GRNs), gene mutations often occur in a stochastic manner. As an important model of GRNs, gene mutations of Boolean networks are always described as function perturbations. This article studies the robust stability and stabilization of Boolean networks with stochastic function perturbations. A kind of parameterized set is constructed, and it is revealed that under the stochastic function perturbations, the property of finite-time stability remains unchanged when the perturbed set and the parameterized set are disjoint. In addition, it is proved that the finite-time stability is reduced to stability in distribution when the intersection of perturbed set and complement set of parameterized set is nonempty. As an application, the robust stabilization problem of Boolean control networks with stochastic function perturbations is discussed, and several necessary and sufficient conditions are presented for the robustness of feedback stabilizers. Finally, the obtained results are used to study the Drosophila melanogaster segmentation polarity gene network and the lac operon in the bacterium Escherichia coil.

Newer applications for Wireless Sensor Networks, such as for video and audio applications, require higher data rates compared to traditional low data rate sensor network applications. Platforms with two radios were proposed to address these new classes of applications: each radio can send data on different routes to achieve high data rates and energy efficiency. In this work, we show that in heterogeneous dual radio networks the use of two disjoint paths is not enough to achieve maximal throughput. We present the novel disjoint paths with the same parity problem and how our system called Two Path Protocol (TPP) can improve throughput in dual radio networks. Our algorithm maintains energy efficiency and uses all the hardware resources available to improve end-to-end data delivery. We compare our design with FastForward, the state-of-the-art protocol for dual-radio in a real testbed. Experimental results confirm that our approach doubled the throughput getting very close to the maximum theoretical limit value.

In this article, we formulate and solve the probabilistic security problem , defined as the probability that a multirobot system (MRS) with probabilistic interaction graphs has realizations that are secure from adversarial attacks. The concept of security is based on the control-theoretic notion of left invertibility, which depends on the existence of disjoint paths and subcuts in the topology describing robot interactions. To model uncertainties in interactions, we associate the existence of edges with a probability distribution. We, then, derive a probability expression based on disjoint paths and subcuts that defines the probability of security of the MRS. The exact probability is computed using the concept of binary decision diagrams (BDDs), a graphical method used to represent Boolean functions. To improve computational complexity, we formulate a combinatorial optimization problem that aims to bound the probability of security. Since MRSs are inherently dynamic, we leverage the graphical properties of BDDs to adapt to any topological changes. To demonstrate the validity of our results, we first track the probability of security of an MRS performing an environmental monitoring task, with Monte Carlo simulations as a baseline for comparison. Finally, we study the behavior of a probabilistic MRS when under attack in three different scenarios.

Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We consider a generalization of their construction, which we call lifted multiplicity codes. These are multivariate polynomial codes whose restriction to any line is a codeword of a multiplicity code (Kopparty, Saraf, Yekhanin 2014). We show that lifted multiplicity codes have a better trade-off between redundancy and a notion of locality called the $t$-disjoint-repair-group property than previously known constructions. More precisely, we show that lifted multiplicity codes with length $N$ and redundancy $O(t^{0.585} \sqrt{N})$ have the property that any symbol of a codeword can be reconstructed in $t$ different ways, each using a disjoint subset of the other coordinates. This gives the best known trade-off for this problem for any super-constant $t < \sqrt{N}$. We also give an alternative analysis of lifted Reed Solomon codes using dual codes, which may be of independent interest., 22 pages; A previous version claimed that a lifted code is exactly the span of all good monomials, but in fact the span of all good monomials only forms a subset of the lifted code. This does not change our main result

Person re-identification (ReID) aims to match pedestrian images across disjoint cameras. Existing supervised ReID methods utilize deep networks and train them with identity-labeled images, which suffer from limited annotations. Recently, clustering-based unsupervised ReID attracts more and more attention. It first clusters unlabeled images and assigns cluster index to the pseudo-identity-labels, then trains a ReID model with the pseudo-identity-labels. However, considering the slight inter-class variations and significant intra-class variations, pseudo-identity-labels learned from clustering algorithms are usually noisy and coarse. To alleviate the problems above, besides clustering pseudo-identity-labels, we propose to learn pseudo-patch-labels, which brings two advantages: (1) Patch naturally alleviates the effect of backgrounds, occlusions, and carryings since they usually occupy small parts in images, thus overcome noisy labels. (2) It is plausible that patches from different pedestrians belong to the same pseudo-identity-label. For example, pedestrians have a high probability of wearing either the same shoes or pants but a low possibility of wearing both. The experiments demonstrate our proposed method achieves the best performance by a large margin on both image- and video-based datasets.

Multinational corporations have multiple databases distributed throughout their branches, which store millions of transactions per day. For business applications, identifying disjoint clusters of similar and relevant databases contributes to learning the common buying patterns among customers and also increases the profits by targeting potential clients in the future. This process is called clustering, which is an important unsupervised technique for big data mining. In this article, we present an effective approach to search for the optimal clustering of multiple transaction databases in a weighted undirected similarity graph. To assess the clustering quality, we use dual gradient descent to minimize a constrained quasi-convex loss function whose parameters will determine the edges needed to form the optimal database clusters in the graph. Therefore, finding the global minimum is guaranteed in a finite and short time compared with the existing non-convex objectives where all possible candidate clusterings are generated to find the ideal clustering. Moreover, our algorithm does not require specifying the number of clusters a priori and uses a disjoint-set forest data structure to maintain and keep track of the clusters as they are updated. Through a series of experiments on public data samples and precomputed similarity matrices, we show that our algorithm is more accurate and faster in practice than the existing clustering algorithms for multi-database mining.

Two-way clustering algorithms use one single set to represent a cluster, which cannot intuitively show the fringe objects of a cluster. Three-way clustering uses the core region and the fringe region to describe a cluster, which divide the universe into three disjoint sets to capture the three types of relationships between a cluster and a sample, namely, belong-to fully, belong-to partially and not belong-to fully. One of the main problems of three-way clustering is to construct the core and the fringe of each cluster. In this paper, we propose a three-way clustering algorithm by using the stability of each sample. In the proposed algorithm, we use a set of base clustering results as inputs to obtain the samples' stability by using the co-association matrix and determinacy function. With this stability, the universe is divided into the universe core and the universe fringe according to a threshold for sample's stability. The universe core is constituted by the samples with high stability and is divided into the core region of each cluster by using kmeans algorithm. Whereas the universe fringe is constituted by the samples with low stability and is assigned into the fringe region of each cluster. Therefore, a three-way explanation of the cluster is naturally formed. The experimental results on UCI data sets show that the proposed algorithm is effective in revealing cluster structures.

All existing solutions to distributed consensus are organised around a Paxos-like structure wherein processes contend for exclusive leadership in one phase, and then either use their dominant position to propose a value in the next phase or elect an alternate leader. This approach may be characterised as adversarial and phase-asymmetric, requiring distinct message schemas and process behaviours for each phase. In over three decades of research, no algorithm has diverged from this basic model, alluding to it perhaps being the only viable solution to consensus. This paper presents a new consensus algorithm named Spire, characterised by a phase-symmetric, cooperative structure. Processes do not contend for leadership; instead, they collude to iteratively establish a dominant value and may do so concurrently without conflicting. Each successive iteration is structured identically to the previous, employing the same messages and invoking the same behaviour. By these characteristics, Spire buckles the trend in protocol design, proving that at least two disjoint cardinal solutions to consensus exist. The resulting phase symmetry halves the number of distinct messages and behaviours, offering a clear intuition and an approachable foundation for learning consensus and building practical systems.

The Set Partitioning Problem (SPP) aims to obtain non-empty disjoint subsets of objects such that their union equals the whole set of objects, and the partition meets some prespecified criteria. The ubiquity of SPP is impressive, given that it has a lot of theoretical and practical motivations. In the theoretical side, the study of the SPP is closely related to Bell numbers, Stirling numbers of the second kind, integer partitions, Eulerian numbers, Restricted Growth Strings (RGS), factoradic number system, power calculations, etc. In the practical side, SPP is intimately related to classification problems, clustering problems, reduction of dimensionality problems, and so on. In this work, three representations for instances of SPP are presented, these representations use: Restricted Growth Strings (RGS), factoradic number system, and a number system with a fixed base. Two cases for these representations will be presented: where the number of subsets is unbounded (i.e. the number of subsets can be the number of objects); and where the number of subsets is less than the number of objects. Bidirectional mappings between these three representations will be introduced, also the mapping among these three representations and the power of a base is defined. Given, that these three representations can be used to solve instances of SPP using exact, greedy, and metaheuristic algorithms, that require to do small changes to one possible solution and/or recombination of two possible solutions, definitions of mutation and recombination operators for the three representations will be shown. In order to motivate the use of the three representations for the solution of particular instances of SPP, it was decided to present their application to solve an instance of a set partition of integers problem (SPIP) using a simple genetic algorithm.

This article studies the batch processing of truss maintenance in large graphs. Trussness is a widely used index in graph analytics for cohesive subgraph mining. It is defined on edges to reflect the closeness of vertices connected by the edges. The trussness maintenance problem, i.e., updating trussness after edge insertions/deletions and avoiding recomputation, was proposed by Cohen (2008) with the assumption that real graphs are continuously evolving in nature and their dynamicity usually only affects few edges. Different from the existing work that mainly focuses on simple single edge/vertex insertion/deletion, we propose batch processing algorithms for truss maintenance with multiedge insertions/deletions. By presenting an edge structure called triangle disjoint set, whose insertion/deletion can make each edge change its trussness by at most 1, we tackle the difficulty in quantifying the trussness changes of the edges in batch processing. More specifically, we propose two indices, namely sustain support and pivotal support, to help measure whether the edges have the potential to change their trussness, such that the search range of the potential edges is greatly reduced. The extensive experiments on real-world graphs illustrate that compared with the single-edge processing approach, our batch processing algorithms can significantly improve the processing efficiency, and the improvement becomes more obvious when more edges are inserted/deleted.

Performance failure has become a major threat for various memory and analog circuits. It is challenging to estimate the extremely small failure probability when failed samples are distributed in multiple disjoint regions. In this article, we propose an adaptive importance sampling (AIS) algorithm. AIS has several iterations of sampling region adjustments, while existing methods predecide a static sampling distribution. We design two adaptive frameworks based on resampling and population Metropolis–Hastings (MH) to iteratively search for failure regions. The experimental results of the AIS method exhibit better efficiency and higher accuracy. For SRAM bit cell with single failure region, the AIS method uses 2– $27{\times }$ fewer samples and reaches better accuracy when compared to several recent methods. For a two-stage amplifier circuit with multiple failure regions, the AIS method is $90{\times }$ faster than Monte Carlo and 7–23 ${\times }$ over other methods. For charge pump circuit and $C^{2}MOS$ master–slave latch circuit, the AIS method can reach 6– $18{\times }$ and 4– $6{\times }$ speedup over other methods, respectively.

A primitive $k$ -batch code encodes a string $\boldsymbol {x}$ of length $n$ into a string $\boldsymbol {y}$ of length $N$ , such that each multiset of $k$ symbols from $\boldsymbol {x}$ has $k$ mutually disjoint recovering sets from $\boldsymbol {y}$ . In this paper, we discuss new constructions of binary primitive batch codes. First, we develop novel explicit and random coding constructions of linear primitive batch codes based on finite geometries. Second, a new explicit coding construction of binary primitive batch codes based on bivariate lifted multiplicity codes is provided. For any $k=n^ \varepsilon $ with $\varepsilon \in (0,0.47)\setminus \{1/5,1/4\}$ , our proposed codes have a better trade-off between the redundancy and the parameters $k,n$ than previously known batch codes.

A linear code is optimal if it has the highest minimum distance of any linear code with a given length and dimension. We construct infinite families of optimal binary linear codes $C_{\Delta ^{c}}$ constructed from simplicial complexes in $\mathbb {F}^{n}_{2}$ , where $\Delta $ is a simplicial complex in $\mathbb {F}^{n}_{2}$ and $\Delta ^{c}$ the complement of $\Delta $ . We first find an explicit computable criterion for $C_{\Delta ^{c}}$ to be optimal; this criterion is given in terms of the 2-adic valuation of $\sum _{i=1}^{s} 2^{|A_{i}|-1}$ , where the $A_{i}$ ’s are maximal elements of $\Delta $ . Furthermore, we obtain much simpler criteria under various specific conditions on the maximal elements of $\Delta $ . In particular, we find that $C_{\Delta ^{c}}$ is a Griesmer code if and only if the maximal elements of $\Delta $ are pairwise disjoint and their sizes are all distinct. Specially, when $\mathcal {F}$ has exactly two maximal elements, we explicitly determine the weight distribution of $C_{\Delta ^{c}}$ . We present many optimal linear codes constructed by our method, and we emphasize that we obtain at least 32 new optimal linear codes.

The byzantine agreement protocol has a disadvantage that there are many limitations on node scalability, because the performance degradation may occur due to a large amount of traffic. Hence, this classical byzantine agreement algorithm seems to be infeasible to achieve scale-out performance with the same level of security as a Bitcoin. In order to improve the performance degradation due to a large amount of traffic, we propose the hierarchical consensus mechanism based on service-zone sharding rather than how all nodes participate in the consensus process. In the proposed consensus mechanism ( SZHBFT ), a disjoint set of transactions is locally processed by a secure consensus subgroup or globally processed between consensus subgroups. Thus, the transactions that occur related to multiple Service-Zone Consensus Groups are updated and maintained in the Inter-Service Zone Public Ledger , whereas service transactions occurring locally are processed in parallel by each Service-Zone Consensus Group and then distributed into a local Service-Zone Private Ledger . The scheme of the proposed SZHBFT mechanism provides the hierarchical agreement solution along with distributed multiledger structure for the scalable byzantine resilient agreement by forming secure consensus subgroups in order to minimize the overhead of overall communication messages.

Shadowed sets, proposed by Pedrycz, provide a three-way approximation scheme for transforming the universe of a fuzzy set into three disjoint areas, i.e., elevated area, reduced area, and shadow area. To calculate a pair of decision-making thresholds, an analytic method was proposed by solving a minimization problem of the uncertainty arising from the three areas. However, some uncertainty will be lost in the process of constructing the shadowed set model using Pedrycz's method. Moreover, few references on how to measure the uncertainty of shadow sets exist. In this article, a comprehensible method for measuring the fuzzy entropy of a shadowed set, i.e., interval fuzzy entropy, is defined. Based on the interval fuzzy entropy, a new shadowed set model, namely, interval shadowed sets, is proposed. Compared with Pedrycz's model, the main difference is that the range of the shadow area in this model is $[\beta,\alpha ]$ $(0 \leq \beta while not [0, 1]. By solving a fuzzy entropy loss-minimization problem, a pair of optimal thresholds, $\alpha$ and $\beta$ , can be obtained. Finally, the results of the instance analysis of different types of representative membership functions and many experiments show that the fuzzy entropy loss of the interval shadowed set is lower than that of the traditional shadowed set of a fuzzy set. These results enrich shadowed set theory from a new perspective.

Big data with a large number of observations (samples) have posed genuine challenges for fuzzy clustering algorithms and fuzzy C-means (FCM), in particular. In this article, we propose an original algorithm referred to as a hyperplane division method to split the entire data set into disjoint subsets. By disjoint subsets, we mean that the data subspaces (parts of the entire data space), each of which is supported or spanned by the data points in the corresponding subset, do not overlap each other. The disjoint subsets turned out to be beneficial to the improvement of the quality of the clusters formed by the clustering algorithms. Moreover, considering that either a large number (say, thousands) or a small number (say, a few) of clusters may be pursued in the clustering task, we propose corresponding strategies (based on the hyperplane division method) to make clustering processes feasible, efficient, and effective. By validating the proposed strategies on both synthetic and publicly available data, we show their superiority (in terms of both efficiency and effectiveness) manifested in a visible way over the method of clustering the entire data and over some representative big data clustering methods.

In a locally recoverable code (LRC), any code symbol can be recovered by accessing at most $r$ other symbols (called a recovery set). In an LRC with availability , any information symbol has $t$ disjoint recovery sets. In this letter, we consider a new class of codes with availability, where the $l^{th}, 1 \leq l \leq t$ disjoint recovery set for any information symbol has locality $r_{l}$ and it is protected by a local code of minimum Hamming distance at least $\delta _{l}$ . We derive an upper-bound on the minimum Hamming distance of these codes. A family of systematic codes with information availability is constructed achieving the bound with equality.

In this paper, we introduce fuzzy granular colors for modeling color categories. Fuzzy granular colors are built by aggregating fuzzy colors having semantic relationships with regard to a certain color category. Our proposal allows us to model color categories which comprise disjoint fuzzy subsets of colors, as well as those having a nonconvex representation in the color space, among other advantages. Such categories are used very often by humans in different real contexts. Fuzzy granular colors are appropriate to provide color models able to deal with ill-defined boundaries, subjectivity, and context-dependence. We illustrate the advantages of our approach with respect to current state of the art with several experiments.

Fast-acting reactive power support from distributed generations (DGs) is a promising approach for tackling rapid voltage fluctuations in distribution networks. However, the voltage regulation range via reactive power of DGs alone is narrow especially in distribution networks with high resistance-reactance ratio. In this paper, a randomized algorithm is proposed to improve the voltage profile in distribution networks via coordinated regulation of the active and reactive power of DGs. To this end, first the variables of the proposed quadratically constrained quadratic programming problem on voltage control are partitioned into disjoint subsets, each of which corresponds to a unique low-dimensional subproblem. Second, these subsets are updated serially in a randomized manner via solving their corresponding subproblems, which overcomes the requirement for system-wide coordination among participating agents and guarantees an optimal solution. Compared with the existing algorithms, the proposed algorithm is resilient to network reconfigurations and achieves a wider voltage regulation range. The effectiveness and convergence performance of the proposed algorithm is validated by the case studies.

We consider wireless device-to-device (D2D) caching networks with single-hop transmissions. Previous work has demonstrated that caching and coded multicasting can significantly increase per user throughput. However, the state-of-the-art coded caching schemes for D2D networks are generally impractical because content files are partitioned into an exponential number of packets with respect to the number of users if both library and memory sizes are fixed. In this paper, we present two combinatorial approaches of D2D coded caching network design with reduced packetizations and desired throughput gain compared to the conventional uncoded unicasting. The first approach uses a “hypercube” design, where each user caches a “hyperplane” in this hypercube and the intersections of “hyperplanes” represent coded multicasting codewords. In addition, we extend the hypercube approach to a decentralized design. The second approach uses the Ruzsa-Szemeredi graph to define the cache placement. Disjoint matchings on this graph represent coded multicasting codewords. Both approaches yield an exponential reduction of packetizations while providing a per-user throughput that is comparable to the state-of-the-art designs in the literature. Furthermore, we apply spatial reuse to the new D2D network designs to further reduce the required packetizations and significantly improve per user throughput for some parameter regimes.

We study the problem of optimal network design in a network of networks, a graph composed of a set of disjoint subgraphs, and a set of designed edges between them. Nodes obey noisy consensus dynamics, and our system model allows for both positive and negative edge weights. We quantify system performance by its coherence, an $H_2$ norm that captures the steady-state variance of the deviation from consensus. We pose the problem of how to connect the subgraphs, by selecting a single connecting node in each subgraph, so that the resulting network of networks has optimal coherence. We then show that this problem can be solved by identifying the connecting node in each subgraph independently of the other nodes and subgraphs. Thus, the problem can be solved in polynomial time in the order of the largest subgraph. We prove that when the connecting topology is a tree, this solution is optimal even under a more general model that allows for multiple connecting nodes per subgraph. We also derive bounds on the best and worst coherence for a general network of networks with all-positive edge weights. Finally, we provide analytical and numerical examples that further explore coherence in a network of networks.

Numerical comparison is often key to verifying the performance of optimization algorithms, especially, global optimization algorithms. However, studies have so far neglected issues concerning comparison strategies necessary to rank optimization algorithms properly. To fill this gap for the first time, we combine voting theory and numerical comparison research areas, which have been disjoint so far, and thus extend the results of the former to the latter for optimization algorithms. In particular, we investigate compatibility issues arising from comparing two and more than two algorithms, termed “C2” and “C2+” in this article, respectively. Through defining and modeling “C2” and “C2+” mathematically, it is uncovered and illustrated that numerical comparison can be incompatible. Further, two possible paradoxes, namely, “cycle ranking” and “survival of the nonfittest,” are discovered and analyzed rigorously. The occurrence probabilities of these two paradoxes are also calculated under the no-free-lunch assumption, which shows the first justifiable use of the impartial culture assumption from voting theory, providing a point of reference to the frequency of the paradoxes occurring. It is also shown that significant influence on these probabilities comes from the number of algorithms and the number of optimization problems studied in the comparison. Further, various limiting probabilities when the number of optimization problems goes to infinity are also derived and characterized. The results would help guide benchmarking and developing optimization and machine learning algorithms.

Relying on a limited power source, WSNs present one of their most challenging concerns as energy consumption. In addition, coverage and connectivity are important quality of service metrics in the networks. In this paper, the problem of connected target coverage (CTC) with an optimistic view of energy usage is investigated. A new 2-phase optimization method is proposed that provides full target coverage and connectivity with the user throughout network lifetime. In the first phase of the algorithm, sensors are organized into maximum achievable disjoint cover sets (CSs) using a new multi-objective integer linear programming (ILP) model. Set of remaining nodes that could not be formed into an independent CS, are allocated to the existing CSs as a subset of potential cluster heads (CHs) i.e., for every active CS, CHs are chosen from its potential CH subset. In the second phase, the algorithm activates CSs one after another to gather information from targets and forward them to the user in a hierarchical manner via a modified multi-objective mixed integer linear programming (MILP) model. Both of the ILP and MILP models are solved using branch-and-bound method. The solutions of the optimization models are solved to optimality. The superiority of the proposed method is proven through numerous experiments in different scenarios compared with two of the most related works.

Community phenomenon is ubiquitous in our social activities. For instance, in a football match, the players are divided into two disjoint teams (i.e., communities) in which the ball is frequently forwarded from one player to another, generating many ball transferring trajectories. It is interesting to do a community detection which is only based on the objective trajectories for some specific purpose such as the fraud player detection. In this brief, we first artificially collect the football trajectories for at least 20 football matches of 2018 FIFA World Cup. Secondly, we build a football transferring network in which the link weight is the number of ball transfers from one player to another. Thirdly, we propose a seed based l ocal b ottom-u p c ommunity d etection (LBPCD) method which discovers new team members gradually by maximizing the defined modularity. Finally, we compose experiments on both the collected football data and an email network to demonstrate the effectiveness of the proposed method.

This paper is concerned with multiple Lagrange stability under perturbation for recurrent neural networks with time-varying delays. This is different from traditional Lagrange stability, which means that multiple Lagrange stability under perturbation holds for any disturbance of initial value and any structural perturbation, within a specified and well-characterized set. In this paper, multiple Lagrange stability under perturbation with respect to a finite number of trivial solutions is established, which has good robustness. Under certain perturbation, the core of the proof of the boundedness of trajectories in mutually disjoint subregions is to employ the generalized differential inequality. The results supplement and extend some previous results, and they are applicable to robust analysis of multiple equilibria. Finally, numerical calculation and simulations are implemented to illustrate the effectiveness of the theoretical results.

External difference families (EDFs for short) are a type of block designs that each nonidentity element arises a fixed number of times as a difference between elements in distinct blocks. An EDF with the property that the union of its blocks covers the nonidentity elements exactly once is called a near-complete EDF. In this letter, we obtain some near-complete EDFs from disjoint difference families and difference unit sets over Galois rings, and explicitly determine their parameters. The obtained EDFs cover some earlier EDFs as special cases. Furthermore, we confirmed the conjecture in Davis et al . (Des. Codes Cryptogr. 87(11): 415-424, 2017).

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, a new combination of codes with locality and codes with multiple disjoint repair sets (also called availability) is introduced. Accordingly, a Singleton-type bound is derived for the new code, which contains those bounds in [9] , [20] , [28] as special cases. Optimal constructions are proposed with respect to the new bound. In addition, these constructions can also generate optimal codes with multiple disjoint repair sets with respect to the bound in [28] , which to the best of our knowledge, are the first explicit constructions that can achieve the bound in [28] .

Many large-scale applications in broad science, engineering, and business domains are generating big data, which must be transferred to remote sites for various storage and analysis purposes. Bandwidth reservation services that discover feasible routing options over dedicated paths in high-performance networks have proved to be effective for such big data transfer. In this paper, we formulate a generic problem of bandwidth scheduling with two variable node-disjoint paths (BS-2VNDP) by exploring the flexibility and capacity of multiple data transfer paths. We further consider two variable paths of either fixed or variable bandwidth with negligible or non-negligible path switching delay, referred to as 2VPFB-0/1 and 2VPVB-0/1, respectively. We prove that all of these four scheduling problems are NP-complete, and then propose a heuristic algorithm for each. For performance comparison, we also design several other heuristic algorithms based on a greedy strategy. These scheduling algorithms are implemented and tested in both simulated and real-life networks, and extensive results show that the proposed heuristic algorithms significantly outperform other algorithms in comparison.

While the majority of methods for community detection produce disjoint communities of nodes, most real-world networks naturally involve overlapping communities. In this paper, a scalable method for the detection of overlapping communities in large networks is proposed. The method is based on an extension of the notion of normalized cut to cope with overlapping communities. A spectral clustering algorithm is formulated to solve the related cut minimization problem. When available, the algorithm may take into account prior information about the likelihood for each node to belong to several communities. This information can either be extracted from the available metadata or from node centrality measures. We also introduce a hierarchical version of the algorithm to automatically detect the number of communities. In addition, a new benchmark model extending the stochastic blockmodel for graphs with overlapping communities is formulated. Our experiments show that the proposed spectral method outperforms the state-of-the-art algorithms in terms of computational complexity and accuracy on our benchmark graph model and on five real-world networks, including a lexical network and large-scale social networks. The scalability of the proposed algorithm is also demonstrated on large synthetic graphs with millions of nodes and edges.