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Routing protocol for Low Power Lossy Network (RPL) is a proactive network layer routing protocol. It is suitable for Internet of Things (IoT). It is also a source routing protocol. It works by creating a tree based network topology called Directed Acyclic Graph (DAG). Based on the position of the nodes from the root, rank value is allocated for each node. Rank is a unique value given to all the nodes in the DAG. It increases in the downward direction from the root. This value is used for prevention of loops, formation and maintenance of topology. Certain malignant nodes use this rank value and introduce a false routing by forcing the neighbors to route the packets through them. The consequences of this attack are more destructive in nature. It decreases throughput and increases delay in communication. Since the devices in IoT are resources constrained, there is an urge to address rank attack immediately. In this paper, a thorough review on the effects of rank attack and its countermeasures are presented.

In this paper, we consider a probability maximizing shortest path problem. For a given directed graph with the length of each arc being an independent normal random variable with rational mean and standard deviation, the problem is to find a simple s − t path that maximizes the probability of arriving at the destination within a given limit. We first prove that the problem is NP -hard even on directed acyclic graphs with the mean of the length of each arc being restricted to an integer. Then, we present pseudo-polynomial time exact algorithms for the problem along with nontrivial special cases that can be solved in polynomial time. Finally, we present a fully polynomial approximation scheme (FPTAS) that iteratively solves deterministic shortest path problems. The structure of the proposed approximation scheme can be applied to devise FPTAS for other probability maximizing combinatorial optimization problems once the corresponding deterministic problems are polynomially solvable.

International audience; Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees. If the literature proposes solutions to enumerate singletons of trees, we study in this article a more general problem, the enumeration of sets of trees -- forests. Specifically, we mainly study irredundant forests, i.e., where no tree is a subtree of another. By compressing each such forest into a Directed Acyclic Graph (DAG), we develop a reverse search like method to enumerate DAGs compressing irredundant forests. Remarkably, we prove that these DAGs are in bijection with the row-Fishburn matrices, a well-studied class of combinatorial objects. In a second step, we derive our irredundant forest enumeration to provide algorithms for tackling related problems: (i) enumeration of forests in their classical sense (where redundancy is allowed); (ii) the enumeration of "subforests" of a forest, and (iii) the frequent "subforest" mining problem. All the methods presented in this article enumerate each item uniquely, up to isomorphism.

The application placement strategies in the hierarchical fog-cloud environment based on the directed acyclic graph (DAG) for rapid execution is an NP-hard optimization problem. Although heuristics have been proposed to generate sub-optimal solutions based on non-preemptive placement policy, merging multiple DAG-based applications into one application is simple but ineffective for minimizing the overall makespan due to the lack of consideration of fairness among multiple DAG-based applications. We design an application placement strategy based on dynamic scheduling that can effectively utilize the schedule gaps in the virtual machines of the different layers to minimize the makespan that meets the deadlines.

Neural architecture search (NAS) has made significant progress in recent years. However, existing methods usually search in a small-scale, well-designed architecture space, discover only one architecture in a single search, and hardly rework, severely limiting their potential. In this paper, we propose a novel neural architecture generator (NAG) that can efficiently sample architectures in a large-scale architecture space. Like a generative adversarial network (GAN), our model consists of two components: (1) a generator that can generate directed acyclic graphs (DAGs) as cells or blocks of neural architectures and (2) a discriminator that can estimate the probability that a DAG comes from cells of real architectures rather than the generator. Furthermore, we employ a random search with NAG (RS-NAG) to discover the optimal architecture with our customized requirements. Experimental results show that the NAG can generate diverse architectures with our customized requirements multiple times after one adversary training. Furthermore, compared with the existing NAS methods, our RS-NAG achieves the competitive results with 2.50% and 25.5% top-1 accuracy on two benchmark datasets – CIFAR-10 and ImageNet.

Due to the excellent performance in complex systems modeling under small samples and uncertainty, Belief Rule Base (BRB) expert system has been widely applied in fault diagnosis. However, the fault diagnosis process for complex mechanical equipment normally needs multiple attributes, which can lead to the rule number explosion problem in BRB, and limit the efficiency and accuracy. To solve this problem, a novel Combination Belief Rule Base (C-BRB) model based on Directed Acyclic Graph (DAG) structure is proposed in this paper. By dispersing numerous attributes into the parallel structure composed of different sub-BRBs, C-BRB can effectively reduce the amount of calculation with acceptable result. At the same time, a path selection strategy considering the accuracy of child nodes is designed in C-BRB to obtain the most suitable sub-models. Finally, a fusion method based on Evidential Reasoning (ER) rule is used to combine the belief rules of C-BRB and generate the final results. To illustrate the effectiveness and reliability of the proposed method, a case study of fault diagnosis of rolling bearing is conducted, and the result is compared with other methods.

In this paper, we study big data-driven Cyber–Physical Systems (CPS) through cloud platforms and design scheduling optimization algorithms to improve the efficiency of the system. A task scheduling scheme for large-scale factory access under cloud–edge collaborative computing architecture is proposed. The method firstly merges the directed acyclic graphs on cloud-side servers and edge-side servers; secondly, divide the tasks using a critical path-based partitioning strategy to effectively improve the allocation accuracy; then achieves load balancing through reasonable processor allocation, and finally compares and analyses the proposed task scheduling algorithm through simulation experiments. The experimental system is thoroughly analysed, hierarchically designed, and modelled, simulated, and the experimental data analysed and compared with related methods. The experimental results prove the effectiveness and correctness of the worst-case execution time analysis method and the idea of big data-driven CPS proposed in this paper and show that big data knowledge can help improve the accuracy of worst-case execution time analysis. This paper implements a big data-driven scheduling optimization algorithm for Cyber–Physical Systems based on a cloud platform, which improves the accuracy and efficiency of the algorithm by about 15% compared to other related studies.

Leukemia is usually diagnosed by viewing the smears of blood and bone marrow using microscopes and complex Cytochemical tests can be used to authorize and classify leukemia. But these methods are costly, slow and affected by the proficiency and expertise of the specialists concerned. Leukemia can be detected with the help of image processing-based methods by analyzing microscopic smear images to detect the presence of leukemic cells and such techniques are simple, fast, cheap and not biased by the specialists. The proposed study presents a computer aided diagnosis system that uses pretrained deep Convolutional Neural Networks (CNNs) for detection of leukemia images against normal images. The use of pretrained networks is comparatively an easy method of applying deep learning for image analysis and the comparison results of the present study can be used to choose appropriate networks for diagnostic tasks. The microscopic images used in the proposed work were downloaded from a public dataset ALL-IDB. In the proposed work, image classification is done without using any image segregation and feature extraction practices and the study used pretrained series network AlexNet, VGG-16, VGG-19, Directed Acyclic Graph (DAG) networks GoogLeNet, Inceptionv3, MobileNet-v2, Xception, DenseNet-201, Inception-ResNet-v2 and residual networks ResNet-18, ResNet-50 and ResNet-101 for performing the classification and comparison. A classification accuracy of 100% is obtained with all the pretrained networks used in the study for ALL_IDB1 dataset and for ALL_IDB2 dataset, 100% accuracy is obtained with all networks except the AlexNet and VGG-16. The efficacy of three optimization algorithms Stochastic Gradient Descent with Momentum (SGDM), Root Mean Square propagation (RMSprop) and Adaptive Moment estimation (ADAM) is also compared in all the classifications performed. The study considered the detection of leukemia in general only, and classification of leukemia into different types can be attempted as a future work.

Using cross-asset return data in global financial markets, we propose a novel empirical framework to identify the causal structure of the asset risk spillover network. The joint return distribution of the global financial system can be characterized using a directed acyclic graph approach. However, since assets tend to be highly correlated during market turbulence, when adopting a nodewise penalized regression approach for neighborhood estimation, parameter estimates will receive large standard errors, and edges cannot be reliably estimated. In this work, we propose a two-stage approach for directed acyclic graph skeleton estimation for highly correlated variables. In the first stage, a variable screening ensemble is incorporated into the sparse partial least squares regression method to both reduce the size of the active variables set and impose an adaptive penalization on the weight vectors. In the second stage, a modified PC algorithm based on Gram-Schmidt orthogonalization is applied to remove the false positive edges. Simulation studies are conducted to demonstrate the effectiveness of the proposed method. Finally, we apply our method to analyze the asset risk spillover channels for international financial assets during the COVID-19 pandemic.

Motion Blur is an important effect of photo-realistic rendering. Distribution ray tracing can simulate motion blur very well by integrating light, both over the spatial and the temporal domain. However, increasing the problem by the temporal dimension entails many challenges, particularly in cinematic multi-bounce path tracing of complex scenes, where heavy-weight geometry with complex lighting and even offscreen elements contribute to the final image. In this paper, we propose the Motion DAG (Directed Acyclic Graph), a novel data structure that filters an entire animation sequence of an object, both in the spatial and temporal domain. These Motion DAGs interleave a temporal interval binary tree for filtering time consecutive data and a sparse voxel octree (SVO), which simplifies spatially nearby data. Motion DAGs are generated in a pre-process and can be easily integrated in a conventional physically based path tracer. Our technique is designed to target motion blur of small objects, where coarse representations are sufficient. Specifically, in this scenario our results show that it is possible to significantly reduce both, memory consumption and render time.

We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a Directed Acyclic Graph (DAG) model. The Linear Non-Gaussian Acyclic Model (LiNGAM) is one of the most successful DAG models, and various estimation methods have been developed. However, existing methods are not efficient for some reasons: (i) the sparse structure is not always incorporated in causal order estimation, and (ii) the information of higher-order moments of the data is not used in parameter estimation. To address these issues, we propose a new estimation method for a linear DAG model with non-Gaussian noises. The proposed method is based on a single statistical criterion that includes the log-likelihood of independent component analysis (ICA) and two penalty terms. The two penalties are related to the sparsity and the consistency condition, respectively. This criterion enables us to leverage the sparse structure and the information of higher-order moments throughout the estimation. For stable and efficient optimization, we propose some devices, such as a modified natural gradient. Numerical experiments show that the proposed method outperforms the existing methods.

The Kirchhoff index K ( G ) of a graph G is one of the most important topological indices in mathematical chemistry. Suppose that G is a unicyclic graph with n vertices and the cycle in G is denoted by C k , where k is the length of this cycle. Let S ( G ) be the unicyclic graph obtained from G by inserting a new vertex to each edge of G . In this paper, we prove that the Kirchhoff index of G equals m ( S ( G ) , n − 2 ) − 2 m ( S ( G ) − C 2 k , n − k − 2 ) ∕ k if 3 ≤ k ≤ n − 2 and equals m ( S ( G ) , n − 2 ) ∕ k if k = n − 1 , n , where m ( S ( G ) , n − 2 ) is the number of matchings of S ( G ) with n − 2 edges and S ( G ) − C 2 k is the acyclic graph obtained from S ( G ) by deleting all vertices of the cycle C 2 k in S ( G ) .

The preview-based leader-following consensus control of distributed multi-agent systems (MAS) with a directed acyclic graph is investigated in this paper. The external disturbance considered in this paper is the step function that can be previewed, and the information of the leader can be obtained in advance. The leader-following consensus control of MAS is solved by using the state augmentation technique and the preview control method that transforms the consensus control problem into the finite horizon linear quadratic regulator (LQR) problem and the infinite horizon LQR problem. In the finite horizon, the minimum principle is utilized to design the optimal controller. In the infinite horizon, the standard infinite horizon LQR is applied to devise the corresponding controller. Assuming the original systems are stabilisable and detectable, the distributed consensus controller guarantees the asymptotic consensus of the preview MAS. The simulation illustrates the effectiveness of the distributed leader-following consensus controller designed in this paper.

In this paper, we introduce a new graph structure named an ST -reachable directed acyclic graph which is a directed acyclic graph (DAG) that guarantees reachability (i.e., a directed path exists) from every sender to every target. When an arbitrarily connected undirected graph G = ( V , E ) and two sets of the vertices, senders S (⊂V) and targets T (⊂V), are given, we consider the construction of a minimal ST -reachable DAG by changing some undirected edges to arcs and removing the remaining edges. In this paper, we present the necessary and sufficient condition under which a minimal ST -reachable DAG can be constructed when | S | ≤ 2 and | T | ≤ 2 , and propose a self-stabilizing algorithm for constructing a minimal ST -reachable DAG (if it exists) when an arbitrarily connected undirected graph, S ( | S | ≤ 2 ) and T ( | T | ≤ 2 ) are given. Moreover, our proposed algorithm can detect the non-existence of any ST -reachable DAG if the ST -reachable DAG of the given graph and two sets of vertices, S and T , do not exist.

Remaining useful life is the estimated continuous normal working time of a component or system from the current moment to the potential failure. The traditional methods have high trial-and-error costs and poor migration capabilities. Fortunately, the neural architecture search (NAS) that has emerged partially solves the problem of automatic construction of network models. However, the search strategy for NAS is reinforcement learning or evolutionary algorithms, which essentially search in discrete space and treating the objective function as a black box, which is very time-consuming. To solve this problem, we proposed a gradient-based neural architecture search method. This method regards a cell in the search space as a directed acyclic graph (DAG) containing N ordered nodes. Each node is a latent representation, and the directed edges represent the conversion operation of two nodes. By mixing the candidate operations (ReLU, tanh) with the softmax function, the search space becomes a continuous space and the objective function becomes a differentiable function, so gradient-based optimization methods can be used to find the optimal structure. A neural architecture search method based on gradient descent for RUL estimation, with extensive experiments showing apparently, outperforms traditional approaches as well as Long Short-Term Memory (LSTM), and it takes much less computing resources than the reinforcement neural architecture search method.

Task allocation in Data Stream Processing Systems (DSPSs) has a significant impact on performance metrics such as data processing latency and system throughput. An application processed by DSPSs can be represented as a Directed Acyclic Graph (DAG), where each vertex represents a task and the edges show the dataflow between the tasks. Task allocation can be defined as the assignment of the vertices in the DAG to the physical compute nodes such that the data movement between the nodes is minimised. Finding an optimal task placement for DSPSs is NP-hard. Thus, approximate scheduling approaches are required to improve the performance of DSPSs. In this paper, we propose a heuristic scheduling algorithm which reliably and efficiently finds highly communicating tasks by exploiting graph partitioning algorithms and a mathematical optimisation software package. We evaluate the communication cost of our method using three micro-benchmarks, showing that we can achieve results that are close to optimal. We further compare our scheduler with two popular existing schedulers, R-Storm and Aniello et al.’s ‘Online scheduler’ using two real-world applications. Our experimental results show that our proposed scheduler outperforms R-Storm, increasing throughput by up to 30%, and improves on the Online scheduler by 20%–86% as a result of finding a more efficient schedule. 1

Although an increasing number of articles examining statistical control variables exist, the use of control variables receives less scrutiny than other methodological topics, and research has yet to show how adding or dropping a control variable can damage causal inferences. By showing the unexpected consequences of including and excluding a control variable, this article challenges the view that additional control variables always strengthens causal conclusions. This study first illustrates the purification role of statistical control variables, and then quantifies the omitted variable bias. Using the Directed Acyclic Graphs (DAG), this essay differentiates confounding bias from overcontrol and endogenous selection bias. While using control variables may at times rule out alternative explanations, it is equally possible that adding control variables introduces overcontrol and endogenous selection biases, creating alternative interpretations rather than ruling them out. This paper concludes by discussing how and whether scholars should include certain control variables.

Animations of virtual items in AR support systems are typically predefined and lack interactions with dynamic physical environments. AR applications rarely consider users’ preferences and do not provide customized spontaneous support under unknown situations. This research focuses on developing adaptive, error-tolerant AR systems based on directed acyclic graphs and error resolving strategies. Using this approach, users will have more freedom of choice during AR supported work, which leads to more efficient workflows. Error correction methods based on CAD models and predefined process data create individual support possibilities. The framework is implemented in the Industry 4.0 model factory at FH Aachen.

This paper studies the following variant of clustering or laying out problems for directed acyclic graphs (DAG for short), called the minimum block transfer problem. The objective of this problem is to find a partition of a node set which satisfies the following two conditions: (i) Each element (called a block) of the partition has a size that is at most B and (ii) the maximum number of external arcs among directed paths from the roots to the leaves is minimized. Here, an external arc is defined as an arc connecting two distinct blocks. This paper mainly studies the case B = 2 . First, we show that the problem is NP-hard even if the height of DAGs is three and its maximum indegree and outdegree are two and three, respectively. Then, we design (i) linear-time optimal algorithms for DAGs of height at most two, (ii) a very simple 2-approximation algorithm, and moreover, (iii) a ( 2 − 2 ∕ h ) -approximation algorithm for the case that the height h of the input DAG is even and the other one for odd h , whose approximation ratio is 2 − 2 ∕ ( h + 1 ) . As for the inapproximability of the problem, for any e > 0 and unless P = NP, we show that the problem does not admit any polynomial time ( 3 ∕ 2 − e ) -approximation ( ( 4 ∕ 3 − e ) -approximation, resp.) algorithm if the height of the input DAGs is restricted to at most five (at least six, resp.). Also, in the case B ≥ 3 , we show the NP-hardness and prove a ( 3 ∕ 2 − e ) -inapproximability of this case.

Given a vertex-colored arc-weighted directed acyclic graph G, the Maximum Colorful Subtree problem (or MCS ) aims at finding an arborescence of maximum weight in G, in which no color appears more than once. The problem was originally introduced in [1] in the context of de novo identification of metabolites by tandem mass spectrometry. However, a thorough analysis of the initial motivation shows that the formal definition of MCS should be amended, since the input graph G actually possesses extra properties, which have been unexploited so far. This leads us to describe in this paper a more precise model that we call Maximum Colorful Arborescence ( MCA ), which we extensively study in terms of algorithmic complexity. In particular, we show that exploiting the implied Color Hierarchy Graph of the input graph G can lead to exact polynomial algorithms and approximation algorithms. We also develop Fixed-Parameter Tractable ( FPT ) algorithms for the problem parameterized by the “dual parameter” l C , defined as the minimum number of vertices of G which are not kept in the solution.

Industrial structure can describe not only the structural relationships between industrial output capacities, but also the structural relationships between industrial economic outputs. Fixed-asset investment affects industrial structure through the formation of capital stock and contemporaneous demand. Based on VAR model, this paper utilizes Granger causality test and other econometric methods to analyze the hysteresis relationships between fixed-asset investment and industrial structure in China from 1991 to 2017. In addition, the contemporaneous relationships are identified by employing the Directed Acyclic Graph (DAG) analysis. The results show that: The hysteresis relationships exist in primary and secondary industries between fixed-asset investment and their respective value added. The fixed-asset investment in primary and tertiary industries are the contemporaneous causes of positive effect to the value added of primary industry. And the value added of secondary industry is the contemporaneous cause of positive effect to its fixed-asset investment.

Internet of Things (IoT) is a heterogeneous, mixed, and uncertain ubiquitous network, which has significantly affected the concept of wireless networking. A large number of wireless devices have connected through the IoT and shared large amounts of data. So, efficient routing and forwarding data packets from the wireless devices toward gateways, which have connected to the Internet, is one of the most important issues in IoT. This paper has focused on routing and forwarding data packets in IoT. Firstly, a learning automata-based cognitive framework has been applied to integrate cognition into IoT; because current IoT lacks intelligence and cannot satisfy the increasing application performance requirements, and also adding cognition into IoT equips it with a brain and high level intelligence. Then, a new routing and forwarding protocol, which benefits from cross-layer optimization between routing and Media Access Control (MAC) layer protocols, has been proposed. In the proposed protocol a network of variable action-set learning automata establishes a route between source nodes and a corresponding gateway, by making a directed acyclic graph toward the gateway. Then, using a set of learning automata, MAC layer protocol parameters are configured to properly forward data packets hop by hop. The proposed protocol has been named VLA-CR (Variable Action-set Learning Automata-based Cognitive Routing Protocol). Based on Martingale theorem, the convergence of VLA-CR has been proved. Finally, extensive simulation experiments have been conducted to show the performance of the proposed protocol. Simulation results show the superiority of VLA-CR over several existing routing protocol in terms of end-to-end reliability, end-to-end delay, power consumption, and routing time.

Identification of stacked retail products from the images of racks of supermarket is a challenging computer vision problem. Regions with convolutional neural network features (R-CNN) generate (mostly overlapped) region proposals around the products on the rack. Subsequently, the region proposals are classified using a convolutional neural network. In the end, R-CNN implements a greedy non-maximal suppression (greedy-NMS) for disambiguating the overlapping proposals. Greedy-NMS discards the proposals (with lower classification scores) that are overlapped with the proposal with higher classification score. This greedy approach often eliminates the (geometrically) better fitted region proposals with (marginally) lower classification scores. This paper introduces a novel graph-based non-maximal suppression (G-NMS) that removes this critical bottleneck of greedy-NMS by looking not only at the classification scores but also at the product classes of the overlapping region proposals. G-NMS first determines the potential confidence scores (pc-scores) of the region proposals by defining the groups of overlapping regions. Subsequently, a directed acyclic graph (DAG) is strategically constructed with the proposals utilizing their pc-scores and overlapping groups. Eventually the maximum weighted path of the DAG provides the products that are present in the rack. The results of our extensive experiments confirm that the proposed scheme is better up to around 7% on one large In-house and three benchmark datasets of retail products. Additionally, the efficacy of our proposed GNMS is also analyzed on four benchmark datasets for detecting generic objects.

Some microfluidic lab-on-chip devices contain modules whose function is to mix two fluids, called reactant and buffer, in desired proportions. In one of the technologies for fluid mixing the process can be represented by a directed acyclic graph whose nodes represent micro-mixers and edges represent micro-channels. A micro-mixer has two input channels and two output channels; it receives two fluid droplets, one from each input, mixes them perfectly, and produces two droplets of the mixed fluid on its output channels. Such a mixing graph converts a set I of input droplets into a set T of output droplets, where the droplets are specified by their reactant concentrations. The most fundamental algorithmic question related to mixing graphs is to determine, given an input set I and a target set T, whether there is a mixing graph that converts I into T. We refer to this decision problem as mix-reachability. While the complexity of this problem remains open, we provide a solution to its natural sub-problem, called perfect mixability, in which we ask whether, given a collection C of droplets, there is a mixing graph that mixes C perfectly, producing only droplets whose concentration is the average concentration of C. We provide a complete characterization of such perfectly mixable sets and an efficient algorithm for testing perfect mixability. Further, we prove that any perfectly mixable set has a perfect-mixing graph of polynomial size, and that this graph can be computed in polynomial time., NSF grant CCF-1536026

With an increase in the number of devices involved in the Industrial Internet, effectively combining the characteristics of industrial scenarios with an edge computing methodology for computation-intensive applications poses a critical challenge. This paper proposes an integrated architecture that allows industrial devices to offload tasks to cloud or edge servers. An offloading problem is also formulated into an energy-cost (EC) minimization problem while satisfying the deadline constraint. To solve the optimization problem, two types of offloading algorithms, namely ASO and Pro-ITGO, are proposed based on the integrated architecture. The ASO algorithm is a lightweight linear programming algorithm that includes subdeadline allocation, topology sorting, and task offloading sub-algorithms. The Pro-ITGO algorithm is a group intelligence heuristic algorithm that is derived from the original ITGO algorithm adapting the offloading scenarios of the Industrial Internet. Experimental results demonstrate that compared with state-of-the-art heuristic algorithms, the proposed algorithms can effectively reduce the energy consumption of industrial devices and cloud computing costs.

Root cause diagnosis is an important step in process monitoring, which aims to identify the sources of process disturbances. The primary challenge is that process disturbances propagate between different operating units because of the flow of material and information. Data-driven causality analysis techniques, such as Granger causality (GC) test, have been widely adopted to construct process causal maps for root cause diagnosis. However, the generated causal map is over-complicated and difficult to interpret because of the existence of process loops and the violation of statistical assumptions. In this work, a two-step procedure is proposed to solve this problem. First, a causal map is built by adopting the conditional GC analysis, which is viewed as a graph in the next step. In this graph, each vertex corresponds to a process variable under investigation, while the weight of the edge connecting two vertices is the F-value calculated by conditional GC. This graph is then simplified by computing its maximum spanning tree. Thus, the results of the causality analysis are transformed into a directed acyclic graph, which eliminates all loops, highlights the root cause variable, and facilitates the diagnosis. The feasibility of this method is illustrated with the application to the Tennessee Eastman benchmark process. In the investigated case studies, the proposed method outperforms the conditional GC test and provides an easy way to identify the root cause of process disturbances.

Objectives Subgroup analyses of clinical trial data can be an important tool for understanding when treatment effects differ across populations. That said, even effect estimates from prespecified subgroups in well-conducted trials may not apply to corresponding subgroups in the source population. While this divergence may simply reflect statistical imprecision, there has been less discussion of systematic or structural sources of misleading subgroup estimates. Study Design and Setting We use directed acyclic graphs to show how selection bias caused by associations between effect measure modifiers and trial selection, whether explicit (e.g., eligibility criteria) or implicit (e.g., self-selection based on race), can result in subgroup estimates that do not correspond to subgroup effects in the source population. To demonstrate this point, we provide a hypothetical example illustrating the sorts of erroneous conclusions that can result, as well as their potential consequences. We also provide a tool for readers to explore additional cases. Conclusion Treating subgroups within a trial essentially as random samples of the corresponding subgroups in the wider population can be misleading, even when analyses are conducted rigorously and all findings are internally valid. Researchers should carefully examine associations between (and consider adjusting for) variables when attempting to identify heterogeneous treatment effects.

The vertex arboricity v a ( G ) of G is the smallest integer k which the acyclic partition of V ( G ) make the vertex set V ( G ) be partitioned into k subsets which each subset induces an acyclic graph. In this paper, we mainly study vertex arboricity of planar graphs, and we prove that if there is without 4-cycles intersecting with 6-cycles, then v a ( G ) ⩽ 2 .

In this paper, we present an incremental variant of the Twin Support Vector Machine (TWSVM) called Fuzzy Bounded Twin Support Vector Machine (FBTWSVM) to deal with large datasets and to learn from data streams. We combine the TWSVM with a fuzzy membership function, so that each input has a different contribution to each hyperplane in a binary classifier. To solve the pair of quadratic programming problems (QPPs), we use a dual coordinate descent algorithm with a shrinking strategy, and to obtain a robust classification with a fast training we propose the use of a Fourier Gaussian approximation function with our linear FBTWSVM. Inspired by the shrinking technique, the incremental algorithm re-utilizes part of the training method with some heuristics, while the decremental procedure is based on a scoring window. The FBTWSVM is also extended for multi-class problems by combining binary classifiers using a Directed Acyclic Graph (DAG) approach. Moreover, we analyzed the theoretical foundation’s properties of the proposed approach and its extension, and the experimental results on benchmark datasets indicate that the FBTWSVM has a fast training and retraining process while maintaining a robust classification performance.

We consider the problem of a maximum probabilistic all-or-nothing network path. Each arc is associated with a profit and a probability and the objective is to select a path with maximum value for the product of probabilities multiplied by the sum of arc profits. The problem can be motivated by applications including serial-system design or subcontracting of key project activities that may fail. When subcontracting such critical success activities, each must be completed on time, according to the specs, and in a satisfactory manner in order for the entire project to be deemed successful. We develop a dynamic programming (DP) method for this problem in the acyclic graph setting, under an independence assumption. Two different fully-polynomial approximation schemes are developed based on the DP formulations, one of which applies repeated rounding and scaling to the input data, while the other uses only rounding. In experiments we compare the DP approach with mixed-integer nonlinear programming (MINLP) using a branch-and-cut method, on synthetic randomly generated instances as well as realistic ones.

International audience; A cooperative game with transferable utility is a situation in which players can generate worth by cooperating and obtain a certain payoff via a sharing rule. In this paper we assume that the cooperation between players is restricted by an acyclic graph. We introduce a new sharing rule for this type of game. We also offer an axiomatization of this sharing rule, based mainly on linearity and a consistency axiom. For unanimity games, this sharing rule identifies the center of the graph.

In this paper, we present Prometheus, a graph partitioning based algorithm that creates multiple variable decompositions efficiently for learning Sum-Product Network structures across both continuous and discrete domains. Prometheus proceeds by creating multiple candidate decompositions that are represented compactly with an acyclic directed graph in which common parts of different decompositions are shared. It eliminates the correlation threshold hyperparameter often used in other structure learning techniques, allowing Prometheus to learn structures that are robust in low data regimes. Prometheus outperforms other structure learning techniques in 30 discrete and continuous domains. We also extend Prometheus to exploit sparsity in correlations between features in order to obtain an efficient sub-quadratic algorithm (w.r.t. the number of features) that scales better to high dimensional datasets.

This paper proves an abstract theorem addressing in a unified manner two important problems in function approximation: avoiding curse of dimensionality and estimating the degree of approximation for out-of-sample extension in manifold learning. We consider an abstract (shallow) network that includes, for example, neural networks, radial basis function networks, and kernels on data defined manifolds used for function approximation in various settings. A deep network is obtained by a composition of the shallow networks according to a directed acyclic graph, representing the architecture of the deep network. In this paper, we prove dimension independent bounds for approximation by shallow networks in the very general setting of what we have called G -networks on a compact metric measure space, where the notion of dimension is defined in terms of the cardinality of maximal distinguishable sets, generalizing the notion of dimension of a cube or a manifold. Our techniques give bounds that improve without saturation with the smoothness of the kernel involved in an integral representation of the target function. In the context of manifold learning, our bounds provide estimates on the degree of approximation for an out-of-sample extension of the target function to the ambient space. One consequence of our theorem is that without the requirement of robust parameter selection, deep networks using a non-smooth activation function such as the ReLU, do not provide any significant advantage over shallow networks in terms of the degree of approximation alone.

Task scheduling, which plays a vital role in cloud computing, is a critical factor that determines the performance of cloud computing. From the booming economy of information processing to the increasing need of quality of service (QoS) in the business of networking, the dynamic task-scheduling problem has attracted worldwide attention. Due to its complexity, task scheduling has been defined and classified as an NP-hard problem. Additionally, most dynamic online task scheduling often manages tasks in a complex environment, which makes it even more challenging to balance and satisfy the benefits of each aspect of cloud computing. In this paper, we propose a novel artificial intelligence algorithm, called deep Q-learning task scheduling (DQTS), that combines the advantages of the Q-learning algorithm and a deep neural network. This new approach is aimed at solving the problem of handling directed acyclic graph (DAG) tasks in a cloud computing environment. The essential idea of our approach uses the popular deep Q-learning (DQL) method in task scheduling, where fundamental model learning is primarily inspired by DQL. Based on developments in WorkflowSim, experiments are conducted that comparatively consider the variance of makespan and load balance in task scheduling. Both simulation and real-life experiments are conducted to verify the efficiency of optimization and learning abilities in DQTS. The result shows that when compared with several standard algorithms precoded in WorkflowSim, DQTS has advantages regarding learning ability, containment, and scalability. In this paper, we have successfully developed a new method for task scheduling in cloud computing.

Temporally Ordered Routing Algorithms (TORA) is one of the most representative on-demand routing protocols in Mobile Ad Hoc Networks (MANET). This protocol is widely used in high-speed mobile MANET because of its robust topology. In order to improve the shortcomings of TORA in routing maintenance, such as high overhead and delay, and make the routing more suitable for emergency and disaster relief network, an adaptive repair algorithm for TORA routing protocol based on flood control strategy (AR-TORA-FCS) is proposed. Firstly, according to the characteristics of the uniform deployment of the nodes in the network, the self-repair process of the self-repair nodes in the directed acyclic graph (DAG) of TORA is transformed into the optimal search problem for the optimal nodes, and the formula is established. According to Ray-Algorithm to search for the optimal node, it is proved that the search result is the optimal solution of the process of searching for the optimal node. Then, a conditional algorithm to determine the self-repair process is given, and the conditional threshold to initiate the self-repair process is determined. The mapping relationship between the repair process of self-repair nodes and the distance between the nodes is established, and the path repair is carried out before the path fails. In order to reduce control overhead, the definition of optimization region is given, and the algorithm to determine the optimization region is proposed. Simulation results show that the algorithm reduces control overhead, improves the packet delivery rate, and improves average end-to-end delay. The mobile device, which is subject to unified deployment, is used as a network node to test the proposed adaptive repair algorithm in the actual rescue and disaster relief environment. The results show that it is basically consistent with the simulation results, and the overall performance is improved significantly.

We study open-shop scheduling for unit jobs under precedence constraints, where if one job precedes another job then it has to be finished before the other job can start to be processed. For the three-machine open-shop to minimize the makespan, we first present a simple 5/3-approximation based on a partition of the job set into agreeable layers using the natural layered representation of the precedence graph. We then show a greedy algorithm to reduce the number of singleton-job layers, resulting in an improved partition, which leads to a 4/3-approximation. Both approximation algorithms apply to the general m-machine open-shops too.

Moving towards comprehensive digitalization of production facilities, it is critical to know the location of work pieces, charges, or other objects of interest that change location over time during production. For the case of a limited traceability of these objects, we first present a theoretical approach that performs a recursive Bayesian estimation of the object’s location over time based on typical passage measurements in production (e. g. light barriers or RFID systems). The probabilistic method is based on a directed acyclic graph modeling the transfer and sojourn of the objects in the production network. Subsequently, the method is validated on simulated data while varying both size and measurement conditions of the process. The results show the benefit of the proposed method against a single estimation and demonstrate its potential for the application in real time scenarios.

The flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem (JSP) in which operations can be performed by a set of candidate capable machines. An extended version of the FJSP, entitled sequencing flexibility, is studied in this work, which considers precedence between the operations in the form of a directed acyclic graph instead of a sequential order. In this work, a mixed integer linear programming (MILP) formulation is presented to minimize weighted tardiness for the FJSP with sequencing flexibility. Due to the NP-hardness of the problem, a novel biomimicry hybrid bacterial foraging optimization algorithm (HBFOA) is developed, which is inspired by the behavior of E. coli bacteria in its search for food. The developed HBFOA search method is hybridized with simulated annealing (SA). Additionally, the algorithm has been enhanced by a local search method based on the manipulation of critical operations. Classical dispatching rules have been employed to create the initial swarm of HBFOA, and a new dispatching rule named minimum number of operations has been devised. The developed approach has been packaged in the form of a decision support system (DSS) developed on top of Microsoft Excel—a tool most small and mid-range enterprises (SME) use heavily for planning. A case study with local industry is presented to validate the proposed HBFOA and MILP. Additional numerical experiments using literature benchmarks are further used for validation. The results demonstrate that the HBFOA outperformed the classical dispatching rules and the best integer solution of MILP when minimizing the weighted tardiness and offered comparable results for the makespan instances.

Data and rules power expert systems and intelligent systems. Rules, as a form of knowledge representation, can be acquired by experts or learned from data. The accuracy and precision of knowledge largely determines the success of the systems, which awakens the concern for causality. The ability to elicit cause–effect rules directly from data is key and difficult to any expert systems and intelligent systems. Rough set theory has succeeded in automatically transforming data into knowledge, where data are often presented as an attribute-value table. However, the existing tools in this theory are currently incapable of interpreting counterfactuals and interventions involved in causal analysis. This paper offers an attempt to characterize the cause–effect relationships between attributes in attribute-value tables with intent to overcome existing limitations. First, we establish the main conditions that attributes need to satisfy in order to estimate the causal effects between them, by employing the back-door criterion and the adjustment formula for a directed acyclic graph. In particular, based on the notion of lower approximation, we extend the back-door criterion to an original data table without any graphical structures. We then identify the effects of the interventions and the counterfactual interpretation of causation between attributes in such tables. Through illustrative studies completed for some attribute-value tables, we show the procedure for identifying the causation between attributes and examine whether the dependency of the attributes can describe causality between them.

We study the allocation problem of a compound request for a service chain in a software defined network that supports network function virtualization. Given a network that contains servers with limited processing power and links with limited bandwidth, a service chain is a sequence of virtual network functions (VNFs) that serve a certain flow request in the network. The allocation of a service chain consists of routing and VNF placement, namely each VNF from the sequence is placed in a server along a path. It is feasible if each server can handle the VNFs that are assigned to it, and if each link on the path can carry the flow that is assigned to it. A request for service is composed of a source and a destination in the network, an upper bound on the total latency, and a specification in the form of a directed acyclic graph (DAG) of VNFs that provides all service chains that are considered valid for this request. In addition, each pair of server and VNF is associated with a cost for placing the VNF in the server. Given a request, the goal is to find a valid service chain of minimum total cost that respects the latency constraint or to identify that such a service chain does not exist. We show that even the feasibility problem is NP-hard in general graphs. Hence we focus on DAGs. We show that the problem is still NP-hard in DAGs even for a very simple network, and even if the VNF specification consists of only one option (i.e., the virtual DAG is a path). On the other hand, we present an FPTAS for the case where the network is a DAG. In addition, based on our FPTAS, we provide algorithms for general instances in which the service chain passes through a bounded number of vertices whose degree is larger than two. Finally, we provide an FPTAS for a fault-tolerant version of the problem.

Many rail terminals have loading areas that are properly equipped to move containers between trains. With the growing throughput of these terminals all the trains involved in a sequence of such movements may not ¿t in the loading area simultaneously, and storage areas are needed to place containers waiting for their destination train, although this storage increases the cost of the transshipment. This increases the complexity of the planning decisions concerning these activities, since now trains need to be packed in groups that ¿t in the loading area, in such a way that the number of containers moved to the storage area is minimized. Additionally, each train is only allowed to enter the loading area once. Similarly to previous authors, we model this situation as an acyclic graph partitioning problem for which we present a new formulation, and several valid inequalities based on its theoretical properties. Our computational experiments show that the new formulation outperforms the previously existing ones, providing results that improve even on the best exact algorithm designed so far for this problem.

An oriented graph D is an orientation of a simple graph, i.e. a directed graph whose underlying graph is simple. A directed path from u to v with minimum number of arcs in D is an (u, v)-geodesic, for every u, v ∈ V(D). A set S ⊆ V(D) is (geodesically) convex if, for every u, v ∈ S, all the vertices in each (u, v)-geodesic and in each (v, u)-geodesic are in S. For every S ⊆ V(D) the (convex) hull of S is the smallest convex set containing S and it is denoted by [S]. A hull set of D is a set S ⊆ V(D) whose hull is V(D). The cardinality of a minimum hull set is the hull number of D and it is denoted by h n → ( D ) . A geodetic set of D is a set S ⊆ V(D) such that each vertex of D lies in an (u, v)-geodesic, for some u, v ∈ S. The cardinality of a minimum geodetic set is the geodetic number of D and it is denoted by g n → ( D ) . In this work, we first present an upper bound for the hull number of oriented split graphs. Then, we turn our attention to the computational complexity of determining such parameters. We first show that computing h n → ( D ) is NP-hard for partial cubes, a subclass of bipartite graphs, and that computing g n → ( D ) is also NP-hard for directed acyclic graphs (DAG). Finally, we present a positive result by showing how to compute such parameters in polynomial time when the input graph is an oriented cactus.

Background Distinguishing between pharmacological and residual effects, this paper considers the problem of causal assessment in the case of a particular model, namely a Sure Outcome of Random Events (SORE) model developed for the analysis of data from a randomized placebo-controlled double-blind trial of a drug. Method This model takes into account two kinds of observable effects, a therapeutic effect and a side-effect. For each observable effect, two latent factors are considered, i.e. a pharmacological (or explained) factor and a residual (or unexplained) one. Results The model presents a plausible mechanism generating the observed and latent outcomes, recursively decomposed into an ordered sequence of sub-mechanisms. Conclusions The characteristics of this model leads to a novel assessment of causality that evaluates the effect of latent variables and of the bias resulting from ignoring the structural features of the data generating process. This approach is illustrated by a numerical example, along with a case study based on a secondary analysis of real data.

Analytic queries are typically compiled into execution plans in the form of directed acyclic graphs (DAGs) of MapReduce jobs. Jobs in the DAGs are dispatched to the MapReduce processing engine as soon as their dependencies are satisfied. MapReduce adopts a job-level scheduling policy to strive for a balanced distribution of tasks and effective utilization of resources. However, such simplistic policy is unable to reconcile the dynamics of different jobs in complex analytic queries, resulting in unfair treatment of different queries, low utilization of system resources, prolonged execution time, and low query throughput. Therefore, we introduce a scheduling framework to address these problems systematically. Our framework includes two techniques: multivariate DAG modeling and two-level query scheduling. Cross-layer semantics percolation allows the flow of query semantics and job dependencies in the DAG to the MapReduce scheduler. With richer semantics information, we build a multivariate model that can accurately predict the execution time of individual MapReduce jobs and gauge the changing size of analytics datasets through selectivity approximation. Furthermore, we introduce two-level query scheduling that can maximize the intra-query job-level concurrency, and at the same time speed up the query-level completion time based on the accurate prediction and queuing of queries. At the job level, we focus on detecting query semantics, predicting the query completion time through an online multivariate linear regression model, thereby increasing job-level parallelism and maximizing data sharing across jobs. At the task level, we focus on balanced data distribution, maximal slot utilization, and optimal data locality of task scheduling. Our experimental results on a set of complex query benchmarks demonstrate that our scheduling framework can significantly improve both fairness and throughput of Hive queries. It can improve query response time by up to 43.9% and 72.8% on average, compared to the Hadoop Fair Scheduling and the Hadoop Capacity Scheduling, respectively. In addition, our two-level scheduler can achieve a query fairness that is, on average, 59.8% better than that of the Hadoop Fair Scheduler.

Cloud services utilize Heterogeneous Clusters as the hardware infrastructure at the backend. Minimal energy consumption in Heterogeneous Cluster System (HCS) is an important but challenging job. It can bring numerous benefits such as drop in operational cost, enhanced system reliability and green environment. Scheduling on HCS, with the objectives of minimizing the energy consumption, is being addressed by the research community at large. This work proposes a scheduling algorithm with green Service Level Agreement (SLA) constrained execution of parallel applications. The green SLA assumes that the tasks are to be scheduled on Dynamic Voltage Frequency Scaling (DVFS) enabled HCS. The proposed algorithm acts in two phases: first, it minimizes the energy consumption for the slacks of the schedule using DVFS technique, and second, a green SLA is made between a customer and service provider to maintain a good energy-performance trade-off. With this strategy, makespan of the schedule is extended a bit but the energy consumption is minimized for the period of extended makespan. It is observed that the decrease in one level of voltage and frequency of high-speed Processing Element (PE) saves more energy compared to that of low-speed PE. To utilize this, jobs running on higher voltage and frequency level of the PE are prioritized first. The performance of the proposed algorithm is studied by simulation on several standard Directed Acyclic Graphs (DAGs) and few other well-known real-world scientific workflows. The comparative study exhibits the effectiveness of the proposed algorithm over state of the art on four real heterogeneous PEs.

For real-world civil infrastructure systems that consist of a large number of functionally and statistically dependent components, such as transportation systems or water distribution networks, the Bayesian Network (BN) can be a powerful tool for probabilistic inference. In a BN, the statistical relationship between multiple random variables (r.v.’s) is modeled through a directed acyclic graph. The complexity of inference in the BN depends not only on the number of r.v.’s, but also the graphical structure. As a consequence, the application of standard BN techniques may become infeasible even with a moderate number of r.v.’s as the size of an event set exponentially increases with the number of r.v.’s. Moreover, when the exhaustive set that is required for full quantification of a discrete BN node becomes intractably large, only approximate inference algorithms are feasible, which do not require the full (explicit) description of all BN nodes. We address both issues in discrete BNs by proposing a matrix-based Bayesian Network (MBN) that facilitates efficient modeling of joint probability mass functions and flexible inference. The MBN is developed for exact as well as approximate BN inference. The efficiency and applicability of the MBN are demonstrated by numerical examples. The supporting source code and data are available for download at https://github.com/jieunbyun/GitHub-MBN-code .

Directed acyclic graphs (DAGs) widely exist in natural biological, industrial, and social networked systems. This brief explores the effects of adding a reverse edge, across a so-called stem, in a DAG on consensus performance. In particular, it quantitatively reveals the effects in terms of the in-degrees of the surpassed stem nodes. The study further enriches the existing results on special chain and grid networks by accommodating more general network topologies. From the application perspective, this brief provides a guidance for an attacking (or conversely anti-attacking) strategy of injecting the most effective malicious reverse edge. It has other potential applications in regulating DAG network convergence performance with reverse edges.

Background Child maltreatment research involves modeling complex relationships between multiple interrelated variables. Directed acyclic graphs (DAGs) are one tool child maltreatment researchers can use to think through relationships among the variables operative in a causal research question and to make decisions about the optimal analytic strategy to minimize potential sources of bias. Objective The purpose of this paper is to highlight the utility of DAGs for child maltreatment research and to provide a practical resource to facilitate and support the use of DAGs in child maltreatment research. Results We first provide an overview of DAG terminology and concepts relevant to child maltreatment research. We describe DAG construction and define specific types of variables within the context of DAGs including confounders, mediators, and colliders, detailing the manner in which each type of variable can be used to inform study design and analysis. We then describe four specific scenarios in which DAGs may yield valuable insights for child maltreatment research: (1) identifying covariates to include in multivariable models to adjust for confounding; (2) identifying unintended effects of adjusting for a mediator; (3) identifying unintended effects of adjusting for multiple types of maltreatment; and (4) identifying potential selection bias in data specific to children involved in the child welfare system. Conclusions Overall, DAGs have the potential to help strengthen and advance the child maltreatment research and practice agenda by increasing transparency about assumptions, illuminating potential sources of bias, and enhancing the interpretability of results for translation to evidence-based practice.

Use of graph theory for enumeration of Epicyclic gear trains (EGTs) is common during conceptual stage. According to theory of structural synthesis of EGTs, two kinds of graphs are defined namely rotation and displacement graphs, for a given number of links and one degree of freedom. In case, all the non-isomorphic rotation graphs are enumerated, then the next stage of synthesis involves the generation of displacement graphs for each rotation graph. To this end, given a rotation graph, the present work proposes an algorithm for generation of all the displacement graphs. Firstly, the rotation graph is decomposed into modules called kinematic units (KUs). Then, for each KU, all the edge-labeling possibilities of turning pairs are evaluated. Finally, displacement graphs are obtained by building the edge labeled KUs in all possible ways. Acyclic graph based representation is employed and displacement graphs with and up to 7 links are enumerated. The enumeration of displacement graphs is treated as two different cases corresponding to rotation graphs enumerated using recursive and non-recursive schemes and the results are in agreement with C.H. Hsu and others.