Incoming Edges Research Articles

On two-variable guarded fragment logic with expressive local Presburger constraints

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges" and captures various description logics with counting, but without constant symbols. We show that the satisfiability problem for this logic is EXP-complete. While the lower bound already holds for the standard two-variable guarded fragment logic, the upper bound is established by a novel, yet simple deterministic graph-based algorithm.

Communication-Efficient Multi-Party Computation for RMS Programs

Despite much progress, general-purpose secure multi-party computation (MPC) with active security may still be prohibitively expensive in settings with large input datasets. This particularly applies to the secure evaluation of graph algorithms, where each party holds a subset of a large graph. Recently, Araki et al. (ACM CCS '21) showed that dedicated solutions may provide significantly better efficiency if the input graph is sparse. In particular, they provide an efficient protocol for the secure evaluation of “message passing” algorithms, such as the PageRank algorithm. Their protocol's computation and communication complexity are both O ~ ( M · B ) instead of the O ( M 2 ) complexity achieved by general-purpose MPC protocols, where M denotes the number of nodes and B the (average) number of incoming edges per node. On the downside, their approach achieves only a relatively weak security notion; 1 -out-of- 3 malicious security with selective abort. In this work, we show that PageRank can instead be captured efficiently as a restricted multiplication straight-line (RMS) program, and present a new actively secure MPC protocol tailored to handle RMS programs. In particular, we show that the local knowledge of the participants can be leveraged towards the first maliciously-secure protocol with communication complexity linear in M , independently of the sparsity of the graph. We present two variants of our protocol. In our communication-optimized protocol, going from semi-honest to malicious security only introduces a small communication overhead, but results in quadratic computation complexity O ( M 2 ) . In our balanced protocol, we still achieve a linear communication complexity O ( M ) , although with worse constants, but a significantly better computational complexity scaling with O ( M · B ) . Additionally, our protocols achieve security with identifiable abort and can tolerate up to n − 1 corruptions.

Partially broken orientations of Eulerian graphs on closed surfaces

In this paper, we discuss orientations given to edges of Eulerian graphs embedded on closed surfaces, and give a characterization of such a graph having a good orientation, i.e., incoming edges and outgoing edges appear alternately around each vertex of the graph. Furthermore, we consider the partially broken orientations of Eulerian graphs embedded on closed surfaces, that is, one in which only for each of specified vertices, incoming edges and outgoing edges appear alternately around it. We discuss a little about good orientations defined for Eulerian graphs drawn on closed surfaces with crossings, and for general connected graphs, i.e., not necessarily Eulerian graphs, embedded on closed surfaces.

Coverings of Graphoids: Existence Theorem and Decomposition Theorems

A graphoid is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each vertex, the mapping restricts to a local bijection on incoming edges and outgoing edges. Naturally, as it appears, this definition displays unusual behaviour since the projection of the corresponding underlying graphs is not necessarily a graph covering. Yet, it is still possible to grasp such coverings algebraically in terms of the action of the fundamental monoid and combinatorially in terms of voltage assignments on arcs. In the present paper, the existence theorem is formulated and proved in terms of the action of the fundamental monoid. A more conventional formulation in terms of the weak fundamental group is possible because the action of the fundamental monoid is permutational. The standard formulation in terms of the fundamental group holds for a restricted class of coverings, called homogeneous. Further, the existence of the universal covering and the problems related to decomposing regular coverings via regular coverings are studied in detail. It is shown that with mild adjustments in the formulation, all the analogous theorems that hold in the context of graphs are still valid in this wider setting.

Predicting Drug-drug Interaction with Graph Mutual Interaction Attention Mechanism

Effective representation of molecules is a crucial step in AI-driven drug design and drug discovery, especially for drug-drug interaction (DDIs) prediction. Previous work usually models the drug information from the drug-related knowledge graph or the single drug molecules, but the interaction information between molecular substructures of drug pair is seldom considered, thus often ignoring the influence of bond information on atom node representation, leading to insufficient drug representation. Moreover, key molecular substructures have significant contribution to the DDIs prediction results. Therefore, in this work, we propose a novel Graph learning framework of Mutual Interaction Attention mechanism (called GMIA) to predict DDIs by effectively representing the drug molecules. Specifically, we build the node-edge message communication encoder to aggregate atom node and the incoming edge information for atom node representation and design the mutual interaction attention decoder to capture the mutual interaction context between molecular graphs of drug pairs. GMIA can bridge the gap between two encoders for the single drug molecules by attention mechanism. We also design a co-attention matrix to analyze the significance of different-size substructures obtained from the encoder-decoder layer and provide interpretability. In comparison with other recent state-of-the-art methods, our GMIA achieves the best results in terms of area under the precision-recall-curve (AUPR), area under the ROC curve (AUC), and F1 score on two different scale datasets. The case study indicates that our GMIA can detect the key substructure for potential DDIs, demonstrating the enhanced performance and interpretation ability of GMIA.

Unsupervised technical phrase extraction by incorporating structure and position information

The vigorous development of patent applications in recent years provides an opportunity to unveil the inherent laws of innovation, but it also puts forward higher requirements for patent mining technology. An essential step for patent text mining is to establish a technology portrait for each patent, that is, identify the technical phrases involved, which can be summarized and represented by the patent from the technical point of view. Currently, there is a large body of work focusing on keyword extraction. However, technical phrase extraction differs from keyword extraction due to the unique properties of technical phrases. Specifically, technical phrases must contain rich technical information and are essential to the entire patent text from a technical perspective. Meanwhile, finding potential relationships between phrases with different technical meanings is challenging for technical phrase extraction. Based on the analysis of the characteristics of technical phrases, we found that the position of technical phrases in the patent text and the structural relationship between technical phrases are crucial, and how to make good use of these two pieces of information is a challenge. Motivated by this, we propose a new Unsupervised Technical phrase Extraction model from the Structure and Position information perspective, named UTESP. Specifically, UTESP includes four key steps: candidate generation, graph construction, candidate score, and candidate selection. The structure information refers to adjusting the incoming edge weight of candidate phrases through the distance relations between candidate phrases and applying the graph ranking algorithm to obtain the structure score of the candidate phrase. The position information simultaneously incorporates the position and frequency of candidate phrases in the patent text to calculate a position score for candidate technical phrases. The effectiveness of our framework has been demonstrated by comparing with seven competitive algorithms on the patent datasets in terms of three evaluation metrics: Precision, Recall, and F1 scores. Besides, our new framework indicated significant improvements in the representation ability of technical phrases by comparing Information Retrieval Efficiency (IRE) with competitive algorithms.

Conservative trees

The conservative number of a graph G is the minimum M such that G admits an orientation and a labeling of its edges with distinct numbers in {1,2,…,M} so that at each vertex of degree at least three, the sum of the labels of the incoming edges minus the sum of the labels of the outgoing edges is zero. A graph is conservative if its conservative number and its size are equal.In this work we determine the conservative number of several classes of trees and study the relation between conservative trees and graceful cycles with chords. We also show that for a given size of its base cycle, shell-type graphs with the maximum number of consecutive 4-faces are graceful.

Improving Envy Freeness up to Any Good Guarantees Through Rainbow Cycle Number

We study the problem of fairly allocating a set of indivisible goods among n agents with additive valuations. Envy freeness up to any good (EFX) is arguably the most compelling fairness notion in this context. However, the existence of an EFX allocation has not been settled and is one of the most important problems in fair division. Toward resolving this question, many impressive results show the existence of its relaxations. In particular, it is known that 0.618-EFX allocations exist and that EFX allocation exists if we do not allocate at most (n-1) goods. Reducing the number of unallocated goods has emerged as a systematic way to tackle the main question. For example, follow-up works on three- and four-agents cases, respectively, allocated two more unallocated goods through an involved procedure. In this paper, we study the general case and achieve sublinear numbers of unallocated goods. Through a new approach, we show that for every [Formula: see text], there always exists a [Formula: see text]-EFX allocation with sublinear number of unallocated goods and high Nash welfare. For this, we reduce the EFX problem to a novel problem in extremal graph theory. We define the notion of rainbow cycle number [Formula: see text] in directed graphs. For all [Formula: see text] is the largest k such that there exists a k-partite graph [Formula: see text], in which each part has at most d vertices (i.e., [Formula: see text] for all [Formula: see text]); for any two parts Vi and Vj, each vertex in Vi has an incoming edge from some vertex in Vj and vice versa; and there exists no cycle in G that contains at most one vertex from each part. We show that any upper bound on [Formula: see text] directly translates to a sublinear bound on the number of unallocated goods. We establish a polynomial upper bound on [Formula: see text], yielding our main result. Furthermore, our approach is constructive, which also gives a polynomial-time algorithm for finding such an allocation. Funding: J. Garg was supported by the Directorate for Computer and Information Science and Engineering [Grant CCF-1942321]. R. Mehta was supported by the Directorate for Computer and Information Science and Engineering [Grant CCF-1750436].

Sexual abuse and psychotic phenomena: a directed acyclic graph analysis of affective symptoms using English national psychiatric survey data.

Sexual abuse and bullying are associated with poor mental health in adulthood. We previously established a clear relationship between bullying and symptoms of psychosis. Similarly, we would expect sexual abuse to be linked to the emergence of psychotic symptoms, through effects on negative affect. We analysed English data from the Adult Psychiatric Morbidity Surveys, carried out in 2007 (N = 5954) and 2014 (N = 5946), based on representative national samples living in private households. We used probabilistic graphical models represented by directed acyclic graphs (DAGs). We obtained measures of persecutory ideation and auditory hallucinosis from the Psychosis Screening Questionnaire, and identified affective symptoms using the Clinical Interview Schedule. We included cannabis consumption and sex as they may determine the relationship between symptoms. We constrained incoming edges to sexual abuse and bullying to respect temporality. In the DAG analyses, contrary to our expectations, paranoia appeared early in the cascade of relationships, close to the abuse variables, and generally lying upstream of affective symptoms. Paranoia was consistently directly antecedent to hallucinations, but also indirectly so, via non-psychotic symptoms. Hallucinosis was also the endpoint of pathways involving non-psychotic symptoms. Via worry, sexual abuse and bullying appear to drive a range of affective symptoms, and in some people, these may encourage the emergence of hallucinations. The link between adverse experiences and paranoia is much more direct. These findings have implications for managing distressing outcomes. In particular, worry may be a salient target for intervention in psychosis.

Recursive State Machine Guided Graph Folding for Context-Free Language Reachability

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.

Nonabelian flows in networks

AbstractIn this work we consider a generalization of graph flows. A graph flow is, in its simplest formulation, a labelling of the directed edges with real numbers subject to various constraints. A common constraint is conservation in a vertex, meaning that the sum of the labels on the incoming edges of this vertex equals the sum of those on the outgoing edges. One easy fact is that if a flow is conserving in all but one vertex, then it is also conserving in the remaining one. In our generalization we do not label the edges with real numbers, but with elements from an arbitrary group, where this fact becomes false in general. As we will show, graphs with the property that conservation of a flow in all but one vertex implies conservation in all vertices are precisely the planar graphs.

Optimal Routing of Unmanned Aerial Vehicle for Joint Goods Delivery and in-Situ Sensing

This paper puts forth a new application of an unmanned aerial vehicle (UAV) to joint goods delivery and in-situ sensing, and proposes a new algorithm that jointly optimizes the route and sensing task selection to minimize the UAV’s energy consumption, maximize its sensing reward, and ensure timely goods delivery. This problem is new and non-trivial due to its nature of mixed integer programming. The key idea behind the new algorithm is that we interpret the possible waypoints of the UAV as location-dependent tasks to incorporate routing and sensing in one task selection process. Another critical aspect is that we construct a new task-time graph to describe the process, where each vertex corresponds to a task associated with its location, time and reward, and each edge indicates the propulsion energy required for the UAV to travel between two tasks. By redistributing the weight of a vertex to its incoming edges, the new UAV routing and sensing task selection problem can be converted to a weighted routing problem in the new task-time graph and solved optimally using the Bellman-Ford algorithm. Validated by a real-world case study, our approach can outperform its alternatives by over 18% in task reward.

Enhanced electroencephalography effective connectivity in frontal low-gamma band correlates of emotional regulation after mindfulness training.

Practicing mindfulness, focusing attention on the internal and external experiences occurring in the present moment with open and nonjudgement stance, can lead to the development of emotional regulation skills. Yet, the effective connectivity of brain regions during mindfulness has been largely unexplored. Studies have shown that mindfulness practice promotes functional connectivity in practitioners, potentially due to improved emotional regulation abilities and increased connectivity in the lateral prefrontal areas. To examine the changes in effective connectivity due to mindfulness training, we analyzed electroencephalogram (EEG) signals taken before and after mindfulness training, focusing on training-related effective connectivity changes in the frontal area. The mindfulness training group participated in an 8-week mindfulness-based stress reduction (MBSR) program. The control group did not take part. Regardless of the specific mindfulness practice used, low-gamma band effective connectivity increased globally after the mindfulness training. High-beta band effective connectivity increased globally only during Breathing. Moreover, relatively higher outgoing effective connectivity strength was seen during Resting and Breathing and Body-scan. By analyzing the changes in outgoing and incoming connectivity edges, both F7 and F8 exhibited strong parietal connectivity during Resting and Breathing. Multiple regression analysis revealed that the changes in effective connectivity of the right lateral prefrontal area predicted mindfulness and emotional regulation abilities. These results partially support the theory that the lateral prefrontal areas have top-down modulatory control, as these areas have high outflow effective connectivity, implying that mindfulness training cultivates better emotional regulation.

Node Importance Recognition Algorithm Based on the Correlation Degree Transmission Contribution Matrix

Based on the importance identification of nodes in a directed weighted network, a node importance recognition algorithm based on the correlation transmission contribution matrix is proposed. The proposed algorithm comprehensively considers the transmission ability of nodes, the correlation degree between nodes and adjacent nodes or indirectly related nodes, and the contribution degree between nodes to construct the correlation degree transmission contribution matrix. This paper combined the algorithm with the node efficiency of the local range of node importance and finally combined it with the global importance index intermediary number centrality to comprehensively evaluate the importance of nodes in the network. For the nodes with only incoming edges in the network, the product of the node mediator centrality and the correlation degree contribution matrix is calculated as the node importance. For nodes with only outgoing edges in the network, the product of node mediator centrality, degree value and node self-efficiency is calculated as node importance. Conducting experimental simulation analysis of the ARPA directed-weighted networks shows that the deliberate attack based on the algorithm results hits the network more obviously, which further proves the effectiveness and accuracy of the proposed algorithm.

Functional Resilience of Mutually Repressing Motifs Embedded in Larger Networks.

Elucidating the design principles of regulatory networks driving cellular decision-making has important implications for understanding cell differentiation and guiding the design of synthetic circuits. Mutually repressing feedback loops between 'master regulators' of cell fates can exhibit multistable dynamics enabling "single-positive" phenotypes: (high A, low B) and (low A, high B) for a toggle switch, and (high A, low B, low C), (low A, high B, low C) and (low A, low B, high C) for a toggle triad. However, the dynamics of these two motifs have been interrogated in isolation in silico, but in vitro and in vivo, they often operate while embedded in larger regulatory networks. Here, we embed these motifs in complex larger networks of varying sizes and connectivity to identify hallmarks under which these motifs maintain their canonical dynamical behavior. We show that an increased number of incoming edges onto a motif leads to a decay in their canonical stand-alone behaviors. We also show that this decay can be exacerbated by adding self-inhibition but not self-activation loops on the 'master regulators'. These observations offer insights into the design principles of biological networks containing these motifs and can help devise optimal strategies for the integration of these motifs into larger synthetic networks.

A Weighted and Normalized Gould-Fernandez brokerage measure.

The Gould and Fernandez local brokerage measure defines brokering roles based on the group membership of the nodes from the incoming and outgoing edges. This paper extends on this brokerage measure to account for weighted edges and introduces the Weighted-Normalized Gould-Fernandez measure (WNGF). The value added of this new measure is demonstrated empirically with both a macro level trade network and a micro level organization network. The measure is first applied to the EUREGIO inter-regional trade dataset and then to an organizational network in a research and development (R&D) group. The results gained from the WNGF measure are compared to those from two dichotomized networks: a threshold and a multiscale backbone network. The results show that the WNGF generates valid results, consistent with those of the dichotomized network. In addition, it provides the following advantages: (i) it ensures information retention; (ii) since no alterations and decisions have to be made on how to dichotomize the network, the WNGF frees the user from the burden of making assumptions; (iii) it provides a nuanced understanding of each node's brokerage role. These advantages are of special importance when the role of less connected nodes is considered. The two empirical networks used here are for illustrative purposes. Possible applications of WNGF span beyond regional and organizational studies, and into all those contexts where retaining weights is important, for example by accounting for persisting or repeating edges compared to one-time interactions. WNGF can also be used to further analyze networks that measure how often people meet, talk, text, like, or retweet. WNGF makes a relevant methodological contribution as it offers a way to analyze brokerage in weighted, directed, and even complete graphs without information loss that can be used across disciplines and different type of networks.

Influence Maximization Revisited: Efficient Sampling with Bound Tightened

Given a social network G with n nodes and m edges, a positive integer k , and a cascade model C , the influence maximization (IM) problem asks for k nodes in G such that the expected number of nodes influenced by the k nodes under cascade model C is maximized. The state-of-the-art approximate solutions run in O(k(n+m) log n/ ε 2 ) expected time while returning a (1 - 1/ e - ε) approximate solution with at least 1 - 1/ n probability. A key phase of these IM algorithms is the random reverse reachable (RR) set generation, and this phase significantly affects the efficiency and scalability of the state-of-the-art IM algorithms. In this article, we present a study on this key phase and propose an efficient random RR set generation algorithm under IC model. With the new algorithm, we show that the expected running time of existing IM algorithms under IC model can be improved to O(k ċ n log n ċ 2 ), when for any node v , the total weight of its incoming edges is no larger than a constant. For the general IC model where the weights are skewed, we present a sampling algorithm SKIP. To the best of our knowledge, it is the first index-free algorithm that achieves the optimal time complexity of the sorted subset sampling problem. Moreover, existing approximate IM algorithms suffer from scalability issues in high influence networks where the size of random RR sets is usually quite large. We tackle this challenging issue by reducing the average size of random RR sets without sacrificing the approximation guarantee. The proposed solution is orders of magnitude faster than states of the art as shown in our experiment. Besides, we investigate the issues of forward propagation and derive its time complexity with our proposed subset sampling techniques. We also present a heuristic condition to indicate when the forward propagation approach should be utilized to estimate the expected influence of a given seed set.

Differential equation for partition functions and a duality pseudo-forest

We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph that contains necessary and sufficient information for computing the full quantum partition function. We derive a second-order differential equation for an extended partition function z[β, β′, J] that describes a transformation from a “parent” partition function z[0, β′, J] (or anti-commutativity graph) to a “child” partition function z[β, 0, J] (or anti-commutativity graph). The procedure can be iterated, and then one forms a pseudo-forest of duality transformations between quantum systems, i.e., a directed graph in which every vertex (or quantum system) has at most one incoming edge (from its parent system). The pseudo-forest has a single tree connected to a constant partition function, many pseudo-trees connected to self-dual systems, and all other pseudo-trees connected to closed cycles of transformations between mutually dual systems. We also show how the differential equation for the extended partition function can be used to study disordered systems.

Density-based structural embedding for anomaly detection in dynamic networks

Dynamic networks continuously change their structure and properties, and anomaly detection methods must identify these structural changes at both local and global levels. Network embedding is considered a powerful tool for low-dimension structural representation of network objects. However, most embedding techniques developed for dynamic networks are incompetent in capturing the changes in global structures. Besides, with incoming edge streams, these techniques change the embeddings of all network objects, including those vertices and edges that do not experience any change in subsequent timestamps. In this paper, we propose an embedding algorithm DSEDN to identify anomalous vertices and edges in dynamic networks utilizing structural changes in networks. The algorithm uses sparse autoencoder to generate network embeddings minimizing the pair-wise and neighborhood distance between vertex representations of every subgraph derived from random walks. The subgraphs have been weighted based on their respective clustering coefficient, and the clustering algorithm is employed to identify network anomalies. The advantages of proposed method include: (i) better accuracy in detecting network anomalies; (ii) structure-preserving embeddings, such that it maintains the local and global structure of every snapshot of growing graphs; (iii) density-based embeddings; (iv) stable embeddings over time such that embeddings of consecutive timestamps do not change much for those network objects that do not experience any change; (v) scalability. We evaluate the proposed algorithm on anomaly detection and graph visualization on five real-world datasets. Our algorithm achieves improvement in AUC, scalability, and stability across all baselines.

Planar L-Drawings of Bimodal Graphs

In a planar L-drawing of a directed graph (digraph) each edge $e$ is represented as a polyline composed of a vertical segment starting at the tail of $e$ and a horizontal segment ending at the head of $e$. Distinct edges may overlap, but not cross. Our main focus is on bimodal graphs, i.e., digraphs admitting a planar embedding in which the incoming and outgoing edges around each vertex are contiguous. We show that every plane bimodal graph without 2-cycles admits a planar L-drawing. This includes the class of upward-plane graphs. Bimodal graphs with 2-cycles admit a planar L-drawing if the underlying undirected graph with merged 2-cycles is a planar 3-tree. Finally, outerplanar digraphs admit a planar L-drawing - although they do not always have a bimodal embedding - but not necessarily with an outerplanar embedding.