Bidirectional Edges Research Articles

Reasoning graph-based reinforcement learning to cooperate mixed connected and autonomous traffic at unsignalized intersections

Cooperation at unsignalized intersections in mixed traffic environments, where Connected and Autonomous Vehicles (CAVs) and Manually Driving Vehicles (MVs) coexist, holds promise for improving safety, efficiency, and energy savings. However, the mixed traffic at unsignalized intersections present huge challenges like MVs’ uncertainties, the chain reaction and diverse interactions. Following the thought of the situation-aware cooperation, this paper proposes a Reasoning Graph-based Reinforcement Learning (RGRL) method, which integrates a Graph Neural Network (GNN) based policy and an environment providing mixed traffic with uncertain behaviors. Firstly, it graphicly represents the observed scenario as a situation using the interaction graph with connected but uncertain (bi-directional) edges. The situation reasoning process is formulated as a Reasoning Graph-based Markov Decision Process which infers the vehicle sequence stage by stage so as to sequentially depict the entire situation. Then, a GNN-based policy is constructed, which uses Graph Convolution Networks (GCN) to capture the interrelated chain reactions and Graph Attentions Networks (GAT) to measure the attention of diverse interactions. Furthermore, an environment block is developed for training the policy, which provides trajectory generators for both CAVs and MVs. A reward function that considers social compliance, collision avoidance, efficiency and energy savings is also provided in this block. Finally, three Reinforcement Learning methods, D3QN, PPO and SAC, are implemented for comparative tests to explore the applicability and strength of the framework. The test results demonstrate that the D3QN outperformed the other two methods with a larger converged reward while maintaining a similar converged speed. Compared to multi-agent RL (MARL), the RGRL approach showed superior performance statistically, reduced the number of severe conflicts by 77.78–94.12 %. The RGRL reduced average and maximum travel times by 13.62–16.02 %, and fuel-consumption by 3.38–6.98 % in medium or high Market Penetration Rates (MPRs). Hardware-in-the-loop (HIL) and Vehicle-in-the-loop (VehIL) experiments were conducted to validate the model effectiveness.

Counting kernels in directed graphs with arbitrary orientations

A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel).Not all directed graphs contain kernels, and computing a kernel or deciding that none exist is NP-complete even on low-degree planar digraphs. The existing polynomial-time algorithms for this problem are all obtained by restricting both the undirected structure and the edge orientations of the input: for example, to chordal graphs without bidirectional edges (Pass-Lanneau, Igarashi and Meunier, Discrete Appl Math 2020) or to permutation graphs where each clique has a sink (Abbas and Saoula, 4OR 2005).By contrast, we count the kernels of a fuzzy circular interval graph in polynomial time, regardless of its edge orientations, and return a kernel when one exists. (Fuzzy circular interval graphs were introduced by Chudnovsky and Seymour in their structure theorem for claw-free graphs.)We also consider kernels on cographs, where we establish NP-hardness in general but linear-time solvability on the subclass of threshold graphs.

Bifurcation and hysteresis in a nonlinear transport model on network motifs

Nonlinear transport has been observed in many real systems, such as international trade, business transactions, human movement, and urban traffic. To understand the fundamental properties of transport in such systems, several models have been proposed in the past few years. These models exhibit complex behavior due to the interplay between nonlinearity and the underlying network topology. We studied a transport equation on three-body network motifs both numerically and analytically, and we found bifurcation on two motifs and hysteresis of a model on one motif. These three motifs show different bifurcation points. The first two motifs have a branching node, i.e., a node with outdegree 2, and the third motif is a fully connected bidirectional triangle. In particular, the hysteresis on the bidirectional triangle is not predictable from the linear stability analysis on the uniform stationary solution. The analysis based on the self-consistency equation of the parameter u [see Eq. (6) for the precise definition] measuring the ratio between sizes on two nodes reveals the following: The bifurcation on the first two motifs is due to supercritical pitchfork bifurcation. The difference between these two motifs comes from the existence of bidirectional edges. The hysteresis on the third motif is due to the combination of the saddle-node and transcritical bifurcation. Our results imply that the nonlinear transport model exhibits nontrivial behavior even in minimal settings and that the bifurcation on large-scale networks becomes far more complex and unpredictable from the underlying network structure. Published by the American Physical Society 2024

Harnessing Artificial Intelligence for Risk Stratification in Acute Myeloid Leukemia (AML): Evaluating the Utility of Longitudinal Electronic Health Record (EHR) Data Via Graph Neural Networks

Background: AML is a life-threatening disease, and to determine which patients need allogeneic stem cell transplantation, hematologists risk-stratify each case. However, standard risk stratification using the European LeukemiaNet (ELN) criteria is focused on baseline mutations and chromosomal aberrations, and the risk estimate is not updated during a patient's course. In other blood cancers, recalculating the risk with treatment response data can help guide the need for more intensive therapy (Kurtz, et al, Cell, 2019). Furthermore, deep learning graph neural networks (GNN) applied to EHR data have strong predictive power in a hematology context (Fouladvand, et al, J Biomed Inform, 2023). Thus, we evaluated the power of a GNN to predict survival in AML using longitudinal EHR data, specifically with labs and histological features that are not included in the ELN but may capture the treatment response. Methods: Patients who were seen at the Stanford Cancer Institute, had EHR data available within six months of diagnosis, and were diagnosed with AML between June 1998 and January 2021 were included in this retrospective analysis. The GNN was trained to predict survival at two years from diagnosis using the first six months of clinical data. Patients were excluded if they were lost to follow-up before two years or died before six months. Data were collected from structured databases associated with Stanford's EHR, except that diagnosis dates were from Stanford's Cancer Registry, and survival data was supplemented with other databases including the Social Security Death Index. Dysplasia, bone marrow cellularity, and bone marrow blast percentages from pathology reports (“pathology report data”) were extracted using text processing algorithms and weakly supervised machine learning (Ratner, et al, ArXiv, 2017). To represent time series information, we framed each patient's timeline as a network (or “graph”) of events. The primary GNN model was a heterogenous graph transformer classifier with two node types: complete blood count (CBC) data and pathology report data (Hu, et al, ArXiv, 2020). Data from the same week were assumed to be from the same timeframe and connected with bidirectional edges. Data separated by longer time periods were connected with unidirectional edges of a separate edge type. The independent test dataset consisted of patients whose ELN 2022 classification was available, and to train the model, the remaining data were divided into train/validation splits of 0.9/0.1. Results: Of the 2,535 patients with survival data, 1,029 met inclusion criteria. Table 1 summarizes the data available in the EHR for each variable, and nearly all patients had CBC and pathology report data. The area under the receiver operating characteristic (AUROC) using the ELN 2022 criteria for predicting survival in the test dataset was 0.79. The AUROC curve for the GNN model was comparable at 0.76, despite not using any variables from the ELN criteria, and the model effectively stratified patients' disease into high- and low-risk in the independent test dataset (hazard ratio [HR] 3.0, log-rank p = 0.0009). Interestingly, despite not having access to mutation or cytogenetic data, the high-risk cases were enriched in known high-risk mutations, like TP53 and RUNX1, and in high-risk chromosomal aberrations, like 5q deletion (Table 1). Although the model predictions correlated with the ELN criteria in some ways, they also stratified the ELN intermediate-risk AML cases into high and low risk (HR 6.1 for model-predicted high risk among ELN intermediate cases, p = 0.07). Conclusions: Risk stratification using artificial intelligence and longitudinal data from the EHR performed comparably to the ELN 2022 criteria and has the potential to further stratify the ELN categories. The model performed well despite only using histological features and lab values, which are more readily available and more frequently updated than next-generation sequencing results. In the future, this approach may further improve with a larger sample size and additional variables, such as measurable residual disease and treatment information. Given the heterogeneity and increasing complexity of AML classification, leveraging artificial intelligence to assist with classification will be crucial, and these results are a step towards a future where data are automatically extracted from the EHR and used for continuously updated risk stratification.

Spatial-temporal knowledge graph network for event prediction

Predicting multiple concurrent events has a remarkable effect on understanding social dynamics and acting in advance to reduce damage. (1) From the perspective of spatial connection, trans-regional implication, which means the cause of the incident is not local but somewhere else, is an important reason for the occurrence of events. However, existing works neglect to model this spatial influence and only leverage the local information for event prediction. (2) From the perspective of temporal connection, future events are triggered by the continuous evolution of the region. Nonetheless, most studies assign events to different timestamps and recognize their sequential patterns, ignoring the continuity of the evolution process. To tackle the above two problems, we propose a spatial and temporal knowledge graph neural network (STKGN). Specifically, to construct the cross-regional connection, we propose a novel spatial-temporal event graph, where each region is denoted as a node and trans-regional influences are reflected by bidirectional edges. To simulate the continuously evolving process, we propose an event-driven memory network to represent the state of each entity and continually update the state embeddings by emerging events. Then we use a broadcast network to spread the local changes in the graph to obtain high-order reasons like the trans-regional implication. Extensive experiments on two real-world datasets demonstrate that STKGN achieves significant improvements over state-of-the-art methods. Further analysis shows the interpretability of the trans-regional implication.

Framework for cyber risk loss distribution of hospital infrastructure: Bond percolation on mixed random graphs approach.

Networks like those of healthcare infrastructure have been a primary target of cyberattacks for over a decade. From just a single cyberattack, a healthcare facility would expect to see millions of dollars in losses from legal fines, business interruption, and loss of revenue. As more medical devices become interconnected, more cyber vulnerabilities emerge, resulting in more potential exploitation that may disrupt patient care and give rise to catastrophic financial losses. In this paper, we propose a structural model of an aggregate loss distribution across multiple cyberattacks on a prototypical hospital network. Modeled as a mixed random graph, the hospital network consists of various patient-monitoring devices and medical imaging equipment as random nodes to account for the variable occupancy of patient rooms and availability of imaging equipment that are connected by bidirectional edges to fixed hospital and radiological information systems. Our framework accounts for the documented cyber vulnerabilities of a hospital's trusted internal network of its major medical assets. To our knowledge, there exist no other models of an aggregate loss distribution for cyber risk in this setting. We contextualize the problem in the probabilistic graph-theoretical framework using a percolation model and combinatorial techniques to compute the mean and variance of the loss distribution for a mixed random network with associated random costs that can be useful for healthcare administrators and cybersecurity professionals to improve cybersecurity management strategies. By characterizing this distribution, we allow for the further utility of pricing cyberrisk.

Finding spatial and temporal features of delay propagation via multi-layer networks

Air traffic system is a typical complex network with dynamic delay propagation between airports. However, difficulties in measuring delay propagation strength and constructing rational networks make investigating the features of delay propagation based on real data from the perspective of complex network is rarely seen. In this paper, using two largest real-world flights dataset of China and the USA over a period of two months in 2018 (from Jul. to Aug.), we construct the delay propagation networks among airports by calculating causality relationship between delay time series of airports. We identify the multilayer structures of networks by k-core decomposition and reveal that a core layer with a few of tightly connected airports dominants delay propagation in the whole systems. Through the analysis on motifs, bidirectional edges are found to be the culprit to expand the scope of delay propagation from airport pairs to local structures. At the system level, we analyze the properties of communities and found that airports geographically close to each other are likely to be classified into a delay propagation community, while the delay propagation between communities is mainly affected by the air traffic flow between them. Moreover, through the comparisons of structures for the delay propagation networks on different days, we reveal the temporal dependence of delay propagation that the more serious the delay propagation in one day, the more similar it will be to that in the next day. Finally, the usefulness of features found is assessed through applying them to predict the delay propagation in the future.

Prior Knowledge-Based Causal Inference Algorithms and Their Applications for China COVID-19 Analysis

Causal inference has become an important research direction in the field of computing. Traditional methods have mainly used Bayesian networks to discover the causal effects between variables. These methods have limitations, namely, on the one hand, the computing cost is expensive if one wants to achieve accurate results, i.e., exponential growth along with the number of variables. On the other hand, the accuracy is not good enough if one tries to reduce the computing cost. In this study, we use prior knowledge iteration or time series trend fitting between causal variables to resolve the limitations and discover bidirectional causal edges between the variables. Subsequently, we obtain real causal graphs, thus establishing a more accurate causal model for the evaluation and calculation of causal effects. We present two new algorithms, namely, the PC+ algorithm and the DCM algorithm. The PC+ algorithm is used to address the problem of the traditional PC algorithm, which needs to enumerate all Markov equivalence classes at a high computational cost or with immediate output of non-directional causal edges. In the PC+ algorithm, the causal tendency among some variables was analyzed via partial exhaustive analysis. By fixing the relatively certain causality as prior knowledge, a causal graph of higher accuracy is the final output at a low running cost. The DCM algorithm uses the d-separation strategy to improve the traditional CCM algorithm, which can only handle the pairwise fitting of variables, and thus identify the indirect causality as the direct one. By using the d-separation strategy, our DCM algorithm achieves higher accuracy while following the basic criteria of Bayesian networks. In this study, we evaluate the proposed algorithms based on the COVID-19 pandemic with experimental and theoretical analysis. The experimental results show that our improved algorithms are effective and efficient. Compared to the exponential cost of the PC algorithm, the time complexity of the PC+ algorithm is reduced to a linear level. Moreover, the accuracies of the PC+ algorithm and DCM algorithm are improved to different degrees; specifically, the accuracy of the PC+ algorithm reaches 91%, much higher than the 33% of the PC algorithm.

Thermodynamic State Machine Network.

We describe a model system—a thermodynamic state machine network—comprising a network of probabilistic, stateful automata that equilibrate according to Boltzmann statistics, exchange codes over unweighted bi-directional edges, update a state transition memory to learn transitions between network ground states, and minimize an action associated with fluctuation trajectories. The model is grounded in four postulates concerning self-organizing, open thermodynamic systems—transport-driven self-organization, scale-integration, input-functionalization, and active equilibration. After sufficient exposure to periodically changing inputs, a diffusive-to-mechanistic phase transition emerges in the network dynamics. The evolved networks show spatial and temporal structures that look much like spiking neural networks, although no such structures were incorporated into the model. Our main contribution is the articulation of the postulates, the development of a thermodynamically motivated methodology addressing them, and the resulting phase transition. As with other machine learning methods, the model is limited by its scalability, generality, and temporality. We use limitations to motivate the development of thermodynamic computers—engineered, thermodynamically self-organizing systems—and comment on efforts to realize them in the context of this work. We offer a different philosophical perspective, thermodynamicalism, addressing the limitations of the model and machine learning in general.

Interest clustering coefficient: a new metric for directed networks like Twitter

AbstractThe clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. But, the clustering coefficient is originally defined for a graph in which the links are undirected, such as friendship links (Facebook) or professional links (LinkedIn). For a graph in which links are directed from a source of information to a consumer of information, it is no more adequate. We show that former studies have missed much of the information contained in the directed part of such graphs. In this article, we introduce a new metric to measure the clustering of directed social graphs with interest links, namely the interest clustering coefficient. We compute it (exactly and using sampling methods) on a very large social graph, a Twitter snapshot with 505 million users and 23 billion links, as well as other various datasets. We additionally provide the values of the formerly introduced directed and undirected metrics, a first on such a large snapshot. We observe a higher value of the interest clustering coefficient than classic directed clustering coefficients, showing the importance of this metric. By studying the bidirectional edges of the Twitter graph, we also show that the interest clustering coefficient is more adequate to capture the interest part of the graph while classic ones are more adequate to capture the social part. We also introduce a new model able to build random networks with a high value of interest clustering coefficient. We finally discuss the interest of this new metric for link recommendation.

Hybrid algorithm for two-terminal reliability evaluation in communication networks

<span>Network reliability is valuable in establishing a survivable communication network. Reliability evaluation algorithms are used in the design stage and during the network deployment. This work presents a new multistage hybrid technique for two-terminal reliability evaluation problem. It is based on a combination of graph reduction techniques and tie-set method. A new approach has been introduced for deducing tie-sets in a network containing both unidirectional and bi-directional edges. The proposed algorithm can be applied for both simple and complex networks without restrictions. The results confirm that new algorithm evaluates network's reliability with decreasing computing time compared to classical algorithms. The results for a case study of a 20-node network have demonstrated that the required time for reliability evaluation is decreased from (t>1 hour) in the case of using a classical algorithm, to (t<1 second) for the new algorithm.</span>

An improvement method for degree and its extending centralities in directed networks

Vital nodes identification in social networks keeps attracting lots of attention in recent years because of its great theoretical and practical significance for many applications. Degree centrality is one of the most efficient neighborhood-based metrics and has been widely used because of its simplicity and low computation complexity. Many other centralities derived from degree have been proposed to try to further improve the accuracy on ranking performance by extending the coverage area of neighbors. But a common problem of degree and its extensional centralities is that the directivity of edges between nodes is not considered. In directed network, nodes’ importance are not only related with their neighbor numbers but also related with the relationships between the nodes and their neighbors. In this paper, we propose a modification method with an adjustable parameter α on degree to improve its ranking accuracy in directed networks. This method redefines the degree of a node by separately taking into account its out-degree and in-degree and uses parameter α to flexibly set the relative weights between out-degree and in-degree when evaluating nodes’ importance in different scenes, which can effectively avoid the situation that too many neighbors from one direction could lead to extreme high value of centrality. We also apply this method on another two centralities: semi-local and k-hop, and for the two centralities that considering multi-step neighbors, the corresponding improvement centralities could eliminate the irrelevant multi-step neighbors when evaluating nodes’ importance. Experimental results in 3 real social networks and 1 artificial network indicate that, setting α to be appropriate value the improvement centralities can better estimate nodes’ connection abilities, propagation abilities and immunization abilities while keeping the same compute complexity with the corresponding original centralities, especially in the network with low percentage of bidirectional edges. Moreover, the improvement method proposed in this paper also can be applied to other centralities, such as eigenvector centrality, neighborhood centrality, Exdegree centrality and percolation based centrality, to improve their performances in directed networks.

Uncovering the nucleus of a massive reciprocal network

Google+ is a directed online social network where nodes have either reciprocal (bidirectional) edges or parasocial (one-way) edges. As reciprocal edges play an important role in the structural properties, formation and evolution of online social networks, we study the core structure of the subgraph formed by them, referred to as the reciprocal network of Google+ — in a sense, a reciprocal network can be viewed as the stable “skeleton” network of a directed online social network that holds it together. We develop an effective three-step procedure to hierarchically extract and unfold the core structure of a network by building up and generalizing ideas from the existing k-shell decomposition and clique percolation approaches. Our scheme produces higher-level representations of the core structure of the Google+ reciprocal network and it reveals that there are ten subgraphs (“communities”) comprising of dense clusters of cliques lying at the center of the core structure of the Google+ reciprocal network. Together they form the core to which “peripheral” sparse subgraphs are attached. Furthermore, our analysis shows that the core structure of the Google+ reciprocal network is very stable as the network evolves. Our results have implications in the design of algorithms for information flow, and in development of techniques for analyzing the vulnerability or robustness of online social networks.

Parameter identifiability-based optimal observation remedy for biological networks

BackgroundTo systematically understand the interactions between numerous biological components, a variety of biological networks on different levels and scales have been constructed and made available in public databases or knowledge repositories. Graphical models such as structural equation models have long been used to describe biological networks for various quantitative analysis tasks, especially key biological parameter estimation. However, limited by resources or technical capacities, partial observation is a common problem in experimental observations of biological networks, and it thus becomes an important problem how to select unobserved nodes for additional measurements such that all unknown model parameters become identifiable. To the best knowledge of our authors, a solution to this problem does not exist until this study.ResultsThe identifiability-based observation problem for biological networks is mathematically formulated for the first time based on linear recursive structural equation models, and then a dynamic programming strategy is developed to obtain the optimal observation strategies. The efficiency of the dynamic programming algorithm is achieved by avoiding both symbolic computation and matrix operations as used in other studies. We also provided necessary theoretical justifications to the proposed method. Finally, we verified the algorithm using synthetic network structures and illustrated the application of the proposed method in practice using a real biological network related to influenza A virus infection.ConclusionsThe proposed approach is the first solution to the structural identifiability-based optimal observation remedy problem. It is applicable to an arbitrary directed acyclic biological network (recursive SEMs) without bidirectional edges, and it is a computerizable method. Observation remedy is an important issue in experiment design for biological networks, and we believe that this study provides a solid basis for dealing with more challenging design issues (e.g., feedback loops, dynamic or nonlinear networks) in the future. We implemented our method in R, which is freely accessible at https://github.com/Hongyu-Miao/SIOOR.

An Empirical Comparison of Algorithms to Find Communities in Directed Graphs and Their Application in Web Data Analytics

Detecting communities in graphs is a fundamental tool to understand the structure of Web-based systems and predict their evolution. Many community detection algorithms are designed to process undirected graphs (i.e., graphs with bidirectional edges) but many graphs on the Web-e.g., microblogging Web sites, trust networks or the Web graph itself-are often directed . Few community detection algorithms deal with directed graphs but we lack their experimental comparison. In this paper we evaluated some community detection algorithms across accuracy and scalability. A first group of algorithms (Label Propagation and Infomap) are explicitly designed to manage directed graphs while a second group (e.g., WalkTrap) simply ignores edge directionality; finally, a third group of algorithms (e.g., Eigenvector) maps input graphs onto undirected ones and extracts communities from the symmetrized version of the input graph. We ran our tests on both artificial and real graphs and, on artificial graphs, WalkTrap achieved the highest accuracy, closely followed by other algorithms; Label Propagation has outstanding performance in scalability on both artificial and real graphs. The Infomap algorithm showcased the best trade-off between accuracy and computational performance and, therefore, it has to be considered as a promising tool for Web Data Analytics purposes.

A GROUP SUM INEQUALITY AND ITS APPLICATION TO POWER GRAPHS

AbstractLet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ be a finite group of order $n$, and let $\text {C}_n$ be the cyclic group of order $n$. For $g\in G$, let ${\mathrm{o}}(g)$ denote the order of $g$. Let $\phi $ denote the Euler totient function. We show that $\sum _{g \in \text {C}_n} \phi ({\mathrm{o}}(g))\geq \sum _{g \in G} \phi ({\mathrm{o}}(g))$, with equality if and only if $G$ is isomorphic to $\text {C}_n$. As an application, we show that among all finite groups of a given order, the cyclic group of that order has the maximum number of bidirectional edges in its directed power graph.

Determining the reduction sequence of Hawaiian quadrangular adzes using 3D approaches: a case study from Moloka'i

Hawaiian adze manufacture requires a great deal of skill and undoubtedly required long apprenticeships to achieve the finesse seen in many finished prehistoric adzes. Despite the presence of more than two dozen adze quarries in Hawai'i, and previous attempts at replicating adze preforms and positing reduction sequences in Polynesia, there is no detailed study that clearly defines the steps and stages of quadrangular adze preform manufacture (the most common form in Hawai'i), and the resulting characteristic debitage. In this paper we examine the sequence of adze production for a population of 109 adzes from Moloka'i, documenting the transition from blanks to preforms to the finished objects that were transported away from quarries. Reduction intensity is measured using the Scar Density Index (Clarkson, 2013) calculated from 3D scans. We document the sequence of cumulative additions of characteristic features to adzes (e.g. bidirectional edges, bevel, poll and tang) as reduction intensity increases. We also note the reasons for adze rejection at each stage of reduction. Our study provides the first detailed analysis of adze reduction in Polynesia facilitated and standardised by 3D scanning technology. Hopefully, it will serve as a useful benchmark for objectively and systematically comparing adze technology in other parts of Hawai'i and across Polynesia, leading to a better understanding of regional and temporal variation in adze technology.

Effects of local structure of neuronal networks on spiking activity in silico

The structure of the neuronal network, including synaptic connectivity, is the basis for information transfer in the network. Various graph-theoretic measures such as degree distribution, mean geodesic path length, clustering coefficient and motif distribution exist for analysing the structure of networks [1], and each of them captures only one perspective of the properties that are crucial regarding the activity in the network. In this work, we vary the local structure of neuronal networks and observe changes in their activity in silico, i.e. in simulations where the activity of single neurons and their interaction is modeled. The local structure is analysed through the occurrence of different motifs, i.e. different patterns of connectivity. The effect of motifs on network dynamics has been widely studied in different types of networks: from the stability point of view in networks with unspecified dynamics [2], in artificial neural networks [3], and from synchronization point of view in spiking neuronal networks [4]. Our work focuses on noise-driven neuronal networks, where the activity can be characterised by spike trains of neurons in the network, and particularly by the bursting behaviour of the network. To study the local structure of networks we consider the occurrences of three separate connectivity patterns: (1) the bidirectional edges, (2) the loops of three nodes, and (3) the feed-forward motifs of triples of nodes. Networks with one of these three local connectivity patterns promoted are generated – we abbreviate these networks (L1), (L2) and (L3). In addition, different distance-dependent networks are generated, including networks with ring topology (RT) and biologically plausible topology, obtained by the NETMORPH [5] simulator (NM). All networks except for NM have binomially distributed in-degree, as is the case with the random networks (RN) that are widely used in neuronal activity simulations. Small illustrations of these network structures are shown in Figure ​Figure1.1. Neuronal activity in these types of networks of size N=100 is simulated using the model presented in [6]. The simulations show a difference in the activity of these networks. Preliminary results indicate, that network bursts occur more frequently in distance dependent networks RT and NM, especially in RT. Accordingly, the overall spiking frequency is high in these networks, but also in L3 networks. Figure 1 Different network structures. Illustration of different networks used in the present work. The red arrows and balls represent characteristics of each network, which are the following: Bidirectional edges in L1, loops of length 3 in L2, feed-forward triples ...

The Compatibility of Binary Characters on Phylogenetic Networks: Complexity and Parameterized Algorithms

In a recent article, Nakhleh, Ringe and Warnow introduced perfect phylogenetic networks—a model of language evolution where languages do not evolve via clean speciation—and formulated a set of problems for their accurate reconstruction. Their new methodology assumes networks, rather than trees, as the correct model to capture the evolutionary history of natural languages. They proved the NP-hardness of the problem of testing whether a network is a perfect phylogenetic one for characters exhibiting at least three states, leaving open the case of binary characters, and gave a straightforward brute-force parameterized algorithm for the problem of running time O(3 k n), where k is the number of bidirectional edges in the network and n is its size. In this paper, we first establish the NP-hardness of the binary case of the problem. Then we provide a more efficient parameterized algorithm for this case running in time O(2 k n 2). The presented algorithm is very simple, and utilizes some structural results and elegant operations developed in this paper that can be useful on their own in the design of heuristic algorithms for the problem. The analysis phase of the algorithm is very elegant using amortized techniques to show that the upper bound on the running time of the algorithm is much tighter than the upper bound obtained under a conservative worst-case scenario assumption. Our results bear significant impact on reconstructing evolutionary histories of languages—particularly from phonological and morphological character data, most of which exhibit at most two states (i.e., are binary), as well as on the design and analysis of parameterized algorithms.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edges--that is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.