Sequence Of Graphs Research Articles

Driver Maneuver Identification with Multi-Representation Learning and Meta Model Update Designs

Driver maneuver identification (DMI), i.e., the task of predicting the driver maneuver classes given sensor measurements (such as IMU sensors from mobile devices), can serve as a key enabler for many ubiquitous driver behavior analysis applications. Despite the prior studies, two major technical challenges remain before an effective DMI system can be deployed: (i) latent complex maneuver behavior feature relations for accuracy enhancement, and (ii) inconsistency and uncertainty in model adaptation given dynamic data collection settings (e.g., given different urban environments, drivers, and mobile devices). To address the aforementioned challenges, we propose MetaDMI, a novel and adaptive driver maneuver identification framework based on multi-representation learning and meta model update, with the case study on the inertial measurement unit (IMU) sensor measurements (i.e., accelerometer and gyroscope). Specifically, we first extract multiple feature representations for each driver maneuver record in the forms of graph, spectral, and time sequence. Next, MetaDMI processes them with a novel multi-representation learning network, extracting complex patterns and feature relations from the driver maneuvers. Finally, to further enhance the adaptivity of our DMI model to external impacts with dynamic data collection, we have designed a regularized meta learning-based training method to regularize the knowledge transfers across the source and target datasets (e.g., across cities/devices, and few-shot initialization) for consistent and robust identification performance. We have conducted extensive experimental studies upon our MetaDMI prototype based on two datasets (one is collected on our own) and shown that our approach outperforms other baseline approaches for DMI in terms of accuracy and adaptivity.

Universality of Nodal Count Distribution in Large Metric Graphs

An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph’s non-trivial topology. This number, called the nodal surplus, is an integer between 0 and the graph’s first Betti number β. We study the distribution of the nodal surplus values in the countably infinite set of the graph’s eigenfunctions. We conjecture that this distribution converges to Gaussian for any sequence of graphs of growing β. We prove this conjecture for several special graph sequences and test it numerically for a variety of well-known graph families. Accurate computation of the distribution is made possible by a formula expressing the nodal surplus distribution as an integral over a high-dimensional torus.

Fold thickness of some classes of graphs

A 1-fold of $G$ is the graph $G'$ obtained from a graph $G$ by identifying two nonadjacent vertices in $G$ having at least one common neighbor and reducing the resulting multiple edges to simple edges. A sequence of graphs $G = G_0, G_1, G_2, \ldots ,G_k$, where $G_{i+1}$ is a 1-fold of $G_{i}$ for $i=0,1,2,\ldots ,k-1$ is called a uniform $k$-folding if all the graphs in the sequence are singular or all of them are nonsingular. The largest $k$ for which there exists a uniform $k$- folding of $G$ is called fold thickness of $G$ and it was first introduced in [Campe{\~n}a, F. J. H.; Gervacio, S. V. On the fold thickness of graphs. \emph{Arab, J. Math. (Springer)} {\bf9} (2020), no. 2, 345--355]. In this paper, we determine fold thickness of $K_n \odot \overline{K_m}$, $K_n + \overline{K_m}$, cone graph and tadpole graph.

Tutte short exact sequences of graphs

We associate two modules, the \(G\)-parking critical module and the toppling critical module, to an undirected connected graph \(G\). The \(G\)-parking critical module and the toppling critical module are canonical modules (with suitable twists) of quotient rings of the well-studied \(G\)-parking function ideal and the toppling ideal, respectively. For each critical module, we establish a Tutte-like short exact sequence relating the modules associated to \(G\), an edge contraction \(G/e\) and an edge deletion \(G \setminus e\) (\(e\) is a non-bridge). We obtain purely combinatorial consequences of Tutte short exact sequences. For instance, we reprove a theorem of Merino that the critical polynomial of a graph is an evaluation of its Tutte polynomial, and relate the vanishing of certain combinatorial invariants (the number of acyclic orientations on connected partition graphs satisfying a unique sink property) of \(G/e\) to the equality of the corresponding invariants of \(G\) and \(G \setminus e\).Mathematics Subject Classifications: 13D02, 05E40Keywords: Tutte polynomials, chip firing games, toppling ideals, \(G\)-parking function ideals, canonical modules

RResolver: efficient short-read repeat resolution within ABySS

BackgroundDe novo genome assembly is essential to modern genomics studies. As it is not biased by a reference, it is also a useful method for studying genomes with high variation, such as cancer genomes. De novo short-read assemblers commonly use de Bruijn graphs, where nodes are sequences of equal length k, also known as k-mers. Edges in this graph are established between nodes that overlap by k - 1 bases, and nodes along unambiguous walks in the graph are subsequently merged. The selection of k is influenced by multiple factors, and optimizing this value results in a trade-off between graph connectivity and sequence contiguity. Ideally, multiple k sizes should be used, so lower values can provide good connectivity in lesser covered regions and higher values can increase contiguity in well-covered regions. However, current approaches that use multiple k values do not address the scalability issues inherent to the assembly of large genomes.ResultsHere we present RResolver, a scalable algorithm that takes a short-read de Bruijn graph assembly with a starting k as input and uses a k value closer to that of the read length to resolve repeats. RResolver builds a Bloom filter of sequencing reads which is used to evaluate the assembly graph path support at branching points and removes paths with insufficient support. RResolver runs efficiently, taking only 26 min on average for an ABySS human assembly with 48 threads and 60 GiB memory. Across all experiments, compared to a baseline assembly, RResolver improves scaffold contiguity (NGA50) by up to 15% and reduces misassemblies by up to 12%.ConclusionsRResolver adds a missing component to scalable de Bruijn graph genome assembly. By improving the initial and fundamental graph traversal outcome, all downstream ABySS algorithms greatly benefit by working with a more accurate and less complex representation of the genome. The RResolver code is integrated into ABySS and is available at https://github.com/bcgsc/abyss/tree/master/RResolver.

Behavior-based detection and classification of malicious software utilizing structural characteristics of group sequence graphs

Behavior-based detection and classification of malicious software utilizing structural characteristics of group sequence graphs

The Large Deviation Principle for Inhomogeneous Erdős–Rényi Random Graphs

Consider the inhomogeneous Erdős-Rényi random graph (ERRG) on n vertices for which each pair i,jin {1,ldots ,n}, ine j, is connected independently by an edge with probability r_n(frac{i-1}{n},frac{j-1}{n}), where (r_n)_{nin mathbb {N}} is a sequence of graphons converging to a reference graphonr. As a generalisation of the celebrated large deviation principle (LDP) for ERRGs by Chatterjee and Varadhan (Eur J Comb 32:1000–1017, 2011), Dhara and Sen (Large deviation for uniform graphs with given degrees, 2020. arXiv:1904.07666) proved an LDP for a sequence of such graphs under the assumption that r is bounded away from 0 and 1, and with a rate function in the form of a lower semi-continuous envelope. We further extend the results by Dhara and Sen. We relax the conditions on the reference graphon to (log r, log (1- r))in L^1([0,1]^2). We also show that, under this condition, their rate function equals a different, more tractable rate function. We then apply these results to the large deviation principle for the largest eigenvalue of inhomogeneous ERRGs and weaken the conditions for part of the analysis of the rate function by Chakrabarty et al. (Large deviation principle for the maximal eigenvalue of inhomogeneous Erdoös-Rényi random graphs, 2020. arXiv:2008.08367).

Convergence of combinatorial gravity

We present a new regularization of Euclidean Einstein gravity in terms of (sequences of) graphs. In particular, we define a discrete Einstein-Hilbert action that converges to its manifold counterpart on sufficiently dense random geometric graphs (more generally on any sequence of graphs that converges suitably to the manifold in the sense of Gromov-Hausdorff). Our construction relies crucially on the Ollivier curvature of optimal transport theory. Our methods also allow us to define an analogous discrete action for Klein-Gordon fields. These results are part of the ongoing program combinatorial approach to quantum gravity where we seek to generate graphs that approximate manifolds as metric-measure structures.

Energy-Efficient Data Transmission in Mobility-Aware Wireless Networks

Data transmission scheme is an effective mode to improve the energy-efficiency in packet delivery. In this paper, we investigate the energy-efficient data transmission over reliable links and unreliable links in mobility-aware wireless networks. The network topologies in mobility-aware wireless networks are changed from one time slot to another, and they could be described by a sequence of static graphs. We first model these network topologies in a time period as a virtual space-time graph. On the virtual space-time graph, energy-efficient data transmission problems over reliable links and unreliable links are defined. The aim of the two data transmission problems is to find a spatial-temporal path with the minimum energy cost. Next, we propose an Energy-Efficient Data Transmission algorithm over Reliable Links (EEDT-RL) to find the optimal space-time path. Based on EEDT-RL, we also develop a heuristic data transmission protocol over unreliable links (named EEDT-UL), in which the path reliability is taken into consideration. Simulation results show that our proposed algorithms perform well in terms of energy cost and transmission count compared with some existing algorithms.

Logarithmic girth expander graphs of $$SL_n({\mathbb {F}}_p)$$

We provide an explicit construction of finite 4-regular graphs $$(\Gamma _k)_{k\in {\mathbb {N}}}$$ with $$\text {girth}\, \Gamma _k\rightarrow \infty $$ as $$k\rightarrow \infty $$ and $$\frac{\text {diam}\,\Gamma _k}{\text {girth}\,\Gamma _k}\leqslant D$$ for some $$D>0$$ and all $$k\in {\mathbb {N}}$$ . For each fixed dimension $$n\geqslant 2,$$ we find a pair of matrices in $$SL_{n}({\mathbb {Z}})$$ such that (i) they generate a free subgroup, (ii) their reductions $$\bmod \, p$$ generate $$SL_{n}({\mathbb {F}}_{p})$$ for all sufficiently large primes p, (iii) the corresponding Cayley graphs of $$SL_{n}({\mathbb {F}}_{p})$$ have girth at least $$c_n\log p$$ for some $$c_n>0$$ . Relying on growth results (with no use of expansion properties of the involved graphs), we observe that the diameter of those Cayley graphs is at most $$O(\log p)$$ . This gives infinite sequences of finite 4-regular Cayley graphs of $$SL_n({\mathbb {F}}_p)$$ as $$p\rightarrow \infty $$ with large girth and bounded diameter-by-girth ratio. These are the first explicit examples in all dimensions $$n\geqslant 2$$ (all prior examples were in $$n=2$$ ). Moreover, they happen to be expanders. Together with Margulis’ and Lubotzky–Phillips–Sarnak’s classical constructions, these new graphs are the only known explicit logarithmic girth Cayley graph expanders.

Graph covers of higher dimensional dynamical systems

We generalize the notion of an inverse sequence of graph covers from the zero-dimensional dynamical systems [8] to any dynamical system.

Federated Dynamic Graph Neural Networks with Secure Aggregation for Video-based Distributed Surveillance

Distributed surveillance systems have the ability to detect, track, and snapshot objects moving around in a certain space. The systems generate video data from multiple personal devices or street cameras. Intelligent video-analysis models are needed to learn dynamic representation of the objects for detection and tracking. Can we exploit the structural and dynamic information without storing the spatiotemporal video data at a central server that leads to a violation of user privacy? In this work, we introduce Federated Dynamic Graph Neural Network (Feddy), a distributed and secured framework to learn the object representations from graph sequences: (1) It aggregates structural information from nearby objects in the current graph as well as dynamic information from those in the previous graph. It uses a self-supervised loss of predicting the trajectories of objects. (2) It is trained in a federated learning manner. The centrally located server sends the model to user devices. Local models on the respective user devices learn and periodically send their learning to the central server without ever exposing the user’s data to server. (3) Studies showed that the aggregated parameters could be inspected though decrypted when broadcast to clients for model synchronizing, after the server performed a weighted average. We design an appropriate aggregation mechanism of secure aggregation primitives that can protect the security and privacy in federated learning with scalability. Experiments on four video camera datasets as well as simulation demonstrate that Feddy achieves great effectiveness and security.

Spatial-Temporal Conv-Sequence Learning With Accident Encoding for Traffic Flow Prediction

In an intelligent transportation system, the key problem of traffic forecasting is how to extract periodic temporal dependencies and complex spatial correlations. Current state-of-the-art methods for predicting traffic flow are based on graph architectures and sequence learning models, but they do not fully exploit dynamic spatial-temporal information in the traffic system. Specifically, the temporal dependencies in the short-range are diluted by recurrent neural networks. Moreover, local spatial information is also ignored by existing sequence models, because their convolution operation uses global average pooling. Besides, accidents may occur during object transition, which will cause congestion in the real world and further decrease prediction accuracy. To overcome these challenges, we propose Spatial-Temporal Conv-sequence Learning (STCL), where a focused temporal block uses unidirectional convolution to capture short-term periodic temporal dependencies effectively, and a spatial-temporal fusion module is responsible for extracting dependencies of interactions and decreasing the feature dimensions. Moreover, as the accidents features have an impact on local traffic congestion, we employ position encoding to detect anomalies in complex traffic situations. We have conducted a large number of experiments on real-world tasks and verified the effectiveness of our proposed method.

Scattering resonances of large weakly open quantum graphs

In this paper, we consider a sequence of open quantum graphs, with uniformly bounded data, and we are interested in the asymptotic distribution of their scattering resonances. Supposing that the number of leads in our quantum graphs is small compared to the total number of edges, we show that most resonances are close to the real axis. More precisely, the asymptotic distribution of resonances of our open quantum graphs is the same as the asymptotic distribution of the square-root of the eigenvalues of the closed quantum graphs obtained by removing all the leads.

CHAPAO: Likelihood and hierarchical reference-based representation of biomolecular sequences and applications to compressing multiple sequence alignments.

High-throughput experimental technologies are generating tremendous amounts of genomic data, offering valuable resources to answer important questions and extract biological insights. Storing this sheer amount of genomic data has become a major concern in bioinformatics. General purpose compression techniques (e.g. gzip, bzip2, 7-zip) are being widely used due to their pervasiveness and relatively good speed. However, they are not customized for genomic data and may fail to leverage special characteristics and redundancy of the biomolecular sequences. We present a new lossless compression method CHAPAO (COmpressing Alignments using Hierarchical and Probabilistic Approach), which is especially designed for multiple sequence alignments (MSAs) of biomolecular data and offers very good compression gain. We have introduced a novel hierarchical referencing technique to represent biomolecular sequences which combines likelihood based analyses of the sequence similarities and graph theoretic algorithms. We performed an extensive evaluation study using a collection of real biological data from the avian phylogenomics project, 1000 plants project (1KP), and 16S and 23S rRNA datasets. We report the performance of CHAPAO in comparison with general purpose compression techniques as well as with MFCompress and Nucleotide Archival Format (NAF)-two of the best known methods especially designed for FASTA files. Experimental results suggest that CHAPAO offers significant improvements in compression gain over most other alternative methods. CHAPAO is freely available as an open source software at https://github.com/ashiq24/CHAPAO. CHAPAO advances the state-of-the-art in compression algorithms and represents a potential alternative to the general purpose compression techniques as well as to the existing specialized compression techniques for biomolecular sequences.

Long time series ozone prediction in China: A novel dynamic spatiotemporal deep learning approach

Ozone pollution is a global environmental problem becoming increasingly prominent in China. It is of great significance to achieve long-term and high-precision ground-level ozone prediction on large scales to improve the efficiency of environmental governance. In this paper, we developed a dynamic graph convolutional and sequence to sequence embedded with the attention mechanism model (DG-ASeqseq) for predicting daily maximum 8-h average ozone (MDA8 O3) concentrations over China the next seven days. In the proposed approach, changeable spatial correlations are modelled by graph convolutional operations on dynamic graphs constructed based on multiple information of historical change, and temporal correlations in long time series are modelled through the sequence to sequence networks embedded with the attention mechanism. Results show the reliability and effectiveness of the proposed model, and it is superior to other benchmark models in simulating long-term spatiotemporal variations of O3 concentrations in large scale areas. Moreover, the proposed model has good prediction capability in severe O3 pollution events. Advancement in this methodology could provide guidance for the government's coordinated control of regional pollution to help improve air quality and jointly safeguard global climate security.

Restriction of the Global IgM Repertoire in Antiphospholipid Syndrome.

The typical anti-phospholipid antibodies (APLA) in the anti-phospholipid syndrome (APS) are reactive with the phospholipid-binding protein β2GPI as well as a growing list of other protein targets. The relation of APLA to natural antibodies and the fuzzy set of autoantigens involved provoked us to study the changes in the IgM repertoire in APS. To this end, peptides selected by serum IgM from a 7-residue linear peptide phage display library (PDL) were deep sequenced. The analysis was aided by a novel formal representation of the Igome (the mimotope set reflecting the IgM specificities) in the form of a sequence graph. The study involved women with APLA and habitual abortions (n=24) compared to age-matched clinically healthy pregnant women (n=20). Their pooled Igomes (297 028 mimotope sequences) were compared also to the global public repertoire Igome of pooled donor plasma IgM (n=2 796 484) and a set of 7-mer sequences found in the J regions of human immunoglobulins (n=4 433 252). The pooled Igome was represented as a graph connecting the sequences as similar as the mimotopes of the same monoclonal antibody. The criterion was based on previously published data. In the resulting graph, identifiable clusters of vertices were considered related to the footprints of overlapping antibody cross-reactivities. A subgraph based on the clusters with a significant differential expression of APS patients’ mimotopes contained predominantly specificities underrepresented in APS. The differentially expressed IgM footprints showed also an increased cross-reactivity with immunoglobulin J regions. The specificities underexpressed in APS had a higher correlation with public specificities than those overexpressed. The APS associated specificities were strongly related also to the human peptidome with 1 072 mimotope sequences found in 7 519 human proteins. These regions were characterized by low complexity. Thus, the IgM repertoire of the APS patients was found to be characterized by a significant reduction of certain public specificities found in the healthy controls with targets representing low complexity linear self-epitopes homologous to human antibody J regions.

Multistage Vertex Cover

The NP-complete Vertex Cover problem asks to cover all edges of a graph by a small (given) number of vertices. It is among the most prominent graph-algorithmic problems. Following a recent trend in studying temporal graphs (a sequence of graphs, so-called layers, over the same vertex set but, over time, changing edge sets), we initiate the study of Multistage Vertex Cover. Herein, given a temporal graph, the goal is to find for each layer of the temporal graph a small vertex cover and to guarantee that two vertex cover sets of every two consecutive layers differ not too much (specified by a given parameter). We show that, different from classic Vertex Cover and some other dynamic or temporal variants of it, Multistage Vertex Cover is computationally hard even in fairly restricted settings. On the positive side, however, we also spot several fixed-parameter tractability results based on some of themost natural parameterizations.

HashWalk: An efficient node classification method based on clique-compressed graph embedding

• Based on homophily and co-citation hypothesis, cliques reflect structural features of a graph. • Considering a clique as a sample unit improves the quality of random walk . • Compressing graph reduces computational cost in graph embedding. • Compressing graph by consistent cliques preserves structural information. In recent years, random walk based embedding has become a popular method for node classification. However, current methods still require a huge computational cost to obtain the representation of a large number of nodes. In addition, walking methods cannot adapt well to diverse network structures. Hence, this paper proposes HashWalk to generate a clique-compressed graph that can be used in random walk based embedding for node classification. Specifically, HashWalk compresses cliques into single nodes, and these single nodes are able to inherit neighbors of cliques. As a result, HashWalk can significantly reduce the number of training nodes and computational cost. Besides, HashWalk uses the random walk mapping method to obtain walking sequences of the clique-compressed graph, which makes random walk adapt to network structure. The experimental results prove that HashWalk provides faster time efficiency and lower space complexity while ensuring the accuracy. In summary, this paper provides a fast and effective method using clique-compressed graph embedding for node classification.

Rare event asymptotics for exploration processes for random graphs

Large deviations for random graph models has been a topic of significant recent research activity. Much work in this area is focused on the class of dense random graph models (number of edges in the graph scale as n2, where n is the number of vertices) where the theory of graphons has emerged as a principal tool in the study of large deviation properties. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is to study an approach for large deviation problems in this regime by establishing large deviation principles (LDP) on suitable path spaces for certain exploration processes of the associated random graph sequence. Exploration processes are an important tool in the study of sparse random graph models and have been used to understand detailed asymptotics of many functionals of sparse random graphs, such as component sizes, surplus, deviations from trees, etc. In the context of rare event asymptotics of interest here, the point of view of exploration process transforms a large deviation analysis of a static random combinatorial structure to the study of a small noise LDP for certain stochastic dynamical systems with jumps. Our work focuses on one particular class of random graph models, namely the configuration model; however, the general approach of using exploration processes for studying large deviation properties of sparse random graph models has broader applicability. The goal is to study asymptotics of probabilities of nontypical behavior in the large network limit. The first key step for this is to establish a LDP for an exploration process associated with the configuration model. A suitable exploration process here turns out to be an infinite-dimensional Markov process with transition probability rates that diminish to zero in certain parts of the state space. Large deviation properties of such Markovian models is challenging due to poor regularity behavior of the associated local rate functions. Our proof of the LDP relies on a representation of the exploration process in terms of a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. Next, using the rate function in the LDP for the exploration process we formulate a calculus of variations problem associated with the asymptotics of component degree distributions. The second key ingredient in our study is a careful analysis of the infinite-dimensional Euler–Lagrange equations associated with this calculus of variations problem. Exact solutions of these systems of nonlinear differential equations are identified which then provide explicit formulas for decay rates of probabilities of nontypical component degree distributions and related quantities.