Expander Graphs Research Articles

Pred-ID: Future event prediction based on event type schema mining by graph induction and deduction

In the field of information management, effective event intelligence management is crucial for its development. With the continuous evolution of events, predicting future events has become a key task in information management. Event Prediction aims to predict upcoming events based on given contextual information. This requires modeling events and their relationships in the context to infer the structure of future events. However, the existing event prediction methods ignore that the event graph schema based on core events can provide more knowledge about history and future for event prediction through induction and deduction, so as to achieve accurate event prediction. In addressing this issue, we directed our focus towards Event Schema Induction. Inspired by it, we propose the Pred-ID model, designed to build event evolutionary pattern through Inductive Event Graph Generation, Deductive Event Graph Expansion, and Graph Fusion for Event Prediction. Specifically, in the Inductive Event Graph Generation phase, Pred-ID extracts the event core subgraph and event developmental trends from the instance event graph, learning the global structure and uncovering the main processes of event development. Then, in the Deductive Event Graph Expansion phase, by expanding future event node and stretching the main processes of event development into future directions, Pred-ID obtains deductive results, so as to construct the event evolutionary pattern. Finally, in the Graph Fusion for Event Prediction phase, aligning and merging the event evolutionary pattern with the instance event graph enables collaborative prediction of future events. The experimental results indicate that our proposed Pred-ID achieves optimal performance in event evolutionary pattern generation and event prediction tasks.

A Generalized Method for Proving Polynomial Calculus Degree Lower Bounds

We study the problem of obtaining lower bounds for polynomial calculus (PC) and polynomial calculus resolution (PCR) on proof degree, and hence by [Impagliazzo et al. ’99] also on proof size. [Alekhnovich and Razborov’03] established that if the clause-variable incidence graph of a conjunctive normal form (CNF) formula F is a good enough expander, then proving that F is unsatisfiable requires high PC/PCR degree. We further develop their techniques to show that if one can “cluster” clauses and variables in a way that “respects the structure” of the formula in a certain sense, then it is sufficient that the incidence graph of this clustered version is an expander. We also show how a weaker structural condition is sufficient to obtain lower bounds on width for the resolution proof system, and give a unified treatment that highlights similarities and differences between resolution and polynomial calculus (PC) lower bounds. As a corollary of our main technical theorem, we prove that the functional pigeonhole principle (FPHP) formulas require high PC/PCR degree when restricted to constant-degree expander graphs. This answers an open question in [Razborov’02], and also implies that the standard CNF encoding of the FPHP formulas require exponential proof size in polynomial calculus resolution (PCR). Thus, while onto-FPHP formulas are easy for polynomial calculus, as shown in [Riis’93], both FPHP and onto-PHP formulas are hard even when restricted to bounded-degree expanders.

Non-holomorphic modular forms from zeta generators

We study non-holomorphic modular forms built from iterated integrals of holomorphic modular forms for SL(2, ℤ) known as equivariant iterated Eisenstein integrals. A special subclass of them furnishes an equivalent description of the modular graph forms appearing in the low-energy expansion of string amplitudes at genus one. Notably the Fourier expansion of modular graph forms contains single-valued multiple zeta values. We deduce the appearance of products and higher-depth instances of multiple zeta values in equivariant iterated Eisenstein integrals, and ultimately modular graph forms, from the appearance of simpler odd Riemann zeta values. This analysis relies on so-called zeta generators which act on certain non-commutative variables in the generating series of the iterated integrals. From an extension of these non-commutative variables we incorporate iterated integrals involving holomorphic cusp forms into our setup and use them to construct the modular completion of triple Eisenstein integrals. Our work represents a fully explicit realisation of the modular graph forms within Brown’s framework of equivariant iterated Eisenstein integrals and reveals structural analogies between single-valued period functions appearing in genus zero and one string amplitudes.

A decentralized control approach in hypergraph distributed optimization decomposition cases

We study the main decomposition approaches (primal, dual and primal–dual) for a distributed optimization problem from a dynamical system perspective where the couplings among the variables of the optimization problem are described by an undirected, unweighted hypergraph. We conduct stability analysis for the respective dynamical systems of the decomposition cases by using non linear decentralized control theoretic techniques and spectral properties of the respective communication matrices, i.e., the incidence and the Laplacian matrices of the hypergraph. Finally, we provide numerical simulations under a specific coalitional setting that demonstrate the superiority of the hypergraph compared to its respective graph analogue, the clique expansion graph, for the given decomposition algorithms in terms of convergence rate and information transmission efficiency.

HILDEGARD Human-in-the-Loop Data Extraction and Graphically Augmented Relation Discovery

This research paper presents HILDEGARD, an application conceived to guide a semi-expert user in the domain of cultural heritage data management toward the creation of a lightweight knowledge graph tailored for supporting Automatic Story Generation (ASG). For this purpose, a subset of CIDOC-CRM classes and properties is preliminarily selected to fit the domain of interest. The input is constituted by one or more seed-heritage objects selected from a knowledge base. In our case study, they are SPARQL-queried from a Linked Open Database for Italian Cultural Heritage. The shortest path algorithm is then run online on all couplets obtained by a combination of the Wikipedia entities from the selected entry-seeds descriptions. The retrieved entities are subsequently linked to their related DBpedia or YAGO-entry in the chosen language, and the relationships among them are automatically retrieved. The proposed tool addresses different knowledge gaps and societal needs simultaneously, such as the lack of solutions tailored for narrative purposes in the cultural heritage domain, that is, to be used in a scenario where objects belonging to the same room must be linked through a narrative, which shall not only be coherent and informative but also engaging and interesting. The prototype, already able to generate the triples required for the following step of the proposed general ASG pipeline, is intended to be graphically enhanced so that the end user may guide the graph expansion interactively.

Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network

Abstract We study the dynamics of the generalized Lotka–Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, g c . In the competitive regime g c serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct.

On the power of local graph expansion grammars with and without additional restrictions

We study graph expansion grammars, a type of graph grammar that has recently been introduced with motivations in natural language processing. Graph expansion generalizes the well-known hyperedge replacement. In contrast to the latter, the former is able to generate graph languages of unbounded treewidth, like the set of all graphs. In an earlier paper, the complexity of the membership problem of the generated languages was studied, the main result being a polynomial parsing algorithm for local DAG expansion grammars (there called local DAG expansion grammars), a subclass of graph expansion grammars that generates directed acyclic graphs. Here, we study the generative power of local graph expansion grammars. While they, unrestricted, are able to simulate Turing machines, we identify natural restrictions that give rise to a pumping lemma and ensure that the generated languages have regular path languages as well as a semi-linear Parikh image.

Strong blocking sets and minimal codes from expander graphs

A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, we explicitly construct strong blocking sets in the ( k − 1 ) (k-1) -dimensional projective space over F q \mathbb {F}_q that have size at most c q k c q k for some universal constant c c . Since strong blocking sets have recently been shown to be equivalent to minimal linear codes, our construction gives the first explicit construction of F q \mathbb {F}_q -linear minimal codes of length n n and dimension k k , for every prime power q q , for which n ≤ c q k n \leq c q k . This solves one of the main open problems on minimal codes.

Explainable graph clustering via expanders in the massively parallel computation model

Explainable clustering provides human-understandable reasons for decisions in black-box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps.Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear.We prove the problem is NP-hard. We give a fixed-parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks.

Graph Atomic Cluster Expansion for Semilocal Interactions beyond Equivariant Message Passing

The atomic cluster expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the atomic cluster expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph atomic cluster expansion for a number of small molecules, clusters, and a general-purpose model for carbon. We further show that the graph atomic cluster expansion scales linearly with the number of neighbors and layer depth of the graph basis functions. Published by the American Physical Society 2024

Coarse equivalence versus bijective coarse equivalence of expander graphs

Coarse equivalence versus bijective coarse equivalence of expander graphs

Quasi‐majority functional voting on expander graphs

AbstractConsider an ‐vertex graph where each vertex holds one of two distinct opinions. We are interested in the consensus time of synchronous voting processes, where each vertex is allowed to update its opinion according to a predefined commonly local updating rule. This article proposes a general class of voting processes called quasi‐majority functional voting and gives upper and lower bounds of the consensus time. Our results cover many previous results on specific processes, for example, best‐of‐two (a.k.a. 2Choices) and best‐of‐three (a.k.a. 3Majority), as special cases. Our key ingredient is a nonlinear extension of the expander mixing lemma, which enables us to estimate expected and variance changes in opinions of quasi‐majority functional voting on expander graphs.

Integration of quantum physics theories to understand open government data (OGD) adoption by the government

PurposeThis paper aims to further the understanding of Open Government Data (OGD) adoption by the government by invoking two quantum physics theories – percolation theory and expander graph theory.Design/methodology/approachExtant research on the barriers to adoption and rollout of OGD is reviewed to drive home the research question for the present study. Both the theories are summarized, and lessons are derived therefrom for answering the research question.FindingsThe percolation theory solves the riddle of why the OGD initiatives find it difficult to seep across the hierarchical and geographical levels of any administrative division. The expander graph theory builds the understanding of the need for having networking among and within the key government personnel for bolstering the motivation and capacity building of the operational personnel linked with the OGD initiative. The theoretical understanding also aids in the implementation and institutionalization of OGD in general.Originality/valueIntersectionality of domains for conducting research on any theme is always a need. Given the fact that there are innumerable challenges regarding the adoption of OGD by the governments across the world, the application of the two theories of quantum physics might solve the quandary in a befitting way.

Research on Driving Scenario Knowledge Graphs

Despite the partial disclosure of driving scenario knowledge graphs, they still fail to meet the comprehensive needs of intelligent connected vehicles for driving knowledge. Current issues include the high complexity of pattern layer construction, insufficient accuracy of information extraction and fusion, and limited performance of knowledge reasoning models. To address these challenges, a hybrid knowledge graph method was adopted in the construction of a driving scenario knowledge graph (DSKG). Firstly, core concepts in the field were systematically sorted and classified, laying the foundation for the construction of a multi-level classified knowledge graph top-level ontology. Subsequently, by deeply exploring and analyzing the Traffic Genome data, 34 entities and 51 relations were extracted and integrated with the ontology layer, achieving the expansion and updating of the knowledge graph. Then, in terms of knowledge reasoning models, an analysis of the training results of the TransE, Complex, Distmult, and Rotate models in the entity linking prediction task of DSKG revealed that the Distmult model performed the best in metrics such as hit rate, making it more suitable for inference in DSKG. Finally, a standardized and widely applicable driving scenario knowledge graph was proposed. The DSKG and related materials have been publicly released for use by industry and academia.

Bipartite Unique Neighbour Expanders via Ramanujan Graphs.

We construct an infinite family of bounded-degree bipartite unique neighbour expander graphs with arbitrarily unbalanced sides. Although weaker than the lossless expanders constructed by Capalbo et al., our construction is simpler and may be closer to being implementable in practice, due to the smaller constants. We construct these graphs by composing bipartite Ramanujan graphs with a fixed-size gadget in a way that generalises the construction of unique neighbour expanders by Alon and Capalbo. For the analysis of our construction, we prove a strong upper bound on average degrees in small induced subgraphs of bipartite Ramanujan graphs. Our bound generalises Kahale's average degree bound to bipartite Ramanujan graphs, and may be of independent interest. Surprisingly, our bound strongly relies on the exact Ramanujan-ness of the graph and is not known to hold for nearly-Ramanujan graphs.

Fast and Perfect Sampling of Subgraphs and Polymer Systems

We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets ) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and works under a percolation subcriticality condition. We show that this condition is optimal in the sense that the task of (approximately) sampling weighted rooted graphlets becomes impossible in finite expected time for infinite graphs and intractable for finite graphs when the condition does not hold. We apply our sampling algorithm as a subroutine to give near linear-time perfect sampling algorithms for polymer models and weighted non-rooted graphlets in finite graphs, two widely studied yet very different problems. This new perfect sampling algorithm for polymer models gives improved sampling algorithms for spin systems at low temperatures on expander graphs and unbalanced bipartite graphs, among other applications.

A local central limit theorem for random walks on expander graphs

A local central limit theorem for random walks on expander graphs

Optimization in graphical small cancellation theory

Gromov (2003) [5] constructed finitely generated groups whose Cayley graphs contain all graphs from a given infinite sequence of expander graphs of unbounded girth and bounded diameter-to-girth ratio. These so-called Gromov monster groups provide examples of finitely generated groups that do not coarsely embed into Hilbert space, among other interesting properties. If graphs in Gromov's construction admit graphical small cancellation labellings, then one gets similar examples of Cayley graphs containing all the graphs of the family as isometric subgraphs. Osajda (2020) [11] recently showed how to obtain such labellings using the probabilistic method. In this short note, we simplify Osajda's approach, decreasing the number of generators of the resulting group significantly.

T-MGCL: Molecule Graph Contrastive Learning Based on Transformer for Molecular Property Prediction.

In recent years, machine learning has gained increasing traction in the study of molecules, enabling researchers to tackle challenging tasks including molecular property prediction and drug design.Consequently, there remains an open challenge to develop a neural network architecture that can make use of extensive amounts of unlabeled data for training while still providing competitive results in various molecular property prediction tasks. To address this challenge, we propose a Molecule Graph Contrastive Learning approach based on the Transformer framework (T-MGCL). Our approach involves expanding numerous unsupervised molecular graphs and using a contrast estimator to ensure consistency among various graph expansions of the same molecule. Transformer framework is employed to consider the distance between atoms and molecular graph attributes, thereby accounting for structural information that may be overlooked by traditional graph neural networks. Our experimental results demonstrate that the T-MGCL model outperforms other models in several molecular property prediction tasks. Additionally, we observe that the attention weight learned by T-MGCL can be easily explained from a chemical perspective.

Automated extraction of domain knowledge in the dairy industry

Three weeks prior to calving to three weeks after calving, the transition period poses challenges for dairy cattle and farmers. Vast changes in housing, feeding, and reproduction might result in milk drop, metabolic and reproductive diseases. Moreover, most of the metabolic processes are intricately linked as many conditions can coexist. This challenge means that dairy producers and their advisors have difficulty drawing concise conclusions because of all aspects and relationships in transition cow management. Herein, machine-learning techniques and knowledge-graph theory were explored with a view to creating a decision-support system that could provide producers and their advisors with knowledge from domain literature. Specifically, knowledge is modelled as entities and relationships in knowledge graph theory, and natural language models were developed to extract information as knowledge graphs. A dataset comprising 1152 sentences from 20 papers was created and split into 922 sentences for training and 230 sentences for testing. Sequentially, two deep learning models were trained to extract entities and relationships respectively. For training results, a Bi-directional Long-Short-Term Memory model was applied for the entity extraction task and obtained an F1 score of 80 %. As for relationship extraction, a Transformer-based model was deployed but yielded a low F1 of 23 %, thus another pre-trained Transformer model with 89 % accuracy was deployed into the system. After feeding the domain literature into the deep-learning models, a knowledge graph of 1,576 nodes and 3,456 edges was constructed and stored in the graph database Neo4j. Afterward, a semantic parsing method was used to allow users to conduct question answering through the knowledge graph in natural language. In addition, to determine the quality of answers that the knowledge built from the papers, answers were sampled and evaluated based on human judgment. On average, answers scored 7.5 out of 10 and proved informative with respect to the original literature. Although the final interactive results demonstrated a high degree of visualization and scalability, this study primarily sought to demonstrate its feasibility. For tailored commercial applications, further improvements could be implemented in knowledge graph expansion and reasoning.