Recursive Aggregation Research Articles

Recursive aggregate segmentation by erosion and reconstitution (RASER) to characterize concrete microstructure using complementarity of X-ray and neutron computed tomography

The reconstruction of concrete microstructure with computed tomography (CT) images is a challenging problem because concrete is associated with poly-mineral aggregates, various aggregate sizes, high volume fraction of aggregates, rough aggregate surface, small and large connected aggregates, and others. To tackle some of the issues in concrete microstructure reconstruction, CT images are obtained using the complementarity of X-ray and neutron while a recursive aggregate segmentation by erosion and reconstitution (RASER) process is proposed to separate connected aggregates for both 3D and 2D. The RASER algorithm is based on the recursive and iterative processes of erosion and reconstitution of aggregate surface while increasing the eroding layer thickness until a constant number of aggregates is reached. Based on the RASER technique, the 3D segmented concrete microstructure illustrates that aggregates are not skewed based on their sizes and locations while neither under- nor over-segmented in this study. Furthermore, we found that most 2D microstructure analysis can lead to over-segmentation because of artificial section segmentation and rough aggregate surface.

KGRLFF: Detecting Drug-Drug Interactions Based on Knowledge Graph Representation Learning and Feature Fusion.

Accurate prediction of drug-drug interactions (DDIs) plays an important role in improving the efficiency of drug development and ensuring the safety of combination therapy. Most existing models rely on a single source of information to predict DDIs, and few models can perform tasks on biomedical knowledge graphs. This paper proposes a new hybrid method, namely Knowledge Graph Representation Learning and Feature Fusion (KGRLFF), to fully exploit the information from the biomedical knowledge graph and molecular structure of drugs to better predict DDIs. KGRLFF first uses a Bidirectional Random Walk sampling method based on the PageRank algorithm (BRWP) to obtain higher-order neighborhood information of drugs in the knowledge graph, including neighboring nodes, semantic relations, and higher-order information associated with triple facts. Then, an embedded representation learning model named Knowledge Graph-based Cyclic Recursive Aggregation (KGCRA) is used to learn the embedded representations of drugs by recursively propagating and aggregating messages with drugs as both the source and destination. In addition, the model learns the molecular structures of the drugs to obtain the structured features. Finally, a Feature Representation Fusion Strategy (FRFS) was developed to integrate embedded representations and structured feature representations. Experimental results showed that KGRLFF is feasible for predicting potential DDIs.

Long short‐distance topology modelling of 3D point cloud segmentation with a graph convolution neural network

Abstract3D point cloud segmentation is a non‐trivial problem due to its irregular, sparse, and unordered data structure. Existing methods only consider structural relationships of a 3D point and its spatial neighbours. However, the inner‐point interactions and long‐distance context of a 3D point cloud have been less investigated. In this study, we propose an effective plug‐and‐play module called the Long Short‐Distance Topologically Modelled (LSDTM) Graph Convolutional Neural Network (GCNN) to learn the underlying structure of 3D point clouds. Specifically, we introduce the concept of subgraph to model the contextual‐point relationships within a short distance. Then the proposed topology can be reconstructed by recursive aggregation of subgraphs, and importantly, to propagate the contextual scope to a long range. The proposed LSDTM can parse the point cloud data with maximisation of preserving the geometric structure and contextual structure, and the topological graph can be trained end‐to‐end through a seamlessly integrated GCNN. We provide a case study of triple‐layer ternary topology and experimental results on ShapeNetPart, Stanford 3D Indoor Semantics and ScanNet datasets, indicating a significant improvement on the task of 3D point cloud segmentation and validating the effectiveness of our research.

On the Foundations of Grounding in Answer Set Programming

AbstractWe provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP’s modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.

Recursive Aggregation and Its Fusion Process for Intuitionistic Fuzzy Numbers Based on Non-Additive Measure

In this paper, the recursive aggregation of OWA operators for intuitionistic fuzzy numbers (IFN) based on a non-additive measure (NAM) with σ−λ rules is constructed and investigated in light of the σ−λ rules of a non-additive measure (NAM). Additionally, an integrator is designed by drawing on the genetic algorithm and the process of calculation is elaborated by an example.

Progressive global perception and local polishing network for lung infection segmentation of COVID-19 CT images

In this paper, a progressive global perception and local polishing (PCPLP) network is proposed to automatically segment the COVID-19-caused pneumonia infections in computed tomography (CT) images. The proposed PCPLP follows an encoder-decoder architecture. Particularly, the encoder is implemented as a computationally efficient fully convolutional network (FCN). In this study, a multi-scale multi-level feature recursive aggregation (mmFRA) network is used to integrate multi-scale features (viz. global guidance features and local refinement features) with multi-level features (viz. high-level semantic features, middle-level comprehensive features, and low-level detailed features). Because of this innovative aggregation of features, an edge-preserving segmentation map can be produced in a boundary-aware multiple supervision (BMS) way. Furthermore, both global perception and local perception are devised. On the one hand, a global perception module (GPM) providing a holistic estimation of potential lung infection regions is employed to capture more complementary coarse-structure information from different pyramid levels by enlarging the receptive fields without substantially increasing the computational burden. On the other hand, a local polishing module (LPM), which provides a fine prediction of the segmentation regions, is applied to explicitly heighten the fine-detail information and reduce the dilution effect of boundary knowledge. Comprehensive experimental evaluations demonstrate the effectiveness of the proposed PCPLP in boosting the learning ability to identify the lung infected regions with clear contours accurately. Our model is superior remarkably to the state-of-the-art segmentation models both quantitatively and qualitatively on a real CT dataset of COVID-19.

Reliability and barrier assessment of series–parallel systems subject to cascading failures

Cascading failures can occur in many technical systems where the components are organized as in series–parallel structures. The failures in these systems may propagate from one component to the other, not only within the same parallel sub-structure but also between different sub-structures. This article presents a recursive aggregation method based on the extended models of reliability block diagram, for analyzing the impacts of cascading failures on the reliability of series–parallel systems. Based on the reliability analysis, the effects of safety barriers on preventing cascading failures are studied, and the importance of safety barriers at different locations is evaluated. One simple example of three components and one practical case from an oil production system are presented. The findings in these case studies illustrate how system designers and safety managers can identify the effective and reasonable ways of installing safety barriers by using the proposed approaches, for the mitigation of cascading failures in series–parallel technical systems.

BigData Applications from Graph Analytics to Machine Learning by Aggregates in Recursion

In the past, the semantic issues raised by the non-monotonic nature of aggregates often prevented their use in the recursive statements of logic programs and deductive databases. However, the recently introduced notion of Pre-mappability (PreM) has shown that, in key applications of interest, aggregates can be used in recursion to optimize the perfect-model semantics of aggregate-stratified programs. Therefore we can preserve the declarative formal semantics of such programs while achieving a highly efficient operational semantics that is conducive to scalable implementations on parallel and distributed platforms. In this paper, we show that with PreM, a wide spectrum of classical algorithms of practical interest, ranging from graph analytics and dynamic programming based optimization problems to data mining and machine learning applications can be concisely expressed in declarative languages by using aggregates in recursion. Our examples are also used to show that PreM can be checked using simple techniques and templatized verification strategies. A wide range of advanced BigData applications can now be expressed declaratively in logic-based languages, including Datalog, Prolog, and even SQL, while enabling their execution with superior performance and scalability.

A Case for Stale Synchronous Distributed Model for Declarative Recursive Computation

AbstractA large class of traditional graph and data mining algorithms can be concisely expressed in Datalog, and other Logic-based languages, once aggregates are allowed in recursion. In fact, for most BigData algorithms, the difficult semantic issues raised by the use of non-monotonic aggregates in recursion are solved byPre-Mappability(${\cal P}$reM), a property that assures that for a program with aggregates in recursion there is an equivalent aggregate-stratified program. In this paper we show that, by bringing together the formal abstract semantics of stratified programs with the efficient operational one of unstratified programs,$\[{\cal P}\]$reMcan also facilitate and improve their parallel execution. We prove that$\[{\cal P}\]$reM-optimized lock-free and decomposable parallel semi-naive evaluations produce the same results as the single executor programs. Therefore,$\[{\cal P}\]$reMcan be assimilated into the data-parallel computation plans of different distributed systems, irrespective of whether these follow bulk synchronous parallel (BSP) or asynchronous computing models. In addition, we show that non-linear recursive queries can be evaluated using a hybrid stale synchronous parallel (SSP) model on distributed environments. After providing a formal correctness proof for the recursive query evaluation with$\[{\cal P}\]$reMunder this relaxed synchronization model, we present experimental evidence of its benefits.

Bucket-based multigrid preconditioner for solving pressure Poisson equation using a particle method

The execution time for incompressible particle methods is dominated by solving large sparse linear systems. In this study, a novel simple bucket-based multigrid (BMG) preconditioner is presented to retrieve linear scaling. In the algorithm, the domain is decomposed into cubic boxes, to enable recursive aggregation of the closest neighboring particles. Under a moving particle semi-implicit (MPS) discretization scheme, parametric, verification, and performance studies were conducted for basic problems. From the parametric study, the BMG preconditioner was accompanied with a Krylov subspace accelerated multigrid cycle strategy and incorporated into a generalized conjugate residual method. Regardless of dimension and degree of particle distribution irregularity, the method significantly outperformed a conjugate gradient (CG), an incomplete Cholesky CG, and a conventional plain aggregation-based algebraic multigrid preconditioned solver. For a dam-break problem with 1.3 M and 2.3 M particles in 2D and 3D, the proposed method, as a linear solver for the MPS method, was 27 and 5.4 times faster than the CG method.

Classifying Incomplete Gene-Expression Data: Ensemble Learning with Non-Pre-Imputation Feature Filtering and Best-First Search Technique.

(1) Background: Gene-expression data usually contain missing values (MVs). Numerous methods focused on how to estimate MVs have been proposed in the past few years. Recent studies show that those imputation algorithms made little difference in classification. Thus, some scholars believe that how to select the informative genes for downstream classification is more important than how to impute MVs. However, most feature-selection (FS) algorithms need beforehand imputation, and the impact of beforehand MV imputation on downstream FS performance is seldom considered. (2) Method: A modified chi-square test-based FS is introduced for gene-expression data. To deal with the challenge of a small sample size of gene-expression data, a heuristic method called recursive element aggregation is proposed in this study. Our approach can directly handle incomplete data without any imputation methods or missing-data assumptions. The most informative genes can be selected through a threshold. After that, the best-first search strategy is utilized to find optimal feature subsets for classification. (3) Results: We compare our method with several FS algorithms. Evaluation is performed on twelve original incomplete cancer gene-expression datasets. We demonstrate that MV imputation on an incomplete dataset impacts subsequent FS in terms of classification tasks. Through directly conducting FS on incomplete data, our method can avoid potential disturbances on subsequent FS procedures caused by MV imputation. An experiment on small, round blue cell tumor (SRBCT) dataset showed that our method found additional genes besides many common genes with the two compared existing methods.

Recursive Aggregation of OWA Operators for Fuzzy Number Based on Non-additive Measure with σ-λ Rules

Recursive Aggregation of OWA Operators for Fuzzy Number Based on Non-additive Measure with σ-λ Rules

Evaluating Answer Set Programming with Non-Convex Recursive Aggregates

Aggregation functions are widely used in answer set programming (ASP) for representing and reasoning on knowledge involving sets of objects collectively. These sets may also depend recursively on the results of the aggregation functions, even if so far the support for such recursive aggregations was quite limited in ASP systems. In fact, recursion over aggregates was restricted to convex aggregates, i.e., aggregates that may have only one transition from false to true, and one from true to false, in this specific order. Recently, such a restriction has been overcome, so that the user can finally use non-convex recursive aggregates in ASP programs, either on purpose or accidentally. A preliminary evaluation of ASP programs with non-convex recursive aggregates is reported in this paper.

Optimal learning with Bernstein online aggregation

We introduce a new recursive aggregation procedure called Bernstein Online Aggregation (BOA). Its exponential weights include a second order refinement. The procedure is optimal for the model selection aggregation problem in the bounded iid setting for the square loss: the excess of risk of its batch version achieves the fast rate of convergence $$\log (M)/n$$log(M)/n in deviation. The BOA procedure is the first online algorithm that satisfies this optimal fast rate. The second order refinement is required to achieve the optimality in deviation as the classical exponential weights cannot be optimal, see Audibert (Advances in neural information processing systems. MIT Press, Cambridge, MA, 2007). This refinement is settled thanks to a new stochastic conversion that estimates the cumulative predictive risk in any stochastic environment with observable second order terms. The observable second order term is shown to be sufficiently small to assert the fast rate in the iid setting when the loss is Lipschitz and strongly convex. We also introduce a multiple learning rates version of BOA. This fully adaptive BOA procedure is also optimal, up to a $$\log \log (n)$$loglog(n) factor.

Discrete and continuous recursive forms of OWA operators

We firstly present an evaluation problem for online shop based on gradually increasing number of inputs. Then we propose a model using Recursive OWA operator with constant orness/andness grade involved. Next, we analyze properties of discrete Recursive OWA operators, show their relationship with Pascal Triangle and further generalize this relationship to Γ function. For the continuous case, we propose a concept of self-similar ordered weighting functions (OWF) and analyze some properties of OWF. Using these concepts, we present the recursive aggregation method of continuous arguments under continuous OWF. We show a relationship of OWF with the Regular Increasing (RIM) quantifier. Furthermore, based on an isomorphism relation between discrete and continuous recursive OWA operators, Left Recursive OWA can be seen as the discrete form of continuous OWF.

Computing secure sets in graphs using answer set programming

Abstract The notion of secure sets is a rather new concept in the area of graph theory. Applied to social network analysis, the goal is to identify groups of entities that can repel any attack or influence from the outside. In this article, we tackle this problem by utilizing Answer Set Programming (ASP). It is known that verifying whether a set is secure in a graph is already co-NP-hard. Therefore, the problem of enumerating all secure sets is challenging for ASP and its systems. In particular, encodings for this problem seem to require disjunction and also recursive aggregates. Here, we provide such encodings and analyse their performance using the Clingo system. Furthermore, we study several problem variants, including multiple secure or insecure sets, and weighted graphs.

Rewriting recursive aggregates in answer set programming: back to monotonicity

AbstractAggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the groundergringo, using the methods presented in this paper.

Investigation of the scattering characteristics from discrete random scatterers based on recursive aggregate T-matrix algorithm

In this paper, we derive in vector form the recursive aggregate T-matrix algorithm based on the principles of electromagnetic wave multipole expansion of vector spherical wave functions and the vector addition theorem. After that we establish a three-dimensional electromagnetic scattering model for multiple spherical scatterers by simulating the scattering of subsurface discrete random scatterers using the derived algorithm. Calculating the scattering from different sizes, randomly distributed spherical scatteres and analyzing the high-order scattering effects, we can conclude that the vector recursive aggregate T-matrix algorithm has a high computation accuracy, and contains the interaction effects among multiple scatterers, therefore we can calculate the total scattering effects accurately from multiple scatterers. The established model can be served as a powerful tool in applications for retrieving the impact caused by the scattering of subsurface discrete random scatterers in soil moisture from radar measurements.

Reliability of Series-Parallel Systems With Random Failure Propagation Time

This paper presents an algorithm for evaluating the reliability and performance distribution of complex non-repairable series-parallel multi-state systems with common cause failures caused by propagation of failures in system elements. The failure propagation can have a selective effect, which means that the failures originating from different elements can cause failures of different subsets of system elements. The failure propagation time is assumed to be a random value with a given distribution. The suggested algorithm is based on the universal generating function approach, and a generalized reliability block diagram method (recursive aggregation of pairs of elements and their replacement by an equivalent one). The evaluation procedure is repeated for each combination of elements affected by the common cause failures. Illustrative examples are provided.

Graph queries in a next-generation Datalog system

Recent theoretical advances have enabled the use of special monotonic aggregates in recursion. These special aggregates make possible the concise expression and efficient implementation of a rich new set of advanced applications. Among these applications, graph queries are particularly important because of their pervasiveness in data intensive application areas. In this demonstration, we present our Deductive Application Language (DeAL) System, the first of a new generation of Deductive Database Systems that support applications that could not be expressed using regular stratification, or could be expressed using XY-stratification (also supported in DeAL) but suffer from inefficient execution. Using example queries, we will (i) show how complex graph queries can be concisely expressed using DeAL and (ii) illustrate the formal semantics and efficient implementation of these powerful new monotonic constructs.