Only rational homology spheres admit Ω(f)\Omega(f) to be union of DE attractors

If there exists a diffeomorphism $f$ on a closed, orientable $n$-manifold $M$ such that the non-wandering set $\Omega(f)$ consists of finitely many orientable $(\pm)$ attractors derived from expanding maps, then $M$ must be a rational homology sphere; moreover all those attractors are of topological dimension $n-2$. Expanding maps are expanding on (co)homologies.Comment: 23 pages, 2 figure

Reasoning about Record Matching Rules

To accurately match records it is often necessary to utilize the semantics of the data. Functional dependencies (FDs) have proven useful in identifying tuples in a clean relation, based on the semantics of the data. For all the reasons that FDs and their inference are needed, it is also important to develop dependencies and their reasoning techniques for matching tuples from unreliable data sources. This paper investigates dependencies and their reasoning for record matching. (a) We introduce a class of matching dependencies (MDs) for specifying the semantics of data in unreliable relations, defined in terms of similarity metrics and a dynamic semantics . (b) We identify a special case of MDs, referred to as relative candidate keys (RCKs), to determine what attributes to compare and how to compare them when matching records across possibly different relations. (c) We propose a mechanism for inferring MDs, a departure from traditional implication analysis, such that when we cannot match records by comparing attributes that contain errors, we may still find matches by using other, more reliable attributes. (d) We provide an O ( n 2 ) time algorithm for inferring MDs, and an effective algorithm for deducing a set of RCKs from MDs. (e) We experimentally verify that the algorithms help matching tools efficiently identify keys at compile time for matching, blocking or windowing, and that the techniques effectively improve both the quality and efficiency of various record matching methods. </jats:p

Graph Homomorphism Revisited for Graph Matching

In a variety of emerging applications one needs to decide whether a graph G matches another G p , i.e. , whether G has a topological structure similar to that of G p . The traditional notions of graph homomorphism and isomorphism often fall short of capturing the structural similarity in these applications. This paper studies revisions of these notions, providing a full treatment from complexity to algorithms. (1) We propose p-homomorphism (p -hom) and 1-1 p -hom, which extend graph homomorphism and subgraph isomorphism, respectively, by mapping edges from one graph to paths in another, and by measuring the similarity of nodes . (2) We introduce metrics to measure graph similarity, and several optimization problems for p -hom and 1-1 p -hom. (3) We show that the decision problems for p -hom and 1-1 p -hom are NP-complete even for DAGs, and that the optimization problems are approximation-hard. (4) Nevertheless, we provide approximation algorithms with provable guarantees on match quality. We experimentally verify the effectiveness of the revised notions and the efficiency of our algorithms in Web site matching, using real-life and synthetic data. </jats:p

Towards Certain Fixes with Editing Rules and Master Data

A variety of integrity constraints have been studied for data cleaning. While these constraints can detect the presence of errors, they fall short of guiding us to correct the errors. Indeed, data repairing based on these constraints may not find certain fixes that are absolutely correct, and worse, may introduce new errors when repairing the data. We propose a method for finding certain fixes, based on master data, a notion of certain regions , and a class of editing rules . A certain region is a set of attributes that are assured correct by the users. Given a certain region and master data, editing rules tell us what attributes to fix and how to update them. We show how the method can be used in data monitoring and enrichment. We develop techniques for reasoning about editing rules, to decide whether they lead to a unique fix and whether they are able to fix all the attributes in a tuple, relative to master data and a certain region. We also provide an algorithm to identify minimal certain regions, such that a certain fix is warranted by editing rules and master data as long as one of the regions is correct. We experimentally verify the effectiveness and scalability of the algorithm. </jats:p

A Review of Layer Based Manufacturing Processes for Metals

The metal layered manufacturing processes have provided industries with a fast method to build functional parts directly from CAD models. This paper compares current metal layered manufacturing technologies from including powder based metal deposition, selective laser sinstering (SLS), wire feed deposition etc. The characteristics of each process, including its industrial applications, advantages/disadvantages, costs etc are discussed. In addition, the comparison between each process in terms of build rate, suitable metal etc. is presented in this paper.Mechanical Engineerin

GMAN: A Graph Multi-Attention Network for Traffic Prediction

Long-term traffic prediction is highly challenging due to the complexity of traffic systems and the constantly changing nature of many impacting factors. In this paper, we focus on the spatio-temporal factors, and propose a graph multi-attention network (GMAN) to predict traffic conditions for time steps ahead at different locations on a road network graph. GMAN adapts an encoder-decoder architecture, where both the encoder and the decoder consist of multiple spatio-temporal attention blocks to model the impact of the spatio-temporal factors on traffic conditions. The encoder encodes the input traffic features and the decoder predicts the output sequence. Between the encoder and the decoder, a transform attention layer is applied to convert the encoded traffic features to generate the sequence representations of future time steps as the input of the decoder. The transform attention mechanism models the direct relationships between historical and future time steps that helps to alleviate the error propagation problem among prediction time steps. Experimental results on two real-world traffic prediction tasks (i.e., traffic volume prediction and traffic speed prediction) demonstrate the superiority of GMAN. In particular, in the 1 hour ahead prediction, GMAN outperforms state-of-the-art methods by up to 4% improvement in MAE measure. The source code is available at https://github.com/zhengchuanpan/GMAN.Comment: AAAI 2020 pape