Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams

While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a problem which lies at the core of many graph mining applications called {\em densest subgraph problem}. We develop an algorithm that achieves time- and space-efficiency for this problem simultaneously. It is one of the first of its kind for graph problems to the best of our knowledge. In a graph $G = (V, E)$, the "density" of a subgraph induced by a subset of nodes $S \subseteq V$ is defined as $|E(S)|/|S|$, where $E(S)$ is the set of edges in $E$ with both endpoints in $S$. In the densest subgraph problem, the goal is to find a subset of nodes that maximizes the density of the corresponding induced subgraph. For any $\epsilon>0$, we present a dynamic algorithm that, with high probability, maintains a $(4+\epsilon)$-approximation to the densest subgraph problem under a sequence of edge insertions and deletions in a graph with $n$ nodes. It uses $\tilde O(n)$ space, and has an amortized update time of $\tilde O(1)$ and a query time of $\tilde O(1)$. Here, $\tilde O$ hides a O(\poly\log_{1+\epsilon} n) term. The approximation ratio can be improved to $(2+\epsilon)$ at the cost of increasing the query time to $\tilde O(n)$. It can be extended to a $(2+\epsilon)$-approximation sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm is the first streaming algorithm that can maintain the densest subgraph in {\em one pass}. The previously best algorithm in this setting required $O(\log n)$ passes [Bahmani, Kumar and Vassilvitskii, VLDB'12]. The space required by our algorithm is tight up to a polylogarithmic factor.Comment: A preliminary version of this paper appeared in STOC 201

aluminum honeycomb sandwich for protective structures of earth moving machines

Abstract The design and the assembly of the vehicles subjected to the risk of crushing from falling objects have to consider such danger and provide the operators with suitable safety systems. Generally, falling object protective structures for earth moving machines consist of vertical elements, connected by transversal elements, covered by a roof. The latter has the aim to protect the operators from falling objects and it is usually made of a steel skeleton with a metal plate. In this study, sandwich panels were proposed as technical solution for the impact protection from falling objects in earth moving machines. A very light and cheap aluminum honeycomb core (AA3003 alloy and cell size = 19 mm) was considered as design solution and was subjected to static and dynamic full-scale tests. The results were analysed according to the performance requirements of ISO 3449 standard. The experimental results confirmed that the honeycomb structures are well suitable for designing absorber devices in vehicles protective structures in order to ensure occupant safety

The K-clique Densest Subgraph Problem

Numerous graph mining applications rely on detecting sub-graphs which are large near-cliques. Since formulations that are geared towards finding large near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem, the poly-time solvable densest subgraph problem which maximizes the average degree over all possible subgraphs “lies at the core of large scale data mining”[10]. However, frequently the densest subgraph prob-lem fails in detecting large near-cliques in networks. In this work, we introduce the k-clique densest subgraph problem, k ≥ 2. This generalizes the well studied dens-est subgraph problem which is obtained as a special case for k = 2. For k = 3 we obtain a novel formulation which we refer to as the triangle densest subgraph problem: given a graph G(V,E), find a subset of vertices S ∗ such that τ(S∗) = max S⊆V t(S

PinnerSage: Multi-Modal User Embedding Framework for Recommendations at Pinterest

Latent user representations are widely adopted in the tech industry for powering personalized recommender systems. Most prior work infers a single high dimensional embedding to represent a user, which is a good starting point but falls short in delivering a full understanding of the user's interests. In this work, we introduce PinnerSage, an end-to-end recommender system that represents each user via multi-modal embeddings and leverages this rich representation of users to provides high quality personalized recommendations. PinnerSage achieves this by clustering users' actions into conceptually coherent clusters with the help of a hierarchical clustering method (Ward) and summarizes the clusters via representative pins (Medoids) for efficiency and interpretability. PinnerSage is deployed in production at Pinterest and we outline the several design decisions that makes it run seamlessly at a very large scale. We conduct several offline and online A/B experiments to show that our method significantly outperforms single embedding methods.Comment: 10 pages, 7 figure

Experimental and theoretical analyses of Iroko wood laminates

This paper reports the experimental tests, which have been carried out to assess the mechanical properties of Iroko wood laminates used for the construction of a large wooden sailing ship. Three-point bending tests have been carried out on different types of specimens: laminates with 3 layers @ 0\ub0 and without scarf joints, laminates with 3 layers @ 0\ub0 having the outer layers with scarf joints, and laminates with 4 layers @ 0\ub0/\ub145\ub0/0\ub0 and no scarf joints. The tests have been performed in compliance with the current EN Standards. The analyses of the experimental data allowed the assessment of the mechanical properties of the laminated Iroko wood as well as the influence of scarf joints. The experimental results demonstrated that the presence of scarf joints only affect the strength of the glued laminate, while the stiffness properties in terms of Young modulus in bending and shear modulus, obtained applying the \u201cmethod of variable support span\u201d, remain essentially the same. The investigated laminates have been also analysed using a 3D computed tomography and an ultrasonic phased array equipment in order to assess the dimensions of possible defects or voids in the adhesive and the dynamic modulus of elasticity. The tomographic measurements of the glue thickness explained the reason of the reduced strength of the scarf joints, due to the inhomogeneity of the glue bond-line. The value of the dynamic modulus of elasticity, obtained by the ultrasonic technique, is slightly higher than the value of the modulus of elasticity obtained by the bending tests. Finally, the experimental findings have been compared with those drawn from both Classical Lamination Theory and Dietz approach, obtaining a good agreement and confirming that the Dietz approach is a fast and easy way to assess the elastic properties of a laminated structure

Spreading Rumours without the Network

In this paper we tackle the following question: is it possible to predict the characteristics of the evolution of an epidemic process in a social network on the basis of the degree distribution alone? We answer this question affirmatively for several diffusion processes-- Push-Pull, Broadcast and SIR-- by showing that it is possible to predict with good accuracy their average evolution. We do this by developing a space efficient predictor that makes it possible to handle very large networks with very limited computational resources. Our experiments show that the prediction is surprisingly good for many instances of real-world networks. The class of real-world networks for which this happens can be characterized in terms of their neighbourhood function, which turns out to be similar to that of random networks. Finally, we analyse real instances of rumour spreading in Twitter and observe that our model describes qualitatively well their evolution

Communities, Random Walks, and Social Sybil Defense

Sybil attacks, in which an adversary forges a potentially unbounded number of identities, are a danger to distributed systems and online social networks. The goal of sybil defense is to accurately identify sybil identities. This paper surveys the evolution of sybil defense protocols that leverage the structural properties of the social graph underlying a distributed system to identify sybil identities. We make two main contributions. First, we clarify the deep connection between sybil defense and the theory of random walks. This leads us to identify a community detection algorithm that, for the first time, offers provable guarantees in the context of sybil defense. Second, we advocate a new goal for sybil defense that addresses the more limited, but practically useful, goal of securely white-listing a local region of the graph

Impact behaviour and non destructive evaluation of 3D printed reinforced composites

The widespread additive manufacturing technology for producing components having complex geometries has increased the attention towards new reinforced materials, whose internal structure can be designed ad hoc on the required mechanical performance. Moreover, fused deposition modelling (FDM) technology allows the building of continuous fibre-reinforced thermoplastic composites. Due to this innovative technology, there is a lack of knowledge mainly about the impact behaviour of these materials, also considering that the main demand comes from the transportation field (automotive, aircraft, etc.), where the impact event is always possible. Thus, the aim of this research is the investigation of the impact behaviour of specimens obtained by continuous fiber fabrication technique, where Onyx and nylon white filaments were used as matrices and glass fibres for reinforcement. Onyx is a nylon mixed with short carbon fibres. An extensive non-destructive evaluation was performed on the specimens subjected to impact tests to assess the impact damage tolerance of these materials and to measure the damage extension as well. Nevertheless, considering that different non-destructive techniques were employed, the research aims also to suggest the most suitable and reliable technique to detect damage, mainly by on-site inspection

Numerical and experimental investigation of corrugated tubes under lateral compression

As a common type of energy absorbers, thin-walled structures have been extensively used in crashworthiness application in many industries. The goal of this research is the optimisation of the crushing parameters of corrugated tubes in terms of the number and shape of corrugations. Six different configurations were experimentally investigated; one refers to the straight tube without configurations and the others to corrugated tubes with different geometrical parameters. First, lateral compression tests were carried out and the experimental results were used to validate the finite element models. Other six different configurations of corrugated tubes were analysed by means of finite element simulations. The obtained results demonstrate the advantage of the corrugated tubes with respect to the straight tube in terms of the total absorbed energy and the crushing load. Moreover, the geometrical shape of corrugation (i.e. the ratio of corrugation base to its depth) plays an important role in enhancing the efficiency of the corrugated tubes. ? 2017, ? 2017 Informa UK Limited, trading as Taylor & Francis Group.Qatar National Research Fund (a member of Qatar Foundation) [grant number GSRA2-1-0611-14034].Scopu