Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio

Towards a Swiss National Research Infrastructure

In this position paper we describe the current status and plans for a Swiss National Research Infrastructure. Swiss academic and research institutions are very autonomous. While being loosely coupled, they do not rely on any centralized management entities. Therefore, a coordinated national research infrastructure can only be established by federating the various resources available locally at the individual institutions. The Swiss Multi-Science Computing Grid and the Swiss Academic Compute Cloud projects serve already a large number of diverse user communities. These projects also allow us to test the operational setup of such a heterogeneous federated infrastructure

POEM: Pricing Longer for Edge Computing in the Device Cloud

Multiple access mobile edge computing has been proposed as a promising technology to bring computation services close to end users, by making good use of edge cloud servers. In mobile device clouds (MDC), idle end devices may act as edge servers to offer computation services for busy end devices. Most existing auction based incentive mechanisms in MDC focus on only one round auction without considering the time correlation. Moreover, although existing single round auctions can also be used for multiple times, users should trade with higher bids to get more resources in the cascading rounds of auctions, then their budgets will run out too early to participate in the next auction, leading to auction failures and the whole benefit may suffer. In this paper, we formulate the computation offloading problem as a social welfare optimization problem with given budgets of mobile devices, and consider pricing longer of mobile devices. This problem is a multiple-choice multi-dimensional 0-1 knapsack problem, which is a NP-hard problem. We propose an auction framework named MAFL for long-term benefits that runs a single round resource auction in each round. Extensive simulation results show that the proposed auction mechanism outperforms the single round by about 55.6% on the revenue on average and MAFL outperforms existing double auction by about 68.6% in terms of the revenue.Comment: 8 pages, 1 figure, Accepted by the 18th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP

For a learnable mathematics in the digital cultures

I begin with some general remarks concerning the co-evolution of representational forms and mathematical meanings. I then discuss the changed roles of mathematics and novel representations that emerge from the ubiquity of computational models, and briefly consider the implications for learning mathematics. I contend that a central component of knowledge required in modern societies involves the development of a meta-epistemological stance – i.e. developing a sense of mechanism for the models that underpin social and professional discourses. I illustrate this point in relation to recent research in which I am investigating the mathematical epistemology of engineering practice. Finally, I map out one implication for the design of future mathematical learning environments with reference to some data from the "Playground Project"

PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures

Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of persistence diagrams is not Hilbert, they end up being difficult inputs for most Machine Learning techniques. To address this concern, several vectorization methods have been put forward that embed persistence diagrams into either finite-dimensional Euclidean space or (implicit) infinite dimensional Hilbert space with kernels. In this work, we focus on persistence diagrams built on top of graphs. Relying on extended persistence theory and the so-called heat kernel signature, we show how graphs can be encoded by (extended) persistence diagrams in a provably stable way. We then propose a general and versatile framework for learning vectorizations of persistence diagrams, which encompasses most of the vectorization techniques used in the literature. We finally showcase the experimental strength of our setup by achieving competitive scores on classification tasks on real-life graph datasets

HPC Cloud for Scientific and Business Applications: Taxonomy, Vision, and Research Challenges

High Performance Computing (HPC) clouds are becoming an alternative to on-premise clusters for executing scientific applications and business analytics services. Most research efforts in HPC cloud aim to understand the cost-benefit of moving resource-intensive applications from on-premise environments to public cloud platforms. Industry trends show hybrid environments are the natural path to get the best of the on-premise and cloud resources---steady (and sensitive) workloads can run on on-premise resources and peak demand can leverage remote resources in a pay-as-you-go manner. Nevertheless, there are plenty of questions to be answered in HPC cloud, which range from how to extract the best performance of an unknown underlying platform to what services are essential to make its usage easier. Moreover, the discussion on the right pricing and contractual models to fit small and large users is relevant for the sustainability of HPC clouds. This paper brings a survey and taxonomy of efforts in HPC cloud and a vision on what we believe is ahead of us, including a set of research challenges that, once tackled, can help advance businesses and scientific discoveries. This becomes particularly relevant due to the fast increasing wave of new HPC applications coming from big data and artificial intelligence.Comment: 29 pages, 5 figures, Published in ACM Computing Surveys (CSUR