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1. Denial-of-Service Attacks on Shared Cache in Multicore: Analysis and Prevention

   Bechtel, Michael G; Yun, Heechul (January 2019, Proceedings - IEEE Real-Time and Embedded Technology and Applications Symposium)

   In this paper we investigate the feasibility of denialof-service (DoS) attacks on shared caches in multicore platforms. With carefully engineered attacker tasks, we are able to cause more than 300X execution time increases on a victim task running on a dedicated core on a popular embedded multicore platform, regardless of whether we partition its shared cache or not. Based on careful experimentation on real and simulated multicore platforms, we identify an internal hardware structure of a nonblocking cache, namely the cache writeback buffer, as a potential target of shared cache DoS attacks. We propose an OS-level solution to prevent such DoS attacks by extending a state-of-the-art memory bandwidth regulation mechanism. We implement the proposed mechanism in Linux on a real multicore platform and show its effectiveness in protecting against cache DoS attacks. 

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2. Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

   https://doi.org/10.1007/s10208-018-09407-7  

   Kanagawa, Motonobu; Sriperumbudur, Bharath K.; Fukumizu, Kenji (January 2019, Foundations of Computational Mathematics)

   This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights, and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand. 

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3. The Gromov–Wasserstein distance between networks and stable network invariants

   https://doi.org/10.1093/imaiai/iaz026  

   Chowdhury, Samir; Mémoli, Facundo (November 2019, Information and Inference: A Journal of the IMA)

   Abstract We define a metric—the network Gromov–Wasserstein distance—on weighted, directed networks that is sensitive to the presence of outliers. In addition to proving its theoretical properties, we supply network invariants based on optimal transport that approximate this distance by means of lower bounds. We test these methods on a range of simulated network datasets and on a dataset of real-world global bilateral migration. For our simulations, we define a network generative model based on the stochastic block model. This may be of independent interest for benchmarking purposes. 

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4. Volume Growth, Curvature, and Buser-Type Inequalities in Graphs

   https://doi.org/10.1093/imrn/rnz305  

   Benson, Brian; Ralli, Peter; Tetali, Prasad (December 2019, International Mathematics Research Notices)

   Abstract We study the volume growth of metric balls as a function of the radius in discrete spaces and focus on the relationship between volume growth and discrete curvature. We improve volume growth bounds under a lower bound on the so-called Ollivier curvature and discuss similar results under other types of discrete Ricci curvature. Following recent work in the continuous setting of Riemannian manifolds (by the 1st author), we then bound the eigenvalues of the Laplacian of a graph under bounds on the volume growth. In particular, $$\lambda _2$$ of the graph can be bounded using a weighted discrete Hardy inequality and the higher eigenvalues of the graph can be bounded by the eigenvalues of a tridiagonal matrix times a multiplicative factor, both of which only depend on the volume growth of the graph. As a direct application, we relate the eigenvalues to the Cheeger isoperimetric constant. Using these methods, we describe classes of graphs for which the Cheeger inequality is tight on the 2nd eigenvalue (i.e. the 1st nonzero eigenvalue). We also describe a method for proving Buser’s Inequality in graphs, particularly under a lower bound assumption on curvature. 

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5. Sampling random graph homomorphisms and applications to network data analysis

   Hanbaek Lyu, Facundo Mémoli (April 2023, Journal of machine learning research)

   Francis Bach (Ed.)

   A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut dis- tance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our frame- work on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels. 

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