When Hashes Met Wedges: A Distributed Algorithm for Finding High Similarity Vectors

Finding similar user pairs is a fundamental task in social networks, with numerous applications in ranking and personalization tasks such as link prediction and tie strength detection. A common manifestation of user similarity is based upon network structure: each user is represented by a vector that represents the user's network connections, where pairwise cosine similarity among these vectors defines user similarity. The predominant task for user similarity applications is to discover all similar pairs that have a pairwise cosine similarity value larger than a given threshold $\tau$. In contrast to previous work where $\tau$ is assumed to be quite close to 1, we focus on recommendation applications where $\tau$ is small, but still meaningful. The all pairs cosine similarity problem is computationally challenging on networks with billions of edges, and especially so for settings with small $\tau$. To the best of our knowledge, there is no practical solution for computing all user pairs with, say $\tau = 0.2$ on large social networks, even using the power of distributed algorithms. Our work directly addresses this challenge by introducing a new algorithm --- WHIMP --- that solves this problem efficiently in the MapReduce model. The key insight in WHIMP is to combine the "wedge-sampling" approach of Cohen-Lewis for approximate matrix multiplication with the SimHash random projection techniques of Charikar. We provide a theoretical analysis of WHIMP, proving that it has near optimal communication costs while maintaining computation cost comparable with the state of the art. We also empirically demonstrate WHIMP's scalability by computing all highly similar pairs on four massive data sets, and show that it accurately finds high similarity pairs. In particular, we note that WHIMP successfully processes the entire Twitter network, which has tens of billions of edges

Higgs boson hadronic branching ratios at the ILC

We present a study of the Higgs boson decay branching ratios to $b\bar{b}$, $c\bar{c}$ and gluons, one of the cornerstones of the physics program at the International Linear Collider (ILC). A standard model Higgs boson of 120\,GeV mass, produced in the Higgs-strahlung process at $\sqrt{s} = 250$\,GeV was investigated using the full detector simulation and reconstruction procedures. The analysis was performed in the framework of the Silicon Detector (SiD) concept with full account of inclusive standard model backgrounds. The selected decay modes contained two heavy flavour jets in the final state and required excellent flavour tagging through precise reconstruction of interaction and decay vertices in the detector. A new signal discrimination technique using correlations of neural network outputs was used to determine the branching ratios and estimate their uncertainties, 4.8\%, 8.4\% and 12.2\% for $b\bar{b}$, $c\bar{c}$ and gluons respectively.Comment: 9 Pages, 5 figures and 5 table

Anomalous Couplings in Double Higgs Production

The process of gluon-initiated double Higgs production is sensitive to non-linear interactions of the Higgs boson. In the context of the Standard Model, studies of this process focused on the extraction of the Higgs trilinear coupling. In a general parametrization of New Physics effects, however, an even more interesting interaction that can be tested through this channel is the (ttbar hh) coupling. This interaction vanishes in the Standard Model and is a genuine signature of theories in which the Higgs boson emerges from a strongly-interacting sector. In this paper we perform a model-independent estimate of the LHC potential to detect anomalous Higgs couplings in gluon-fusion double Higgs production. We find that while the sensitivity to the trilinear is poor, the perspectives of measuring the new (ttbar hh) coupling are rather promising.Comment: 22 pages, 9 figures. v2: plots of Figs.8 and 9 redone to include experimental uncertainty on the Higgs couplings, references adde

The scalar sector of the Randall-Sundrum model

We derive the effective potential for the Standard Model Higgs-boson sector interacting with Kaluza-Klein excitations of the graviton ($h_\mu^{\nu n}$) and the radion ($\phi$) and show that {\it only} the Standard Model vacuum solution of $\partial V(h)/\partial h =0$ (h is the Higgs field) is allowed. We then consider the consequences of the curvature-scalar mixing xi R \Hhat^\dagger \Hhat$(where$\Hhat$is a Higgs doublet field on the visible brane), which causes the physical mass eigenstates h and$\phi$to be mixtures of the original Higgs and radion fields. First, we discuss the theoretical constraints on the allowed parameter space. Next, we give precise procedures for computing the h and$\phi$couplings given the {\it physical} eigenstate masses, mh and$\mphi$, xi and the new physics scales of the model. We show that LEP/LEP2 data implies that not both the h and$\phi$can be light. In the allowed region of parameter space, we examine numerically the couplings and branching ratios of the h and$\phi$for several cases with$\mh=120\gev$and$\mphi\leq 300\gev$. The resulting prospects for detection of the h and$\phi$at the LHC, a future LC and a$\gam\gam$collider are reviewed. For moderate$|\xi|$, both the anomalous$h\to gg$coupling and (when$\mh>2\mphi$) the non-standard decay channel$h \to \phi\phi$can substantially impact h discovery. Presence of the latter is a direct signature for non-zero xi. We find that$BR(h \to \phi\phi)$as large as$30 \div 40 %$is possible when$|\xi|$is large. Conversely, if$\mphi>2\mh$then$BR(\phi\to hh)$is generally large. The feasibility of experimentally measuring the anomalous gg and$\gam\gam$couplings of the h and$\phi$ is examined.Comment: 62 page, 30 figures. Because some figures had to be reduced in resolution, they will only accurately appear in magnified ghostview. For full abstract see pape