Bipartite graph partitioning and data clustering

Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. We point out the connection of our clustering algorithm to correspondence analysis used in multivariate analysis. We also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, we apply our clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.Comment: Proceedings of ACM CIKM 2001, the Tenth International Conference on Information and Knowledge Management, 200

Radiative Neutrino Mass, Dark Matter and Leptogenesis

We propose an extension of the standard model, in which neutrinos are Dirac particles and their tiny masses originate from a one-loop radiative diagram. The new fields required by the neutrino mass-generation also accommodate the explanation for the matter-antimatter asymmetry and dark matter in the universe.Comment: 4 pages, 3 figures. Revised version with improved model. Accepted by PR

Dimensions of Copeland-Erdos Sequences

The base-$k$ {\em Copeland-Erd\"os sequence} given by an infinite set $A$ of positive integers is the infinite sequence \CE_k(A) formed by concatenating the base-$k$ representations of the elements of $A$ in numerical order. This paper concerns the following four quantities. The {\em finite-state dimension} \dimfs (\CE_k(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. The {\em finite-state strong dimension} \Dimfs(\CE_k(A)), a finite-state version of classical packing dimension introduced in 2004. This is a dual of \dimfs(\CE_k(A)) satisfying \Dimfs(\CE_k(A)) \geq \dimfs(\CE_k(A)). The {\em zeta-dimension} \Dimzeta(A), a kind of discrete fractal dimension discovered many times over the past few decades. The {\em lower zeta-dimension} \dimzeta(A), a dual of \Dimzeta(A) satisfying \dimzeta(A)\leq \Dimzeta(A). We prove the following. \dimfs(\CE_k(A))\geq \dimzeta(A). This extends the 1946 proof by Copeland and Erd\"os that the sequence \CE_k(\mathrm{PRIMES}) is Borel normal. \Dimfs(\CE_k(A))\geq \Dimzeta(A). These bounds are tight in the strong sense that these four quantities can have (simultaneously) any four values in $[0,1]$ satisfying the four above-mentioned inequalities.Comment: 19 page

Revisiting the hydrogen storage behavior of the Na-O-H system

Solid-state reactions between sodium hydride and sodium hydroxide are unusual among hydride-hydroxide systems since hydrogen can be stored reversibly. In order to understand the relationship between hydrogen uptake/release properties and phase/structure evolution, the dehydrogenation and hydrogenation behavior of the Na-O-H system has been investigated in detail both ex- and in-situ. Simultaneous thermogravimetric-differential thermal analysis coupled to mass spectrometry (TG-DTA-MS) experiments of NaH-NaOH composites reveal two principal features: Firstly, an H2 desorption event occurring between 240 and 380 °C and secondly an additional endothermic process at around 170 °C with no associated weight change. In-situ high-resolution synchrotron powder X-ray diffraction showed that NaOH appears to form a solid solution with NaH yielding a new cubic complex hydride phase below 200 °C. The Na-H-OH phase persists up to the maximum temperature of the in-situ diffraction experiment shortly before dehydrogenation occurs. The present work suggests that not only is the inter-phase synergic interaction of protic hydrogen (in NaOH) and hydridic hydrogen (in NaH) important in the dehydrogenation mechanism, but that also an intra-phase Hδ+… Hδ– interaction may be a crucial step in the desorption process

Neutrino masses, leptogenesis and dark matter in hybrid seesaw

We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the leptogenesis mechanism.Comment: 4 page