Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data.Comment: To appear as a part of an upcoming textbook on dimensionality reduction and manifold learning. v2: corrected some typo

Unfolding simulations reveal the mechanism of extreme unfolding cooperativity in the kinetically stable alpha-lytic protease.

Kinetically stable proteins, those whose stability is derived from their slow unfolding kinetics and not thermodynamics, are examples of evolution's best attempts at suppressing unfolding. Especially in highly proteolytic environments, both partially and fully unfolded proteins face potential inactivation through degradation and/or aggregation, hence, slowing unfolding can greatly extend a protein's functional lifetime. The prokaryotic serine protease alpha-lytic protease (alphaLP) has done just that, as its unfolding is both very slow (t(1/2) approximately 1 year) and so cooperative that partial unfolding is negligible, providing a functional advantage over its thermodynamically stable homologs, such as trypsin. Previous studies have identified regions of the domain interface as critical to alphaLP unfolding, though a complete description of the unfolding pathway is missing. In order to identify the alphaLP unfolding pathway and the mechanism for its extreme cooperativity, we performed high temperature molecular dynamics unfolding simulations of both alphaLP and trypsin. The simulated alphaLP unfolding pathway produces a robust transition state ensemble consistent with prior biochemical experiments and clearly shows that unfolding proceeds through a preferential disruption of the domain interface. Through a novel method of calculating unfolding cooperativity, we show that alphaLP unfolds extremely cooperatively while trypsin unfolds gradually. Finally, by examining the behavior of both domain interfaces, we propose a model for the differential unfolding cooperativity of alphaLP and trypsin involving three key regions that differ between the kinetically stable and thermodynamically stable classes of serine proteases

Ultra high energy neutrino-nucleon cross section from cosmic ray experiments and neutrino telescopes

We deduce the cosmogenic neutrino flux by jointly analysing ultra high energy cosmic ray data from HiRes-I and II, AGASA and the Pierre Auger Observatory. We make two determinations of the neutrino flux by using a model-dependent method and a model-independent method. The former is well-known, and involves the use of a power-law injection spectrum. The latter is a regularized unfolding procedure. We then use neutrino flux bounds obtained by the RICE experiment to constrain the neutrino-nucleon inelastic cross section at energies inaccessible at colliders. The cross section bounds obtained using the cosmogenic fluxes derived by unfolding are the most model-independent bounds to date.Comment: 20 pages, 6 figures, 2 table

Multiparticle azimuthal correlations for extracting event-by-event elliptic and triangular flow in Au + Au collisions at sNN =200 GeV

We present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity 1<|η|<3 in Au + Au collisions at sNN=200 GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients v2{2},v2{4},v2{6}, and v2{8}, and triangular flow coefficients v3{2} and v3{4}. Using the small-variance limit, we estimate the mean and variance of the event-by-event v2 distribution from v2{2} and v2{4}. In a complementary analysis, we also use a folding procedure to study the distributions of v2 and v3 directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final-state momentum distributions are discussed