Optimal Data-Dependent Hashing for Approximate Near Neighbors

We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an $n$-point data set in a $d$-dimensional space our data structure achieves query time $O(d n^{\rho+o(1)})$ and space $O(n^{1+\rho+o(1)} + dn)$, where $\rho=\tfrac{1}{2c^2-1}$ for the Euclidean space and approximation $c>1$. For the Hamming space, we obtain an exponent of $\rho=\tfrac{1}{2c-1}$. Our result completes the direction set forth in [AINR14] who gave a proof-of-concept that data-dependent hashing can outperform classical Locality Sensitive Hashing (LSH). In contrast to [AINR14], the new bound is not only optimal, but in fact improves over the best (optimal) LSH data structures [IM98,AI06] for all approximation factors $c>1$. From the technical perspective, we proceed by decomposing an arbitrary dataset into several subsets that are, in a certain sense, pseudo-random.Comment: 36 pages, 5 figures, an extended abstract appeared in the proceedings of the 47th ACM Symposium on Theory of Computing (STOC 2015

Predictability of large future changes in a competitive evolving population

The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a generic multi-agent population competing for a limited resource, and find that the level of predictability actually increases prior to a large change. These large changes hence arise as a predictable consequence of information encoded in the system's global state.Comment: 10 pages, 3 figure

Excitation energies, hyperfine constants, E1, E2, M1 transition rates, and lifetimes of (6s2)nl states in Tl I and Pb II

Energies of np (n=6-9), ns (n=7-9), nd (n=6-8), and nf (n=5-6) states in Tl I and Pb II are obtained using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 72 possible electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to obtain np(3/2) - mp(1/2) (n,m=6,7) transition rates. Hyperfine constants A are evaluated for a number of states in 205Tl. First-, second-, third-, and all-order corrections to the energies and matrix elements and first- and second-order Breit corrections to energies are calculated. In our implementation of the all-order method, single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. These calculations provide a theoretical benchmark for comparison with experiment and theory.Comment: twelve tables, no figure

Structure of human transthyretin complexed with bromophenols: a new mode of binding

The binding of two organohalogen substances, pentabromophenol (PBP) and 2,4,6-tribromophenol (TBP), to human transthyretin (TTR), a thyroid hormone transport protein, has been studied by in vitro competitive binding assays and by X-ray crystallography. Both compounds bind to TTR with high affinity, in competition with the natural ligand thyroxine (

Syndecan-4 knockout leads to reduced extracellular transglutaminase-2 and protects against tubulointerstitial fibrosis

Transglutaminase type 2 (TG2) is an extracellular matrix crosslinking enzyme with a pivotal role in kidney fibrosis. The interaction of TG2 with the heparan sulfate proteoglycan syndecan-4 (Sdc4) regulates the cell surface trafficking, localization, and activity of TG2 in vitro but remains unstudied in vivo. We tested the hypothesis that Sdc4 is required for cell surface targeting of TG2 and the development of kidney fibrosis in CKD. Wild-type and Sdc4-null mice were subjected to unilateral ureteric obstruction and aristolochic acid nephropathy (AAN) as experimental models of kidney fibrosis. Analysis of renal scarring by Masson trichrome staining, kidney hydroxyproline levels, and collagen immunofluorescence demonstrated progressive fibrosis associated with increases in extracellular TG2 and TG activity in the tubulointerstitium in both models. Knockout of Sdc-4 reduced these effects and prevented AAN-induced increases in total and active TGF-b1. In wild-type mice subjected to AAN, extracellular TG2 colocalized with Sdc4 in the tubular interstitium and basement membrane, where TG2 also colocalized with heparan sulfate chains. Heparitinase I, which selectively cleaves heparan sulfate, completely abolished extracellular TG2 in normal and diseased kidney sections. In conclusion, the lack of Sdc4 heparan sulfate chains in the kidneys of Sdc4-null mice abrogates injury-induced externalization of TG2, thereby preventing profibrotic crosslinking of extracellular matrix and recruitment of large latent TGF-b1. This finding suggests that targeting the TG2- Sdc4 interaction may provide a specific interventional strategy for the treatment of CKD

Developing number sense with Fingu: a preschooler’s embodied mathematics during interactions with a multi-touch digital game

Early number sense, including subitizing and composition, is a foundation for mathematics, and bodies, especially fingers, are integral to number sense. Multi-touch technology offers innovative opportunities for developing and studying number sense, especially using conceptually congruent gestures that match the mathematics. However, there have been few investigations of the development of early number sense, particularly in embodied forms. Therefore, this mixed-methods study explores a preschooler’s development of early number sense during a month of interactions with the multi-touch digital mathematics game Fingu. Key findings related to the development of early number sense include relevance of configuration and quantity, relationships among gestures and quantities, and development of estimation and precision. This research adds new perspectives to our understandings of early number sense research and practice, calling for consideration of embodiment and conceptually congruent gestures

A study of rotating globular clusters - the case of the old, metal-poor globular cluster NGC 4372

Aims: We present the first in-depth study of the kinematic properties and derive the structural parameters of NGC 4372 based on the fit of a Plummer profile and a rotating, physical model. We explore the link between internal rotation to different cluster properties and together with similar studies of more GCs, we put these in the context of globular cluster formation and evolution. Methods: We present radial velocities for 131 cluster member stars measured from high-resolution FLAMES/GIRAFFE observations. Their membership to the GC is additionally confirmed from precise metallicity estimates. Using this kinematic data set we build a velocity dispersion profile and a systemic rotation curve. Additionally, we obtain an elliptical number density profile of NGC 4372 based on optical images using a MCMC fitting algorithm. From this we derive the cluster's half-light radius and ellipticity as r_h=3.4'+/-0.04' and e=0.08+/-0.01. Finally, we give a physical interpretation of the observed morphological and kinematic properties of this GC by fitting an axisymmetric, differentially rotating, dynamical model. Results: Our results show that NGC 4372 has an unusually high ratio of rotation amplitude to velocity dispersion (1.2 vs. 4.5 km/s) for its metallicity. This, however, puts it in line with two other exceptional, very metal-poor GCs - M 15 and NGC 4590. We also find a mild flattening of NGC 4372 in the direction of its rotation. Given its old age, this suggests that the flattening is indeed caused by the systemic rotation rather than tidal interactions with the Galaxy. Additionally, we estimate the dynamical mass of the GC M_dyn=2.0+/-0.5 x 10^5 M_Sun based on the dynamical model, which constrains the mass-to-light ratio of NGC 4372 between 1.4 and 2.3 M_Sun/L_Sun, representative of an old, purely stellar population.Comment: Accepted for publication in A&A, 12 pages, 14 figures, 2 table

Holographic Coulomb Branch Flows with N=1 Supersymmetry

We obtain a large, new class of N=1 supersymmetric holographic flow backgrounds with U(1)^3 symmetry. These solutions correspond to flows toward the Coulomb branch of the non-trivial N=1 supersymmetric fixed point. The massless (complex) chiral fields are allowed to develop vevs that are independent of their two phase angles, and this corresponds to allowing the brane to spread with arbitrary, U(1)^2 invariant, radial distributions in each of these directions. Our solutions are "almost Calabi-Yau:" The metric is hermitian with respect to an integrable complex structure, but is not Kahler. The "modulus squared" of the holomorphic (3,0)-form is the volume form, and the complete solution is characterized by a function that must satisfy a single partial differential equation that is closely related to the Calabi-Yau condition. The deformation from a standard Calabi-Yau background is driven by a non-trivial, non-normalizable 3-form flux dual to a fermion mass that reduces the supersymmetry to N=1. This flux also induces dielectric polarization of the D3-branes into D5-branes.Comment: 22 pages; harvmac. Typos corrected;small improvements in presentatio

Universal magneto-orbital ordering in the divalent AA-site quadruple perovskite manganites AAMn7_7O12_{12} (AA = Ca, Sr, Cd, and Pb)

Through analysis of variable temperature neutron powder diffraction data, we present solutions for the magnetic structures of SrMn$_7$O$_{12}$, CdMn$_7$O$_{12}$, and PbMn$_7$O$_{12}$ in all long-range ordered phases. The three compounds were found to have magnetic structures analogous to that reported for CaMn$_7$O$_{12}$. They all feature a higher temperature lock-in phase with \emph{commensurate} magneto-orbital coupling, and a delocked, multi-\textbf{k} magnetic ground state where \emph{incommensurate} magneto-orbital coupling gives rise to a constant-moment magnetic helix with modulated spin helicity. CdMn$_7$O$_{12}$ represents a special case in which the orbital modulation is commensurate with the crystal lattice and involves stacking of fully and partially polarized orbital states. Our results provide a robust confirmation of the phenomenological model for magneto-orbital coupling previously presented for CaMn$_7$O$_{12}$. Furthermore, we show that the model is universal to the $A^{2+}$ quadruple perovskite manganites synthesised to date, and that it is tunable by selection of the $A$-site ionic radius

5-micron photometry of late-type dwarfs

We present narrowband-M photometry of nine low-mass dwarfs with spectral types ranging from M2.5 to L0.5. Combining the (L'-M') colours derived from our observations with data from the literature, we find colours consistent with a Rayleigh-Jeans flux distribution for spectral types earlier than M5, but enhanced F_3.8/F_4.7 flux ratios (negative (L'-M') colours) at later spectral types. This probably reflects increased absorption at M' due to the CO fundamental band. We compare our results against recent model predictions and briefly discuss the implications.Comment: accepted for the Astronomical Journa