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

Effect of sintering temperature and heat treatment on electrical properties of indium oxide based ceramics

Indium oxide based ceramics with bismuth oxide addition were sintered in air in the temperature range 800-1300 ºC. Current-voltage characteristics of In2O3-Bi2O3 ceramics sintered at different temperatures are weakly nonlinear. After an additional heat treatment in air at about 200 ºC samples sintered at a temperature within the narrow range of about 1050-1100 ºC exhibit a current-limiting effect accompanied by low-frequency current oscillations. It is shown that the observed electrical properties are controlled by the grain-boundary barriers and the heat treatment in air at 200 ºC leads to the decrease in the barrier height. Electrical measurements, scanning electron microscopy and X-ray photoelectron spectroscopy results suggest that the current-limiting effect observed in In2O3-Bi2O3 can be explained in terms of the modified barrier model proposed earlier for the explanation of similar effect in In2O3-SrO ceramics

Dust in a few southern H II regions

The property of dust in four southern H II region/molecular cloud complexes (RCW 108, RCW 57, RCW 122, and G351.6-1.3) was discussed. These regions were observed at an effective wavelength of 150 micron using TIFR balloon borne 1 m telescope and deconvolved maps with a resolution of 1 min were obtained. The data were combined with other available data to derive the properties of the infrared emitting dust in these regions

Distribution of dust in W31 complex

W31 is a H II region/molecular cloud complex in the galactic plane at a distance of 6 Kpc. This complex consists of two prominent radio continuum sources (G10.2-0.3 and G10.3-0.1) representing H II regions. An extended region covering both these H II regions was mapped in the Far IR (FIR) using the TIFR 1 m balloon-borne telescope with an angular resolution of approx. 1 min and a dynamic range of 100. The resulting flux density distribution at an effective wavelength of 160 microns is presented. The coadded IRAS survey scan data at 60 and 100 microns were deconvolved using a maximum entropy method to generate the flux density maps of the same region. These 60 and 100 micron maps are given and are briefly discussed

Far-infrared observations of Circinus and NGC 4945 galaxies

Circinus and NGC 4945 are two galaxies luminous in the infrared and are characterized by compact non thermal radio nuclei, deep silicate absorption features and unusually strong water vapor maser luminosities. Moorwood and Glass (1984) have observed these galaxies extensively in the 1 to 20 micron range. In the far-infrared, observations up to 100 microns are available from the Infrared Astronomy Satellite (IRAS). In order to study the cool dust component of these galaxies, researchers observed them at 150 microns using the Tata Institute of Fundamental Research (TIFR) 100 cm balloon-borne telescope. Here, they report observations along with deconvolved maps at 50 and 100 microns obtained from the Chopped Photometric Channel (CPC) on board IRAS

Algebraic Aspects of Abelian Sandpile Models

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G, and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of toppling matrix. We construct scalar functions, linear in height variables of the pile, that are invariant toppling at any site. These invariants provide convenient coordinates to label the recurrent configurations of the sandpile. For an L X L square lattice, we show that g = L. In this case, we observe that the system has nontrivial symmetries coming from the action of the cyclotomic Galois group of the (2L+2)th roots of unity which operates on the set of eigenvalues of the toppling matrix. These eigenvalues are algebraic integers, whose product is the order |G|. With the help of this Galois group, we obtain an explicit factorizaration of |G|. We also use it to define other simpler, though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3

Measurement of Spin of Projectiles

Hitherto the spin of the projectile has been measured with the help of spin loop method (for magnetised projectiles) and Multishot Ballistic Synchro method (for magnetised and non-magnetised projectiles). This paper discusses the method of measurement of spinwith a single ballistic synchro picture; the advantage of this method is that it dispenses with elaborate and precise optical alignment, required for Multishot Ballistic Synchro method

Reactions of Hafnium Tetrachloride with Benzoyl Hydrazones

Hafnium tetrachloride reacts with monofunctional bidentate (BHyH) and bifunctional tridentate (BHy\u27H2) benzoyl hydrazones (derived from the condensation of benzoyl hydrazine with different aldehydes/ketones) in refluxing dichloromethane to form products of the type, HfC13(BHy), HfC12(BHy)2 and HfCb(BHy\u27). These reaction products have been characterized on the basis of elemental analysis, electrical conductance measurements and spectral (infrared and electronic) data