24,312 research outputs found
Fast Exact Search in Hamming Space with Multi-Index Hashing
There is growing interest in representing image data and feature descriptors
using compact binary codes for fast near neighbor search. Although binary codes
are motivated by their use as direct indices (addresses) into a hash table,
codes longer than 32 bits are not being used as such, as it was thought to be
ineffective. We introduce a rigorous way to build multiple hash tables on
binary code substrings that enables exact k-nearest neighbor search in Hamming
space. The approach is storage efficient and straightforward to implement.
Theoretical analysis shows that the algorithm exhibits sub-linear run-time
behavior for uniformly distributed codes. Empirical results show dramatic
speedups over a linear scan baseline for datasets of up to one billion codes of
64, 128, or 256 bits
A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations
In this paper, we prove a new identity for the least-square solution of an
over-determined set of linear equation , where is an
full-rank matrix, is a column-vector of dimension , and (the number
of equations) is larger than or equal to (the dimension of the unknown
vector ). Generally, the equations are inconsistent and there is no feasible
solution for unless belongs to the column-span of . In the
least-square approach, a candidate solution is found as the unique that
minimizes the error function .
We propose a more general approach that consist in considering all the
consistent subset of the equations, finding their solutions, and taking a
weighted average of them to build a candidate solution. In particular, we show
that by weighting the solutions with the squared determinant of their
coefficient matrix, the resulting candidate solution coincides with the least
square solution
Double point self-intersection surfaces of immersions
A self-transverse immersion of a smooth manifold M^{k+2} in R^{2k+2} has a
double point self-intersection set which is the image of an immersion of a
smooth surface, the double point self-intersection surface. We prove that this
surface may have odd Euler characteristic if and only if k is congruent to 1
modulo 4 or k+1 is a power of 2. This corrects a previously published result by
Andras Szucs.
The method of proof is to evaluate the Stiefel-Whitney numbers of the double
point self-intersection surface. By earier work of the authors these numbers
can be read off from the Hurewicz image h(\alpha ) in H_{2k+2}\Omega ^{\infty
}\Sigma ^{\infty }MO(k) of the element \alpha in \pi _{2k+2}\Omega ^{\infty
}\Sigma ^{\infty }MO(k) corresponding to the immersion under the
Pontrjagin-Thom construction.Comment: 22 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper4.abs.htm
An algorithmic proof for the completeness of two-dimensional Ising model
We show that the two dimensional Ising model is complete, in the sense that
the partition function of any lattice model on any graph is equal to the
partition function of the 2D Ising model with complex coupling. The latter
model has all its spin-spin coupling equal to i\pi/4 and all the parameters of
the original model are contained in the local magnetic fields of the Ising
model. This result has already been derived by using techniques from quantum
information theory and by exploiting the universality of cluster states. Here
we do not use the quantum formalism and hence make the completeness result
accessible to a wide audience. Furthermore our method has the advantage of
being algorithmic in nature so that by following a set of simple graphical
transformations, one is able to transform any discrete lattice model to an
Ising model defined on a (polynomially) larger 2D lattice.Comment: 18 pages, 15 figures, Accepted for publication in Physical Review
Hydrogen adsorption in metal-organic frameworks: the role of nuclear quantum effects
The role of nuclear quantum effects on the adsorption of molecular hydrogen
in metal-organic frameworks (MOFs) has been investigated on grounds of
Grand-Canonical Quantized Liquid Density-Functional Theory (GC-QLDFT)
calculations. For this purpose, we have carefully validated classical H2 -host
interaction potentials that are obtained by fitting Born-Oppenheimer ab initio
reference data. The hydrogen adsorption has first been assessed classically
using Liquid Density-Functional Theory (LDFT) and the Grand-Canonical Monte
Carlo (GCMC) methods. The results have been compared against the semi-classical
treatment of quantum effects by applying the Feynman-Hibbs correction to the
Born-Oppenheimer-derived potentials, and by explicit treatment within the
Grand-Canonical Quantized Liquid Density-Functional Theory (GC-QLDFT). The
results are compared with experimental data and indicate pronounced quantum and
possibly many-particle effects. After validation calculations have been carried
out for IRMOF-1 (MOF-5), GC-QLDFT is applied to study the adsorption of H2 in a
series of MOFs, including IRMOF-4, -6, -8, -9, -10, -12, -14, -16, -18 and
MOF-177. Finally, we discuss the evolution of the H2 quantum fluid with
increasing pressure and lowering temperature
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