40,567 research outputs found
Multi-Scale Link Prediction
The automated analysis of social networks has become an important problem due
to the proliferation of social networks, such as LiveJournal, Flickr and
Facebook. The scale of these social networks is massive and continues to grow
rapidly. An important problem in social network analysis is proximity
estimation that infers the closeness of different users. Link prediction, in
turn, is an important application of proximity estimation. However, many
methods for computing proximity measures have high computational complexity and
are thus prohibitive for large-scale link prediction problems. One way to
address this problem is to estimate proximity measures via low-rank
approximation. However, a single low-rank approximation may not be sufficient
to represent the behavior of the entire network. In this paper, we propose
Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can
handle massive networks. The basis idea of MSLP is to construct low rank
approximations of the network at multiple scales in an efficient manner. Based
on this approach, MSLP combines predictions at multiple scales to make robust
and accurate predictions. Experimental results on real-life datasets with more
than a million nodes show the superior performance and scalability of our
method.Comment: 20 pages, 10 figure
A Divide-and-Conquer Solver for Kernel Support Vector Machines
The kernel support vector machine (SVM) is one of the most widely used
classification methods; however, the amount of computation required becomes the
bottleneck when facing millions of samples. In this paper, we propose and
analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the
division step, we partition the kernel SVM problem into smaller subproblems by
clustering the data, so that each subproblem can be solved independently and
efficiently. We show theoretically that the support vectors identified by the
subproblem solution are likely to be support vectors of the entire kernel SVM
problem, provided that the problem is partitioned appropriately by kernel
clustering. In the conquer step, the local solutions from the subproblems are
used to initialize a global coordinate descent solver, which converges quickly
as suggested by our analysis. By extending this idea, we develop a multilevel
Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction
strategy, which outperforms state-of-the-art methods in terms of training
speed, testing accuracy, and memory usage. As an example, on the covtype
dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in
obtaining the exact SVM solution (to within relative error) which
achieves 96.15% prediction accuracy. Moreover, with our proposed early
prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes,
which is more than 100 times faster than LIBSVM
Laser-induced spin protection and switching in a specially designed magnetic dot: A theoretical investigation
Most laser-induced femtosecond magnetism investigations are done in magnetic
thin films. Nanostructured magnetic dots, with their reduced dimensionality,
present new opportunities for spin manipulation. Here we predict that if a
magnetic dot has a dipole-forbidden transition between the lowest occupied
molecular orbital (LUMO) and the highest unoccupied molecular orbital (HOMO),
but a dipole-allowed transition between LUMO+1 and HOMO, electromagnetically
inducedtransparency can be used to prevent ultrafast laser-induced spin
momentum reduction, or spin protection. This is realized through a strong dump
pulse to funnel the population into LUMO+1. If the time delay between the pump
and dump pulses is longer than 60 fs, a population inversion starts and spin
switching is achieved. Thesepredictions are detectable experimentally.Comment: 6 pages, three figur
Mapping class group and U(1) Chern-Simons theory on closed orientable surfaces
U(1) Chern-Simons theory is quantized canonically on manifolds of the form
, where is a closed orientable surface. In
particular, we investigate the role of mapping class group of in the
process of quantization. We show that, by requiring the quantum states to form
representation of the holonomy group and the large gauge transformation group,
both of which are deformed by quantum effect, the mapping class group can be
consistently represented, provided the Chern-Simons parameter satisfies an
interesting quantization condition. The representations of all the discrete
groups are unique, up to an arbitrary sub-representation of the mapping class
group. Also, we find a duality of the representations.Comment: 17 pages, 3 figure
Hot spin spots in the laser-induced demagnetization
Laser-induced femtosecond magnetism or femtomagnetism simultaneously relies
on two distinctive contributions: (a) the optical dipole interaction (ODI)
between a laser field and a magnetic system and (b) the spin expectation value
change (SEC) between two transition states. Surprisingly, up to now, no study
has taken both contributions into account simultaneously. Here we do so by
introducing a new concept of the optical spin generator, a product of SEC and
ODI between transition states. In ferromagnetic nickel, our first-principles
calculation demonstrates that the larger the value of optical spin generator
is, the larger the dynamic spin moment change is. This simple generator
directly links the time-dependent spin moment change {\Delta}Mk z (t) at every
crystal- momentum k point to its intrinsic electronic structure and magnetic
properties. Those hot spin spots are a direct manifestation of the optical spin
generator, and should be the focus of future research.Comment: 10 pages, 2 figures, [email protected]
On pairwise comparison matrices that can be made consistent by the modification of a few elements
Pairwise comparison matrices are often used in Multi-attribute Decision Making forweighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comparison matrix can be made consistent is examined. From practical point of view, the modification of 1, 2, or, for larger matrices, 3 elements seems to be relevant. These cases are characterized by using the graph representation of the matrices. Empirical examples illustrate that pairwise comparison matrices that can be made consistent by the modification of a few elements are present in the applications
- …