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 $10^{-6}$ 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 $M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In particular, we investigate the role of mapping class group of $\Sigma$ 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 $k$ 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 $k\leftrightarrow1/k$ 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