5,248 research outputs found
M-Theory Inflation from Multi M5-Brane Dynamics
We derive inflation from M-theory on S^1/Z_2 via the non-perturbative
dynamics of N M5-branes. The open membrane instanton interactions between the
M5-branes give rise to exponential potentials which are too steep for inflation
individually but lead to inflation when combined together. The resulting type
of inflation, known as assisted inflation, facilitates considerably the
requirement of having all moduli, except the inflaton, stabilized at the
beginning of inflation. During inflation the distances between the M5-branes,
which correspond to the inflatons, grow until they reach the size of the
S^1/Z_2 orbifold. At this stage the M5-branes will reheat the universe by
dissolving into the boundaries through small instanton transitions. Further
flux and non-perturbative contributions become important at this late stage,
bringing inflation to an end and stabilizing the moduli. We find that with
moderate values for N, one obtains both a sufficient amount of e-foldings and
the right size for the spectral index.Comment: 30 pages, 3 figures; v3: one comment and refs adde
Methods of Hierarchical Clustering
We survey agglomerative hierarchical clustering algorithms and discuss
efficient implementations that are available in R and other software
environments. We look at hierarchical self-organizing maps, and mixture models.
We review grid-based clustering, focusing on hierarchical density-based
approaches. Finally we describe a recently developed very efficient (linear
time) hierarchical clustering algorithm, which can also be viewed as a
hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference
Monte Carlo Study of the Precipitation Kinetics of Al3zr in Al-Zr
Zr precipitates in Al to form the phase Al3Zr. For a low supersaturation in
Zr of the fcc solid solution, it has been observed that during the
precipitation first steps the Al3Zr precipitates have the metastable L12
structure and that they transform themselves to the stable DO23 structure for
long enough annealing time. The aim of this study is to model the kinetics of
precipitation during this nucleation stage. We use FP-LMTO (Full-Potential
Linear-Mu n-Tin-Orbitals) calculations to fit a generalized Ising model
describing thermodynamics of the Al-Zr system. As we are interested in the
nucleation stage, the structures considered to obtain the interactions of the
Ising model are lying on a perfect fcc lattice having the lattice parameter of
Al. This allows us to stabilize the L12 structure with respect to the DO23. In
order to be able to take into account the influence of local environment on
kinetics, interactions for the tetrahedron of first nearest-neighbors are
considered, and for the pair of second nearest neighbours so as to stabilize
the L12 structure. We then generalize our description of the configurational
energy of the binary Al-Zr to the one of the ternary Al-Zr-Vacancy system by
including interactions with vacancies. Saddle point energies for the migration
of the vacancy are fitted using experimental di usion coe cients. This model is
then employed in a kinetic Monte Carlo simulation which considers the di usion
through the jumps of a vacancy. Thus we are able to study the Al3Zr kinetics of
nucleation.Comment: Proceeding of the Third International Alloy Conference, Lisbon 2002.
Published in P.E.A. Turchi, A. Gonis, K. Rajan and A. Meike (Eds.), Complex
Inorganic Solids - Structural, Stability, and Magnetic Properties of Alloys,
(Springer Verlag, New York, 2005), pp. 215-24
MRPR: a MapReduce solution for prototype reduction in big data classification
In the era of big data, analyzing and extracting knowledge from large-scale data sets is a very interesting and challenging task. The application of standard data mining tools in such data sets is not straightforward. Hence, a new class of scalable mining method that embraces the huge storage and processing capacity of cloud platforms is required. In this work, we propose a novel distributed partitioning methodology for prototype reduction techniques in nearest neighbor classification. These methods aim at representing original training data sets as a reduced number of instances. Their main purposes are to speed up the classification process and reduce the storage requirements and sensitivity to noise of the nearest neighbor rule. However, the standard prototype reduction methods cannot cope with very large data sets. To overcome this limitation, we develop a MapReduce-based framework to distribute the functioning of these algorithms through a cluster of computing elements, proposing several algorithmic strategies to integrate multiple partial solutions (reduced sets of prototypes) into a single one. The proposed model enables prototype reduction algorithms to be applied over big data classification problems without significant accuracy loss. We test the speeding up capabilities of our model with data sets up to 5.7 millions of instances. The results show that this model is a suitable tool to enhance the performance of the nearest neighbor classifier with big data
Evolution of networks
We review the recent fast progress in statistical physics of evolving
networks. Interest has focused mainly on the structural properties of random
complex networks in communications, biology, social sciences and economics. A
number of giant artificial networks of such a kind came into existence
recently. This opens a wide field for the study of their topology, evolution,
and complex processes occurring in them. Such networks possess a rich set of
scaling properties. A number of them are scale-free and show striking
resilience against random breakdowns. In spite of large sizes of these
networks, the distances between most their vertices are short -- a feature
known as the ``small-world'' effect. We discuss how growing networks
self-organize into scale-free structures and the role of the mechanism of
preferential linking. We consider the topological and structural properties of
evolving networks, and percolation in these networks. We present a number of
models demonstrating the main features of evolving networks and discuss current
approaches for their simulation and analytical study. Applications of the
general results to particular networks in Nature are discussed. We demonstrate
the generic connections of the network growth processes with the general
problems of non-equilibrium physics, econophysics, evolutionary biology, etc.Comment: 67 pages, updated, revised, and extended version of review, submitted
to Adv. Phy
Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in
which magnetic frustration promotes the formation of local singlets. Our
results include a theory for 2d valence-bond solids subject to weak bond
randomness, as well as extensions to stronger disorder regimes where we make
connections with quantum spin liquids. We find, on various lattices, that the
destruction of a valence-bond solid phase by weak quenched disorder leads
inevitably to the nucleation of topological defects carrying spin-1/2 moments.
This renormalizes the lattice into a strongly random spin network with
interesting low-energy excitations. Similarly when short-ranged valence bonds
would be pinned by stronger disorder, we find that this putative glass is
unstable to defects that carry spin-1/2 magnetic moments, and whose residual
interactions decide the ultimate low energy fate. Motivated by these results we
conjecture Lieb-Schultz-Mattis-like restrictions on ground states for
disordered magnets with spin-1/2 per statistical unit cell. These conjectures
are supported by an argument for 1d spin chains. We apply insights from this
study to the phenomenology of YbMgGaO, a recently discovered triangular
lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We
instead explore a description based on the present theory. Experimental
signatures, including unusual specific heat, thermal conductivity, and
dynamical structure factor, and their behavior in a magnetic field, are
predicted from the theory, and compare favorably with existing measurements on
YbMgGaO and related materials.Comment: v2: Stylistic revisions to improve clarity. 22 pages, 8 figures, 2
tables main text; 13 pages, 3 figures appendice
k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)
Perhaps the most straightforward classifier in the arsenal or machine
learning techniques is the Nearest Neighbour Classifier -- classification is
achieved by identifying the nearest neighbours to a query example and using
those neighbours to determine the class of the query. This approach to
classification is of particular importance because issues of poor run-time
performance is not such a problem these days with the computational power that
is available. This paper presents an overview of techniques for Nearest
Neighbour classification focusing on; mechanisms for assessing similarity
(distance), computational issues in identifying nearest neighbours and
mechanisms for reducing the dimension of the data.
This paper is the second edition of a paper previously published as a
technical report. Sections on similarity measures for time-series, retrieval
speed-up and intrinsic dimensionality have been added. An Appendix is included
providing access to Python code for the key methods.Comment: 22 pages, 15 figures: An updated edition of an older tutorial on kN
Nearest-neighbor resonating valence bonds in YbMgGaO4
Since its proposal by Anderson, resonating valence bonds (RVB) formed by a
superposition of fluctuating singlet pairs have been a paradigmatic concept in
understanding quantum spin liquids (QSL). Here, we show that excitations
related to singlet breaking on nearest-neighbor bonds describe the high-energy
part of the excitation spectrum in YbMgGaO4, the effective spin-1/2 frustrated
antiferromagnet on the triangular lattice, as originally considered by
Anderson. By a thorough single-crystal inelastic neutron scattering (INS)
study, we demonstrate that nearest-neighbor RVB excitations account for the
bulk of the spectral weight above 0.5 meV. This renders YbMgGaO4 the first
experimental system where putative RVB correlations restricted to nearest
neighbors are observed, and poses a fundamental question of how complex
interactions on the triangular lattice conspire to form this unique many-body
state.Comment: To be published in Nature Communication
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