4,466 research outputs found
A Harmonic Extension Approach for Collaborative Ranking
We present a new perspective on graph-based methods for collaborative ranking
for recommender systems. Unlike user-based or item-based methods that compute a
weighted average of ratings given by the nearest neighbors, or low-rank
approximation methods using convex optimization and the nuclear norm, we
formulate matrix completion as a series of semi-supervised learning problems,
and propagate the known ratings to the missing ones on the user-user or
item-item graph globally. The semi-supervised learning problems are expressed
as Laplace-Beltrami equations on a manifold, or namely, harmonic extension, and
can be discretized by a point integral method. We show that our approach does
not impose a low-rank Euclidean subspace on the data points, but instead
minimizes the dimension of the underlying manifold. Our method, named LDM (low
dimensional manifold), turns out to be particularly effective in generating
rankings of items, showing decent computational efficiency and robust ranking
quality compared to state-of-the-art methods
How random is your heart beat?
We measure the content of random uncorrelated noise in heart rate variability
using a general method of noise level estimation using a coarse grained
entropy. We show that usually - except for atrial fibrillation - the level of
such noise is within 5 - 15% of the variance of the data and that the
variability due to the linearly correlated processes is dominant in all cases
analysed but atrial fibrillation. The nonlinear deterministic content of heart
rate variability remains significant and may not be ignored.Comment: see http://urbanowicz.org.p
About the fastest growth of Order Parameter in Models of Percolation
Can there be a `Litmus test' for determining the nature of transition in
models of percolation? In this paper we argue that the answer is in the
affirmative. All one needs to do is to measure the `growth exponent' of
the largest component at the percolation threshold; or
determines if the transition is continuous or discontinuous. We show that a
related exponent which describes how the average maximal jump
sizes in the Order Parameter decays on increasing the system size, is the
single exponent that describes the finite-size scaling of a number of
distributions related to the fastest growth of the Order Parameter in these
problems. Excellent quality scaling analysis are presented for the two single
peak distributions corresponding to the Order Parameters at the two ends of the
maximal jump, the bimodal distribution constructed by interpolation of these
distributions and for the distribution of the maximal jump in the Order
Parameter.Comment: 8 pages, 9 figure
Exchange interaction effects in the thermodynamic properties of quantum dots
We study electron-electron interaction effects in the thermodynamic
properties of quantum-dot systems. We obtain the direct and exchange
contributions to the specific heat C_v in the self-consistent Hartree-Fock
approximation at finite temperatures. An exchange-induced phase transition is
observed and the transition temperature is shown to be inversely proportional
to the size of the system. The exchange contribution to C_v dominates over the
direct and kinetic contributions in the intermediate regime of interaction
strength (r_s ~ 1). Furthermore, the electron-electron interaction modifies
both the amplitude and the period of magnetic field induced oscillations in
C_v.Comment: 4 pages, 4 figures; To appear in Phys. Rev.
Aspectos Sobre Os Hábitos de Nidificação e Atividades de Forrageio de Bombus Transversalis ( Olivier, 1789)
Levy distribution and long correlation times in supermarket sales
Sales data in a commodity market (supermarket sales to consumers) has been
analysed by studying the fluctuation spectrum and noise correlations. Three
related products (ketchup, mayonnaise and curry sauce) have been analysed. Most
noise in sales is caused by promotions, but here we focus on the fluctuations
in baseline sales. These characterise the dynamics of the market. Four hitherto
unnoticed effects have been found that are difficult to explain from simple
econometric models. These effects are: (1) the noise level in baseline sales is
much higher than can be expected for uncorrelated sales events; (2) weekly
baseline sales differences are distributed according to a broad non-Gaussian
function with fat tails; (3) these fluctuations follow a Levy distribution of
exponent alpha = 1.4, similar to financial exchange markets and in stock
markets; and (4) this noise is correlated over a period of 10 to 11 weeks, or
shows an apparent power law spectrum. The similarity to stock markets suggests
that models developed to describe these markets may be applied to describe the
collective behaviour of consumers.Comment: 19 pages, 7 figures, accepted for publication in Physica
Spontaneous symmetry breaking in amnestically induced persistence
We investigate a recently proposed non-Markovian random walk model
characterized by loss of memories of the recent past and amnestically induced
persistence. We report numerical and analytical results showing the complete
phase diagram, consisting of 4 phases, for this system: (i) classical
nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence
and (iv) log-periodic persistence driven by negative feedback. The first two
phases possess continuous scale invariance symmetry, however log-periodicity
breaks this symmetry. Instead, log-periodic motion satisfies discrete scale
invariance symmetry, with complex rather than real fractal dimensions. We find
for log-periodic persistence evidence not only of statistical but also of
geometric self-similarity.Comment: 4 pages, 2 color fig
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