5,589 research outputs found
Distribution of Mutual Information
The mutual information of two random variables i and j with joint
probabilities t_ij is commonly used in learning Bayesian nets as well as in
many other fields. The chances t_ij are usually estimated by the empirical
sampling frequency n_ij/n leading to a point estimate I(n_ij/n) for the mutual
information. To answer questions like "is I(n_ij/n) consistent with zero?" or
"what is the probability that the true mutual information is much larger than
the point estimate?" one has to go beyond the point estimate. In the Bayesian
framework one can answer these questions by utilizing a (second order) prior
distribution p(t) comprising prior information about t. From the prior p(t) one
can compute the posterior p(t|n), from which the distribution p(I|n) of the
mutual information can be calculated. We derive reliable and quickly computable
approximations for p(I|n). We concentrate on the mean, variance, skewness, and
kurtosis, and non-informative priors. For the mean we also give an exact
expression. Numerical issues and the range of validity are discussed.Comment: 8 page
On a q-difference Painlev\'e III equation: II. Rational solutions
Rational solutions for a -difference analogue of the Painlev\'e III
equation are considered. A Determinant formula of Jacobi-Trudi type for the
solutions is constructed.Comment: Archive version is already official. Published by JNMP at
http://www.sm.luth.se/math/JNMP
Formation of homophily in academic performance: Students change their friends rather than performance
Homophily, the tendency of individuals to associate with others who share similar traits, has been identified as a major driving force in the formation and evolution of social ties. In many cases, it is not clear if homophily is the result of a socialization process, where individuals change their traits according to the dominance of that trait in their local social networks, or if it results from a selection process, in which individuals reshape their social networks so that their traits match those in the new environment. Here we demonstrate the detailed temporal formation of strong homophily in academic achievements of high school and university students. We analyze a unique dataset that contains information about the detailed time evolution of a friendship network of 6,000 students across 42 months. Combining the evolving social network data with the time series of the academic performance (GPA) of individual students, we show that academic homophily is a result of selection: students prefer to gradually reorganize their social networks according to their performance levels, rather than adapting their performance to the level of their local group. We find no signs for a pull effect, where a social environment of good performers motivates bad students to improve their performance. We are able to understand the underlying dynamics of grades and networks with a simple model. The lack of a social pull effect in classical educational settings could have important implications for the understanding of the observed persistence of segregation, inequality and social immobility in societies
Reentrant Spin-Peierls Transition in Mg-Doped CuGeO_3
We report a synchrotron x-ray scattering study of the diluted spin-Peierls
(SP) material Cu_{1-x}Mg_xGeO_3. In a recent paper we have shown that the SP
dimerization attains long-range order only for x < x_c = 0.022(0.001). Here we
report that the SP transition is reentrant in the vicinity of the critical
concentration x_c. This is manifested by broadening of the SP dimerization
superlattice peaks below the reentrance temperature, T_r, which may mean either
the complete loss of the long-range SP order or the development of a
short-range ordered component within the long-range ordered SP state. Marked
hysteresis and very large relaxation times are found in the samples with Mg
concentrations in the vicinity of x_c. The reentrant transition is likely
related to the competing Neel transition which occurs at a temperature similar
to T_r. We argue that impurity-induced competing interchain interactions play
an essential role in these phenomena.Comment: 5 pages, 4 embedded eps figure
Reentrant Spin-Peierls Transition in Mg-Doped CuGeO_3
We report a synchrotron x-ray scattering study of the diluted spin-Peierls
(SP) material Cu_{1-x}Mg_xGeO_3. In a recent paper we have shown that the SP
dimerization attains long-range order only for x < x_c = 0.022(0.001). Here we
report that the SP transition is reentrant in the vicinity of the critical
concentration x_c. This is manifested by broadening of the SP dimerization
superlattice peaks below the reentrance temperature, T_r, which may mean either
the complete loss of the long-range SP order or the development of a
short-range ordered component within the long-range ordered SP state. Marked
hysteresis and very large relaxation times are found in the samples with Mg
concentrations in the vicinity of x_c. The reentrant transition is likely
related to the competing Neel transition which occurs at a temperature similar
to T_r. We argue that impurity-induced competing interchain interactions play
an essential role in these phenomena.Comment: 5 pages, 4 embedded eps figure
59Co-NQR study on superconducting NaxCoO2.yH2O
Layered Co oxide NaxCoO2.yH2O with a superconducting transition temperature
Tc =4.5 K has been studied by 59Co NQR. The nuclear spin relaxation rate 1/59T1
is nearly proportional to temperature T in the normal state. In the
superconducting state, it exhibits the coherence peak and decreases with
decreasing T below ~0.8Tc. Detailed comparison of the 1/T1T values and the
magnetic susceptibilities between NaxCoO2.yH2O and NaxCoO2 implies that the
metallic state of the former system is closer to a ferromagnetic phase than
that of the latter. These experimental results impose a restriction on the
mechanism of the superconductivity.Comment: 7 pages, 5 figures. to be published in J. Phys. Soc. Jpn. 72 (2003)
No.
Numerical study of pi-junction using spin filtering barriers
We numerically investigate the Josephson transport through ferromagnetic
insulators (FIs) by taking into account its band structure. By use of the
recursive Green's function method, we found the formation of the pi junction in
the case of the fully spin-polarized FI (FPFI), e.g., LaBaCuO.
Moreover, the 0-pi transition is induced by increasing the thickness of FPFI.
On the other hand, Josephson current through the Eu chalcogenides shows the pi
junction behavior in the case of the strong d-f hybridization between the
conduction d and the localized f electrons of Eu. Such FI-based Josephson
junctions may become a element in the architecture of future quantum
information devices.Comment: 9 pages, 5 figure
Ocean Planet or Thick Atmosphere: On the Mass-Radius Relationship for Solid Exoplanets with Massive Atmospheres
The bulk composition of an exoplanet is commonly inferred from its average
density. For small planets, however, the average density is not unique within
the range of compositions. Variations of a number of important planetary
parameters--which are difficult or impossible to constrain from measurements
alone--produce planets with the same average densities but widely varying bulk
compositions. We find that adding a gas envelope equivalent to 0.1%-10% of the
mass of a solid planet causes the radius to increase 5-60% above its gas-free
value. A planet with a given mass and radius might have substantial water ice
content (a so-called ocean planet) or alternatively a large rocky-iron core and
some H and/or He. For example, a wide variety of compositions can explain the
observed radius of GJ 436b, although all models require some H/He. We conclude
that the identification of water worlds based on the mass-radius relationship
alone is impossible unless a significant gas layer can be ruled out by other
means.Comment: 5 pages, 3 figures, accepted to Ap
Regulation of Inositol 1,4,5 Trisphosphate Receptors by InsP3 Receptor-Associated cGMP Kinase Substrate (IRAG)
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