52,872 research outputs found
Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory
Bayes statistics and statistical physics have the common mathematical
structure, where the log likelihood function corresponds to the random
Hamiltonian. Recently, it was discovered that the asymptotic learning curves in
Bayes estimation are subject to a universal law, even if the log likelihood
function can not be approximated by any quadratic form. However, it is left
unknown what mathematical property ensures such a universal law. In this paper,
we define a renormalizable condition of the statistical estimation problem, and
show that, under such a condition, the asymptotic learning curves are ensured
to be subject to the universal law, even if the true distribution is
unrealizable and singular for a statistical model. Also we study a
nonrenormalizable case, in which the learning curves have the different
asymptotic behaviors from the universal law
Formation of hydrogen peroxide and water from the reaction of cold hydrogen atoms with solid oxygen at 10K
The reactions of cold H atoms with solid O2 molecules were investigated at 10
K. The formation of H2O2 and H2O has been confirmed by in-situ infrared
spectroscopy. We found that the reaction proceeds very efficiently and obtained
the effective reaction rates. This is the first clear experimental evidence of
the formation of water molecules under conditions mimicking those found in cold
interstellar molecular clouds. Based on the experimental results, we discuss
the reaction mechanism and astrophysical implications.Comment: 12 pages, 3 Postscript figures, use package amsmath, amssymb,
graphic
The Complexity of Kings
A king in a directed graph is a node from which each node in the graph can be
reached via paths of length at most two. There is a broad literature on
tournaments (completely oriented digraphs), and it has been known for more than
half a century that all tournaments have at least one king [Lan53]. Recently,
kings have proven useful in theoretical computer science, in particular in the
study of the complexity of the semifeasible sets [HNP98,HT05] and in the study
of the complexity of reachability problems [Tan01,NT02].
In this paper, we study the complexity of recognizing kings. For each
succinctly specified family of tournaments, the king problem is known to belong
to [HOZZ]. We prove that this bound is optimal: We construct a
succinctly specified tournament family whose king problem is
-complete. It follows easily from our proof approach that the problem
of testing kingship in succinctly specified graphs (which need not be
tournaments) is -complete. We also obtain -completeness
results for k-kings in succinctly specified j-partite tournaments, , and we generalize our main construction to show that -completeness
holds for testing k-kingship in succinctly specified families of tournaments
for all
Single-electron transistors in electromagnetic environments
The current-voltage (I-V) characteristics of single-electron transistors
(SETs) have been measured in various electromagnetic environments. Some SETs
were biased with one-dimensional arrays of dc superconducting quantum
interference devices (SQUIDs). The purpose was to provide the SETs with a
magnetic-field-tunable environment in the superconducting state, and a
high-impedance environment in the normal state. The comparison of SETs with
SQUID arrays and those without arrays in the normal state confirmed that the
effective charging energy of SETs in the normal state becomes larger in the
high-impedance environment, as expected theoretically. In SETs with SQUID
arrays in the superconducting state, as the zero-bias resistance of the SQUID
arrays was increased to be much larger than the quantum resistance R_K = h/e^2
= 26 kohm, a sharp Coulomb blockade was induced, and the current modulation by
the gate-induced charge was changed from e periodic to 2e periodic at a bias
point 0<|V|<2D_0/e, where D_0 is the superconducting energy gap. The author
discusses the Coulomb blockade and its dependence on the gate-induced charge in
terms of the single Josephson junction with gate-tunable junction capacitance.Comment: 8 pages with 10 embedded figures, RevTeX4, published versio
Transition from Band insulator to Bose-Einstein Condensate superfluid and Mott State of Cold Fermi Gases with Multiband Effects in Optical Lattices
We study two models realized by two-component Fermi gases loaded in optical
lattices. We clarify that multi-band effects inevitably caused by the optical
lattices generate a rich structure, when the systems crossover from the region
of weakly bound molecular bosons to the region of strongly bound atomic bosons.
Here the crossover can be controlled by attractive fermion interaction. One of
the present models is a case with attractive fermion interaction, where an
insulator-superfluid transition takes place. The transition is characterized as
the transition between a band insulator and a Bose-Einstein condensate (BEC)
superfluid state. Differing from the conventional BCS superfluid transition,
this transition shows unconventional properties. In contrast to the one
particle excitation gap scaled by the superfluid order parameter in the
conventional BCS transition, because of the multi-band effects, a large gap of
one-particle density of states is retained all through the transition although
the superfluid order grows continuously from zero. A reentrant transition with
lowering temperature is another unconventionality. The other model is the case
with coexisting attractive and repulsive interactions. Within a mean field
treatment, we find a new insulating state, an orbital ordered insulator. This
insulator is one candidate for the Mott insulator of molecular bosons and is
the first example that the orbital internal degrees of freedom of molecular
bosons appears explicitly. Besides the emergence of a new phase, a coexisting
phase also appears where superfluidity and an orbital order coexist just by
doping holes or particles. The insulating and superfluid particles show
differentiation in momentum space as in the high-Tc cuprate superconductors.Comment: 13 pages, 10 figure
Boolean Operations, Joins, and the Extended Low Hierarchy
We prove that the join of two sets may actually fall into a lower level of
the extended low hierarchy than either of the sets. In particular, there exist
sets that are not in the second level of the extended low hierarchy, EL_2, yet
their join is in EL_2. That is, in terms of extended lowness, the join operator
can lower complexity. Since in a strong intuitive sense the join does not lower
complexity, our result suggests that the extended low hierarchy is unnatural as
a complexity measure. We also study the closure properties of EL_ and prove
that EL_2 is not closed under certain Boolean operations. To this end, we
establish the first known (and optimal) EL_2 lower bounds for certain notions
generalizing Selman's P-selectivity, which may be regarded as an interesting
result in its own right.Comment: 12 page
Quantum Valence Criticality as Origin of Unconventional Critical Phenomena
It is shown that unconventional critical phenomena commonly observed in
paramagnetic metals YbRh2Si2, YbRh2(Si0.95Ge0.05)2, and beta-YbAlB4 is
naturally explained by the quantum criticality of Yb-valence fluctuations. We
construct the mode coupling theory taking account of local correlation effects
of f electrons and find that unconventional criticality is caused by the
locality of the valence fluctuation mode. We show that measured low-temperature
anomalies such as divergence of uniform spin susceptibility \chi T^{-\zeta)
with giving rise to a huge enhancement of the Wilson ratio and the
emergence of T-linear resistivity are explained in a unified way.Comment: 5 pages, 3 figures, to be published in Physical Review Letter
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