2,438 research outputs found
Statistical Mechanics of Dictionary Learning
Finding a basis matrix (dictionary) by which objective signals are
represented sparsely is of major relevance in various scientific and
technological fields. We consider a problem to learn a dictionary from a set of
training signals. We employ techniques of statistical mechanics of disordered
systems to evaluate the size of the training set necessary to typically succeed
in the dictionary learning. The results indicate that the necessary size is
much smaller than previously estimated, which theoretically supports and/or
encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 figure
Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution
We study evolutionary canalization using a spin-glass model with replica
theory, where spins and their interactions are dynamic variables whose
configurations correspond to phenotypes and genotypes, respectively. The spins
are updated under temperature T_S, and the genotypes evolve under temperature
T_J, according to the evolutionary fitness. It is found that adaptation occurs
at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S <
T_S^{RS}. The replica symmetric phase implies canalization, and replica
symmetry breaking at lower temperatures indicates loss of robustness.Comment: 5pages, 2 figure
About the maximal rank of 3-tensors over the real and the complex number field
High dimensional array data, tensor data, is becoming important in recent
days. Then maximal rank of tensors is important in theory and applications. In
this paper we consider the maximal rank of 3 tensors. It can be attacked from
various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and
Atkinson-Lloyd(1980). They treated the problem in the complex field, and we
will present various bounds over the real field by proving several lemmas and
propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen
Funnel landscape and mutational robustness as a result of evolution under thermal noise
In biological systems, expression dynamics to shape a fitted phenotype for
function has evolved through mutations to genes, as observed in the evolution
of funnel landscape in protein. We study this evolutionary process with a
statistical-mechanical model of interacting spins, where the fitted phenotype
is represented by a configuration of a given set of "target spins" and
interaction matrix J among spins is genotype evolving over generations. The
expression dynamics is given by stochastic process with temperature T_S to
decrease energy for a given set of J. The evolution of J is also stochastic
with temperature T_J, following mutation in J and selection based on a fitness
given by configurations of the target spins. Below a certain temperature
T_S^{c2}, the highly adapted J evolves, whereasanother phase transition
characterised by frustration occurs at T_S^{c1}<T_S^{c2}. At temperature lower
than T_S^{c1}, the Hamiltonian exhibits a spin-glass like phase, where the
dynamics requires long time steps to produce the fitted phenotype, and the
fitness often decreases drastically by single mutation. In contrast, in the
intermediate temperature phase between T_S^{c1} and T_S^{c2}, the evolved
genotypes, that have no frustration around the target spins (we call "local
Mattis state"), give a funnel-like rapid expression dynamics and are robust to
mutation. These results imply that evolution under thermal noise beyond a
certain level leads to funnel dynamics and mutational robustness. We will
explain its mechanism with the statistical-mechanical method.Comment: 4pages, 4figure
Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model
The aim of this work is to study the spectral statistics of the asymmetric
rotor model (triaxial rigid rotator). The asymmetric top is classically
integrable and, according to the Berry-Tabor theory, its spectral statistics
should be Poissonian. Surprisingly, our numerical results show that the nearest
neighbor spacing distribution and the spectral rigidity do
not follow Poisson statistics. In particular, shows a sharp peak at
while for small values of follows the Poissonian
predictions and asymptotically it shows large fluctuations around its mean
value. Finally, we analyze the information entropy, which shows a dissolution
of quantum numbers by breaking the axial symmetry of the rigid rotator.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
Influence of nonlocal electrodynamics on the anisotropic vortex pinning in
We have studied the pinning force density Fp of YNi_2B_2C superconductors for
various field orientations. We observe anisotropies both between the c-axis and
the basal plane and within the plane, that cannot be explained by usual mass
anisotropy. For magnetic field , the reorientation structural
transition in the vortex lattice due to nonlocality, which occurs at a field
, manifests itself as a kink in Fp(H). When , Fp is
much larger and has a quite different H dependence, indicating that other
pinning mechanisms are present. In this case the signature of nonlocal effects
is the presence of a fourfold periodicity of Fp within the basal plane.Comment: 4 pages, 3 figure
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