3,662 research outputs found
Optimisation of on-line principal component analysis
Different techniques, used to optimise on-line principal component analysis,
are investigated by methods of statistical mechanics. These include local and
global optimisation of node-dependent learning-rates which are shown to be very
efficient in speeding up the learning process. They are investigated further
for gaining insight into the learning rates' time-dependence, which is then
employed for devising simple practical methods to improve training performance.
Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure
Spin texture on the Fermi surface of tensile strained HgTe
We present ab initio and k.p calculations of the spin texture on the Fermi
surface of tensile strained HgTe, which is obtained by stretching the
zincblende lattice along the (111) axis. Tensile strained HgTe is a semimetal
with pointlike accidental degeneracies between a mirror symmetry protected
twofold degenerate band and two nondegenerate bands near the Fermi level. The
Fermi surface consists of two ellipsoids which contact at the point where the
Fermi level crosses the twofold degenerate band along the (111) axis. However,
the spin texture of occupied states indicates that neither ellipsoid carries a
compensating Chern number. Consequently, the spin texture is locked in the
plane perpendicular to the (111) axis, exhibits a nonzero winding number in
that plane, and changes winding number from one end of the Fermi ellipsoids to
the other. The change in the winding of the spin texture suggests the existence
of singular points. An ordered alloy of HgTe with ZnTe has the same effect as
stretching the zincblende lattice in the (111) direction. We present ab initio
calculations of ordered Hg_xZn_1-xTe that confirm the existence of a spin
texture locked in a 2D plane on the Fermi surface with different winding
numbers on either end.Comment: 8 pages, 8 figure
Equilibration through local information exchange in networks
We study the equilibrium states of energy functions involving a large set of
real variables, defined on the links of sparsely connected networks, and
interacting at the network nodes, using the cavity and replica methods. When
applied to the representative problem of network resource allocation, an
efficient distributed algorithm is devised, with simulations showing full
agreement with theory. Scaling properties with the network connectivity and the
resource availability are found.Comment: v1: 7 pages, 1 figure, v2: 4 pages, 2 figures, simplified analysis
and more organized results, v3: minor change
Colouring random graphs and maximising local diversity
We study a variation of the graph colouring problem on random graphs of
finite average connectivity. Given the number of colours, we aim to maximise
the number of different colours at neighbouring vertices (i.e. one edge
distance) of any vertex. Two efficient algorithms, belief propagation and
Walksat are adapted to carry out this task. We present experimental results
based on two types of random graphs for different system sizes and identify the
critical value of the connectivity for the algorithms to find a perfect
solution. The problem and the suggested algorithms have practical relevance
since various applications, such as distributed storage, can be mapped onto
this problem.Comment: 10 pages, 10 figure
Inference by replication in densely connected systems
An efficient Bayesian inference method for problems that can be mapped onto
dense graphs is presented. The approach is based on message passing where
messages are averaged over a large number of replicated variable systems
exposed to the same evidential nodes. An assumption about the symmetry of the
solutions is required for carrying out the averages; here we extend the
previous derivation based on a replica symmetric (RS) like structure to include
a more complex one-step replica symmetry breaking (1RSB)-like ansatz. To
demonstrate the potential of the approach it is employed for studying critical
properties of the Ising linear perceptron and for multiuser detection in Code
Division Multiple Access (CDMA) under different noise models. Results obtained
under the RS assumption in the non-critical regime give rise to a highly
efficient signal detection algorithm in the context of CDMA; while in the
critical regime one observes a first order transition line that ends in a
continuous phase transition point. Finite size effects are also observed. While
the 1RSB ansatz is not required for the original problems, it was applied to
the CDMA signal detection problem with a more complex noise model that exhibits
RSB behaviour, resulting in an improvement in performance.Comment: 47 pages, 7 figure
Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
The spectrum of the non-hermitian asymmetric XXZ-chain with additional
non-diagonal boundary terms is studied. The lowest lying eigenvalues are
determined numerically. For the ferromagnetic and completely asymmetric chain
that corresponds to a reaction-diffusion model with input and outflow of
particles the smallest energy gap which corresponds directly to the inverse of
the temporal correlation length shows the same properties as the spatial
correlation length of the stationary state. For the antiferromagnetic chain
with both boundary terms, we find a conformal invariant spectrum where the
partition function corresponds to the one of a Coulomb gas with only magnetic
charges shifted by a purely imaginary and a lattice-length dependent constant.
Similar results are obtained by studying a toy model that can be diagonalized
analytically in terms of free fermions.Comment: LaTeX, 26 pages, 1 figure, uses ioplppt.st
Derivation of tropospheric methane from TCCON CHâ‚„ and HF total column observations
The Total Carbon Column Observing Network (TCCON) is a global ground-based network of Fourier transform spectrometers that produce precise measurements of column-averaged dry-air mole fractions of atmospheric methane (CHâ‚„). Temporal variability in the total column of CHâ‚„ due to stratospheric dynamics obscures fluctuations and trends driven by tropospheric transport and local surface fluxes that are critical for understanding CHâ‚„ sources and sinks. We reduce the contribution of stratospheric variability from the total column average by subtracting an estimate of the stratospheric CHâ‚„ derived from simultaneous measurements of hydrogen fluoride (HF). HF provides a proxy for stratospheric CHâ‚„ because it is strongly correlated to CHâ‚„ in the stratosphere, has an accurately known tropospheric abundance (of zero), and is measured at most TCCON stations. The stratospheric partial column of CHâ‚„ is calculated as a function of the zonal and annual trends in the relationship between CHâ‚„ and HF in the stratosphere, which we determine from ACE-FTS satellite data. We also explicitly take into account the CHâ‚„ column averaging kernel to estimate the contribution of stratospheric CHâ‚„ to the total column. The resulting tropospheric CHâ‚„ columns are consistent with in situ aircraft measurements and augment existing observations in the troposphere
Parallel Arnoldi method for the construction of a Krylov subspace basis: An application in magnetohydrodynamics
Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective
Inference and optimization of real-value edge variables in sparse graphs are
studied using the Bethe approximation and replica method of statistical
physics. Equilibrium states of general energy functions involving a large set
of real edge-variables that interact at the network nodes are obtained in
various cases. When applied to the representative problem of network resource
allocation, efficient distributed algorithms are also devised. Scaling
properties with respect to the network connectivity and the resource
availability are found, and links to probabilistic Bayesian approximation
methods are established. Different cost measures are considered and algorithmic
solutions in the various cases are devised and examined numerically. Simulation
results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated,
Figs. 1 to 3 replace
Dynamical replica theoretic analysis of CDMA detection dynamics
We investigate the detection dynamics of the Gibbs sampler for code-division
multiple access (CDMA) multiuser detection. Our approach is based upon
dynamical replica theory which allows an analytic approximation to the
dynamics. We use this tool to investigate the basins of attraction when phase
coexistence occurs and examine its efficacy via comparison with Monte Carlo
simulations.Comment: 18 pages, 2 figure
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