35 research outputs found
Generating functional analysis of CDMA detection dynamics
We investigate the detection dynamics of the parallel interference canceller
(PIC) for code-division multiple-access (CDMA) multiuser detection, applied to
a randomly spread, fully syncronous base-band uncoded CDMA channel model with
additive white Gaussian noise (AWGN) under perfect power control in the
large-system limit. It is known that the predictions of the density evolution
(DE) can fairly explain the detection dynamics only in the case where the
detection dynamics converge. At transients, though, the predictions of DE
systematically deviate from computer simulation results. Furthermore, when the
detection dynamics fail to convergence, the deviation of the predictions of DE
from the results of numerical experiments becomes large. As an alternative,
generating functional analysis (GFA) can take into account the effect of the
Onsager reaction term exactly and does not need the Gaussian assumption of the
local field. We present GFA to evaluate the detection dynamics of PIC for CDMA
multiuser detection. The predictions of GFA exhibits good consistency with the
computer simulation result for any condition, even if the dynamics fail to
convergence.Comment: 14 pages, 3 figure
The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles
It is shown that an exact solution of the transient dynamics of an
associative memory model storing an infinite number of limit cycles with l
finite steps by means of the path-integral analysis. Assuming the Maxwell
construction ansatz, we have succeeded in deriving the stationary state
equations of the order parameters from the macroscopic recursive equations with
respect to the finite-step sequence processing model which has retarded
self-interactions. We have also derived the stationary state equations by means
of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must
assume that crosstalk noise of an input to spins obeys a Gaussian distribution.
On the other hand, the path-integral method does not require such a Gaussian
approximation of crosstalk noise. We have found that both the signal-to-noise
analysis and the path-integral analysis give the completely same result with
respect to the stationary state in the case where the dynamics is
deterministic, when we assume the Maxwell construction ansatz.
We have shown the dependence of storage capacity (alpha_c) on the number of
patterns per one limit cycle (l). Storage capacity monotonously increases with
the number of steps, and converges to alpha_c=0.269 at l ~= 10. The original
properties of the finite-step sequence processing model appear as long as the
number of steps of the limit cycle has order l=O(1).Comment: 24 pages, 3 figure
Statistical mechanics of lossy compression using multilayer perceptrons
Statistical mechanics is applied to lossy compression using multilayer
perceptrons for unbiased Boolean messages. We utilize a tree-like committee
machine (committee tree) and tree-like parity machine (parity tree) whose
transfer functions are monotonic. For compression using committee tree, a lower
bound of achievable distortion becomes small as the number of hidden units K
increases. However, it cannot reach the Shannon bound even where K -> infty.
For a compression using a parity tree with K >= 2 hidden units, the rate
distortion function, which is known as the theoretical limit for compression,
is derived where the code length becomes infinity.Comment: 12 pages, 5 figure
Photoemission Orbital Tomography Using Robust Sparse PhaseLift
Photoemission orbital tomography (POT) from photoelectron momentum maps
(PMMs) has enabled detailed analysis of the shape and energy of molecular
orbitals in the adsorbed state. This study proposes a new POT method based on
the PhaseLift. Molecular orbitals, including three-dimensional phases, can be
identified from a single PMM by actively providing atomic positions and basis.
Moreover, our method is robust to noise and can perfectly discriminate
adsorption-induced molecular deformations with an accuracy of 0.05 [angstrom].
Our new method enables simultaneous analysis of the three-dimensional shapes of
molecules and molecular orbitals and thus paves the way for advanced
quantum-mechanical interpretation of adsorption-induced electronic state
changes and photo-excited inter-molecular interactions.Comment: 9 pages, 5 figure
Error correcting code using tree-like multilayer perceptron
An error correcting code using a tree-like multilayer perceptron is proposed.
An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0
using a tree-like committee machine (committee tree) or a tree-like parity
machine (parity tree). Based on these architectures, several schemes featuring
monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is
then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by
noise. The analytical performance of these schemes is investigated using the
replica method of statistical mechanics. Under some specific conditions, some
of the proposed schemes are shown to saturate the Shannon bound at the infinite
codeword length limit. The influence of the monotonicity of the units on the
performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise
Statistical mechanics of lossy compression for non-monotonic multilayer perceptrons
A lossy data compression scheme for uniformly biased Boolean messages is
investigated via statistical mechanics techniques. We utilize tree-like
committee machine (committee tree) and tree-like parity machine (parity tree)
whose transfer functions are non-monotonic. The scheme performance at the
infinite code length limit is analyzed using the replica method. Both committee
and parity treelike networks are shown to saturate the Shannon bound. The AT
stability of the Replica Symmetric solution is analyzed, and the tuning of the
non-monotonic transfer function is also discussed.Comment: 29 pages, 7 figure
Integrated analysis of cell shape and movement in moving frame
形を変えながら動く3次元物体の解析手法の提唱 --動くから形が変わるのか、形を変えることで動くのか--. 京都大学プレスリリース. 2021-03-31.The cell's movement and morphological change are two interrelated cellular processes. An integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell's trajectory can be described by its speed, curvature, and torsion. On the other hand, the three-dimensional (3D) cell shape can be studied by using a shape descriptor such as spherical harmonic (SH) descriptor, which is an extension of a Fourier transform in 3D space. We propose a novel method using parallel-transport (PT) to integrate these shape-movement data by using moving frames as the 3D-shape coordinate system. This moving frame is purely determined by the velocity vector. On this moving frame, the movement change will influence the coordinate system for shape analysis. By analyzing the change of the SH coefficients over time in the moving frame, we can observe the relationship between shape and movement. We illustrate the application of our approach using simulated and real datasets in this paper