82 research outputs found
On the non-ergodicity of the Swendsen-Wang-Kotecky algorithm on the kagome lattice
We study the properties of the Wang-Swendsen-Kotecky cluster Monte Carlo
algorithm for simulating the 3-state kagome-lattice Potts antiferromagnet at
zero temperature. We prove that this algorithm is not ergodic for symmetric
subsets of the kagome lattice with fully periodic boundary conditions: given an
initial configuration, not all configurations are accessible via Monte Carlo
steps. The same conclusion holds for single-site dynamics.Comment: Latex2e. 22 pages. Contains 11 figures using pstricks package. Uses
iopart.sty. Final version accepted in journa
Metastates in mean-field models with random external fields generated by Markov chains
We extend the construction by Kuelske and Iacobelli of metastates in
finite-state mean-field models in independent disorder to situations where the
local disorder terms are are a sample of an external ergodic Markov chain in
equilibrium. We show that for non-degenerate Markov chains, the structure of
the theorems is analogous to the case of i.i.d. variables when the limiting
weights in the metastate are expressed with the aid of a CLT for the occupation
time measure of the chain. As a new phenomenon we also show in a Potts example
that, for a degenerate non-reversible chain this CLT approximation is not
enough and the metastate can have less symmetry than the symmetry of the
interaction and a Gaussian approximation of disorder fluctuations would
suggest.Comment: 20 pages, 2 figure
Design of experiments in medical physics: Application to the AAA beam model validation
Purpose
The purpose of this study is to evaluate the usefulness of the design of experiments in the analysis of multiparametric problems related to the quality assurance in radiotherapy. The main motivation is to use this statistical method to optimize the quality assurance processes in the validation of beam models.
Method
Considering the Varian Eclipse system, eight parameters with several levels were selected: energy, MLC, depth, X, Y1 and Y2 jaw dimensions, wedge and wedge jaw. A Taguchi table was used to define 72 validation tests. Measurements were conducted in water using a CC04 on a TrueBeam STx, a TrueBeam Tx, a Trilogy and a 2300IX accelerator matched by the vendor. Dose was computed using the AAA algorithm. The same raw data was used for all accelerators during the beam modelling.
Results
The mean difference between computed and measured doses was 0.1 ± 0.5% for all beams and all accelerators with a maximum difference of 2.4% (under the 3% tolerance level). For all beams, the measured doses were within 0.6% for all accelerators. The energy was found to be an influencing parameter but the deviations observed were smaller than 1% and not considered clinically significant.
Conclusion
Designs of experiment can help define the optimal measurement set to validate a beam model. The proposed method can be used to identify the prognostic factors of dose accuracy. The beam models were validated for the 4 accelerators which were found dosimetrically equivalent even though the accelerator characteristics differ
A new robust statistical method for treatment planning systems validation using experimental designs
Introduction
Dose computation verification is an important part of acceptance testing. The IAEA Tecdoc 1540 and 1583 suggest comparing computed dose to measurements for several beam configurations. However, this process is time-consuming and results out of tolerance are often left unexplained.
Purpose
To validate a treatment planning system using experimental designs which allow evaluating several parameters in a few tests selected by a robust statistical method.
Materials and methods
The Taguchi table L36 (211 × 312) was used to determine the 72 beams needed to test the 7 parameters chosen: energy, MLC, depth, jaw field size in X, Y1 and Y2 directions and wedge. Measurements were conducted in water using a CC04 (IBA) on a TrueBeam STx, a TrueBeam Tx, a Trilogy and a C-serie clinac (Varian). Dose was computed using the AAA algorithm (Eclipse, version 11). The same raw data was used for all accelerators during the algorithm configuration.
Results
The mean difference between computed and measured doses was 0.1 ±± 0.5% for all tested beams and all linacs with a maximum difference of 2.4% (under the 3% tolerance level). For all beams, the measured doses were within 0.6% for all linacs. No studied parameter led to statistically significant deviation between computed and measured doses.
Conclusion
Experimental design is a robust statistical method to validate an algorithm. Only 2 h of measurements were needed to evaluate 7 parameters. Furthermore, the commissioned accelerators were found dosimetrically equivalent even though the linac characteristics differ
Networks become navigable as nodes move and forget
We propose a dynamical process for network evolution, aiming at explaining
the emergence of the small world phenomenon, i.e., the statistical observation
that any pair of individuals are linked by a short chain of acquaintances
computable by a simple decentralized routing algorithm, known as greedy
routing. Previously proposed dynamical processes enabled to demonstrate
experimentally (by simulations) that the small world phenomenon can emerge from
local dynamics. However, the analysis of greedy routing using the probability
distributions arising from these dynamics is quite complex because of mutual
dependencies. In contrast, our process enables complete formal analysis. It is
based on the combination of two simple processes: a random walk process, and an
harmonic forgetting process. Both processes reflect natural behaviors of the
individuals, viewed as nodes in the network of inter-individual acquaintances.
We prove that, in k-dimensional lattices, the combination of these two
processes generates long-range links mutually independently distributed as a
k-harmonic distribution. We analyze the performances of greedy routing at the
stationary regime of our process, and prove that the expected number of steps
for routing from any source to any target in any multidimensional lattice is a
polylogarithmic function of the distance between the two nodes in the lattice.
Up to our knowledge, these results are the first formal proof that navigability
in small worlds can emerge from a dynamical process for network evolution. Our
dynamical process can find practical applications to the design of spatial
gossip and resource location protocols.Comment: 21 pages, 1 figur
Binomial parameters differ across neocortical layers and with different classes of connections in adult rat and cat neocortex
Non-Equilibrium Statistical Physics of Currents in Queuing Networks
We consider a stable open queuing network as a steady non-equilibrium system
of interacting particles. The network is completely specified by its underlying
graphical structure, type of interaction at each node, and the Markovian
transition rates between nodes. For such systems, we ask the question ``What is
the most likely way for large currents to accumulate over time in a network
?'', where time is large compared to the system correlation time scale. We
identify two interesting regimes. In the first regime, in which the
accumulation of currents over time exceeds the expected value by a small to
moderate amount (moderate large deviation), we find that the large-deviation
distribution of currents is universal (independent of the interaction details),
and there is no long-time and averaged over time accumulation of particles
(condensation) at any nodes. In the second regime, in which the accumulation of
currents over time exceeds the expected value by a large amount (severe large
deviation), we find that the large-deviation current distribution is sensitive
to interaction details, and there is a long-time accumulation of particles
(condensation) at some nodes. The transition between the two regimes can be
described as a dynamical second order phase transition. We illustrate these
ideas using the simple, yet non-trivial, example of a single node with
feedback.Comment: 26 pages, 5 figure
Online detection and sorting of extracellularly recorded action potentials in human medial temporal lobe recordings, in vivo
Understanding the function of complex cortical circuits requires the
simultaneous recording of action potentials from many neurons in awake and
behaving animals. Practically, this can be achieved by extracellularly
recording from multiple brain sites using single wire electrodes. However, in
densely packed neural structures such as the human hippocampus, a single
electrode can record the activity of multiple neurons. Thus, analytic
techniques that differentiate action potentials of different neurons are
required. Offline spike sorting approaches are currently used to detect and
sort action potentials after finishing the experiment. Because the
opportunities to record from the human brain are relatively rare, it is
desirable to analyze large numbers of simultaneous recordings quickly using
online sorting and detection algorithms. In this way, the experiment can be
optimized for the particular response properties of the recorded neurons. Here
we present and evaluate a method that is capable of detecting and sorting
extracellular single-wire recordings in realtime. We demonstrate the utility of
the method by applying it to an extensive data set we acquired from
chronically-implanted depth electrodes in the hippocampus of human epilepsy
patients. This dataset is particularly challenging because it was recorded in a
noisy clinical environment. This method will allow the development of
closed-loop experiments, which immediately adapt the experimental stimuli
and/or tasks to the neural response observed.Comment: 9 figures, 2 tables. Journal of Neuroscience Methods 2006 (in press).
Journal of Neuroscience Methods, 2006 (in press
Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model
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