5,881 research outputs found
Optimal Capacity of the Blume-Emery-Griffiths perceptron
A Blume-Emery-Griffiths perceptron model is introduced and its optimal
capacity is calculated within the replica-symmetric Gardner approach, as a
function of the pattern activity and the imbedding stability parameter. The
stability of the replica-symmetric approximation is studied via the analogue of
the Almeida-Thouless line. A comparison is made with other three-state
perceptrons.Comment: 10 pages, 8 figure
A spherical Hopfield model
We introduce a spherical Hopfield-type neural network involving neurons and
patterns that are continuous variables. We study both the thermodynamics and
dynamics of this model. In order to have a retrieval phase a quartic term is
added to the Hamiltonian. The thermodynamics of the model is exactly solvable
and the results are replica symmetric. A Langevin dynamics leads to a closed
set of equations for the order parameters and effective correlation and
response function typical for neural networks. The stationary limit corresponds
to the thermodynamic results. Numerical calculations illustrate our findings.Comment: 9 pages Latex including 3 eps figures, Addition of an author in the
HTML-abstract unintentionally forgotten, no changes to the manuscrip
Von Neumann's expanding model on random graphs
Within the framework of Von Neumann's expanding model, we study the maximum
growth rate r achievable by an autocatalytic reaction network in which
reactions involve a finite (fixed or fluctuating) number D of reagents. r is
calculated numerically using a variant of the Minover algorithm, and
analytically via the cavity method for disordered systems. As the ratio between
the number of reactions and that of reagents increases the system passes from a
contracting (r1). These results extend the
scenario derived in the fully connected model (D\to\infinity), with the
important difference that, generically, larger growth rates are achievable in
the expanding phase for finite D and in more diluted networks. Moreover, the
range of attainable values of r shrinks as the connectivity increases.Comment: 20 page
On the transition to efficiency in Minority Games
The existence of a phase transition with diverging susceptibility in batch
Minority Games (MGs) is the mark of informationally efficient regimes and is
linked to the specifics of the agents' learning rules. Here we study how the
standard scenario is affected in a mixed population game in which agents with
the `optimal' learning rule (i.e. the one leading to efficiency) coexist with
ones whose adaptive dynamics is sub-optimal. Our generic finding is that any
non-vanishing intensive fraction of optimal agents guarantees the existence of
an efficient phase. Specifically, we calculate the dependence of the critical
point on the fraction of `optimal' agents focusing our analysis on three
cases: MGs with market impact correction, grand-canonical MGs and MGs with
heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the
World through Spin Glasses" in honour of David Sherrington on the occasion of
his 65th birthda
Gardner optimal capacity of the diluted Blume-Emery-Griffiths neural network
The optimal capacity of a diluted Blume-Emery-Griffiths neural network is
studied as a function of the pattern activity and the embedding stability using
the Gardner entropy approach. Annealed dilution is considered, cutting some of
the couplings referring to the ternary patterns themselves and some of the
couplings related to the active patterns, both simultaneously (synchronous
dilution) or independently (asynchronous dilution). Through the de
Almeida-Thouless criterion it is found that the replica-symmetric solution is
locally unstable as soon as there is dilution. The distribution of the
couplings shows the typical gap with a width depending on the amount of
dilution, but this gap persists even in cases where a particular type of
coupling plays no role in the learning process.Comment: 9 pages Latex, 2 eps figure
Accuracy of liquid-based brush cytology and HPV detection for the diagnosis and management of patients with oropharyngeal and oral cancer.
Objectives This study aims to evaluate the usefulness of liquid-based brush cytology for malignancy diagnosis and HPV detection in patients with suspected oropharyngeal and oral carcinomas, as well as for the diagnosis of tumoral persistence after treatment. Material and methods Seventy-five patients with suspicion of squamous cell carcinoma of the oropharynx or oral cavity were included. Two different study groups were analyzed according to the date of the sample collection: (1) during the first endoscopy exploration and (2) in the first control endoscopy after treatment for squamous cell carcinoma. Sensitivity, specificity, positive predictive value, negative predictive value, and accuracy for malignancy diagnosis as well as for HPV-DNA detection on brush cytologies were assessed. Results Before treatment, the brush cytology showed a sensitivity of 88%, specificity of 100%, and accuracy of 88%. After treatment, it showed a sensitivity of 71%, specificity of 77%, and accuracy of 75%. HPV-DNA detection in cytology samples showed a sensitivity of 85%, specificity of 100%, and accuracy of 91% before treatment and an accuracy of 100% after treatment. Conclusions Liquid-based brush cytology showed good accuracy for diagnosis of oropharyngeal and oral squamous cell carcinoma before treatment, but its value decreases after treatment. Nevertheless, it is useful for HPV-DNA detection, as well as to monitor the patients after treatment. Clinical relevance Brush cytology samples are reliable for the detection of HPV-DNA before and after treatment and may be a useful method to incorporate in the HPV testing guidelines
Criticality in diluted ferromagnet
We perform a detailed study of the critical behavior of the mean field
diluted Ising ferromagnet by analytical and numerical tools. We obtain
self-averaging for the magnetization and write down an expansion for the free
energy close to the critical line. The scaling of the magnetization is also
rigorously obtained and compared with extensive Monte Carlo simulations. We
explain the transition from an ergodic region to a non trivial phase by
commutativity breaking of the infinite volume limit and a suitable vanishing
field. We find full agreement among theory, simulations and previous results.Comment: 23 pages, 3 figure
Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices
We calculate equilibrium solutions for Ising spin models on `small world'
lattices, which are constructed by super-imposing random and sparse Poissonian
graphs with finite average connectivity c onto a one-dimensional ring. The
nearest neighbour bonds along the ring are ferromagnetic, whereas those
corresponding to the Poisonnian graph are allowed to be random. Our models thus
generally contain quenched connectivity and bond disorder. Within the replica
formalism, calculating the disorder-averaged free energy requires the
diagonalization of replicated transfer matrices. In addition to developing the
general replica symmetric theory, we derive phase diagrams and calculate
effective field distributions for two specific cases: that of uniform sparse
long-range bonds (i.e. `small world' magnets), and that of (+J/-J) random
sparse long-range bonds (i.e. `small world' spin-glasses).Comment: 22 pages, LaTeX, IOP macros, eps figure
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