Time evolution of the extremely diluted Blume-Emery-Griffiths neural network

The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases. It is shown that saddle-point solutions associated with fluctuation overlaps slow down considerably the flow of the network states towards the retrieval fixed points. A comparison of the performance with other three-state networks is also presented.Comment: 8 pages, 5 figure

Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution

The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, $\alpha = P/N$, and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to $\alpha \sim O(1)$. The most relevant results are: (1) the simulation supports the validity of the analytical prediction, and (2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of $\alpha$.Comment: 6 pages, 8 figures, LaTeX fil

Beyond Diagnosis: Evolving Prostate Biopsy in the Era of Focal Therapy

Despite decades of use as the “gold standard” in the detection of prostate cancer, the optimal biopsy regimen is still not universally agreed upon. While important aspects such as the need for laterally placed biopsies and the importance of apical cancer are known, repeated studies have shown significant patients with cancer on subsequent biopsy when the original biopsy was negative and an ongoing suspicion of cancer remained. Attempts to maximise the effectiveness of repeat biopsies have given rise to the alternate approaches of saturation biopsy and the transperineal approach. Recent interest in focal treatment of prostate cancer has further highlighted the need for accurate detection of prostate cancer, and in response, the introduction of transperineal template-guided biopsy. While the saturation biopsy approach and the transperineal template approach increase the detection rate of cancer in men with a previous negative biopsy and appear to have acceptable morbidity, there is a lack of clinical trials evaluating the different biopsy strategies. This paper reviews the evolution of prostatic biopsy and current controversies

Controlling chaos in diluted networks with continuous neurons

Diluted neural networks with continuous neurons and nonmonotonic transfer function are studied, with both fixed and dynamic synapses. A noisy stimulus with periodic variance results in a mechanism for controlling chaos in neural systems with fixed synapses: a proper amount of external perturbation forces the system to behave periodically with the same period as the stimulus.Comment: 11 pages, 8 figure

Self-control in Sparsely Coded Networks

A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for sparsely coded models this mechanism is shown to considerably improve the storage capacity, the basins of attraction and the mutual information content of the network.Comment: 4 pages, 6 Postscript figure

Optimally adapted multi-state neural networks trained with noise

The principle of adaptation in a noisy retrieval environment is extended here to a diluted attractor neural network of Q-state neurons trained with noisy data. The network is adapted to an appropriate noisy training overlap and training activity which are determined self-consistently by the optimized retrieval attractor overlap and activity. The optimized storage capacity and the corresponding retriever overlap are considerably enhanced by an adequate threshold in the states. Explicit results for improved optimal performance and new retriever phase diagrams are obtained for Q=3 and Q=4, with coexisting phases over a wide range of thresholds. Most of the interesting results are stable to replica-symmetry-breaking fluctuations.Comment: 22 pages, 5 figures, accepted for publication in PR

Test of Information Theory on the Boltzmann Equation

We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.Comment: 12 page