Storage of correlated patterns in a perceptron

We calculate the storage capacity of a perceptron for correlated gaussian patterns. We find that the storage capacity $\alpha_c$ can be less than 2 if similar patterns are mapped onto different outputs and vice versa. As long as the patterns are in general position we obtain, in contrast to previous works, that $\alpha_c \geq 1$ in agreement with Cover's theorem. Numerical simulations confirm the results.Comment: 9 pages LaTeX ioplppt style, figures included using eps

Statistical mechanics of the multi-constraint continuous knapsack problem

We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the number of constraints. We study the stability of the replica symmetric (RS) solution and find that the RS calculation cannot estimate the optimal number of items in knapsack correctly if many constraints are required.In order to obtain a consistent solution in the RS region,we try the zero entropy approximation for this continuous solution space and get a stable solution within the RS ansatz.On the other hand, in replica symmetry breaking (RSB) region, the one step RSB solution is found by Parisi's scheme. It turns out that this problem is closely related to the problem of optimal storage capacity and of generalization by maximum stability rule of a spherical perceptron.Comment: Latex 13 pages using IOP style file, 5 figure

Storage capacity of a constructive learning algorithm

Upper and lower bounds for the typical storage capacity of a constructive algorithm, the Tilinglike Learning Algorithm for the Parity Machine [M. Biehl and M. Opper, Phys. Rev. A {\bf 44} 6888 (1991)], are determined in the asymptotic limit of large training set sizes. The properties of a perceptron with threshold, learning a training set of patterns having a biased distribution of targets, needed as an intermediate step in the capacity calculation, are determined analytically. The lower bound for the capacity, determined with a cavity method, is proportional to the number of hidden units. The upper bound, obtained with the hypothesis of replica symmetry, is close to the one predicted by Mitchinson and Durbin [Biol. Cyber. {\bf 60} 345 (1989)].Comment: 13 pages, 1 figur

Do divorcing couples become happier by breaking up?

Divorce is a leap in the dark. The paper investigates whether people who split up actually become happier. Using the British Household Panel Survey, we can observe an individual's level of psychological well-being in the years before and after divorce. Our results show that divorcing couples reap psychological gains from the dissolution of their marriages. Men and women benefit equally. The paper also studies the effects of bereavement, of having dependant children and of remarriage. We measure well-being by using general health questionnaire and life satisfaction scores

Polarization observations in a low synchrotron emission field at 1.4 GHz

We present the first observation of the diffuse polarized synchrotron radiation of a patch ($\sim 3^\circ \times 3^\circ$) in the BOOMERanG field, one of the areas with the lowest CMB foreground emission. The work has been carried out with the Australia Telescope Compact Array at 1.4 GHz with 3.4 arcmin resolution and sensitivity of $\sim 0.18$ mJy beam$^{-1}$. The mean polarized signal has been found to be $P_{rms} = \sqrt{(Q_{rms}^2 + U_{rms}^2)} = 11.6 \pm 0.6$ mK, nearly one order of magnitude below than in the Galactic Plane. Extrapolations to frequencies of interest for cosmological investigations suggest that polarized synchrotron foreground noise should allow the detection of the CMB Polarization $E$--mode already at 32 GHz and make us confident that, at 90 GHz, it is accessible with no relevant foreground contamination. Last but not least, even the $B$--mode detection for $T/S > 0.01$ is not ruled out in such a low emission patch.Comment: Uses emulateapj.sty, onecolfloat.sty, 5 pages 4 fig., accepted for publication in ApJ