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

Correlated patterns in non-monotonic graded-response perceptrons

The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the overall performance of the perceptrons.Comment: 4 pages, 4 figure

A GBT Survey of the HALOGAS Galaxies and Their Environments I: Revealing the full extent of HI around NGC891, NGC925, NGC4414 & NGC4565

We present initial results from a deep neutral hydrogen (HI) survey of the HALOGAS galaxy sample, which includes the spiral galaxies NGC891, NGC925, NGC4414, and NGC4565, performed with the Robert C. Byrd Green Bank Telescope (GBT). The resulting observations cover at least four deg$^2$ around these galaxies with an average 5$\sigma$ detection limit of 1.2$\times$10$^{18}$ cm$^{-2}$ over a velocity range of 20 km s$^{-1}$ and angular scale of 9.1$'$. In addition to detecting the same total flux as the GBT data, the spatial distribution of the GBT and original Westerbork Synthesis Radio Telescope (WSRT) data match well at equal spatial resolutions. The HI mass fraction below HI column densities of 10$^{19}$ cm$^{-2}$ is, on average, 2\%. We discuss the possible origins of low column density HI of nearby spiral galaxies. The absence of a considerable amount of newly detected HI by the GBT indicates these galaxies do not have significant extended diffuse HI structures, and suggests future surveys planned with the SKA and its precursors must go \textit{at least} as deep as 10$^{17}$ cm$^{-2}$ in column density to significantly increase the probability of detecting HI associated with the cosmic web and/or cold mode accretion.Comment: Accepted for publication in The Astrophysical Journal; 28 pages, 15 figure

Network Power Fault Detection

Network power fault detection. At least one first network device is instructed to temporarily disconnect from a power supply path of a network, and at least one characteristic of the power supply path of the network is measured at a second network device connected to the network while the at least one first network device is temporarily disconnected from the network

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page

A morphological algorithm for improving radio-frequency interference detection

A technique is described that is used to improve the detection of radio-frequency interference in astronomical radio observatories. It is applied on a two-dimensional interference mask after regular detection in the time-frequency domain with existing techniques. The scale-invariant rank (SIR) operator is defined, which is a one-dimensional mathematical morphology technique that can be used to find adjacent intervals in the time or frequency domain that are likely to be affected by RFI. The technique might also be applicable in other areas in which morphological scale-invariant behaviour is desired, such as source detection. A new algorithm is described, that is shown to perform quite well, has linear time complexity and is fast enough to be applied in modern high resolution observatories. It is used in the default pipeline of the LOFAR observatory.Comment: Accepted for publication in A&