Optimal learning rules for discrete synapses

There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity

Memory, space and time: Researching children's lives

This article discusses the research approach in 'Pathways through Childhood', a small qualitative study drawing on memories of childhood. The research explores how wider social arrangements and social change influence children's everyday lives.The article discusses the way that the concepts of social memory, space and time have been drawn on to access and analyse children's experiences, arguing that attention to the temporal and spatial complexity of childhood reveals less visible yet formative influences and connections. Children's everyday engagements involve connections between past and present time, between children, families, communities and nations, and between different places. Children carve out space and time for themselves from these complex relations. © The Author(s) 2010

Multiple zero modes of the Dirac operator in three dimensions

One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the construction of multiple zero modes has been sucessfully carried out only very recently. Here we generalise these results by discussing a much wider class of Dirac operators together with their zero modes. Further we show that those Dirac operators that do admit zero modes may be related to Hopf maps, where the Hopf index is related to the number of zero modes in a simple way.Comment: Latex file, 20 pages, no figure

Hohenberg-Kohn theorem for the lowest-energy resonance of unbound systems

We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT) can be extended to the lowest-energy resonance of unbound systems. Using the Gel'fand Levitan theorem, the extended version of the HKT can also be applied to systems that support a finite number of bound states. The extended version of the HKT provides an adequate framework to carry out DFT calculations of negative electron affinities.Comment: 4 pages, 3 figure

Seismicity along the western part of the Eurasia-Nubian plate boundary

The seismicity along the western part of the Eurasia-Nubian plate boundary is characterized by a very complex pattern. In average, the motion is transtensional in the Azores, dextral along the Gloria transform zone and convergent between the SW Portuguese Atlantic margin and the Ibero-Maghrebian zone. To constraint the factors controlling the seismicity, we provide a new seismotectonic synthesis using several significant seismic events. We show that the studied area can be divided into six different regions, each one characterized by a coherent seismicity pattern. The total seismic moment tensor and the average slip velocities are provided for each one of them. To understand the spatial distribution of the seismicity, we compute for each event from the focal mechanism the slip vector and compare it to the relative velocity between the Eurasia and Nubia plates, deduced from global kinematics models. Despite local departures in the Alboran Sea and in the proximity of the Mid Atlantic Ridge, we find a good correlation between these two independent vectors sets. Quantitatively, the slip velocities display a linear, non-affine correlation with the norms of the relative kinematics velocities. The norm of the slip velocities seems to also depend on the tectonic regime and on the morphology of the plates’ boundary

Chern-Simons action for zero-mode supporting gauge fields in three dimensions

Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized values for gauge fields that lead to zero modes of the corresponding Dirac operator. Here we show that this conjecture is wrong by constructing an explicit counter-example.Comment: version as published in PRD, minor change

Resonant scattering and recombination of pseudo-degenerate WIMPs

We consider the direct and indirect detection signatures of WIMPs \chi^0 in kinematic regimes with a heavier, but nearly degenerate, charged state \chi^{+-}. For small splittings of O(10) MeV, the scattering of WIMPs off nuclei may be dominated by inelastic recombination processes mediated by the formation of (\chi^- N) bound states, leading to a distinct signature for direct detection. These cross-sections are bound primarily by limits on the abundance of heavy isotopes, and may be considerably larger than the elastic scattering cross section in more conventional models. If the mass splitting is too large for recombination to occur, there may still be a significant resonant enhancement of loop-induced electromagnetic form-factors of the WIMP, which can enhance the elastic scattering cross-section. We also discuss how this regime affects the annihilation cross-section and indirect detection signatures, and note the possibility of a significant mono-energetic \gamma-signal, mediated by resonant processes near the (\chi^+\chi^-) bound state threshold.Comment: 22 pages, 6 figures; v2: typos corrected, to appear in Phys. Rev.

Dirac lattice

We study the emergence of Dirac fermionic field in the low energy description of non-relativistic dynamical models on graphs admitting continuum limit. The Dirac fermionic field appears as the effective field describing the excitations above point-like Fermi surface. Together with the Dirac fermionic field an effective space-time metric is also emerging. We analyze the conditions for such Fermi points to appear in general, paying special attention to the cases of two and three spacial dimensions.Comment: 26 pages, 4 figures; typo and grammatical corrections, new reference(s) added, version accepted for publicatio