Simple Analyses of the Sparse Johnson-Lindenstrauss Transform

For every n-point subset X of Euclidean space and target distortion 1+eps for 0l_2^m where f(x) = Ax for A a matrix with m rows where (1) m = O((log n)/eps^2), and (2) each column of A is sparse, having only O(eps m) non-zero entries. Though the constructions given for such A in (Kane, Nelson, J. ACM 2014) are simple, the analyses are not, employing intricate combinatorial arguments. We here give two simple alternative proofs of their main result, involving no delicate combinatorics. One of these proofs has already been tested pedagogically, requiring slightly under forty minutes by the third author at a casual pace to cover all details in a blackboard course lecture

The more often you see an object, the easier it becomes to track it

Is it easier to track objects that you have seen repeatedly? We compared repeated blocks, where identities were the same from trial to trial, to unrepeated blocks, where identities varied. People were better in tracking objects that they saw repeatedly. We tested four hypotheses to explain this repetition benefit. First, perhaps the repeated condition benefits from consistent mapping of identities to target and distractor roles. However, the repetition benefit persisted even when both the repeated and the unrepeated conditions used consistent mapping. Second, repetition might improve the ability to recover targets that have been lost, or swapped with distractors. However, we observed a larger repetition benefit for color-color conjunctions, which do not benefit from such error recovery processes, than for unique features, which do. Furthermore, a repetition benefit was observed even in the absence of distractors. Third, perhaps repetition frees up resources by reducing memory load. However, increasing memory load by masking identities during the motion phase reduced the repetition benefit. The fourth hypothesis is that repetition facilitates identity tracking, which in turn improves location tracking. This hypothesis is consistent with all our results. Thus, our data suggest that identity and location tracking share a common resource

Gauged supersymmetric \gs--models and soft breaking terms

Supersymmetric non--linear \gs--models in four dimensions with a $D$--term potentials can sometimes have singular kinetic metric terms. As the kinetic terms of scalar fields and their chiral fermionic partners are determine by this metric, it follow that their kinetic energy vanishes in the vacuum. In previous work, it has been shown in a simple model that soft supersymmetry breaking terms can lift the degenerate the sigma-model metric and provide a consistent mass-spectra. In this letter I introduce soft breaking terms in a more realistic models based on SO(10) and $E_6$ and compute the resulting mass spectrum.Comment: Latex 6 pages, added references, typos corrected; final published versio

The Nuclear Sigma Term in the Skyrme Model: Pion-Nucleus Interaction

The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the NN interaction with respect to the quark mass, $m_q\frac{\partial V_{NN}}{\partial m_q}$. The NN potential is evaluated in the skyrmion-skyrmion picture within the quantized product ansatz. The contribution of the NN potential to the nuclear sigma term provides repulsion to the pion-nucleus interaction. The strength of the s-wave pion-nucleus optical potential is estimated including such contribution. The results are consistent with the analysis of the experimental data.Comment: 16 pages (latex), 3 figures (eps), e-mail: [email protected] and [email protected]

Soft-bed experiments beneath Engabreen, Norway: regelation infiltration, basal slip and bed deformation

To avoid some of the limitations of studying soft-bed processes through boreholes, a prism of simulated till (1.8 m × 1.6 m × 0.45 m) with extensive instrumentation was constructed in a trough blasted in the rock bed of Engabreen, a temperate glacier in Norway. Tunnels there provide access to the bed beneath 213 m of ice. Pore-water pressure was regulated in the prism by pumping water to it. During experiments lasting 7–12 days, the glacier regelated downward into the prism to depths of 50– 80 mm, accreting ice-infiltrated till at rates predicted by theory. During periods of sustained high pore water pressure (70–100% of overburden), ice commonly slipped over the prism, due to a water layer at the prism surface. Deformation of the prism was activated when this layer thinned to a sub-millimeter thickness. Shear strain in the till was pervasive and decreased with depth. A model of slip by ploughing of ice-infiltrated till across the prism surface accounts for the slip that occurred when effective pressure was sufficiently low or high. Slip at low effective pressures resulted from water-layer thickening that increased non-linearly with decreasing effective pressure. If sufficiently widespread, such slip over soft glacier beds, which involves no viscous deformation resistance, may instigate abrupt increases in glacier velocity