Constructive Provability Logic

We present constructive provability logic, an intuitionstic modal logic that validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and CPL*, are presented in natural deduction and sequent calculus forms which are then shown to be equivalent. In addition, we discuss the use of constructive provability logic to justify stratified negation in logic programming within an intuitionstic and structural proof theory.Comment: Extended version of IMLA 2011 submission of the same titl

Tine options for alleviating compaction in wheelings

Repeated trafficking and harvesting operations lead to high levels of compaction in inter-row wheelings used in asparagus (Asparagus officinalis) production. This reduces soil porosity and infiltration resulting in water ponding on the soil surface. Even on gently sloping land this can result in runoff generation and an increased risk of soil erosion. A winged tine (WT) is currently used by a leading asparagus grower to loosen compacted inter-row wheelings. In order to test the effectiveness of this tine for alleviating compaction and implications for runoff and soil erosion control, it was evaluated alongside several other tine configurations. These were a narrow tine (NT); a narrow tine with two shallow leading tines (NSLT); a winged tine with two shallow leading tines (WSLT); and a modified para-plough (MPP). Testing was conducted under controlled conditions on a sandy loam soil in the Soil Management Facility at Cranfield University, Bedfordshire, UK. Tine performance was assessed at 3 depths (175, 250 and 300 mm) by draught force; soil disturbance (both above and below ground); specific draught for a given level of soil disturbance; surface roughness; and estimated change in soil bulk density. The effectiveness of tines for compaction alleviation and potential for mitigating runoff and soil erosion varied with depth. The most effective tines were found to be the MPP NSLT and the WSLT at 175 mm, 250 mm and 300 mm depth, respectively

Factorization of correlations in two-dimensional percolation on the plane and torus

Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, in agreement with the numerical value 1.022 found previously in a study of R on the conformally equivalent cylinder. In this paper we confirm the factorization on the plane numerically using periodic lattices (tori) of very large size, which locally approximate a plane. We also investigate the general behavior of R on the torus, and find a minimum value of R approx. 1.0132 when the three points are maximally separated. In addition, we present a simplified expression for R on the plane as a function of the SLE parameter kappa.Comment: Small corrections (final version). In press, J. Phys.

Anchored Critical Percolation Clusters and 2-D Electrostatics

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find that they are given by simple functions of the potentials of 2-D electrostatic dipoles, and that a kind of superposition {\it cum} factorization applies. Our results broaden this connection, already known from previous studies, and we present evidence that it is more generally valid. An exact result similar to the Kirkwood superposition approximation emerges.Comment: 4 pages, 1 (color) figure. More numerics, minor corrections, references adde

Measurement of phosphorus segregation in silicon at the atomic-scale using STM

In order to fabricate precise atomic-scale devices in silicon using a combination of scanning tunnelling microscopy (STM) and molecular beam epitaxy it is necessary to minimize the segregation/diffusion of dopant atoms during silicon encapsulation. We characterize the surface segregation/diffusion of phosphorus atoms from a $\delta$-doped layer in silicon after encapsulation at 250$^{\circ}$C and room temperature using secondary ion mass spectrometry (SIMS), Auger electron spectroscopy (AES), and STM. We show that the surface phosphorus density can be reduced to a few percent of the initial $\delta$-doped density if the phosphorus atoms are encapsulated with 5 or 10 monolayers of epitaxial silicon at room temperature. We highlight the limitations of SIMS and AES to determine phosphorus segregation at the atomic-scale and the advantage of using STM directly

Long-term deficits in cortical circuit function after asphyxial cardiac arrest and resuscitation in developing rats

AbstractCardiac arrest is a common cause of global hypoxic-ischemic brain injury. Poor neurologic outcome among cardiac arrest survivors results not only from direct cellular injury but also from subsequent long-term dysfunction of neuronal circuits. Here, we investigated the long-term impact of cardiac arrest during development on the function of cortical layer IV (L4) barrel circuits in the rat primary somatosensory cortex. We used multielectrode single-neuron recordings to examine responses of presumed excitatory L4 barrel neurons to controlled whisker stimuli in adult (8 ± 2-mo-old) rats that had undergone 9 min of asphyxial cardiac arrest and resuscitation during the third postnatal week. Results indicate that responses to deflections of the topographically appropriate principal whisker (PW) are smaller in magnitude in cardiac arrest survivors than in control rats. Responses to adjacent whisker (AW) deflections are similar in magnitude between the two groups. Because of a disproportionate decrease in PW-evoked responses, receptive fields of L4 barrel neurons are less spatially focused in cardiac arrest survivors than in control rats. In addition, spiking activity among L4 barrel neurons is more correlated in cardiac arrest survivors than in controls. Computational modeling demonstrates that experimentally observed disruptions in barrel circuit function after cardiac arrest can emerge from a balanced increase in background excitatory and inhibitory conductances in L4 neurons. Experimental and modeling data together suggest that after a hypoxic-ischemic insult, cortical sensory circuits are less responsive and less spatially tuned. Modulation of these deficits may represent a therapeutic approach to improving neurologic outcome after cardiac arrest.</jats:p