A syntactic and functional correspondence between reduction semantics and reduction-free full normalisers

Olivier Danvy and others have shown the syntactic correspondence between reduction semantics (a small-step semantics) and abstract machines, as well as the functional correspondence between reduction-free normalisers (a big-step semantics) and abstract machines. The correspondences are established by program transformation (so-called interderivation) techniques. A reduction semantics and a reduction-free normaliser are interderivable when the abstract machine obtained from them is the same. However, the correspondences fail when the underlying reduction strategy is hybrid, i.e., relies on another sub-strategy. Hybridisation is an essential structural property of full-reducing and complete strategies. Hybridisation is unproblematic in the functional correspondence. But in the syntactic correspondence the refocusing and inlining-of-iterate-function steps become context sensitive, preventing the refunctionalisation of the abstract machine. We show how to solve the problem and showcase the interderivation of normalisers for normal order, the standard, full-reducing and complete strategy of the pure lambda calculus. Our solution makes it possible to interderive, rather than contrive, full-reducing abstract machines. As expected, the machine we obtain is a variant of Pierre Crégut s full Krivine machine KN.

Binocular vision in insects: How mantids solve the correspondence problem

Praying mantids use binocular cues to judge whether their prey is in striking distance. When there are several moving targets within their binocular visual field, mantids need to solve the correspondence problem. They must select between the possible pairings of retinal images in the two eyes so that they can strike at a single real target. In this study, mantids were presented with two targets in various configurations, and the resulting fixating saccades that precede the strike were analyzed. The distributions of saccades show that mantids consistently prefer one out of several possible matches. Selection is in part guided by the position and the spatiotemporal features of the target image in each eye. Selection also depends upon the binocular disparity of the images, suggesting that insects can perform local binocular computations. The pairing rules ensure that mantids tend to aim at real targets and not at “ghost” targets arising from false matches.

Computation of Surface Electrical Potentials of Plant Cell Membranes : Correspondence to Published Zeta Potentials from Diverse Plant Sources

A Gouy-Chapman-Stern model has been developed for the computation of surface electrical potential (ψ0) of plant cell membranes in response to ionic solutes. The present model is a modification of an earlier version developed to compute the sorption of ions by wheat (Triticum aestivum L. cv Scout 66) root plasma membranes. A single set of model parameters generates values for ψ0 that correlate highly with published ζ potentials of protoplasts and plasma membrane vesicles from diverse plant sources. The model assumes ion binding to a negatively charged site (R− = 0.3074 μmol m−2) and to a neutral site (P0 = 2.4 μmol m−2) according to the reactions R− + IΖ ⇌ RIΖ−1 and P0 + IΖ ⇌ PIΖ, where IΖ represents an ion of charge Ζ. Binding constants for the negative site are 21,500 m−1 for H+, 20,000 m−1 for Al3+, 2,200 m−1 for La3+, 30 m−1 for Ca2+ and Mg2+, and 1 m−1 for Na+ and K+. Binding constants for the neutral site are 1/180 the value for binding to the negative site. Ion activities at the membrane surface, computed on the basis of ψ0, appear to determine many aspects of plant-mineral interactions, including mineral nutrition and the induction and alleviation of mineral toxicities, according to previous and ongoing studies. A computer program with instructions for the computation of ψ0, ion binding, ion concentrations, and ion activities at membrane surfaces may be requested from the authors.

Close correspondence between the action spectra for the blue light responses of the guard cell and coleoptile chloroplasts, and the spectra for blue light-dependent stomatal opening and coleoptile phototropism.

Fluorescence spectroscopy was used to characterize blue light responses from chloroplasts of adaxial guard cells from Pima cotton (Gossypium barbadense) and coleoptile tips from corn (Zea mays). The chloroplast response to blue light was quantified by measurements of the blue light-induced enhancement of a red light-stimulated quenching of chlorophyll a fluorescence. In adaxial (upper) guard cells, low fluence rates of blue light applied under saturating fluence rates of red light enhanced the red light-stimulated fluorescence quenching by up to 50%. In contrast, added blue light did not alter the red light-stimulated quenching from abaxial (lower) guard cells. This response pattern paralleled the blue light sensitivity of stomatal opening in the two leaf surfaces. An action spectrum for the blue light-induced enhancement of the red light-stimulated quenching showed a major peak at 450 nm and two minor peaks at 420 and 470 nm. This spectrum matched closely an action spectrum for blue light-stimulated stomatal opening. Coleoptile chloroplasts also showed an enhancement by blue light of red light-stimulated quenching. The action spectrum of this response, showing a major peak at 450 nm, a minor peak at 470 nm, and a shoulder at 430 nm, closely matched an action spectrum for blue light-stimulated coleoptile phototropism. Both action spectra match the absorption spectrum of zeaxanthin, a chloroplastic carotenoid recently implicated in blue light photoreception of both guard cells and coleoptiles. The remarkable similarity between the action spectra for the blue light responses of guard cells and coleoptile chloroplasts and the spectra for blue light-stimulated stomatal opening and phototropism, coupled to the recently reported evidence on a role of zeaxanthin in blue light photoreception, indicates that the guard cell and coleoptile chloroplasts specialize in sensory transduction.

Correspondence between long-range and short-range spin glasses

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power σ of the distance. We show that there is a value of σ of the long-range model for which the critical behavior is very similar to that of the short range model in four dimensions. We also study a value of σ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.