Policies to Protect Food Safety and Animal Health

Food Consumption/Nutrition/Food Safety, Livestock Production/Industries, Q16, Q17, Q18,

Complements of hypersurfaces, variation maps and minimal models of arrangements

We prove the minimality of the CW-complex structure for complements of hyperplane arrangements in $\mathbb C^n$ by using the theory of Lefschetz pencils and results on the variation maps within a pencil of hyperplanes. This also provides a method to compute the Betti numbers of complements of arrangements via global polar invariants

Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction

A model describing the role of transversal and longitudinal diffusion of cGMP and Ca2+ in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP CGMP and Ca2+ in the interdiscal spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 μm, consistent with experimental data. This approach represents a tool to analyze pointwise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics

Control and Dynamic Competition of Bright and Dark Lasing States in Active Nanoplasmonic Metamaterials

Active nanoplasmonic metamaterials support bright and dark modes that compete for gain. Using a Maxwell-Bloch approach incorporating Langevin noise we study the lasing dynamics in an active nano-fishnet structure. We report that lasing of the bright negative-index mode is possible if the higher-Q dark mode is discriminated by gain, spatially or spectrally. The nonlinear competition during the transient phase is followed by steady-state emission where bright and dark modes can coexist. We analyze the influence of pump intensity and polarization and explore methods for mode control.Comment: 5 pages, 4 figure

Electoral Reforms, Membership Stability and the Existence of Committee Property Rights in American State Legislatures

One of the most creative theories advanced about legislative organization in recent years is Katz and Sala\u27s linkage of the development of committee property rights in the US House of Representatives to the introduction of the Australian ballot. Katz and Sala argue that the Australian ballot – a government-printed ballot cast in secret that replaced a party-produced ballot that was cast in public – gave members of the House an incentive to pursue personal constituency votes. This, in turn, led to the rise of committee property rights as members sought to keep their committee assignments from term to term because of the potential electoral benefits they derived from them. In this Note we use the state legislative committee membership dataset collected by Hamm and Hedlund and their colleagues to test whether committee property rights appeared in American state legislatures at roughly the same time as Katz and Sala find they emerged in the US House. State legislatures were, of course, exposed to the same electoral innovation at the same time. But, while in some ways state legislatures were much like Congress as organizations, in other ways they were very different. Our cross-sectional data and the variance in important institutional variables they provide allow us to test a critical proposition about the importance of membership stability rates in mediating the rise of committee property rights. We also go beyond Katz and Sala\u27s analysis by testing to see if differences in Australian ballot design (office column and party bloc) across the states influenced the behaviour of legislators in the way their theory suggests

All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy

A combination of spatial interference patterns and spectral interferometry are used to find the global phase for non-collinear two-dimensional Fourier-transform (2DFT) spectra. Results are compared with those using the spectrally resolved transient absorption (STRA) method to find the global phase when excitation is with co-linear polarization. Additionally cross-linear polarized 2DFT spectra are correctly phased using the all-optical technique, where the SRTA is not applicable.Comment: 6 pages, 7 figures, journal publicatio

Kinetics of rhodopsin deactivation and its role in regulating recovery and reproducibility of rod photoresponse

The single photon response (SPR) in vertebrate phototransduction is regulated by the dynamics of R* during its lifetime, including the random number of phosphorylations, the catalytic activity and the random sojourn time at each phosphorylation level. Because of this randomness the electrical responses are expected to be inherently variable. However the SPR is highly reproducible. The mechanisms that confer to the SPR such a low variability are not completely understood. The kinetics of rhodopsin deactivation is investigated by a Continuous Time Markov Chain (CTMC) based on the biochemistry of rhodopsin activation and deactivation, interfaced with a spatio-temporal model of phototransduction. The model parameters are extracted from the photoresponse data of both wild type and mutant mice, having variable numbers of phosphorylation sites and, with the same set of parameters, the model reproduces both WT and mutant responses. The sources of variability are dissected into its components, by asking whether a random number of turnoff steps, a random sojourn time between steps, or both, give rise to the known variability. The model shows that only the randomness of the sojourn times in each of the phosphorylated states contributes to the Coefficient of Variation (CV) of the response, whereas the randomness of the number of R* turnoff steps has a negligible effect. These results counter the view that the larger the number of decay steps of R*, the more stable the photoresponse is. Our results indicate that R* shutoff is responsible for the variability of the photoresponse, while the diffusion of the second messengers acts as a variability suppressor

Self-consistent solution for the polarized vacuum in a no-photon QED model

We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted as the polarized vacuum and it solves a self-consistent equation. In a recent paper math-ph/0403005, we proved the convergence of the iterative fixed-point scheme naturally associated with this equation to a global minimizer of the BDF functional, under some restrictive conditions on the external potential, the ultraviolet cut-off $\Lambda$ and the bare fine structure constant $\alpha$. In the present work, we improve this result by showing the existence of the minimizer by a variational method, for any cut-off $\Lambda$ and without any constraint on the external field. We also study the behaviour of the minimizer as $\Lambda$ goes to infinity and show that the theory is "nullified" in that limit, as predicted first by Landau: the vacuum totally kills the external potential. Therefore the limit case of an infinite cut-off makes no sense both from a physical and mathematical point of view. Finally, we perform a charge and density renormalization scheme applying simultaneously to all orders of the fine structure constant $\alpha$, on a simplified model where the exchange term is neglected.Comment: Final version, to appear in J. Phys. A: Math. Ge

Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction

The single photon response in vertebrate phototransduction is highly reproducible despite a number of random components of the activation cascade, including the random activation site, the random walk of an activated receptor, and its quenching in a random number of steps. Here we use a previously generated and tested spatiotemporal mathematical and computational model to identify possible mechanisms of variability reduction. The model permits one to separate the process into modules, and to analyze their impact separately. We show that the activation cascade is responsible for generation of variability, whereas diffusion of the second messengers is responsible for its suppression. Randomness of the activation site contributes at early times to the coefficient of variation of the photoresponse, whereas the Brownian path of a photoisomerized rhodopsin (Rh*) has a negligible effect. The major driver of variability is the turnoff mechanism of Rh*, which occurs essentially within the first 2-4 phosphorylated states of Rh*. Theoretically increasing the number of steps to quenching does not significantly decrease the corresponding coefficient of variation of the effector, in agreement with the biochemical limitations on the phosphorylated states of the receptor. Diffusion of the second messengers in the cytosol acts as a suppressor of the variability generated by the activation cascade. Calcium feedback has a negligible regulatory effect on the photocurrent variability. A comparative variability analysis has been conducted for the phototransduction in mouse and salamander, including a study of the effects of their anatomical differences such as incisures and photoreceptors geometry on variability generation and suppression. © 2008 by the Biophysical Society