“Guardian of Civil Rights … Medieval Relic”: The Civil Jury in Canada

Bogart offers some explanations of why Canadian civil juries exist only at the margins by examining the availability of civil juries, empirical evidence regarding their use and cost in Ontario Canada and academic and policy debates concerning their role

Circuit operates as sine function generator

Electronic circuit drives sine function generator using square wave and sawtooth sweep generators. The circuit replaces electromechanical driver and increases accuracy

An improved analysis of sphere transmission experiments for average capture cross sections

Monte Carlo and Bethe methods for calculating neutron cross sections with effective scattering cross section

Multiscale metabolic modeling of C4 plants: connecting nonlinear genome-scale models to leaf-scale metabolism in developing maize leaves

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, here the predicted fluxes achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems. We suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data.Comment: 57 pages, 14 figures; submitted to PLoS Computational Biology; source code available at http://github.com/ebogart/fluxtools and http://github.com/ebogart/multiscale_c4_sourc

A lower bound for the determinantal complexity of a hypersurface

We prove that the determinantal complexity of a hypersurface of degree $d > 2$ is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least $5$. As a result, we obtain that the determinantal complexity of the $3 \times 3$ permanent is $7$. We also prove that for $n> 3$, there is no nonsingular hypersurface in $\mathbf{P}^n$ of degree $d$ that has an expression as a determinant of a $d \times d$ matrix of linear forms while on the other hand for $n \le 3$, a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is $5$.Comment: 7 pages, 0 figure

Equality of Graver bases and universal Gr\"obner bases of colored partition identities

Associated to any vector configuration A is a toric ideal encoded by vectors in the kernel of A. Each toric ideal has two special generating sets: the universal Gr\"obner basis and the Graver basis. While the former is generally a proper subset of the latter, there are cases for which the two sets coincide. The most prominent examples among them are toric ideals of unimodular matrices. Equality of universal Gr\"obner basis and Graver basis is a combinatorial property of the toric ideal (or, of the defining matrix), providing interesting information about ideals of higher Lawrence liftings of a matrix. Nonetheless, a general classification of all matrices for which both sets agree is far from known. We contribute to this task by identifying all cases with equality within two families of matrices; namely, those defining rational normal scrolls and those encoding homogeneous primitive colored partition identities.Comment: minor revision; references added; introduction expanded