DE MINIMIS NON CURAT LEX

An age-old maxim often applied but infrequently rationalized is that of de minimus non curat lex. In the recent case of Steve Anderson v. Mt. Clemens Pottery Company, the United States Supreme Court focused attention upon the doctrine by ruling that it should be applied in determining whether walking time and other preliminary activities constitute work for which employees are entitled to compensation under the Fair Labor Standards Act of 1938. The so-called portal-to-portal problems which have arisen as a result of the last mentioned ruling make timely a discussion of the origin, meaning, function and application of the maxim

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Can additive beta-diversity be reliably partitioned into nestedness and turnover components?

Aims: Quantifying β‐diversity (differences in the composition of communities) is central to many ecological studies. There are many β‐diversity metrics, falling mostly into two approaches: variance‐based (e.g., the Sørensen index), or diversity partitioning (e.g., additive β‐diversity). The former cannot be used when species–sites matrices are unavailable (which is often the case in island biogeography in particular) and only species richness data are provided. Recently, efforts have been made to partition additive β‐diversity, a metric calculated using only α‐diversity and γ‐diversity, into nestedness and turnover components (termed here “richness‐only β‐diversity partitioning”). We set out to test whether this form of β‐diversity partitioning generates interpretable results, comparable with metrics based on species incidence β‐diversity partitioning. Location: Global. Time period: Present day. Major taxa studied: Multiple taxa. Methods: We first provide a brief review of β‐diversity partitioning methods, with a particular focus on the development of richness‐only β‐diversity partitioning. Second, we use 254 empirical incidence matrices (provided with the paper) sourced from the literature to measure turnover and nestedness using incidence β‐diversity partitioning, comparing the resulting values with those calculated using richness‐only β‐diversity. Results: We provide an account of the emergence of β‐diversity partitioning, with particular reference to the analysis of richness‐only datasets, and to the definition and usage of the relevant metrics. Analytically, we report weak correlations between turnover and nestedness calculated using the two different approaches. We show that this is because identical values of α‐diversity and γ‐diversity can correspond to incidence matrices with a range of different structures. Main conclusions: Our results demonstrate that the use of richness‐only β‐diversity partitioning to measure turnover and nestedness is problematic and can produce patterns unrelated to conventional measures of turnover and nestedness. We therefore recommend that more accurate definitions are adopted for these terms in future studies.</br

Shapes of polyhedra, mixed volumes and hyperbolic geometry

We generalize to higher dimensions the Bavard–Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d -dimensional polyhedra with fixed directions of facet normals has a decomposition into type cones that correspond to different combinatorial types of polyhedra. This decomposition is a subfan of the secondary fan of a vector configuration and can be analyzed with the help of Gale diagrams. We construct a family of quadratic forms on each of the type cones using the theory of mixed volumes. The Alexandrov–Fenchel inequalities ensure that these forms have exactly one positive eigenvalue. This introduces a piecewise hyperbolic structure on the space of similarity classes of polyhedra with fixed directions of facet normals. We show that some of the dihedral angles on the boundary of the resulting cone-manifold are equal to π/2

NMR Structures of Apo L. casei Dihydrofolate Reductase and Its Complexes with Trimethoprim and NADPH: Contributions to Positive Cooperative Binding from Ligand-Induced Refolding, Conformational Changes, and Interligand Hydrophobic Interactions

bS Supporting Information The enzyme dihydrofolate reductase (DHFR; 5,6,7,8-tetra-hydrofolate:NADPH oxidoreductase, EC 1.5.1.3) catalyzes the reduction of 7,8-dihydrofolate (DHF) to 5,6,7,8-tetrahydro-folate (THF) using NADPH as coenzyme.1 Since THF and its metabolites are precursors of purine and pyrimidine bases, the normal functioning of this enzyme is essential for proliferating cells. This makes DHFR an excellent target for antifolate drugs such as methotrexate (anticancer), pyrimethamine (antimalarial), and trimethoprim (antibacterial). Such agents act by inhibiting the enzyme in parasitic or malignant cells.1,2 The cooperative binding of ligands to DHFR plays an important role not only in the enzyme catalytic cycle (negative cooperativity in THF/ NADPH binding)3 but also in enzyme inhibition (positive cooperativity in antifolate/NADPH binding).4 The effects of positive cooperative binding in controlling enzyme inhibition ar