Semiotics, Analogical Legal Reasoning, and the Cf. Citation: Getting Our Signals Uncrossed

The Bluebook\u27s introductory citation signals are essential to effective legal discourse. The choice of signal can influence not only the interpretation of cited cases, but also the path of the law. In this Article, Professor Ira Robbins examines one commonly used signal: the cf. After exploring its semiotic function, he details the multitude of ways in which this signal has been used and misused. He argues that lawyers\u27 and judges\u27 careless use of the cf. leads to confusing and often incoherent developments in the law, and concludes by proposing a precise working definition for this irksome, but potentially powerful, citation signal

On the Areas of Cyclic and Semicyclic Polygons

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain variety derived from the variety of binary (2m-1)-forms having m-1 double roots. Thus we obtain explicit formulas for the areas of cyclic heptagons and octagons, and illuminate some mysterious features of Robbins' formulas for the areas of cyclic pentagons and hexagons. We also introduce a companion family of polynomials that relate the squared area of an n-gon inscribed in a circle, one of whose sides is a diameter, to the squared lengths of the other sides. By similar algebraic techniques we obtain explicit formulas for these polynomials for all n <= 7.Comment: 22 page

Nanoindentation of virus capsids in a molecular model

A molecular-level model is used to study the mechanical response of empty cowpea chlorotic mottle virus (CCMV) and cowpea mosaic virus (CPMV) capsids. The model is based on the native structure of the proteins that consitute the capsids and is described in terms of the C-alpha atoms. Nanoindentation by a large tip is modeled as compression between parallel plates. Plots of the compressive force versus plate separation for CCMV are qualitatively consistent with continuum models and experiments, showing an elastic region followed by an irreversible drop in force. The mechanical response of CPMV has not been studied, but the molecular model predicts an order of magnitude higher stiffness and a much shorter elastic region than for CCMV. These large changes result from small structural changes that increase the number of bonds by only 30% and would be difficult to capture in continuum models. Direct comparison of local deformations in continuum and molecular models of CCMV shows that the molecular model undergoes a gradual symmetry breaking rotation and accommodates more strain near the walls than the continuum model. The irreversible drop in force at small separations is associated with rupturing nearly all of the bonds between capsid proteins in the molecular model while a buckling transition is observed in continuum models.Comment: 18 figure

Torsion and bending of nucleic acids studied by subnanosecond time-resolved fluorescence depolarization of intercalated dyes

Subnanosecond time‐resolved fluorescence depolarization has been used to monitor the reorientation of ethidium bromide intercalated in native DNA, synthetic polynucleotide complexes, and in supercoiled plasmid DNA. The fluorescence polarization anisotropy was successfully analyzed with an elastic model of DNA dynamics, including both torsion and bending, which yielded an accurate value for the torsional rigidity of the different DNA samples. The dependence of the torsional rigidity on the base sequence, helical structure, and tertiary structure was experimentally observed. The magnitude of the polyelectrolyte contribution to the torsional rigidity of DNA was measured over a wide range of ionic strength, and compared with polyelectrolyte theories for the persistence length. We also observed a rapid initial reorientation of the intercalated ethidium which had a much smaller amplitude in RNA than in DNA