The dynamics of patent citations

The use of patent citations as a measure of patent "quality" increased dramatically in recent years. I estimate the hazard of patent citation, and find evidence of unobserved heterogeneity. Hazard estimation provides a means to separate patent quality from citation "inflation."

A Theory of the IMF for Star Formation in Molecular Clouds

We present models for the initial mass function (IMF) for stars forming within molecular clouds. These models use the idea that stars determine their own masses through the action of powerful stellar outflows. This concept allows us to calculate a semi-empirical mass formula (SEMF), which provides the transformation between initial conditions in molecular clouds and the final masses of forming stars. For a particular SEMF, a given distribution of initial conditions predicts a corresponding IMF. We consider several different descriptions for the distribution of initial conditions in star forming molecular clouds. We first consider the limiting case in which only one physical variable -- the effective sound speed -- determines the initial conditions. In this limit, we use observed scaling laws to determine the distribution of sound speed and the SEMF to convert this distribution into an IMF. We next consider the opposite limit in which many different independent physical variables play a role in determining stellar masses. In this limit, the central limit theorem shows that the IMF approaches a log-normal form. Realistic star forming regions contain an intermediate number of relevant variables; we thus consider intermediate cases between the two limits. Our results show that this picture of star formation and the IMF naturally produces stellar mass distributions that are roughly consistent with observations. This paper thus provides a calculational framework to construct theoretical models of the IMF.Comment: 34 pages, 7 figures available on reques

The Extended Fock Basis of Clifford Algebra

We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of \Gamma. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).Comment: Minimal corrections to the published versio

Deterministic Controlled-NOT gate for single-photon two-qubit quantum logic

We demonstrate a robust implementation of a deterministic linear-optical Controlled-NOT (CNOT) gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45$^{\circ}$-oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The CNOT gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.Comment: 10 pages, 4 figures. Typos corrected, referee comments and correction

Kelo, Cuno, and the Broken Window

In June 2005, the Supreme Court made one of its least popular decisions in recent history. In Kelo v. New London, the Court missed a simple point: that local decision makers make local decisions.

Uncertainty Analysis of Feature Extraction from Expired Gas Traces

Noninvasive medical analyses are a convenient method to study several pathologies even though their indirect nature often requires a complex processing to determine the relevant health "indicators". The usefulness of such indicators depends on the employed model, but also on the uncertainty that is connected to the complex processing involved in the indicator determination. This paper deals with the problems related to the estimation of the uncertainty when the indicators are computed by means of a nontrivial processing on recorded traces of clinical parameters. The paper is focused on the analysis of expired gas traces, but the procedure can also be applied to many other cases where the processing involves manual or automatic selection of suitable "key points" on repetitive traces

A Parametric Framework for the Comparison of Methods of Very Robust Regression

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression data and the outliers. We introduce a parameter $\lambda$ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of $\lambda$, the variance and squared bias of five estimators and we also consider their power when used in the detection of outliers. This systematic approach provides tools for gaining knowledge and better understanding of the properties of robust estimators.Comment: Published in at http://dx.doi.org/10.1214/13-STS437 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

QCD and spin effects in black hole airshowers

In models with large extra dimensions, black holes may be produced in high-energy particle collisions. We revisit the physics of black hole formation in extensive airshowers from ultrahigh-energy cosmic rays, focusing on collisional QCD and black hole emissivity effects. New results for rotating black holes are presented. Monte Carlo simulations show that QCD effects and black hole spin produce no observable signatures in airshowers. These results further confirm that the main characteristics of black hole-induced airshowers do not depend on the fine details of micro black hole models.Comment: 6 pages, 2 figures, accepted for publication in Physical Review