Head as metaphor in Paul

Since the 1980s there has been a debate among New Testament scholars about the meaning of the Greek word “kephal?” (“head”) in the Pauline epistles. Some scholars defend the traditional view that it means “leader”, while others argue that it should be understood to mean “source”. One result of this debate is that it is now clear that both the traditional and the new interpretation of kephal? have very little support in general Greek usage before the New Testament. This article seeks to advance the debate by showing that the phenomenon of “semantic borrowing” can explain why the meaning “source” is effectively limited to one passage in Herodotus,and the meaning “leader” is only found in Greek works written by bilingual Jews. The passage in Herodotus probably reflects a semantic loan from Old Persian *sar while various places in the Septuagint, Philo, Josephus and Paul reflect a semantic loan from Hebrew “ro’sh” (or Aramaic “re’sh”). Because the latter semantic loan (“head” meaning “leader”) is embedded in the Greek Bible (both in the Septuagint and Paul),the authority and prestige of the latter can account for the fact that the new meaning of kephal?, though unknown in previous pagan Greek writings, gradually became widespread in postbiblical Greek as Christianity spread

Analysis of the entanglement between two individual atoms using global Raman rotations

Making use of the Rydberg blockade, we generate entanglement between two atoms individually trapped in two optical tweezers. In this paper we detail the analysis of the data and show that we can determine the amount of entanglement between the atoms in the presence of atom losses during the entangling sequence. Our model takes into account states outside the qubit basis and allows us to perform a partial reconstruction of the density matrix describing the two atom state. With this method we extract the amount of entanglement between pairs of atoms still trapped after the entangling sequence and measure the fidelity with respect to the expected Bell state. We find a fidelity $F_{\rm pairs} =0.74(7)$ for the 62% of atom pairs remaining in the traps at the end of the entangling sequence

A Greedy Algorithm for Unimodal Kernel Density Estimation by Data Sharpening

We consider the problem of nonparametric density estimation where estimates are constrained to be unimodal. Though several methods have been proposed to achieve this end, each of them has its own drawbacks and none of them have readily-available computer codes. The approach of Braun and Hall (2001), where a kernel density estimator is modified by data sharpening, is one of the most promising options, but optimization difficulties make it hard to use in practice. This paper presents a new algorithm and MATLAB code for finding good unimodal density estimates under the Braun and Hall scheme. The algorithm uses a greedy, feasibility-preserving strategy to ensure that it always returns a unimodal solution. Compared to the incumbent method of optimization, the greedy method is easier to use, runs faster, and produces solutions of comparable quality. It can also be extended to the bivariate case

A Greedy Algorithm for Unimodal Kernel Density Estimation by Data Sharpening

Nonparametric methods for smoothing, regression, and density estimation produce estimators with great shape flexibility. Although this flexibility is an advantage, the practical value of nonparametric methods would be increased if qualitative constraints—natural-language shape restrictions—could also be imposed on the estimator. In density estimation, the most common such constraints are monotonicity (the density must be nondecreasing or nonincreasing) and unimodality (the density must have only one peak). The work presented here takes unimodal kernel density estimation as a representative problem in constrained nonparametric estimation. The method proposed for handling the constraint is data sharpening. A greedy algorithm is described for achieving the unimodality constraint. The algorithm is deterministic and runs quickly. It can find solutions that are competitive with the incumbent method, sequential quadratic programming

Methods for Shape-Constrained Kernel Density Estimation

Nonparametric density estimators are used to estimate an unknown probability density while making minimal assumptions about its functional form. Although the low reliance of nonparametric estimators on modelling assumptions is a benefit, their performance will be improved if auxiliary information about the density\u27s shape is incorporated into the estimate. Auxiliary information can take the form of shape constraints, such as unimodality or symmetry, that the estimate must satisfy. Finding the constrained estimate is usually a difficult optimization problem, however, and a consistent framework for finding estimates across a variety of problems is lacking. It is proposed to find shape-constrained density estimates by starting with a pilot estimate obtained by standard methods, and subsequently adjusting its shape until the constraints are satisfied. This strategy is part of a general approach, in which a constrained estimation problem is defined by an estimator, a method of shape adjustment, a constraint, and an objective function. Optimization methods are developed to suit this approach, with a focus on kernel density estimation under a variety of constraints. Two methods of shape adjustment are examined in detail. The first is data sharpening, for which two optimization algorithms are proposed: a greedy algorithm that runs quickly but can handle a limited set of constraints, and a particle swarm algorithm that is suitable for a wider range of problems. The second is the method of adjustment curves, for which it is often possible to use quadratic programming to find optimal estimates. The methods presented here can be used for univariate or higher-dimensional kernel density estimation with shape constraints. They can also be extended to other estimators, in both the density estimation and regression settings. As such they constitute a step toward a truly general optimizer, that can be used on arbitrary combinations of estimator and constraint

A Genetic Algorithm for Selection of Fixed-Size Subsets with Application to Design Problems

The R function kofnGA conducts a genetic algorithm search for the best subset of k items from a set of n alternatives, given an objective function that measures the quality of a subset. The function fills a gap in the presently available subset selection software, which typically searches over a range of subset sizes, restricts the types of objective functions considered, or does not include freely available code. The new function is demonstrated on two types of problem where a fixed-size subset search is desirable: design of environmental monitoring networks, and D-optimal design of experiments. Additionally, the performance is evaluated on a class of constructed test problems with a novel design that is interesting in its own right

Metal contacts to lowly doped Si and ultra thin SOI

We present our investigations on the fabrication of ohmic and Schottky contacts of several metals on lowly doped bulk Si and SOI wafers. Through this paper we evaluate the fabrication of rectifying devices in which no doping is intentionally introduced