Evaluating prose style transfer with the Bible

In the prose style transfer task a system, provided with text input and a target prose style, produces output which preserves the meaning of the input text but alters the style. These systems require parallel data for evaluation of results and usually make use of parallel data for training. Currently, there are few publicly available corpora for this task. In this work, we identify a high-quality source of aligned, stylistically distinct text in different versions of the Bible. We provide a standardized split, into training, development and testing data, of the public domain versions in our corpus. This corpus is highly parallel since many Bible versions are included. Sentences are aligned due to the presence of chapter and verse numbers within all versions of the text. In addition to the corpus, we present the results, as measured by the BLEU and PINC metrics, of several models trained on our data which can serve as baselines for future research. While we present these data as a style transfer corpus, we believe that it is of unmatched quality and may be useful for other natural language tasks as well

Endotrivial modules for the symmetric and alternating groups.

In this paper we determine the group of endotrivial modules for certain symmetric and alternating groups in characteristic $p$. If $p=2$, then the group is generated by the class of $\Omega^n(k)$ except in a few low degrees. If $p >2$, then the group is only determined for degrees less than $p^2$. In these cases we show that there are several Young modules which are endotrivial

Real Cubic Surfaces and Real Hyperbolic Geometry

The moduli space of stable real cubic surfaces is the quotient of real hyperbolic four-space by a discrete, nonarithmetic group. The volume of the moduli space is 37\pi^2/1080 in the metric of constant curvature -1. Each of the five connected components of the moduli space can be described as the quotient of real hyperbolic four-space by a specific arithmetic group. We compute the volumes of these components.Comment: 4 pages, one figur

Hyperbolic geometry and moduli of real cubic surfaces

Let M_0^R be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H^4 and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in PO(4,1). We also derive several new and several old results on the topology of M_0^R. Let M_s^R be the moduli space of real cubic surfaces that are stable in the sense of geometric invariant theory. We show that this space carries a hyperbolic structure whose restriction to M_0^R is that just mentioned. The corresponding lattice in PO(4,1), for which we find an explicit fundamental domain, is nonarithmetic.Comment: Major revision, including several new or completely rewritten sections. 56 page

Job vacancy chains in metropolitan labor markets

Metropolitan Labor markets are characterized by gross flows, much larger than the traditional net measures of employment change might suggest. Standard impact analyses of employment change tend to either ignore these flows or treat them as a matter of 'job churning'. But in a metropolitan area experiencing involuntary unemployment and underemployment, these flows may offer real opportunities for individuals to improve their employment positions. Such improvement occurs along 'job chains' in which a new vacancy opens a sequence of job changes allowing workers to move closer to their full employment wage. Not all chains are of the same length, nor does every chain produce the same welfare gain. This paper presents a model of job chaims which addresses chain length, welfare gains and distributional effects. The application of the model is illustrated using a hypothetical case of a new manufacturing firm in the Chicago metropolitan area. The job chains approach to estimating multiplier, efficiency and distributional effects associated with the firm, is compared with conventional impact analysis estimates. The conclusions discuss the implications of these estimates for the evaluation of local economic development projects.