Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

An Open Mapping Theorem

It is proved that any surjective morphism $f: \mathbb{Z}^\kappa \to K$ onto a locally compact group $K$ is open for every cardinal $\kappa$. This answers a question posed by Karl Heinrich Hofmann and the second author

String-Like Lagrangians from a Generalized Geometry

This note will use Hitchin's generalized geometry and a model of axionic gravity developed by Warren Siegel in the mid-nineties to show that the construction of Lagrangians based on the inner product arising from the pairing of a vector and its dual can lead naturally to the low-energy Lagrangian of the bosonic string.Comment: Conclusions basically unchanged, but presentation streamlined significantly. Published versio

Mobility Measurements Probe Conformational Changes in Membrane Proteins due to Tension

The function of membrane-embedded proteins such as ion channels depends crucially on their conformation. We demonstrate how conformational changes in asymmetric membrane proteins may be inferred from measurements of their diffusion. Such proteins cause local deformations in the membrane, which induce an extra hydrodynamic drag on the protein. Using membrane tension to control the magnitude of the deformations and hence the drag, measurements of diffusivity can be used to infer--- via an elastic model of the protein--- how conformation is changed by tension. Motivated by recent experimental results [Quemeneur et al., Proc. Natl. Acad. Sci. USA, 111 5083 (2014)] we focus on KvAP, a voltage-gated potassium channel. The conformation of KvAP is found to change considerably due to tension, with its `walls', where the protein meets the membrane, undergoing significant angular strains. The torsional stiffness is determined to be 26.8 kT at room temperature. This has implications for both the structure and function of such proteins in the environment of a tension-bearing membrane.Comment: Manuscript: 4 pages, 4 figures. Supplementary Material: 8 pages, 1 figur

Network simulation using the simulation language for alternate modeling (SLAM 2)

The simulation language for alternate modeling (SLAM 2) is a general purpose language that combines network, discrete event, and continuous modeling capabilities in a single language system. The efficacy of the system's network modeling is examined and discussed. Examples are given of the symbolism that is used, and an example problem and model are derived. The results are discussed in terms of the ease of programming, special features, and system limitations. The system offers many features which allow rapid model development and provides an informative standardized output. The system also has limitations which may cause undetected errors and misleading reports unless the user is aware of these programming characteristics

Fiscal policies aimed at spurring capital formation: a framework for analysis

In recent years, policymakers have proposed various fiscal policies to spur long-run economic growth through increased capital formation. The Bush Administration, for example, proposed lowering the capital gains tax rate. The Clinton Administration, among other measures in its economic package, proposed reinstituting the investment tax credit. These proposals stem from heightened concerns that the U.S. economy has been growing by less than its long-run potential, and from the judgment that this subpar growth is due in part to deficient capital formation.> Chirinko and Morris present a framework for examining fiscal policies aimed at spurring capital formation and highlight the conditions for their success. First, they show why capital formation is an important determinant of economic growth. Second, they show how the optimal amount of capital formation, and therefore economic growth, is determined. Third, they show how economic distortions can cause capital formation to fall short of the socially optimal amount. Finally, they discuss several fiscal policies that have been proposed to raise capital formation.Capital ; Economic development ; Fiscal policy