Unifying Cubical Models of Univalent Type Theory

We present a new constructive model of univalent type theory based on cubical sets. Unlike prior work on cubical models, ours depends neither on diagonal cofibrations nor connections. This is made possible by weakening the notion of fibration from the cartesian cubical set model, so that it is not necessary to assume that the diagonal on the interval is a cofibration. We have formally verified in Agda that these fibrations are closed under the type formers of cubical type theory and that the model satisfies the univalence axiom. By applying the construction in the presence of diagonal cofibrations or connections and reversals, we recover the existing cartesian and De Morgan cubical set models as special cases. Generalizing earlier work of Sattler for cubical sets with connections, we also obtain a Quillen model structure

Billiards in Nearly Isosceles Triangles

We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some self-similarity phenomena in irrational triangular billiards. Our analysis illustrates the surprising fact that billiards on a triangle near a Veech triangle is extremely complicated even though Billiards on a Veech triangle is very well understood.Comment: Errors have been corrected in Section 9 from the prior and published versions of this paper. In particular, the formulas associated to homology classes of curves corresponding to stable periodic billiard paths in obtuse Veech triangles were corrected. See Remark 9.1 of the paper for more information. The main results and the results from other sections are unaffected. 82 pages, 43 figure

The Case for Liberal Spectrum Licenses: A Technical and Economic Perspective

The traditional system of radio spectrum allocation has inefficiently restricted wireless services. Alternatively, liberal licenses ceding de facto spectrum ownership rights yield incentives for operators to maximize airwave value. These authorizations have been widely used for mobile services in the U.S. and internationally, leading to the development of highly productive services and waves of innovation in technology, applications and business models. Serious challenges to the efficacy of such a spectrum regime have arisen, however. Seeing the widespread adoption of such devices as cordless phones and wi-fi radios using bands set aside for unlicensed use, some scholars and policy makers posit that spectrum sharing technologies have become cheap and easy to deploy, mitigating airwave scarcity and, therefore, the utility of exclusive rights. This paper evaluates such claims technically and economically. We demonstrate that spectrum scarcity is alive and well. Costly conflicts over airwave use not only continue, but have intensified with scientific advances that dramatically improve the functionality of wireless devices and so increase demand for spectrum access. Exclusive ownership rights help direct spectrum inputs to where they deliver the highest social gains, making exclusive property rules relatively more socially valuable. Liberal licenses efficiently accommodate rival business models (including those commonly associated with unlicensed spectrum allocations) while mitigating the constraints levied on spectrum use by regulators imposing restrictions in traditional licenses or via use rules and technology standards in unlicensed spectrum allocations.

The dynamic impact of fundamental tax reform part 1: the basic model

The Internal Revenue Service remains unpopular, the U.S. savings rate remains low, and pressure to efficiently raise significant new tax revenues seems certain to grow once the baby boom generation reaches retirement age. Consequently, it is likely that alternatives to the current income tax system will receive substantial political and media attention in coming years. In this first of two articles on the economic impact of fundamental tax reform, Evan Koenig and Gregory Huffman describe a framework for analyzing how the adoption of a flat-rate consumption tax would affect the economy over time. Their analysis indicates that replacing the income tax with a consumption tax would have an immediate positive impact on saving and lead, in the long run, to higher levels of consumption, wages, and stock prices and to lower interest rates. In the short run, however, interest rates would probably rise, and consumption and stock prices would probably decline.Taxation

The dynamic impact of fundamental tax reform part 2 : extensions

In this second of two articles on the economic impact of fundamental tax reform, Gregory Huffman and Evan Koenig extend their earlier framework for analyzing how the adoption of a flat-rate consumption tax would affect the economy over time. They argue that if tax reform is to be successful in stimulating investment and raising long-run living standards, then it is important that ways be found to avoid increasing the rate of labor-income taxation. Increases in labor-income tax rates can undo the positive economic effects of a cut in the rate of capital-income taxation. Conversely, cuts in labor-income tax rates reinforce savings incentives and contribute to higher steady-state levels of consumption. Huffman and Koenig also demonstrate that the economy’s immediate response to tax reform is muted—and the overall adjustment process can be substantially prolonged—when firms find it expensive to add quickly to their stocks of plant and equipment.Taxation ; Tax auditing ; Tax reform

Doubly stochastic continuous-time hidden Markov approach for analyzing genome tiling arrays

Microarrays have been developed that tile the entire nonrepetitive genomes of many different organisms, allowing for the unbiased mapping of active transcription regions or protein binding sites across the entire genome. These tiling array experiments produce massive correlated data sets that have many experimental artifacts, presenting many challenges to researchers that require innovative analysis methods and efficient computational algorithms. This paper presents a doubly stochastic latent variable analysis method for transcript discovery and protein binding region localization using tiling array data. This model is unique in that it considers actual genomic distance between probes. Additionally, the model is designed to be robust to cross-hybridized and nonresponsive probes, which can often lead to false-positive results in microarray experiments. We apply our model to a transcript finding data set to illustrate the consistency of our method. Additionally, we apply our method to a spike-in experiment that can be used as a benchmark data set for researchers interested in developing and comparing future tiling array methods. The results indicate that our method is very powerful, accurate and can be used on a single sample and without control experiments, thus defraying some of the overhead cost of conducting experiments on tiling arrays.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS248 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org