Splicing systems and the Chomsky hierarchy

In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we show that it is decidable, given a circular splicing language and a regular language, whether they are equal. Second, we prove the language generated by an alphabetic splicing system is context-free. Alphabetic splicing systems are a generalization of simple and semi-simple splicin systems already considered in the literature

Changes in Purkinje cell firing and gene expression precede behavioral pathology in a mouse model of SCA2.

Spinocerebellar ataxia type 2 (SCA2) is an autosomal dominantly inherited disorder, which is caused by a pathological expansion of a polyglutamine (polyQ) tract in the coding region of the ATXN2 gene. Like other ataxias, SCA2 most overtly affects Purkinje cells (PCs) in the cerebellum. Using a transgenic mouse model expressing a full-length ATXN2(Q127)-complementary DNA under control of the Pcp2 promoter (a PC-specific promoter), we examined the time course of behavioral, morphologic, biochemical and physiological changes with particular attention to PC firing in the cerebellar slice. Although motor performance began to deteriorate at 8 weeks of age, reductions in PC number were not seen until after 12 weeks. Decreases in the PC firing frequency first showed at 6 weeks and paralleled deterioration of motor performance with progression of disease. Transcription changes in several PC-specific genes such as Calb1 and Pcp2 mirrored the time course of changes in PC physiology with calbindin-28 K changes showing the first small, but significant decreases at 4 weeks. These results emphasize that in this model of SCA2, physiological and behavioral phenotypes precede morphological changes by several weeks and provide a rationale for future studies examining the effects of restoration of firing frequency on motor function and prevention of future loss of PCs

Challenges of Trending Time Series Econometrics

We discuss some challenges presented by trending data in time series econometrics. To the empirical economist there is little guidance from theory about the source of trend behavior and even less guidance about practical formulations. Moreover, recent proximity theorems reveal that trends are more elusive to model empirically than stationary processes, with the upshot that optimal forecasts are also harder to estimate when the data involve trends. These limitations are implicitly acknowledged in much practical modeling and forecasting work, where adaptive methods are often used to help keep models on track as trends evolve. The paper discusses these broader issues and limitations of econometrics and o.ers some thoughts on new practical possibilities for data analysis in the absence of good theory models for trends. In particular, a new concept of coordinate cointegration is introduced and some new econometric methodology is suggested for analyzing trends and comovement and for producing forecasts in a general way that is agnostic about the specific nature of the trend process. Some simulation exercises are conducted and some long historical series on prices and yields on long securities are used to illustrate the methods.Coordinate instrumental variables, coordinate reduced rank regression, coordinate trend functions, limitations of econometrics, nonstationarity, trend

What Do CFTs Tell Us About Anti-de Sitter Spacetimes?

The AdS/CFT conjecture relates quantum gravity on Anti-de Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk S-matrix. Our first approach finds the bulk S-matrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geodesics obstructs a standard LSZ prescription for scattering within global AdS. To avoid this subtlety we partition global AdS into patches within which CFT correlators reconstruct transition amplitudes of AdS states. Finally, we use the AdS/CFT duality to propose a large N collective field theory that describes local, perturbative supergravity. Failure of locality in quantum gravity should be related to the difference between the collective 1/N expansion and genuine finite N dynamics.Comment: 33 pages, 7 figures, uses harvmac, reference adde

Modeling and analysis of RNA-seq data: a review from a statistical perspective

Background: Since the invention of next-generation RNA sequencing (RNA-seq) technologies, they have become a powerful tool to study the presence and quantity of RNA molecules in biological samples and have revolutionized transcriptomic studies. The analysis of RNA-seq data at four different levels (samples, genes, transcripts, and exons) involve multiple statistical and computational questions, some of which remain challenging up to date. Results: We review RNA-seq analysis tools at the sample, gene, transcript, and exon levels from a statistical perspective. We also highlight the biological and statistical questions of most practical considerations. Conclusion: The development of statistical and computational methods for analyzing RNA- seq data has made significant advances in the past decade. However, methods developed to answer the same biological question often rely on diverse statical models and exhibit different performance under different scenarios. This review discusses and compares multiple commonly used statistical models regarding their assumptions, in the hope of helping users select appropriate methods as needed, as well as assisting developers for future method development

Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed