On the undefinability of Tsirelson's space and its descendants

We prove that Tsirelson's space cannot be defined explicitly from the classical Banach sequence spaces. We also prove that any Banach space that is explicitly definable from a class of spaces that contain $\ell_p$ or $c_0$ must contain $\ell_p$ or $c_0$ as well

Rolling ES cells down the Waddington landscape with Oct4 and Sox2

Embryonic stem cell (ESC) pluripotency is maintained by core transcriptional circuits whereby critical factors sustain their own expression while preventing the expression of genes required for differentiation. Thomson et al. (2011) now show that two core components of the pluripotency circuit, Oct4 and Sox2, are also critical for germ layer fate choice

Ultraproducts and metastability

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory

Nonlinearities in Exchange rates: Double EGARCH Threshold Models for Forecasting Volatility

This paper illustrates how to specify and test a Double Threshold EGARCH Model for some important exchange rates. The analysis is monthly and refers to the period 1990.01-2007.06. The procedure involves testing for Threshold effects the residuals of a linear autoregressive model of the exchange rate that is taken as the starting point. If this preliminary testing is favourable to the hypothesis off nonlinearity one then specifies and estimates a threshold model using Tong (1983,1990) algorithm, Tong algorithm allows to specify separately two AR regimes and helps locating both the delay and the parameters of the regimes using a search procedure based on the AIC. Residual for the SETAR model are then further tested for conditional heteroskedasticity. If it is present then a Double symmetric EGARCH is fitted to the data by maximum likelihood. The result is compared with an AR GARCH model both in sample and out of sample to asses whether there is any forecasting superiority of the more complex model. Reported results favour this outcome. In the text of the paper we report explicitly the results for the Japanese yen and the British pound exchange rates vis a vis the US dollar, but the same procedure has been applied to many other exchange rate series with results favourable to the double variance model in more than 50% of the cases. We report the complete results in the appendix. We conclude that the proposed model is both feasible and of wide applicability to the analysis of volatility of exchange rates. We add two provisos: data are monthly and the period of estimation reflects only the most recent experience.non linearity; forecasting volatility; exchange rates