The Small-Is-Very-Small Principle

The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable cut, then it shows that the property has a very small witness: i.e. a witness below a given standard number. We draw various consequences from the central result. For example (in rough formulations): (i) Every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative w.r.t. formulas of complexity $\leq n$. (ii) Every sequential model has, for any $n$, an extension that is elementary for formulas of complexity $\leq n$, in which the intersection of all definable cuts is the natural numbers. (iii) We have reflection for $\Sigma^0_2$-sentences with sufficiently small witness in any consistent restricted theory $U$. (iv) Suppose $U$ is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential $V$ that locally inteprets $U$, globally interprets $U$. Then, $U$ is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations

Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure

This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics into a forecast equation for daily volatility. Analysis of S&P 500 index tick data over the years 1988-2006 shows that taking into account the downward movements improves forecast accuracy significantly. The R2 statistic for evaluating daily volatility forecasts attains a value of 0.80, both for in-sample and out-of-sample prediction.volatility proxy; downward absolute power variation; log-Garch; volatility asymmetry; leverage effect; SP500; volatility forecasting; high-frequency data

Apical dominance in Alstroemeria cultured in vitro

Apical dominance in Alstroemeria is studied to develop an improved propagation protocol for this crop. Four types of explants were prepared: an intact rhizome with two intact shoots (+R+2S), an intact rhizome with two decapitated shoots (+R-2S), a decapitated rhizome with two intact shoots (-R+2S), and a decapitated rhizome with two decapitated shoots (-R-2S). The explants were cultivated on solid MS medium with 9 µM 6-benzylaminopurine (BAP). -R-2S explants showed the highest and +R+2S the lowest axillary-bud outgrowth. Outgrowth in -R+2S and +R-2S explants was intermediate. So, axillary buds are released by removal of the rhizome tip and by removal of the shoot tips. In both decapitated shoots and decapitated rhizomes, application of lanolin with 3-indolebutyric acid (IBA) to the cut end restored apical dominance. This indicates that both tips exert an effect via basipetally transported auxi

Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed anisotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, the beta factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.Comment: 5 pages, 3 figure