Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for $\nu_e$ $\to$ $\nu_{\mu}$ transition can be written in the form $P(\nu_e \to \nu_{\mu})=A_{e\mu}\cos\delta+B_{e\mu}\sin\delta+C_{e\mu}$ without any approximation using CP phase $\delta$. For $\nu_{\mu}$ $\to$ $\nu_{\tau}$ transition, the linear term of $\cos 2\delta$ is added and the probability can be written in the form $P(\nu_{\mu} \to \nu_{\tau})=A_{\mu\tau}\cos\delta+B_{\mu\tau} \sin\delta+C_{\mu\tau}+D_{\mu\tau}\cos 2\delta$. We give the CP dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to $\delta$ as in vacuum. It means that matter effects just modify the coefficients $A$, $B$, $C$ and $D$. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to CP dependences are reproduced from the effective mixing angles and the effective CP phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.Comment: 12 pages, RevTeX4 style, changed title, minor correction

Processing efficiency in anxiety: evidence from eye-movements during visual search

It is generally held that anxiety is characterized by an attentional bias for threatening information. In recent years there has been an important debate whether these biases reside at the level of attentional selection (threat detection) or attentional processing after threat detection (attentional disengagement). In a visual search task containing emotional facial expressions, eye-movements were examined before and after threat detection in high and low trait anxious individuals to further elucidate the temporal unfolding of attentional bias. Results indicated that high-anxious individuals neither showed facilitated orienting to threat nor impaired disengagement of visual attention from threat. Interestingly, the presence of threat in the visual search display was associated with increased decision times in high-anxious individuals. These results challenge some of the current views on attentional bias to threat but indicate that emotional information reduces processing efficiency in anxiety

The North Court of the Erechtheion and the Ritual of the Plynteria

The north side of the uncanonical Temple of Athena Polias at Athens, conventionally called the Erechtheion, included a small paved court with banks of steps on the east and on the north against the Acropolis wall. The details of construction indicate that both the marble paving and the steps were built as part of the Erechtheion. This small, secluded North Court is a likely venue for the solemn ceremonies of the Plynteria and the Kallynteria, in which the ancient olive-wood statue of Athena Polias was taken out of the temple, bathed, and adorned. The unroofed, tightly integrated North Court reinforces the status of the Erechtheion as an innovative architectural composition