On the time-dependent analysis of Gamow decay

Gamow's explanation of the exponential decay law uses complex 'eigenvalues' and exponentially growing 'eigenfunctions'. This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any wavefunction is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover, the presentation can well be used in physics lectures to students.

Granger causality of coupled climate processes: Ocean feedback on the North Atlantic oscillation

This study uses a Granger causality time series modeling approach to quantitatively diagnose the feedback of daily sea surface temperatures (SSTs) on daily values of the North Atlantic Oscillation (NAO) as simulated by a realistic coupled general circulation model (GCM). Bivariate vector autoregressive time series models are carefully fitted to daily wintertime SST and NAO time series produced by a 50-yr simulation of the Third Hadley Centre Coupled Ocean-Atmosphere GCM (HadCM3). The approach demonstrates that there is a small yet statistically significant feedback of SSTs oil the NAO. The SST tripole index is found to provide additional predictive information for the NAO than that available by using only past values of NAO-the SST tripole is Granger causal for the NAO. Careful examination of local SSTs reveals that much of this effect is due to the effect of SSTs in the region of the Gulf Steam, especially south of Cape Hatteras. The effect of SSTs on NAO is responsible for the slower-than-exponential decay in lag-autocorrelations of NAO notable at lags longer than 10 days. The persistence induced in daily NAO by SSTs causes long-term means of NAO to have more variance than expected from averaging NAO noise if there is no feedback of the ocean on the atmosphere. There are greater long-term trends in NAO than can be expected from aggregating just short-term atmospheric noise, and NAO is potentially predictable provided that future SSTs are known. For example, there is about 10%-30% more variance in seasonal wintertime means of NAO and almost 70% more variance in annual means of NAO due to SST effects than one would expect if NAO were a purely atmospheric process.

Study of the lactation curve in dairy cattle on farms in Central Mexico

Accurate knowledge of lactation curves has an important relevance to management and research of dairy production systems. A number of equations have been proposed to describe the lactation curve, the most widely applied being the gamma equation. The objective of this work was to compare and evaluate candidate functions for their predictive ability in describing lactation curves from central Mexican dairy cows reared under 2 contrasting management systems. Five equations were considered: Gaines ( exponential decay), Wood ( gamma equation), Rook ( Michaelis-Menten x exponential), and 2 more mechanistic ones (Dijkstra and Pollott). A database consisting of 701 and 1283 records of cows in small-scale and intensive systems, respectively, was used in the analysis. Before analysis, the database was divided into 6 groups representing first, second, and third and higher parity cows in both systems. In all cases except second and above parity cows in small-scale systems, all models improved on the Gaines equation. The Wood equation explained much of the variation, but its parameters do not have direct biological interpretation. Although the Rook equation fitted the data well, some of the parameter estimates were not significant. The Dijkstra equation consistently gave better predictions, and its parameters were usually statistically significant and lend themselves to physiological interpretation. As such, the differences between systems and parity could be explained due to variations in theoretical initial milk production at parturition, specific rates of secretory cell proliferation and death, and rate of decay, all of which are parameters in the model. The Pollott equation, although containing the most biology, was found to be over-parameterized and resulted in nonsignificant parameter estimates. For central Mexican dairy cows, the Dijkstra equation was the best option to use in describing the lactation curve.

Classification and fault detection methods for fuel cell monitoring and quality control

In this paper, various types of fault detection methods for fuel cells are compared. For example, those that use a model based approach or a data driven approach or a combination of the two. The potential advantages and drawbacks of each method are discussed and comparisons between methods are made. In particular, classification algorithms are investigated, which separate a data set into classes or clusters based on some prior knowledge or measure of similarity. In particular, the application of classification methods to vectors of reconstructed currents by magnetic tomography or to vectors of magnetic field measurements directly is explored. Bases are simulated using the finite integration technique (FIT) and regularization techniques are employed to overcome ill-posedness. Fisher's linear discriminant is used to illustrate these concepts. Numerical experiments show that the ill-posedness of the magnetic tomography problem is a part of the classification problem on magnetic field measurements as well. This is independent of the particular working mode of the cell but influenced by the type of faulty behavior that is studied. The numerical results demonstrate the ill-posedness by the exponential decay behavior of the singular values for three examples of fault classes.

Movement intention detection from autocorrelation of EEG for BCI

Movement intention detection is important for development of intuitive movement based Brain Computer Interfaces (BCI). Various complex oscillatory processes are involved in producing voluntary movement intention. In this paper, temporal dynamics of electroencephalography (EEG) associated with movement intention and execution were studied using autocorrelation. It was observed that the trend of decay of autocorrelation of EEG changes before and during the voluntary movement. A novel feature for movement intention detection was developed based on relaxation time of autocorrelation obtained by fitting exponential decay curve to the autocorrelation. This new single trial feature was used to classify voluntary finger tapping trials from resting state trials with peak accuracy of 76.7%. The performance of autocorrelation analysis was compared with Motor-Related Cortical Potentials (MRCP).

The influence of bottom topography on the decay of modeled Agulhas rings

The influence of a large meridional submarine ridge on the decay of Agulhas rings is investigated with a 1 and 2-layer setup of the isopycnic primitive-equation ocean model MICOM. In the single-layer case we show that the SSH decay of the ring is primarily governed by bottom friction and secondly by the radiation of Rossby waves. When a topographic ridge is present, the effect of the ridge on SSH decay and loss of tracer from the ring is negligible. However, the barotropic ring cannot pass the ridge due to energy and vorticity constraints. In the case of a two-layer ring the initial SSH decay is governed by a mixed barotropic–baroclinic instability of the ring. Again, radiation of barotropic Rossby waves is present. When the ring passes the topographic ridge, it shows a small but significant stagnation of SSH decay, agreeing with satellite altimetry observations. This is found to be due to a reduction of the growth rate of the m = 2 instability, to conversions of kinetic energy to the upper layer, and to a decrease in Rossby-wave radiation. The energy transfer is related to the fact that coherent structures in the lower layer cannot pass the steep ridge due to energy constraints. Furthermore, the loss of tracer from the ring through filamentation is less than for a ring moving over a flat bottom, related to a decrease in propagation speed of the ring. We conclude that ridges like the Walvis Ridge tend to stabilize a multi-layer ring and reduce its decay.

Aberrant mRNA Transcripts and the Nonsense-Mediated Decay Proteins UPF2 and UPF3 Are Enriched in the Arabidopsis Nucleolus

The eukaryotic nucleolus is multifunctional and involved in the metabolism and assembly of many different RNAs and ribonucleoprotein particles as well as in cellular functions, such as cell division and transcriptional silencing in plants. We previously showed that Arabidopsis thaliana exon junction complex proteins associate with the nucleolus, suggesting a role for the nucleolus in mRNA production. Here, we report that the plant nucleolus contains mRNAs, including fully spliced, aberrantly spliced, and single exon gene transcripts. Aberrant mRNAs are much more abundant in nucleolar fractions, while fully spliced products are more abundant in nucleoplasmic fractions. The majority of the aberrant transcripts contain premature termination codons and have characteristics of nonsense-mediated decay (NMD) substrates. A direct link between NMD and the nucleolus is shown by increased levels of the same aberrant transcripts in both the nucleolus and in Up-frameshift (upf) mutants impaired in NMD. In addition, the NMD factors UPF3 and UPF2 localize to the nucleolus, suggesting that the Arabidopsis nucleolus is therefore involved in identifying aberrant mRNAs and NMD.