Merging for inhomogeneous finite Markov chains, part II: Nash and log-Sobolev inequalities

We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOP572 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Time inhomogeneous Markov chains with wave-like behavior

Starting from a given Markov kernel on a finite set $V$ and a bijection $g$ of $V$, we construct and study a time inhomogeneous Markov chain whose kernel at time $n$ is obtained from $K$ by transport of $g^{n-1}$. We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.Comment: Published in at http://dx.doi.org/10.1214/09-AAP661 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Barry Smith an sich

Festschrift in Honor of Barry Smith on the occasion of his 65th Birthday. Published as issue 4:4 of the journal Cosmos + Taxis: Studies in Emergent Order and Organization. Includes contributions by Wolfgang Grassl, Nicola Guarino, John T. Kearns, Rudolf Lüthe, Luc Schneider, Peter Simons, Wojciech Żełaniec, and Jan Woleński

The mid-infrared extinction law in the darkest cores of the Pipe Nebula

Context. The properties of dust grains, in particular their size distribution, are expected to differ from the interstellar medium to the high-density regions within molecular clouds. Aims. We measure the mid-infrared extinction law produced by dense material in molecular cloud cores. Since the extinction at these wavelengths is caused by dust, the extinction law in cores should depart from that found in low-density environments if the dust grains have different properties. Methods. We use the unbiased LINES method to measure the slope of the reddening vectors in color-color diagrams. We derive the mid-infrared extinction law toward the dense cores B59 and FeSt 1-457 in the Pipe Nebula over a range of visual extinction between 10 and 50 magnitudes, using a combination of Spitzer/IRAC, and ESO NTT/VLT data. Results. The mid-infrared extinction law in both cores departs significantly from a power-law between 3.6 and 8 micron, suggesting that these cores contain dust with a considerable fraction of large dust grains. We find no evidence for a dependence of the extinction law with column density up to 50 magnitudes of visual extinction in these cores, and no evidence for a variation between our result and those for other clouds at lower column densities reported elsewhere in the literature. This suggests that either large grains are present even in low column density regions, or that the existing dust models need to be revised at mid-infrared wavelengths. We find a small but significant difference in the extinction law of the two cores, that we tentatively associate with the onset of star formation in B59.Comment: 8 pages, 6 figures. Accepted to A&

Seasonal Effects and Volume-yield Relationship in the Central Bank Indexed Promissory Notes

This article analyzes information on yields and volume on daily transactions of Central Bank indexed promissory notes (PRBC) from July 1995 to June 1998. Daily yields increase on Mondays, reaching maximum values on Wednesdays, followed by a decline to minimum values on Fridays. The highest weekly yield is observed in the last week of the month, with a general upward trend in yields observed from the start to the end of the month. With regard to PRBC’s volume-yield relation, I found that higher yields correspond to more active trading periods and yields rise strongly with the aggregation of trading data. Central Bank monetary policy, through the monetary policy rate, accounts on average for 6% of this relation. Finally, the volume-yield relation is sensitive to the type of data aggregation, and may show an inverse relation when data is ordered according to days to maturity.