Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

A Tale of Two Forecasts: An Analysis of Mandatory and Voluntary Effective Tax Rate Forecasts

We exploit a setting where firms provide two forecasts of the same underlying metric – effective tax rates (ETRs) – to examine the interaction between voluntary and mandatory disclosures. The integral method (ASC 740-270) requires firms to forecast de facto annual ETRs while some firms additionally provide voluntary ETR forecasts in earnings calls. Using a self-constructed dataset of voluntary ETR forecasts, we document that managers are more likely to issue voluntary ETR forecasts when tax complexity is higher. More importantly, voluntary ETR forecasts are incrementally informative over mandatory ETR forecasts as analysts revise their ETR forecasts based on the news in voluntary ETR forecasts, especially for voluntary non-GAAP ETR forecasts and in the presence of discrete tax items. Overall, our results suggest that managers resort to voluntary disclosure when mandatory disclosure constrains their ability to convey private information, thus we offer new insights on the interaction between voluntary and mandatory forward-looking disclosures

Models of emission line profiles and spectral energy distributions to characterize the multi-frequency properties of active galactic nuclei

The spectra of Active Galactic Nuclei (AGNs) are often characterized by a wealth of emission lines with different profiles and intensity ratios that led to a complicated classification. Their electro-magnetic radiation spans more than 10 orders of magnitude in frequency. In spite of the differences between various classes, the origin of their activity is attributed to a combination of emitting components, surrounding an accreting Super Massive Black Hole, in the so called Unified Model. Currently, the execution of sky surveys, with instruments operating at various frequencies, provides the possibility to detect and to investigate the properties of AGNs on very large statistical samples. Thanks to the spectroscopic surveys that allow investigation of many objects, we have the opportunity to place new constraints on the nature and evolution of AGNs. In this contribution we present the results obtained by working on multi-frequency data and we discuss their relations with the available optical spectra. We compare our findings with the AGN Unified Model predictions, and we present a revised technique to select AGNs of different types from other line emitting objects. We discuss the multi-frequency properties in terms of the innermost structures of the sources.Comment: 11 pages, 4 figures. Proceedings of the XI Serbian Conference on Spectral Line Shapes in Astrophysics. Accepted for publication on Atom

Wnt3 and Wnt3a are required for induction of the mid-diencephalic organizer in the caudal forebrain

Abstract Background A fundamental requirement for development of diverse brain regions is the function of local organizers at morphological boundaries. These organizers are restricted groups of cells that secrete signaling molecules, which in turn regulate the fate of the adjacent neural tissue. The thalamus is located in the caudal diencephalon and is the central relay station between the sense organs and higher brain areas. The mid-diencephalic organizer (MDO) orchestrates the development of the thalamus by releasing secreted signaling molecules such as Shh. Results Here we show that canonical Wnt signaling in the caudal forebrain is required for the formation of the Shh-secreting MD organizer in zebrafish. Wnt signaling induces the MDO in a narrow time window of 4 hours - between 10 and 14 hours post fertilization. Loss of Wnt3 and Wnt3a prevents induction of the MDO, a phenotype also observed upon blockage of canonical Wnt signaling per se. Pharmaceutical activation of the canonical Wnt pathways in Wnt3/Wnt3a compound morphant embryos is able to restore the lack of the MDO. After blockage of Wnt signaling or knock-down of Wnt3/Wnt3a we find an increase of apoptotic cells specifically within the organizer primordium. Consistently, blockage of apoptosis restores the thalamus organizer MDO in Wnt deficient embryos. Conclusion We have identified canonical Wnt signaling as a novel pathway, that is required for proper formation of the MDO and consequently for the development of the major relay station of the brain - the thalamus. We propose that Wnt ligands are necessary to maintain the primordial tissue of the organizer during somitogenesis by suppressing Tp53-mediated apoptosis. </jats:sec