Recursions for rational q,t-Catalan numbers

We give a simple recursion labeled by binary sequences which computes rational q,t-Catalan power series, both in relatively prime and non relatively prime cases. It is inspired by, but not identical to recursions due to B. Elias, M. Hogancamp, and A. Mellit, obtained in their study of link homology. We also compare our recursion with the Hogancamp-Mellit's recursion and verify a connection between the Khovanov-Rozansky homology of N,M-torus links and the rational q,t-Catalan power series for general positive N,M

Affine permutations and rational slope parking functions

We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to two previously known combinatorial constructions: Haglund’s bijection ζ exchanging the pairs of statistics (area, dinv) and (bounce, area) on Dyck paths, and the Pak-Stanley labeling of the regions of k-Shi hyperplane arrangements by k-parking functions. Essentially, our approach can be viewed as a generalization and a unification of these two constructions. We also relate our combinatorial constructions to representation theory. We derive new formulas for the Poincaré polynomials of certain affine Springer fibers and describe a connection to the theory of finite-dimensional representations of DAHA and non-symmetric Macdonald polynomials

Ground-based detectors in very-high-energy gamma-ray astronomy

Following the discovery of the cosmic rays by Victor Hess in 1912, more than 70 years and numerous technological developments were needed before an unambiguous detection of the first very-high-energy gamma-ray source in 1989 was made. Since this discovery the field on very-high-energy gamma-ray astronomy experienced a true revolution: A second, then a third generation of instruments were built, observing the atmospheric cascades from the ground, either through the atmospheric Cherenkov light they comprise, or via the direct detection of the charged particles they carry. Present arrays, 100 times more sensitive than the pioneering experiments, have detected a large number of astrophysical sources of various types, thus opening a new window on the non-thermal Universe. New, even more sensitive instruments are currently being built; these will allow us to explore further this fascinating domain. In this article we describe the detection techniques, the history of the field and the prospects for the future of ground-based very-high-energy gamma-ray astronomy.Comment: 21 pages, 13 figure

Competitions in layered ruthenates: ferro- vs. antiferromagnetism and triplet vs. singlet pairing

Ru based perovskites demonstrate an amazing richness in their magnetic properties, including 3D and quasi-2D ferromagnetism, antiferromagnetism, and unconventional superconductivity. Tendency to ferromagnetism, stemming from the unusually large involvement of O in magnetism in ruthenates, leads to ferromagnetic spin fluctuations in Sr2RuO4 and eventually to p-wave superconductivity. A related compound Ca2RuO4 was measured to be antiferromagnetic, suggesting a possibility of antiferromagnetic fluctuations in Sr2RuO4 as well. Here we report first principles calculations that demonstrate that in both compounds the ferro- and antiferromagnetic fluctuations coexist, leading to an actual instability in Ca2RuO4 and to a close competition between p-wave and d-wave superconducting symmetries in Sr2RuO4. The antiferromagnetism in this system appears to be mostly related with the nesting, which is the strongest at Q=(2pi/3,2pi/3,0). Surprisingly, for the Fermiology of Sr2RuO4 the p-wave state wins over the d-wave one everywhere except in close vicinity of the antiferromagnetic instability. The most stable state within the d-wave channel has vanishing order parameter at one out of three Fermi surfaces in Sr2RuO4, while in the p channel its amplitude is comparable at all three of them.Comment: 4 Revtex pages with 4 embedded postscript figure. Some figures are color, but should look OK in B&W as wel

Unresolved problems in superconductivity of CaC6

We discuss the current status of the theory of the "high-temperature" superconductivity in intercalated graphites YbC6 and CaC6. We emphasize that while the general picture of conventional, phonon-driven superconductivity has already emerged and is generally accepted, there are still interesting problems with this picture, such as weak-coupling regime inferred from specific heat suggesting coupling exclusively with high-energy carbon phonons coming in direct contradiction with the isotope effect measurements suggesting coupling exclusively with the low-energy intercalant modes. At the same time, the first principle calculations, while explaining Tc, contradict both of the experiments above by predicting equal coupling with both groups of phonons.Comment: Contribution to the Proceedings of the M2S Conference in Dresden, 200

Asset Market Liquidity Risk Management: A Generalized Theoretical Modeling Approach for Trading and Fund Management Portfolios

Asset market liquidity risk is a significant and perplexing subject and though the term market liquidity risk is used quite chronically in academic literature it lacks an unambiguous definition, let alone understanding of the proposed risk measures. To this end, this paper presents a review of contemporary thoughts and attempts vis-à-vis asset market/liquidity risk management. Furthermore, this research focuses on the theoretical aspects of asset liquidity risk and presents critically two reciprocal approaches to measuring market liquidity risk for individual trading securities, and discusses the problems that arise in attempting to quantify asset market liquidity risk at a portfolio level. This paper extends research literature related to the assessment of asset market/liquidity risk by providing a generalized theoretical modeling underpinning that handle, from the same perspective, market and liquidity risks jointly and integrate both risks into a portfolio setting without a commensurate increase of statistical postulations. As such, we argue that market and liquidity risk components are correlated in most cases and can be integrated into one single market/liquidity framework that consists of two interrelated sub-components. The first component is attributed to the impact of adverse price movements, while the second component focuses on the risk of variation in transactions costs due to bid-ask spreads and it attempts to measure the likelihood that it will cost more than expected to liquidate the asset position. We thereafter propose a concrete theoretical foundation and a new modeling framework that attempts to tackle the issue of market/liquidity risk at a portfolio level by combining two asset market/liquidity risk models. The first model is a re-engineered and robust liquidity horizon multiplier that can aid in producing realistic asset market liquidity losses during the unwinding period. The essence of the model is based on the concept of Liquidity-Adjusted Value-at-Risk (L-VaR) framework, and particularly from the perspective of trading portfolios that have both long and short trading positions. Conversely, the second model is related to the transactions cost of liquidation due to bid-ask spreads and includes an improved technique that tackles the issue of bid-ask spread volatility. As such, the model comprises a new approach to contemplating the impact of time-varying volatility of the bid-ask spread and its upshot on the overall asset market/liquidity risk.Economic Capital; Emerging Markets; Financial Engineering; Financial Risk Management; Financial Markets; Liquidity Risk; Portfolio Management; Liquidity Adjusted Value at Risk

Optical depth for VHE gamma-rays from distant sources from a generic EBL density

Very-high-energy (VHE; E>100GeV) gamma-rays from distant sources suffer attenuation through pair-production with low energy photons from the diffuse extragalactic photon fields in the ultraviolet (UV) to far-infrared (FIR) (commonly referred to as Extragalactic Background Light; EBL). When modeling the intrinsic spectra of the VHE gamma-ray sources it is crucial to correctly account for the attenuation. Unfortunately, direct measurements of the EBL are difficult and the knowledge about the EBL over certain wavelength ranges is poor. To calculate the EBL attenuation usually predictions from theoretical models are used. Recently, the limits on the EBL from direct and indirect methods have narrowed down the possible EBL range and many of the previous models are in conflict with these limits. We propose a new generic EBL density (not a complete model), which is in compliance with the new EBL limits. EBL evolution with redshift is included in the calculation in a very simple but effective ad-hoc way. Properties of this generic EBL are discussed.Comment: Proceedings of the workshop 'High Energy Phenomena in Relativistic Outflows' (HEPRO), Dublin, 24-28 September 200

On the distance of PG 1553+11. A lineless BL Lac object active in the TeV band

Context: The redshift of PG 1553+11, a bright BL Lac object (V~14), is still unknown. It has been recently observed in the TeV band, a fact that offers an upper limit for the redshift z<0.4. Aims: We intend to provide a lower limit for the distance of the object. Methods: We used a chi^2 procedure to constrain the apparent magnitude of the host galaxy in archived HST images. Supposing that the host galaxy is typical of BL Lac objects (M_{R} -22.8), a lower limit to the distance can be obtained from the limit on the apparent magnitude of the host galaxy. Results: Using the 3 sigma limit on the host galaxy magnitude, the redshift is found to be greater or equal to 0.25. Conlusions: The redshift of PG 1553+11 is probably in the range z=0.3-0.4, making this object the most distant extragalactic source so far detected in the TeV energies. We suggest that other bright BL Lac objects of unknown redshift and similar spectroscopic characteristics may be interesting targets for TeV observations.Comment: Accepted for publication in A&A letters, 4 pages, 5 figure

The electronic structure of the Nax_xCoO2_2 surface

The idea that surface effects may play an important role in suppressing $e_g'$ Fermi surface pockets on Na$_x$CoO$_2$ $(0.333 \le x \le 0.75)$ has been frequently proposed to explain the discrepancy between LDA calculations (performed on the bulk compound) which find $e_g$' hole pockets present and ARPES experiments, which do not observe the hole pockets. Since ARPES is a surface sensitive technique it is important to investigate the effects that surface formation will have on the electronic structure of Na$_{1/3}$CoO$_2$ in order to more accurately compare theory and experiment. We have calculated the band structure and Fermi surface of cleaved Na$_{1/3}$CoO$_2$ and determined that the surface non-trivially affects the fermiology in comparison to the bulk. Additionally, we examine the likelihood of possible hydroxyl cotamination and surface termination. Our results show that a combination of surface formation and contamination effects could resolve the ongoing controversy between ARPES experiments and theory.Comment: 4 pages, 2 figure