Combinatorial proofs on the joint distribution of descents and inverse descents

Let $A_{n,i,j}$ be the number of permutations on $[n]$ with $i-1$ descents and $j-1$ inverse descents. Carlitz, Roselle and Scoville in 1966 first revealed some combinatorial and arithmetic properties of $A_{n,i,j}$, which contain a recurrence of $A_{n,i,j}$. Using the idea of balls in boxes, Petersen gave a combinatorial interpretation for the generating function of $A_{n,i,j}$, and obtained the same recurrence of $A_{n,i,j}$ from its generating function. Subsequently, Petersen asked whether there is a visual way to understand this recurrence. In this paper, after observing the internal structures of permutation grids, we present a combinatorial proof of the recurrence of $A_{n,i,j}$. Let $I_{n,k}$ and $J_{n,k}$ count the number of involutions and fixed-point free involutions on $[n]$ with $k$ descents, respectively. With the help of generating functions, Guo and Zeng derived two recurrences of $I_{n,k}$ and $J_{2n,k}$ that play an essential role in the proof of their unimodal properties. Unexpectedly, the constructive approach to the recurrence of $A_{n,i,j}$ is found to fuel the combinatorial interpretations of these two recurrences of $I_{n,k}$ and $J_{2n,k}$

Far Ultraviolet Observations of the Dwarf Nova VW Hyi in Quiescence

We present a 904-1183 A spectrum of the dwarf nova VW Hydri taken with the Far Ultraviolet Spectroscopic Explorer during quiescence, eleven days after a normal outburst, when the underlying white dwarf accreter is clearly exposed in the far ultraviolet. However, model fitting show that a uniform temperature white dwarf does not reproduce the overall spectrum, especially at the shortest wavelengths. A better approximation to the spectrum is obtained with a model consisting of a white dwarf and a rapidly rotating ``accretion belt''. The white dwarf component accounts for 83% of the total flux, has a temperature of 23,000K, a v sin i = 400 km/s, and a low carbon abundance. The best-fit accretion belt component accounts for 17% of the total flux, has a temperature of about 48,000-50,000K, and a rotation rate Vrot sin i around 3,000-4,000 km/s. The requirement of two components in the modeling of the spectrum of VW Hyi in quiescence helps to resolve some of the differences in interpretation of ultraviolet spectra of VW Hyi in quiescence. However, the physical existence of a second component (and its exact nature) in VW Hyi itself is still relatively uncertain, given the lack of better models for spectra of the inner disk in a quiescent dwarf nova.Comment: 6 figures, 10 printed page in the journal, to appear in APJ, 1 Sept. 2004 issue, vol. 61

Kerr-Newman Black Hole Thermodynamical State Space: Blockwise Coordinates

A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordstrom and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric.Comment: 4 pages incl 2 figs. Accepted by Gen. Rel. Grav. Replaced with Accepted version (minor corrections

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energy. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.Comment: review, 31 pages, 15 figure

Novel insights into the cardio-protective effects of FGF21 in lean and obese rat hearts

Aims: Fibroblast growth factor 21 (FGF21) is a hepatic metabolic regulator with pleotropic actions. Its plasma concentrations are increased in obesity and diabetes; states associated with an increased incidence of cardiovascular disease. We therefore investigated the direct effect of FGF21 on cardio-protection in obese and lean hearts in response to ischemia. Methods and Results: FGF21, FGF21-receptor 1 (FGFR1) and beta-Klotho (βKlotho) were expressed in rodent, human hearts and primary rat cardiomyocytes. Cardiac FGF21 was expressed and secreted (real time RT-PCR/western blot and ELISA) in an autocrine-paracrine manner, in response to obesity and hypoxia, involving FGFR1-βKlotho components. Cardiac-FGF21 expression and secretion were increased in response to global ischemia. In contrast βKlotho was reduced in obese hearts. In isolated adult rat cardiomyocytes, FGF21 activated PI3K/Akt (phosphatidylinositol 3-kinase/Akt), ERK1/2(extracellular signal-regulated kinase) and AMPK (AMP-activated protein kinase) pathways. In Langendorff perfused rat [adult male wild-type wistar] hearts, FGF21 administration induced significant cardio-protection and restoration of function following global ischemia. Inhibition of PI3K/Akt, AMPK, ERK1/2 and ROR-α (retinoic-acid receptor alpha) pathway led to significant decrease of FGF21 induced cardio-protection and restoration of cardiac function in response to global ischemia. More importantly, this cardio-protective response induced by FGF21 was reduced in obesity, although the cardiac expression profiles and circulating FGF21 levels were increased. Conclusion: In an ex vivo Langendorff system, we show that FGF21 induced cardiac protection and restoration of cardiac function involving autocrine-paracrine pathways, with reduced effect in obesity. Collectively, our findings provide novel insights into FGF21-induced cardiac effects in obesity and ischemia

A Man with Labile Blood Pressure

Ronald Ma and colleagues discuss the differential diagnosis and management of a patient who presented with recurrent episodes of chest discomfort, palpitations, and labile blood pressure

The secreted triose phosphate isomerase of Brugia malayi is required to sustain microfilaria production in vivo

Human lymphatic filariasis is a major tropical disease transmitted through mosquito vectors which take up microfilarial larvae from the blood of infected subjects. Microfilariae are produced by long-lived adult parasites, which also release a suite of excretory-secretory products that have recently been subject to in-depth proteomic analysis. Surprisingly, the most abundant secreted protein of adult Brugia malayi is triose phosphate isomerase (TPI), a glycolytic enzyme usually associated with the cytosol. We now show that while TPI is a prominent target of the antibody response to infection, there is little antibody-mediated inhibition of catalytic activity by polyclonal sera. We generated a panel of twenty-three anti-TPI monoclonal antibodies and found only two were able to block TPI enzymatic activity. Immunisation of jirds with B. malayi TPI, or mice with the homologous protein from the rodent filaria Litomosoides sigmodontis, failed to induce neutralising antibodies or protective immunity. In contrast, passive transfer of neutralising monoclonal antibody to mice prior to implantation with adult B. malayi resulted in 60–70% reductions in microfilarial levels in vivo and both oocyte and microfilarial production by individual adult females. The loss of fecundity was accompanied by reduced IFNγ expression by CD4+ T cells and a higher proportion of macrophages at the site of infection. Thus, enzymatically active TPI plays an important role in the transmission cycle of B. malayi filarial parasites and is identified as a potential target for immunological and pharmacological intervention against filarial infections