Eigenfunctions of GL(N,\RR) Toda chain: The Mellin-Barnes representation

The recurrent relations between the eigenfunctions for GL(N,\RR) and GL(N-1,\RR) quantum Toda chains is derived. As a corollary, the Mellin-Barnes integral representation for the eigenfunctions of a quantum open Toda chain is constructed for the $N$-particle case.Comment: Latex+amssymb.sty, 7 pages; corrected some typos published in Pis'ma v ZhETF (2000), vol. 71, 338-34

Quantum Algebraic Approach to Refined Topological Vertex

We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W_{1+infty} introduced by Miki. Our construction involves trivalent intertwining operators Phi and Phi^* associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors in Z^2 is attached to each intertwining operator, which satisfy the Calabi-Yau and smoothness conditions. It is shown that certain matrix elements of Phi and Phi^* give the refined topological vertex C_{lambda mu nu}(t,q) of Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined topological vertex C_{lambda mu}^nu(q,t) of Awata-Kanno. The gluing factors appears correctly when we consider any compositions of Phi and Phi^*. The spectral parameters attached to Fock spaces play the role of the K"ahler parameters.Comment: 27 page

Particle interactions and lattice dynamics: Scenarios for efficient bidirectional stochastic transport?

Intracellular transport processes driven by molecular motors can be described by stochastic lattice models of self-driven particles. Here we focus on bidirectional transport models excluding the exchange of particles on the same track. We explore the possibility to have efficient transport in these systems. One possibility would be to have appropriate interactions between the various motors' species, so as to form lanes. However, we show that the lane formation mechanism based on modified attachment/detachment rates as it was proposed previously is not necessarily connected to an efficient transport state and is suppressed when the diffusivity of unbound particles is finite. We propose another interaction mechanism based on obstacle avoidance that allows to have lane formation for limited diffusion. Besides, we had shown in a separate paper that the dynamics of the lattice itself could be a key ingredient for the efficiency of bidirectional transport. Here we show that lattice dynamics and interactions can both contribute in a cooperative way to the efficiency of transport. In particular, lattice dynamics can decrease the interaction threshold beyond which lanes form. Lattice dynamics may also enhance the transport capacity of the system even when lane formation is suppressed.Comment: 25 pages, 17 figures, 2 table

The double Ringel-Hall algebra on a hereditary abelian finitary length category

In this paper, we study the category $\mathscr{H}^{(\rho)}$ of semi-stable coherent sheaves of a fixed slope $\rho$ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of $\mathscr{H}^{(\rho)}$ and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.Comment: 29 page

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

Treatment of Fabry Disease: Outcome of a Comparative Trial with Agalsidase Alfa or Beta at a Dose of 0.2 mg/kg

Two different enzyme preparations, agalsidase alfa (Replagal(TM), Shire) and beta (Fabrazyme(TM), Genzyme), are registered for treatment of Fabry disease. We compared the efficacy of and tolerability towards the two agalsidase preparations administered at identical protein dose in a randomized controlled open label trial.Thirty-four Fabry disease patients were treated with either agalsidase alfa or agalsidase beta at equal dose of 0.2 mg/kg biweekly. Primary endpoint was reduction in left ventricular mass after 12 and 24 months of treatment. Other endpoints included occurrence of treatment failure (defined as progression of cardiac, renal or cerebral disease), glomerular filtration rate, pain, anti-agalsidase antibodies, and globotriaosylceramide levels in plasma and urine. After 12 and 24 months of treatment no reduction in left ventricular mass was seen, which was not different between the two treatment groups. Also, no differences in glomerular filtration rate, pain and decline in globotriaosylceramide levels were found. Antibodies developed only in males (4/8 in the agalsidase alfa group and 6/8 in the agalsidase beta group). Treatment failure within 24 months of therapy was seen in 8/34 patients: 6 male patients (3 in each treatment group) and 2 female patients (both agalsidase alfa). The occurrence of treatment failures did not differ between the two treatment groups; chi(2) = 0.38 p = 0.54.Our study revealed no difference in reduction of left ventricular mass or other disease parameters after 12 and 24 months of treatment with either agalsidase alfa or beta at a dose of 0.2 mg/kg biweekly. Treatment failure occurred frequently in both groups and seems related to age and severe pre-treatment disease.International Standard Randomized Clinical Trial ISRCTN45178534 [http://www.controlled-trials.com/ISRCTN45178534]

The historical development of zoo elephant survivorship

In the discussion about zoo elephant husbandry, the report of Clubb et al. (2008, Science 322: 1649) that zoo elephants had a “compromised survivorship” compared to certain non-zoo populations is a grave argument, and was possibly one of the triggers of a large variety of investigations into zoo elephant welfare, and changes in zoo elephant management. A side observation of that report was that whereas survivorship in African elephants (Loxodonta africana) improved since 1960, this was not the case in Asian elephants (Elephas maximus). We used historical data (based on the Species360 database) to revisit this aspect, including recent developments since 2008. Assessing the North American and European populations from 1910 until today, there were significant improvements of adult (≥10 years) survivorship in both species. For the period from 1960 until today, survivorship improvement was significant for African elephants and close to a significant improvement in Asian elephants; Asian elephants generally had a higher survivorship than Africans. Juvenile (<10 years) survivorship did not change significantly since 1960 and was higher in African elephants, most likely due to the effect of elephant herpes virus on Asian elephants. Current zoo elephant survivorship is higher than some, and lower than some other non-zoo populations. We discuss that in our view, the shape of the survivorship curve, and its change over time, are more relevant than comparisons with specific populations. Zoo elephant survivorship should be monitored continuously, and the expectation of a continuous trend towards improvement should be met

Prognostic value of lymph node ratio and extramural vascular invasion on survival for patients undergoing curative colon cancer resection

There was no study funding. We are grateful to Tony Rafferty (Tailored Information for the People of Scotland, TIPs) for providing survival data.Peer reviewedPublisher PD