Twisted traces of quantum intertwiners and quantum dynamical R-matrices corresponding to generalized Belavin-Drinfeld triples

This paper is a continuation of math.QA/9907181 and math.QA/9908115. We consider traces of intertwiners between certain representations of the quantized enveloping algebra associated to a semisimple complex Lie algebra g, which are twisted by a ``generalized Belavin-Drinfeld triple'', i.e a triple consisting of two subdiagrams of the Dynkin diagram of g together with an isomorphism between them. The generating functions F(lambda,mu) for such traces depend on two weights lambda and mu. We show that F(lambda,mu) satisfy two sets of difference equations in the variable lambda: the Macdonald-Ruijsenaars (MR) equations and the quantum Knizhnik-Zamolodchikov (qKZB) equations. These equations involve as a main ingredient the quantum dynamical R-matrices constructed in math.QA/9912009. When the generalized Belavin-Drinfeld triple is an automorphism, we show that F(lambda,mu) satisfy another two sets of difference equations with respect to the weight mu. These dual MR and dual qKZB equations involve the usual Felder's dynamical R-matrix. These results were first obtained by the first author and A. Varchenko in the special case of the trivial Belavin-Drinfeld triple. However, the symmetry between lambda and mu which exists in that case is destroyed in the twisted setting. At the end, we brielfly treat the (simialr) case of Kac-Moody algebras g and derive the classical limits of all the previous results.Comment: 30 pages, late

An open-label clinical trial of agalsidase alfa enzyme replacement therapy in children with Fabry disease who are naïve to enzyme replacement therapy.

BackgroundFollowing a drug manufacturing process change, safety/efficacy of agalsidase alfa were evaluated in enzyme replacement therapy (ERT)-naïve children with Fabry disease.MethodsIn an open-label, multicenter, Phase II study (HGT-REP-084; Shire), 14 children aged ≥7 years received 0.2 mg/kg agalsidase alfa every other week for 55 weeks. Primary endpoints: safety, changes in autonomic function (2-hour Holter monitoring). Secondary endpoints: estimated glomerular filtration rate, left ventricular mass index (LVMI), midwall fractional shortening, pharmacodynamic parameters, and patient-reported quality-of-life.ResultsAmong five boys (median 10.2 [range 6.7, 14.4] years) and nine girls (14.8 [10.1, 15.9] years), eight patients experienced infusion-related adverse events (vomiting, n=4; nausea, n=3; dyspnea, n=3; chest discomfort, n=2; chills, n=2; dizziness, n=2; headache, n=2). One of these had several hypersensitivity episodes. However, no patient discontinued for safety reasons and no serious adverse events occurred. One boy developed immunoglobulin G (IgG) and neutralizing antidrug antibodies. Overall, no deterioration in cardiac function was observed in seven patients with low/abnormal SDNN (standard deviation of all filtered RR intervals; <100 ms) and no left ventricular hypertrophy: mean (SD) baseline SDNN, 81.6 (20.9) ms; mean (95% confidence interval [CI]) change from baseline to week 55, 17.4 (2.9, 31.9) ms. Changes in SDNN correlated with changes in LVMI (r=-0.975). No change occurred in secondary efficacy endpoints: mean (95% CI) change from baseline at week 55 in LVMI, 0.16 (-3.3, 3.7) g/m(2.7); midwall fractional shortening, -0.62% (-2.7%, 1.5%); estimated glomerular filtration rate, 0.15 (-11.4, 11.7) mL/min/1.73 m(2); urine protein, -1.8 (-6.0, 2.4) mg/dL; urine microalbumin, 0.6 (-0.5, 1.7) mg/dL; plasma globotriaosylceramide (Gb3), -5.71 (-10.8, -0.6) nmol/mL; urinary Gb3, -1,403.3 (-3,714.0, 907.4) nmol/g creatinine, or clinical quality-of-life outcomes.ConclusionFifty-five weeks' agalsidase alfa ERT at 0.2 mg/kg every other week was well tolerated. Disease progression may be slowed when ERT is started prior to major organ dysfunction.Trial registrationhttps://ClinicalTrials.gov identifier NCT01363492

Asymmetric simple exclusion process in one-dimensional chains with long-range links

We study the boundary-driven asymmetric simple exclusion process (ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting $pL$ different pairs of sites selected randomly where $L$ and $p$ denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at rate $\alpha$ and out of a chain at the other boundary at rate $\beta$, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low density, high density, and maximal current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases; an empty phase with $\rho = 0$, a jammed phase with $\rho = 1$, and a shock phase with $0<\rho<1$ where $\rho$ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the non-equilibrium phase transition is explained by an analytic theory based on a mean-field approximation and an annealed approximation.Comment: revised version (16 pages and 6 eps figures

Loss of APC induces polyploidy as a result of a combination of defects in mitosis and apoptosis

Mutations in the adenomatous polyposis coli (APC) tumor suppressor gene initiate a majority of colorectal cancers. Acquisition of chromosomal instability is an early event in these tumors. We provide evidence that the loss of APC leads to a partial loss of interkinetochore tension at metaphase and alters mitotic progression. Furthermore, we show that inhibition of APC in U2OS cells compromises the mitotic spindle checkpoint. This is accompanied by a decrease in the association of the checkpoint proteins Bub1 and BubR1 with kinetochores. Additionally, APC depletion reduced apoptosis. As expected from this combination of defects, tetraploidy and polyploidy are consequences of APC inhibition in vitro and in vivo. The removal of APC produced the same defects in HCT116 cells that have constitutively active β-catenin. These data show that the loss of APC immediately induces chromosomal instability as a result of a combination of mitotic and apoptotic defects. We suggest that these defects amplify each other to increase the incidence of tetra- and polyploidy in early stages of tumorigenesis

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

An Experimental and Simulation Study of Early Flame Development in a Homogeneous-Charge Spark-Ignition Engine

An integrated experimental and Large-Eddy Simulation (LES) study is presented for homogeneous premixed combustion in a spark-ignition engine. The engine is a single-cylinder two-valve optical research engine with transparent liner and piston: the Transparent Combustion Chamber (TCC) engine. This is a relatively simple, open engine configuration that can be used for LES model development and validation by other research groups. Pressure-based combustion analysis, optical diagnostics and LES have been combined to generate new physical insight into the early stages of combustion. The emphasis has been on developing strategies for making quantitative comparisons between high-speed/high-resolution optical diagnostics and LES using common metrics for both the experiments and the simulations, and focusing on the important early flame development period. Results from two different LES turbulent combustion models are presented, using the same numerical methods and computational mesh. Both models yield Cycle-to-Cycle Variations (CCV) in combustion that are higher than what is observed in the experiments. The results reveal strengths and limitations of the experimental diagnostics and the LES models, and suggest directions for future diagnostic and simulation efforts. In particular, it has been observed that flame development between the times corresponding to the laminar-to-turbulent transition and 1% mass-burned fraction are especially important in establishing the subsequent combustion event for each cycle. This suggests a range of temporal and spatial scales over which future experimental and simulation efforts should focus

Variants Cause Spastic Paraplegia Associated with Cerebral Hypomyelination

Oculodentodigital dysplasia is an autosomal dominant disorder due to variants characterized by dysmorphic features. Neurologic symptoms have been described in some patients but without a clear neuroimaging pattern. To understand the pathophysiology underlying neurologic deficits in oculodentodigital dysplasia, we studied 8 consecutive patients presenting with hereditary spastic paraplegia due to variants. Clinical disease severity was highly variable. Cerebral MR imaging revealed variable white matter abnormalities, consistent with a hypomyelination pattern, and bilateral hypointense signal of the basal ganglia on T2-weighted images and/or magnetic susceptibility sequences, as seen in neurodegeneration with brain iron accumulation diseases. Patients with the more prominent basal ganglia abnormalities were the most disabled ones. This study suggests that -related hereditary spastic paraplegia is a complex neurodegenerative disease affecting both the myelin and the basal ganglia. variants should be considered in patients with hereditary spastic paraplegia presenting with brain hypomyelination, especially if associated with neurodegeneration and a brain iron accumulation pattern

Phase diagram of two-lane driven diffusive systems

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail