Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed $K_C$-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent $K_C$-orbits, which is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference

Body composition is associated with tacrolimus pharmacokinetics in kidney transplant recipients

PURPOSE: A population pharmacokinetic (popPK) model may be used to improve tacrolimus dosing and minimize under- and overexposure in kidney transplant recipients. It is unknown how body composition parameters relate to tacrolimus pharmacokinetics and which parameter correlates best with tacrolimus exposure. The aims of this study were to investigate which body composition parameter has the best association with the pharmacokinetics of tacrolimus and to describe this relationship in a popPK model. METHODS: Body composition was assessed using bio-impedance spectroscopy (BIS). Pharmacokinetic analysis was performed using nonlinear mixed effects modeling (NONMEM). Lean tissue mass, adipose tissue mass, over-hydration, and phase angle were measured with BIS and then evaluated as covariates. The final popPK model was evaluated using goodness-of-fit plots, visual predictive checks, and a bootstrap analysis. RESULTS: In 46 kidney transplant recipients, 284 tacrolimus concentrations were measured. The base model without body composition parameters included age, plasma albumin, plasma creatinine, CYP3A4 and CYP3A5 genotypes, and hematocrit as covariates. After full forward inclusion and backward elimination, only the effect of the phase angle on clearance (dOFV =  − 13.406; p < 0.01) was included in the final model. Phase angle was positively correlated with tacrolimus clearance. The inter-individual variability decreased from 41.7% in the base model to 34.2% in the final model. The model was successfully validated. CONCLUSION: The phase angle is the bio-impedance spectroscopic parameter that correlates best with tacrolimus pharmacokinetics. Incorporation of the phase angle in a popPK model can improve the prediction of an individual’s tacrolimus dose requirement after transplantation. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00228-022-03323-0

Crystal Graphs and qq-Analogues of Weight Multiplicities for the Root System AnA_n

We give an expression of the $q$-analogues of the multiplicities of weights in irreducible \sl_{n+1}-modules in terms of the geometry of the crystal graph attached to the corresponding U_q(\sl_{n+1})-modules. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostant's generalized exponents.Comment: LaTeX file with epic, eepic pictures, 17 pages, November 1994, to appear in Lett. Math. Phy

Nonequilibrium spectral diffusion due to laser heating in stimulated photon echo spectroscopy of low temperature glasses

A quantitative theory is developed, which accounts for heating artifacts in three-pulse photon echo (3PE) experiments. The heat diffusion equation is solved and the average value of the temperature in the focal volume of the laser is determined as a function of the 3PE waiting time. This temperature is used in the framework of nonequilibrium spectral diffusion theory to calculate the effective homogeneous linewidth of an ensemble of probe molecules embedded in an amorphous host. The theory fits recently observed plateaus and bumps without introducing a gap in the distribution function of flip rates of the two-level systems or any other major modification of the standard tunneling model.Comment: 10 pages, Revtex, 6 eps-figures, accepted for publication in Phys. Rev.

A population pharmacokinetic model to predict the individual starting dose of tacrolimus in adult renal transplant recipients

Aims: The aims of this study were to describe the pharmacokinetics of tacrolimus immediately after kidney transplantation, and to develop a clinical tool for selecting the best starting dose for each patient. Methods: Data on tacrolimus exposure were collected for the first 3 months following renal transplantation. A population pharmacokinetic analysis was conducted using nonlinear mixed-effects modelling. Demographic, clinical and genetic parameters were evaluated as covariates. Results: A total of 4527 tacrolimus blood samples collected from 337 kidney transplant recipients were available. Data were best described using a two-compartment model. The mean absorption rate was 3.6 h-1 , clearance was 23.0 l h-1 (39% interindividual variability, IIV), central volume of distribution was 692 l (49% IIV) and the peripheral volume of distribution 5340 l (53% IIV). Interoccasion variability was added to clearance (14%). Higher body surface area (BSA), lower serum creatinine, younger age, higher albumin and lower haematocrit levels were identified as covariates enhancing tacrolimus clearance. Cytochrome P450 (CYP) 3A5 expressers had a significantly higher tacrolimus clearance (160%), whereas CYP3A4*22 carriers had a significantly lower clearance (80%). From these significant covariates, age, BSA, CYP3A4 and CYP3A5 genotype were incorporated in a second model to individualize the tacrolimus starting dose: [Formula: see text] Both models were successfully internally and externally validated. A clinical trial was simulated to demonstrate the added value of the starting dose model. Conclusions: For a good prediction of tacrolimus pharmacokinetics, age, BSA, CYP3A4 and CYP3A5 genotype are important covariates. These covariates explained 30% of the variability in CL/F. The model proved effective in calculating the optimal tacrolimus dose based on these parameters and can be used to individualize the tacrolimus dose in the early period after transplantation

The orbit structure of Dynkin curves

Let G be a simple algebraic group over an algebraically closed field k; assume that Char k is zero or good for G. Let \cB be the variety of Borel subgroups of G and let e in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e in G on the Springer fibre \cB_e = {B' in \cB | e in Lie B'} associated to e. In this paper we consider the case, where e lies in the subregular nilpotent orbit; in this case \cB_e is a Dynkin curve. We give a complete description of the C_G(e)-orbits in \cB_e. In particular, we classify the irreducible components of \cB_e on which C_G(e) acts with finitely many orbits. In an application we obtain a classification of all subregular orbital varieties admitting a finite number of B-orbits for B a fixed Borel subgroup of G.Comment: 12 pages, to appear in Math

Removing the physician from the equation:Patient-controlled, home-based therapeutic drug self-monitoring of tacrolimus

The dosing of tacrolimus, which forms the backbone of immunosuppressive therapy after kidney transplantation, is complex. This is due to its variable pharmacokinetics (both between and within individual patients), narrow therapeutic index, and the severe consequences of over- and underexposure, which may cause toxicity and rejection, respectively. Tacrolimus is, therefore, routinely dosed by means of therapeutic drug monitoring (TDM). TDM is performed for as long as the transplant functions and frequent and often lifelong sampling is therefore the rule. This puts a significant burden on patients and transplant professionals and is associated with high healthcare-associated costs. Furthermore, by its very nature, TDM is reactive and has no predictive power. Finally, the current practice of TDM does not foresee in an active role for patients themselves. Rather, the physician or pharmacist prescribes the next tacrolimus dose after obtaining the concentration measurement test results. In this article, we propose a strategy of patient-controlled, home-based, self-TDM of the immunosuppressant tacrolimus after transplantation. We argue that with the combined use of population tacrolimus pharmacokinetic models, home-based sampling by means of dried blood spotting and implementation of telemedicine, this may become a feasible approach in the near future

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

First measurements of the ^16O(e,e'pn)^14N reaction

This paper reports on the first measurement of the ^16O(e,e'pn)^14N reaction. Data were measured in kinematics centred on a super-parallel geometry at energy and momentum transfers of 215 MeV and 316 MeV/c. The experimental resolution was sufficient to distinguish groups of states in the residual nucleus but not good enough to separate individual states. The data show a strong dependence on missing momentum and this dependence appears to be different for two groups of states in the residual nucleus. Theoretical calculations of the reaction using the Pavia code do not reproduce the shape or the magnitude of the data.Comment: 10 pages, 11 figures, 2 tables, Accepted for publication in EPJ