Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5≥ν≥1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν?1/3 and at ν?2/5 identify a structure of lowest spin-split Landau levels of composite fermions (CFs) that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν=1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.     

Intrinsic volumes of symmetric cones and applications in convex programming

Mathematical Programming - We express the probability distribution of the solution of a random (standard Gaussian) instance of a convex cone program in terms of the intrinsic volumes and curvature...     

Efficient terahertz coupling lens based on planar photonic crystals on silicon on insulator

We present a promising coupling device, namely, a terahertz (THz) planar photonic crystal (PhC) lens based on the effective refractive-index contrast between the PhC and the surrounding unpatterned area. Three-dimensional finite-difference time-domain calculations show a 90% power transfer from a 100-microm silicon waveguide to a 10-microm waveguide, and 45% coupling efficiency is confirmed experimentally. These results demonstrate the utility of the PhC lens as an effective approach to coupling into PhC THz circuits.     

On robust cross-validation for nonparametric smoothing

An essential problem in nonparametric smoothing of noisy data is a proper choice of the bandwidth or window width, which depends on a smoothing parameter $k$ . One way to choose $k$ based on the data is leave-one-out-cross-validation. The selection of the cross-validation criterion is similarly important as the choice of the smoother. Especially, when outliers are present, robust cross-validation criteria are needed. So far little is known about the behaviour of robust cross-validated smoothers in the presence of discontinuities in the regression function. We combine different smoothing procedures based on local constant fits with each of several cross-validation criteria. These combinations are compared in a simulation study under a broad variety of data situations with outliers and abrupt jumps. There is not a single overall best cross-validation criterion, but we find Boente-cross-validation to perform well in case of large percentages of outliers and the Tukey-criterion in case of data situations with jumps, even if the data are contaminated with outliers.     

Products of mixed covering arrays of strength two

A covering array CA(N;t,k, v is an N × k array such that every N × t subarray contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple “cut‐and‐paste” construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t = 2 is derived. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 124–138, 2006     

Compact complex homogeneous manifolds with large automorphism groups

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n. Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F _m , m∈N, for which dimAut(F _m )=m+5, see, e.g. [2, Example 2.4.2]. If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2) ⁿ . For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P ⁿ . It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous manifolds. In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3 ^m , so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6, 7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that caused such examples to be previously overlooked. Oblatum 13-X-97 & 24-X-1997     

Manifolds with almost nonnegative curvature operator and principal bundles

We study closed manifolds with almost nonnegative curvature operator (ANCO) and derive necessary and/or sufficient conditions for the total spaces of principal bundles over (A)NCO manifolds to admit ANCO connection metrics. In particular, we provide first examples of closed simply connected ANCO manifolds which do not admit metrics with nonnegative curvature operator.     

Highly sensitive and rapid determination of tacrolimus in peripheral blood mononuclear cells by liquid chromatography–tandem mass spectrometry

After solid organ transplantation, tacrolimus is given to prevent rejection. Therapeutic drug monitoring is used to reach target concentrations of tacrolimus in whole blood. Because the site of action of tacrolimus is the lymphocyte, and tacrolimus binds ~80% to erythrocytes, the intracellular tacrolimus concentration in lymphocytes is possibly more relevant. For this purpose, we aimed to develop, improve and validate a UPLC–MS/MS method to measure tacrolimus concentrations in isolated peripheral blood mononuclear cells (PBMCs). PBMCs were isolated using a Ficoll separation technique, followed by a washing step using red blood cell lysis. A cell suspension of 50 μL containing 1 million PBMCs was used in combination with MagSiMUS‐TDM^PREP. To each sample we added 30 μL lysis buffer, 20 μL reconstitution buffer containing ¹³C²H₄‐tacrolimus as internal standard, 40 μL MagSiMUS‐TDM^PREP Type I Particle Mix and 175 μL Organic Precipitation Reagent VI for methanol‐based protein precipitation. A 10 μL aliquot of the supernatant was injected into the UPLC–MS/MS system. The method was validated, resulting in high sensitivity and specificity. The method was linear (r² = 0.997) over the range 5.0–1250 pg/1 × 10⁶ PBMCs. The inaccuracy was <5% and the imprecision was <15%. The washing steps following Ficoll isolation could be performed at either room temperature or on ice, with no effect of the temperature on the results. A method for the analysis of tacrolimus concentrations in PBMCs was developed and successfully validated. Further research will be performed to investigate the correlation between concentrations in PBMCs and clinical outcome.     

Determination of a novel antifibrotic small molecule GDC‐3280 in human plasma and urine by liquid chromatography tandem mass spectrometry to support its first‐in‐human clinical trial

A specific and robust LC–MS/MS method was developed and validated for the quantitative determination of GDC‐3280 in human plasma and urine. The nonspecific binding associated with urine samples was overcome by the addition of CHAPS. The sample volume was 25 μL for either matrix, and supported liquid extraction was employed for analyte extraction. d6‐GDC‐3280 was used as the internal standard. Linear standard curves (R² > 0.9956) were established from 5.00 to 5000 ng/mL in both matrices with quantitation extended to 50,000 ng/mL through dilution. In plasma matrix, the precision (RSD) ranged from 1.5 to 9.9% (intra‐run) and from 2.4 to 7.2% (inter‐run); the accuracy (RE) ranged from 96.1 to 107% (intra‐run) and from 96.7 to 104% (inter‐run). Similarly, in urine the precision was 1.5–6.2% (intra‐run) and 1.9–6.1% (inter‐run); the accuracy was 83.1–99.3% (intra‐run) and 87.1–98.3% (inter‐run). Good recovery (>94%) and negligible matrix effect were achieved in both matrices. Long‐term matrix stability was established for at least 703 days in plasma and 477 days in urine. Bench‐top stability of 25 h and five freeze–thaw cycles were also confirmed in both matrices. The method was successfully implemented in GDC‐3280's first‐in‐human trial for assessing its pharmacokinetic profiles.     

Synthesis of α-fluoro-α,β-unsaturated esters monitored by 1D and 2D benchtop NMR spectroscopy

For optimization and control of pharmaceutically and industrially important reactions, chemical information is required in real time. Instrument size, handling, and operation costs are important criteria to be considered when choosing a suitable analytical method apart from sensitivity and resolution. This present study explores the use of a robust and compact nuclear magnetic resonance (NMR) spectrometer to monitor the stereo-selective formation of α-fluoro-α,β-unsaturated esters from α-fluoro-β-keto esters via deprotonation and deacylation in real time. These compounds are precursors of various pharmaceutically active substances. The real-time study revealed the deprotonation and deacylation steps of the reaction. The reaction was studied at temperatures ranging from 293 to 333 K by interleaved one-dimensional ¹H and ¹⁹F and two-dimensional ¹H–¹H COSY experiments. The kinetic rate constants were evaluated using a pseudo first-order kinetic model. The activation energies for the deprotonation and deacylation steps were determined to 28 ± 2 and 63.5 ± 8 kJ/mol, respectively. This showed that the deprotonation step is fast compared with the deacylation step and that the deacylation step determines the rate of the overall reaction. The reaction was repeated three times at 293 K to monitor the repeatability and stability of the system. The compact NMR spectrometer provided detailed information on the mechanism and kinetics of the reaction, which is essential for optimizing the synthetic routes for stepwise syntheses of pharmaceutically active substances.