Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

Discovery of Novel Symmetrical 1,4-Dihydropyridines as Inhibitors of Multidrug-Resistant Protein (MRP4) Efflux Pump for Anticancer Therapy

Despite the development of targeted therapies in cancer, the problem of multidrug resistance (MDR) is still unsolved. Most patients with metastatic cancer die from MDR. Transmembrane efflux pumps as the main cause of MDR have been addressed by developed inhibitors, but early inhibitors of the most prominent and longest known efflux pump P-glycoprotein (P-gp) were disappointing. Those inhibitors have been used without knowledge about the expression of P-gp by the treated tumor. Therefore the use of inhibitors of transmembrane efflux pumps in clinical settings is reconsidered as a promising strategy in the case of the respective efflux pump expression. We discovered novel symmetric inhibitors of the symmetric efflux pump MRP4 encoded by the ABCC4 gene. MRP4 is involved in many kinds of cancer with resistance to anticancer drugs. All compounds showed better activities than the best known MRP4 inhibitor MK571 in an MRP4-overexpressing cell line assay, and the activities could be related to the various substitution patterns of aromatic residues within the symmetric molecular framework. One of the best compounds was demonstrated to overcome the MRP4-mediated resistance in the cell line model to restore the anticancer drug sensitivity as a proof of concept.     

Long-wavelength Ultraviolet A1 and Visible Light Photoprotection: A Multimodality Assessment of Dose and Response

Human skin is exposed to visible light (VL; 400–700 nm) and long-wavelength ultraviolet A1 (UVA1) radiation (370–400 nm) after the application of organic broad-spectrum sunscreens. The biologic effects of these wavelengths have been demonstrated; however, a dose–response has not been investigated. Ten subjects with Fitzpatrick skin phototype IV-VI were enrolled. Subjects were irradiated with 2 light sources (80–480 J cm⁻²): one comprising VL with less than 0.5% UVA1 (VL+UVA1) and the other pure VL. Skin responses were evaluated for 2 weeks using clinical and spectroscopic assessments. 4-mm punch biopsies were obtained from nonirradiated skin and sites irradiated with 480 J cm⁻² of VL+UVA1 and pure VL 24 h after irradiation. Clinical and spectroscopic assessments demonstrated a robust response at VL+UVA1 sites compared with pure VL. Histology findings demonstrated a statistically significant increase in the marker of inflammation (P < 0.05) and proliferation (P < 0.05) at the irradiated sites compared with nonirradiated control. Threshold doses of VL+UVA1 resulting in biologic responses were calculated. Results indicate that approximately 2 h of sun exposure, which equates to VL+UVA1 dose (~400 J cm⁻²), is capable of inducing inflammation, immediate erythema and delayed tanning. These findings reinforce the need of photoprotection beyond the UV range.     

Real-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.     

S 1 actions and elliptic genera

A proof is given of Witten's conjectures for the rigidity of the index of the Dirac-Ramond operator on the loop space of a spin manifold which admits anS ¹ symmetry.Research supported in part by the National Science Foundation     

Patterns—a fundamental idea of mathematical thinking and learning

Taking advantage of patterns is typical of our everyday experience as well as our mathematical thinking and learning. For example a working day or a morning at school displays a certain structure, which can be described in terms of patterns. On the one hand regular structures give us the feeling of permanence and enable us to make predictions. On the other hand they also provide a chance to be creative and to vary common procedures. School students usually encounter patterns in math classes either as number patterns or geometric patterns. There are also patterns that teachers can find in analyzing the errors students make during their calculations (error patterns) as well as patterns that are inherent to mathematical problems. One could even go so far as to say that identifying and describing patterns is elementary for mathematics (cf. Devlin 2003). Practising good interacting with patterns supports not only the active learning of mathematics but also a deeper understanding of the world in general. Patterns can be explored, identified, extended, reproduced, compared, varied, represented, described and created. This paper provides some examples of pattern utilization and detailed analyses thereof. These ideas serve as “hooks” to encourage the good use of patterns to facilitate active learning processes in mathematics.     

Modules of piecewise polynomials and their freeness

Partially supported by NSF Grant DMS-9004123 and ARO through MSI Cornell (DAAG 29-85-C-0018)     

The coexistence of γ(γ′) and θ alumina observed by STM and LEED on top of oxide layer grown on CoAl(1 0 0)

We report the coexistence of γ(γ′) and θ alumina grown on the CoAl(1 0 0) surface. Both phases were observed after annealing of alumina at 1150 K by means of scanning tunnelling microscopy (STM). The crystal structures of γ(γ′) and θ alumina were indexed based on low energy electron diffraction (LEED) and STM experimental data.