Discrete mathematics in primary and secondary schools in the United States

This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies for engaging their students in the study of mathematics.     

The isolation of new norcycloartene triterpenoids from the tropical marine alga Tydemaniaexpeditionitis (chlorophyta)

Three new Δ³-norcycloartene triterpenoids, with differing side chain functionalities, have been isolated from the tropical green alga $\text{Tydemania}$$\text{expeditionitis}$ collected in Guam. The structures of these new compounds were secured by x-ray crystallography and by chemical interconversion.     

Calculating the knowledge-based similarity of functional groups using crystallographic data

A knowledge-based method for calculating the similarity of functional groups is described and validated. The method is based on experimental information derived from small molecule crystal structures. These data are used in the form of scatterplots that show the likelihood of a non-bonded interaction being formed between functional group A (the `central group') and functional group B (the `contact group' or `probe'). The scatterplots are converted into three-dimensional maps that show the propensity of the probe at different positions around the central group. Here we describe how to calculate the similarity of a pair of central groups based on these maps. The similarity method is validated using bioisosteric functional group pairs identified in the Bioster database and Relibase. The Bioster database is a critical compilation of thousands of bioisosteric molecule pairs, including drugs, enzyme inhibitors and agrochemicals. Relibase is an object-oriented database containing structural data about protein-ligand interactions. The distributions of the similarities of the bioisosteric functional group pairs are compared with similarities for all the possible pairs in IsoStar, and are found to be significantly different. Enrichment factors are also calculated showing the similarity method is statistically significantly better than random in predicting bioisosteric functional group pairs.     

Physical,chemical and immunological characteristics of continuous-density lipoproteins isolated by single-spin gradient ultracentrifugation

The isolation of various lipoproteins of very low, intermediate, low and high density from 5 ml of serum was obtained by single-step ultracentrifugation in a potassium bromide density gradient obtained by smoothing a discontinuous gradient during the run (120 000g, 48 h, 4°C; Beckman SW27 rotor). The density profiles were reproducible. The lipoproteins were characterized by electron microscopy, fluorescence polarization, polyacrylamide gel electrophoresis and complete chemical assays. The composition of the entire lipoprotein spectrum was in accordance with previous results. The lipoprotein molecular mass, particle size distribution, Apo AI/AII ratio and microviscosity varied according to the density range.     

The molecular mechanism of stabilization of proteins by TMAO and its ability to counteract the effects of urea

Trimethylamine n-oxide (TMAO) is a naturally occurring osmolyte that stabilizes proteins and offsets the destabilizing effects of urea. To investigate the molecular mechanism of these effects, we have studied the thermodynamics of interaction between TMAO and protein functional groups. The solubilities of a homologous series of cyclic dipeptides were measured by differential refractive index and the dissolution heats were determined calorimetrically as a function of TMAO concentration at 25 degrees C. The transfer free energy of the amide unit (-CONH-) from water to 1 M TMAO is large and positive, indicating an unfavorable interaction between the TMAO solution and the amide unit. This unfavorable interaction is enthalpic in origin. The interaction between TMAO and apolar groups is slightly favorable. The transfer free energy of apolar groups from water to TMAO consists of favorable enthalpic and unfavorable entropic contributions. This is in contrast to the contributions for the interaction between urea and apolar groups. Molecular dynamics simulations were performed to provide a structural framework for the interpretation of these results. The simulations show enhancement of water structure by TMAO in the form of a slight increase in the number of hydrogen bonds per water molecule, stronger water hydrogen bonds, and long-range spatial ordering of the solvent. These findings suggest that TMAO stabilizes proteins via enhancement of water structure, such that interactions with the amide unit are discouraged.     

Local Structure Analysis and Modelling of Lignin-Based Carbon Composites through the Hierarchical Decomposition of the Radial Distribution Function

Carbonized lignin has been proposed as a sustainable and domestic source of activated, amorphous, graphitic, and nanostructured carbon for many industrial applications as the structure can be tuned through processing conditions. However, the inherent variability of lignin and its complex physicochemical structure resulting from feedstock and pulping selection make the Process-Structure-Property-Performance (PSPP) relationships hard to define. In this work, radial distribution functions (RDFs) from synchrotron X-ray and neutron scattering of lignin-based carbon composites (LBCCs) are investigated using the Hierarchical Decomposition of the Radial Distribution Function (HDRDF) modelling method to characterize the local atomic environment and develop quantitative PSPP relationships. PSPP relationships for LBCCs defined by this work include crystallite size dependence on lignin feedstock as well as increasing crystalline volume fraction, nanoscale composite density, and crystallite size with increasing reduction temperature.     

Capillary Atmospheric Pressure Electron Capture Ionization (cAPECI): A Highly Efficient Ionization Method for Nitroaromatic Compounds

We report on a novel method for atmospheric pressure ionization of compounds with elevated electron affinity (e.g., nitroaromatic compounds) or gas phase acidity (e.g., phenols), respectively. The method is based on the generation of thermal electrons by the photo-electric effect, followed by electron capture of oxygen when air is the gas matrix yielding O₂ ^– or of the analyte directly with nitrogen as matrix. Charge transfer or proton abstraction by O₂ ^– leads to the ionization of the analytes. The interaction of UV-light with metals is a clean method for the generation of thermal electrons at atmospheric pressure. Furthermore, only negative ions are generated and neutral radical formation is minimized, in contrast to discharge- or dopant assisted methods. Ionization takes place inside the transfer capillary of the mass spectrometer leading to comparably short transfer times of ions to the high vacuum region of the mass spectrometer. This strongly reduces ion transformation processes, resulting in mass spectra that more closely relate to the neutral analyte distribution. cAPECI is thus a soft and selective ionization method with detection limits in the pptV range. In comparison to standard ionization methods (e.g., PTR), cAPECI is superior with respect to both selectivity and achievable detection limits. cAPECI demonstrates to be a promising ionization method for applications in relevant fields as, for example, explosives detection and atmospheric chemistry.

Anti-Inflammatory Dysidazirine Carboxylic Acid from the Marine Cyanobacterium Caldora sp. Collected from the Reefs of Fort Lauderdale,Florida

Dysidazirine carboxylic acid (1) was isolated from the lipophilic extract of a collection of the benthic marine cyanobacterium Caldora sp. from reefs near Fort Lauderdale, Florida. The planar structure of this new compound was determined by spectroscopic methods and comparisons between HRMS and NMR data with its reported methyl ester. The absolute configuration of the single chiral center was determined by the conversion of 1 to the methyl ester and the comparison of its specific rotation data with the two known methyl ester isomers, 2 and 3. Molecular sequencing with 16S rDNA indicated that this cyanobacterium differs from Caldora penicillata (Oscillatoriales) and represents a previously undocumented and novel Caldora species. Dysidazirine (2) showed weak cytotoxicity against HCT116 colorectal cancer cells (IC₅₀ 9.1 µM), while dysidazirine carboxylic acid (1) was non-cytotoxic. Similar cell viability patterns were observed in RAW264.7 cells with dysidazirine only (2), displaying cytotoxicity at the highest concentration tested (50 µM). The non-cytotoxic dysidazirine carboxylic acid (1) demonstrated anti-inflammatory activity in RAW264.7 cells stimulated with LPS. After 24 h, 1 inhibited the production of NO by almost 50% at 50 µM, without inducing cytotoxicity. Compound 1 rapidly decreased gene expression of the pro-inflammatory gene iNOS after 3 h post-LPS treatment and in a dose-dependent manner (IC₅₀ ~1 µM); the downregulation of iNOS persisted at least until 12 h.     

A comparison of stochastic and effective medium approaches to the backscattered signal from a porous layer in a solid matrix

This paper reports a study of the backscattering behavior of a solid layer containing randomly spaced spherical cavities in the long wavelength limit. The motivation for the work arises from a need to model the responses of porous composite materials in ultrasonic NDE procedures. A comparison is made between models based on a summation over discrete scatterers, which show interesting emergent properties, and an integral formulation based on an ensemble average, and with a simple slab effective medium approximation. The similarities and differences between these three models are demonstrated. A simple quantitative criterion is established which sets the maximum frequency at which ensemble average or equivalent homogeneous medium models can represent echo signal generation in a porous layer for given interpore spacing, or equivalently, given pore size and concentration.     

Optimal control of a birth and death epidemic process

We employ a birth and death process to describe the spread of an infectious disease through a closed population. Control of the epidemic can be effected at any instant by varying the birth and death rates to represent quarantine and medical care programs. An optimal strategy is one which minimizes the expected discounted losses and costs resulting from the epidemic process and the control programs over an infinite horizon. We formulate the problem as a continuous-time Markov decision model. Then we present conditions ensuring that optimal quarantine and medical care program levels are nonincreasing functions of the number of infectives in the population. We also analyze the dependence of the optimal strategy on the model parameters. Finally, we present an application of the model to the control of a rumor.