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 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.     

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.     

Fuzzy processing in transitivity development

We review the literature on the development of transitive reasoning, and note three historical stages. Stage 1 was dominated by the Piagetian idea that transitive inference is logical reasoning in which relationships between adjacent terms figure as premises. Stage 2 was dominated by the information-processing view that memory for relationships between adjacent terms is determinative in transitivity performance. Stage 3 has produced data that are inconsistent with both the logic and memery positions, leading to a new theory that is designed to account for such findings, fuzzy-trace theory. The basic assumption of fuzzytrace theory is that reasoners rely on global patterns, or gist. We describe the tenets of fuzzytrace theory, and explore its implications for different theoretical conceptions of logical competence, concluding that young children possess transitivity competence. We discuss the connection between transitivity competence (cognition) and intransitive preferences (metacognition).     

Qualitative operators for reasoning maps: Evaluating multi-criteria options with networks of reasons

Cognitive/causal maps have been widely used as a powerful way of capturing decision-makers’ views about a problem, representing it as a cause–effect discourse. Several ways of making causal inferences from this type of model have been proposed in the Operational Research and Artificial Intelligence literatures, but none, as far as we are aware, has attempted to use a causal map structure to perform a multi-criteria evaluation of decision alternatives. Recently, we have proposed a new multi-criteria method, denominated as a Reasoning Map, which permits the use of decision-makers’ reasoning, structured as a network of means-and-ends (a particular type of causal map) to perform such an evaluation. In this manner, the model resembles the way that people talk and think about decisions in practice. The method also pays explicit attention to the cognitive limitations of decision-makers in providing preference information. Thus it employs qualitative assessment of preferences, utilises aggregation operators for qualitative data and provides also qualitative outputs. In this paper we discuss and evaluate possible ways of aggregating qualitative performance information in Reasoning Maps.     

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.     

2-Mercaptomethyl-thiazolidines use conserved aromatic–S interactions to achieve broad-range inhibition of metallo-β-lactamases

Infections caused by multidrug resistant (MDR) bacteria are a major public health threat. Carbapenems are among the most potent antimicrobial agents that are commercially available to treat MDR bacteria. Bacterial production of carbapenem-hydrolysing metallo-β-lactamases (MBLs) challenges their safety and efficacy, with subclass B1 MBLs hydrolysing almost all β-lactam antibiotics. MBL inhibitors would fulfil an urgent clinical need by prolonging the lifetime of these life-saving drugs. Here we report the synthesis and activity of a series of 2-mercaptomethyl-thiazolidines (MMTZs), designed to replicate MBL interactions with reaction intermediates or hydrolysis products. MMTZs are potent competitive inhibitors of B1 MBLs in vitro (e.g., K_i = 0.44 μM vs. NDM-1). Crystal structures of MMTZ complexes reveal similar binding patterns to the most clinically important B1 MBLs (NDM-1, VIM-2 and IMP-1), contrasting with previously studied thiol-based MBL inhibitors, such as bisthiazolidines (BTZs) or captopril stereoisomers, which exhibit lower, more variable potencies and multiple binding modes. MMTZ binding involves thiol coordination to the Zn(ii) site and extensive hydrophobic interactions, burying the inhibitor more deeply within the active site than d/l-captopril. Unexpectedly, MMTZ binding features a thioether–π interaction with a conserved active-site aromatic residue, consistent with their equipotent inhibition and similar binding to multiple MBLs. MMTZs penetrate multiple Enterobacterales, inhibit NDM-1 in situ, and restore carbapenem potency against clinical isolates expressing B1 MBLs. Based on their inhibitory profile and lack of eukaryotic cell toxicity, MMTZs represent a promising scaffold for MBL inhibitor development. These results also suggest sulphur–π interactions can be exploited for general ligand design in medicinal chemistry.

Metallo-β-lactamases (MBLs) are major culprits of resistance to carbapenems in bacteria. A series of thiazolidines are potent MBL inhibitors, restoring the activity of carbapenems. Metal binding and sulphur–π interactions are key to inhibition.     

Competing Effects of Chlorination on the Strength of Te⋅⋅⋅O Chalcogen Bonds Select the Structure of Mixed Supramolecular Macrocyclic Aggregates of Iso-Tellurazole N-Oxides

Chlorination of 3-methyl-5-phenyl-1,2-tellurazole-2-oxide yielded the λ⁴Te dichloro derivative. Its crystal structure demonstrates that the heterocycle retains its ability to autoassociate by chalcogen bonding (ChB) forming macrocyclic tetramers. The corresponding Te⋅⋅⋅O ChB distances are 2.062 Å, the shortest observed to date in aggregates of this type. DFT−D3 calculations indicate that while the halogenated molecule is stronger as a ChB donor it also is a weaker ChB acceptor; the overall effect is that the ChBs in the chlorinated homotetramer are not significantly stronger. However, partial halogenation or scrambling selectively yield the 2 : 2 heterotetramer with alternating λ⁴Te and λ²Te centers, which calculations identified as the thermodynamically preferred arrangement.     

A short path synthesis of [13C/15N] multilabeled pyrimidine nucleosides starting from glucopyranose nucleosides

The synthesis of fully [13C/15N] labeled pyrimidine nucleosides has been achieved from 13C-glucose and labeled nucleobases. The reaction scheme leads directly to the protected nucleosides without the need for the inversion of configuration of C-3 of 13C-glucose. This was achieved by an oxitative ring-opening reaction removing the carbon with the wrong configuration.