Molecular transformations and self-association in anthocyanin pigment patterns.

Spatial patterns of red, purple, and blue colors due to plant pigments called anthocyanins appear in a wide variety of flower petals. Activator and inhibitor proteins involved in anthocyanin synthesis in Mimulus (monkeyflowers) have been identified, and an activator-inhibitor system based on the classic Gierer-Meinhardt system has been proposed as a mathematical model. Analysis in this paper provides a prediction for the critical value of a dimensionless parameter, the ratio of the degradation rate constants of the inhibitor and activator, for pattern formation to occur, and numerical simulations demonstrate the potential for this system to form disordered hexagonal or stripe patterns. We provide experimental evidence for spatial variation in total anthocyanin concentration and for concentration-dependent anthocyanin association. Extending the mathematical model to include anthocyanin transport and diffusion, a series of molecular transformations encompassing acid-base and hydration (speciation) reactions, and self association, we predict that spatial color patterns are accompanied by complex spatial variation in the degree of self association. An important consequence of these studies is a proposal that anthocyanin association allows for colored anthocyanin species to be present in large mole fractions in cell vacuoles despite the fact that the typical vacuolar pH range favors the formation of colorless species.

Spatially extended dislocations produced by the dispersive Swift-Hohenberg equation.

Motivated by previous results showing that the addition of a linear dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a dramatic effect on the pattern formation, we study the Swift-Hohenberg equation with an added linear dispersive term, the dispersive Swift-Hohenberg equation (DSHE). The DSHE produces stripe patterns with spatially extended defects that we call seams. A seam is defined to be a dislocation that is smeared out along a line segment that is obliquely oriented relative to an axis of reflectional symmetry. In contrast to the dispersive Kuramoto-Sivashinsky equation, the DSHE has a narrow band of unstable wavelengths close to an instability threshold. This allows for analytical progress to be made. We show that the amplitude equation for the DSHE close to threshold is a special case of the anisotropic complex Ginzburg-Landau equation (ACGLE) and that seams in the DSHE correspond to spiral waves in the ACGLE. Seam defects and the corresponding spiral waves tend to organize themselves into chains, and we obtain formulas for the velocity of the spiral wave cores and for the spacing between them. In the limit of strong dispersion, a perturbative analysis yields a relationship between the amplitude and wavelength of a stripe pattern and its propagation velocity. Numerical integrations of the ACGLE and the DSHE confirm these analytical results.

Topological measures of order for imperfect two-dimensional Bravais lattices.

Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point distributions, are the key components for defining these measures. The measures generalize previous measures of order using persistent homology that were applicable only to imperfect hexagonal lattices in two dimensions. We illustrate the sensitivities of these measures to the degree of perturbation of perfect hexagonal, square, and rhombic Bravais lattices. We also study imperfect hexagonal, square, and rhombic lattices produced by numerical simulations of pattern-forming partial differential equations. These numerical experiments serve to compare the measures of lattice order and reveal differences in the evolution of the patterns in various partial differential equations.

Theory of the oscillatory instability of a rigid tip scraped over a polymer surface.

The patterns produced by dragging an atomic force microscope (AFM) tip over a polymer surface are studied using a mesoscopic model introduced by Gnecco and co-workers [E. Gnecco et al., New J. Phys. 17, 032001 (2015)1367-263010.1088/1367-2630/17/3/032001]. We show that the problem can be reduced to solving a closed integrodifferential equation for a single degree of freedom, the position of the AFM tip. We find the steady-state solution to this equation and then carry out a linear stability analysis of it. The steady state is only stable if the dimensionless indentation rate α is less than a critical value α_{c} which depends on the dimensionless velocity of the rigid support r. Conversely, for α>α_{c}, periodic stick-slip motion sets in after a transient. Simulations show that the amplitude of these oscillations is proportional to (α-α_{c})^{1/2} for α just above α_{c}. Our analysis also yields a closed equation that can be solved for the critical value α_{c}=α_{c}(r). If the steady-state motion is perturbed, as long as the deviation from the steady state is small, the deviation of the tip's position from the steady state can be written as a linear superposition of terms of the form exp(λ_{k}t), where the complex constants λ_{k} are solutions to an integral equation. Finally, we demonstrate that the results obtained for the two-dimensional model of Gnecco et al. carry over in a straightforward way to the generalization of the model to three dimensions.

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach.

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of "how well do we know our parameters, along with their uncertainties?." The results reveal that Bayesian inversion statistical analysis on an example, prototype Ir0n nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a "Gold Standard" Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

Determining the contributions of protein synthesis and breakdown to muscle atrophy requires non-steady-state equations.

BACKGROUND: Ageing and cachexia cause a loss of muscle mass over time, indicating that protein breakdown exceeds protein synthesis. Deuterium oxide (D2 O) is used for studies of protein turnover because of the advantages of long-term labelling, but these methods introduce considerations that have been largely overlooked when studying conditions of protein gain or loss. The purpose of this study was to demonstrate the importance of accounting for a change in protein mass, a non-steady state, during D2 O labelling studies while also exploring the contribution of protein synthesis and breakdown to denervation-induced muscle atrophy. METHODS: Adult (6 months) male C57BL/6 mice (n = 14) were labelled with D2 O for a total of 7 days following unilateral sciatic nerve transection to induce denervation of hindlimb muscles. The contralateral sham limb and nonsurgical mice (n = 5) were used as two different controls to account for potential crossover effects of denervation. We calculated gastrocnemius myofibrillar and collagen protein synthesis and breakdown assuming steady-state or using non-steady-state modelling. We measured RNA synthesis rates to further understand ribosomal turnover during atrophy. RESULTS: Gastrocnemius mass was less in denervated muscle (137 ± 9 mg) compared with sham (174 ± 15 mg; P < 0.0001) or nonsurgical control (162 ± 5 mg; P < 0.0001). With steady-state calculations, fractional synthesis and breakdown rates (FSR and FBR) were lower in the denervated muscle (1.49 ± 0.06%/day) compared with sham (1.81 ± 0.09%/day; P < 0.0001) or nonsurgical control (2.27 ± 0.04%/day; P < 0.0001). When adjusting for change in protein mass, FSR was 4.21 ± 0.19%/day in denervated limb, whereas FBR was 4.09 ± 0.22%/day. When considering change in protein mass (ksyn ), myofibrillar synthesis was lower in denervated limb (2.44 ± 0.14 mg/day) compared with sham (3.43 ± 0.22 mg/day; P < 0.0001) and non-surgical control (3.74 ± 0.12 mg/day; P < 0.0001), whereas rate of protein breakdown (kdeg, 1/t) was greater in denervated limb (0.050 ± 0.003) compared with sham (0.019 ± 0.001; P < 0.0001) and nonsurgical control (0.023 ± 0.000; P < 0.0001). Muscle collagen breakdown was completely inhibited during denervation. There was a strong correlation (r = 0.83, P < 0.001) between RNA and myofibrillar protein synthesis in sham but not denervated muscle. CONCLUSIONS: We show conflicting results between steady- and non-steady-state calculations on myofibrillar protein synthesis and breakdown during periods of muscle loss. We also found that collagen accumulation was largely from a decrease in collagen breakdown. Comparison between sham and non-surgical control demonstrated a crossover effect of denervation on myofibrillar protein synthesis and ribosomal biogenesis, which impacts study design for unilateral atrophy studies. These considerations are important because not accounting for them can mislead therapeutic attempts to maintain muscle mass.

National Estimates of Prevalence, Time-Trend, and Correlates of Smoking in US People Living with HIV (NHANES 1999-2016).

OBJECTIVE: Approximately one in four deaths among people living with HIV (PLWH) in the United States can be attributed to cigarette smoking. Using a nationally representative sample of PLWH, this study examines the prevalence, time-trends, and correlates of current cigarette smoking among PLWH compared to people without HIV. DESIGN: Secondary analysis of population-based cross-sectional biobehavioral survey. METHODS: Data were pooled from the 1999-2016 National Health and Nutrition Examination Survey (NHANES). All adults (20-59 years) who self-reported their smoking status and were tested for HIV (HIV+ = 152; HIV- = 26 305) were included in the analysis. Prevalence with 95% confidence interval (95% CI), trend analysis by year and group (HIV+/HIV-), and multivariable logistic regression analyses were performed with the complex survey design adjustments. RESULTS: Overall, 47.0% of PLWH were current smokers compared to 25.5% of those without HIV. From 1999 to 2016, the decline in smoking in PLWH was comparable to those without HIV (10.7% vs. 8.0%). PLWH smokers were more likely than PLWH nonsmokers to be substance users (adjusted odds ratio [aOR] = 17.52; 95% CI = 2.04 to 27.8). Compared to smokers without HIV, PLWH smokers were more likely to be older (1.10; 1.06 to 1.14), males (7.96; 2.50 to 25.40), non-Hispanic Black (10.45; 4.13 to 26.45), with depression (Patient Health Questionnaire-9 sum score ≥5) (3.79; 1.22 to 11.79), and less likely to be gay (0.02; 0.00 to 0.07). CONCLUSION: Cigarette smoking among PLWH is a major public health problem in the United States. Targeted and tailored smoking cessation interventions that incorporate assessment and treatment of depression and co-occurring substance use are critical for PLWH, especially among those who are disproportionately affected by smoking and HIV (sexual minority). IMPLICATIONS: This study offers important research implications in four areas:1. The decline in smoking among PLWH over 18 years has been modest, and half of PLWH are still smokers.2. More resources and efforts should be allocated to reduce cigarette smoking among PLWH.3. There is a critical need to develop and test culturally tailored smoking cessation interventions for minority subgroups who are most impacted by HIV infection and smoking (non-Hispanic Blacks and men who have sex with men)4. Smoking cessation interventions designed for PLWH should incorporate assessment and treatment of depression and substance use.

Dust Effects on Ir(0)n Nanoparticle Formation Nucleation and Growth Kinetics and Particle Size-Distributions: Analysis by and Insights from Mechanism-Enabled Population Balance Modeling.

The effects of microfiltration removal of filterable dust on nanoparticle formation kinetics and particle-size distribution, in a polyoxometalate polyanion (P2W15Nb3O629-)-stabilized Ir(0)n nanoparticle formation system, are analyzed by the newly developed method of Mechanism-Enabled Population Balance Modeling (ME-PBM). The [(Bu4N)5Na3(1,5-COD)Ir·P2W15Nb3O62] precatalyst system produces on average Ir(0)∼200 nanoparticles of 1.74 ± 0.33 nm and hence a particle-size distribution (PSD) of ±19% dispersion when the precatalyst is reduced under H2 in unfiltered propylene carbonate solvent. But if the precatalyst is reduced in microfiltered solvent and microfiltered reagent solutions (where the filtered solvent is then also used to rinse dust from the glassware), then larger Ir(0)∼300 1.96 ± 0.16 nm nanoparticles are produced with a remarkable, 2.4-fold lowered ±8% dispersion. The results and effects of the microfiltration reduction of dust are analyzed by the newly developed method of ME-PBM. More specifically, the studies reported herein address eight outstanding questions that are listed in the Introduction. Those questions include: how easy or difficult it is to fit PSD data? What is the ability of the recently discovered alternative termolecular nucleation and two size-dependent growth steps mechanism to account for the effects of dust on the PSD? What types and amount of PSD kinetics data are needed to deconvolute the PSD into the parameters of the ME-PBM? What is the reliability of the resulting rate constants? Additional questions addressed include: if the ME-PBM results offer insights into the remarkable 2.4-fold narrowing of the PSD post simple microfiltration lowering of the dust, and if the results are likely to be more general? The Summary and Conclusions section lists nine specific insights that include comments on needed future studies.

Mechanism-Enabled Population Balance Modeling of Particle Formation en Route to Particle Average Size and Size Distribution Understanding and Control.

The concept of Mechanism-Enabled Population Balance Modeling (ME-PBM) is reported, illustrated by its application to a prototype Ir(0)n nanoparticle formation reaction. ME-PBM is defined herein as the use of now available, experimentally established, disproof-based, deliberately minimalistic mechanisms of particle formation as the required input for more rigorous Population Balance models, critically including an experimentally established nucleation mechanism. ME-PBM achieves the long-sought goal of connecting such now available experimental minimum mechanisms to the understanding and rational control of particles size and size distributions. Twelve pseudoelementary step, particle-formation mechanisms are considered so that the approach to the ME-PBM is also extensively disproof-based. Resurrection of Smoluchowski's 1918 full Ordinary Differential Equation (ODE) approach to the PBM is another, critical aspect of our approach which, in turn, allows unbiased fitting of the information-laden particle-size distribution (PSD) including its shape. The results provide one solution to the "inverse problem" in which the PSD informs one as to the correct particle formation mechanism: A new, deliberately minimalistic 3-step particle-formation mechanism has been uncovered that is a single-additional-step expansion of the now broadly used Finke-Watzky (FW) 2-step mechanism, the new 3-step mechanism being: A → B (rate constant k1), A + B → C (rate constant k2), and A + C → 1.5C (rate constant k3), where A represents the monomeric nanoparticle precursor, B represents "small" nanoparticles, and C represents "larger" nanoparticles. The results strongly support three paradigm shifts for nucleation and growth of particles, the most critical paradigm shift being that the "burst" nucleation assumption in LaMer's 1950s model of particle formation is not required to produce narrow, near-monodisperse PSDs. Instead, narrow PSDs can be and are achieved despite continuous nucleation because smaller particles grow faster than larger ones, k2 > k3, thereby allowing the smaller particles to catch up in size to the more slowly growing larger particles.

The counterdiffusion of HCl and NH3: An experimental and modeling analysis of topochemistry, diffusion, reaction, and phase transitions.

Vapor-phase ammonia, NH3(g), and hydrochloric acid, HCl(g), undergo a series of complex reactions, including nucleation and growth, to form solid ammonium chloride, NH4Cl(s). The counterdiffusional experiment, whereby HCl(g) and NH3(g) diffuse from opposite ends of a tube and react to form spatiotemporally complex patterns, has a rich history of study. In this paper, we combine experimental data, molecular simulations, and analysis and simulations of a partial differential equation model to address the questions of where the first unobserved vapor product NH4Cl(g) and visually observable precipitate NH4Cl(s) form and how these positions depend on experimental parameters. These analyses yield a consistent picture which involves a moving reaction front as well as previously unobserved heterogeneous nucleation, wall nucleation, and homogeneous nucleation. The experiments combined with modeling allow for an estimate of the heterogeneous and homogeneous nucleation thresholds for the vapor-to-solid phase transition. The results, synthesized with the literature on this vapor-to-particle reaction, inform a discussion of the details of the reaction mechanism, including the role of water, which concludes the paper.

Enhanced skeletal muscle regrowth and remodelling in massaged and contralateral non-massaged hindlimb.

KEY POINTS: Muscle fibre cross sectional area is enhanced with massage in the form of cyclic compressive loading during regrowth after atrophy. Massage enhances protein synthesis of the myofibrillar and cytosolic, but not the mitochondrial fraction, in muscle during regrowth. Focal adhesion kinase activation and satellite cell number are elevated in muscles undergoing massage during regrowth. Muscle fibre cross sectional area and protein synthesis of the myofibrillar fraction, but not DNA synthesis, are elevated in muscle of the contralateral non-massaged limb. Massage in the form of cyclic compressive loading is a potential anabolic intervention during muscle regrowth after atrophy. ABSTRACT: Massage, in the form of cyclic compressive loading (CCL), is associated with multiple health benefits, but its potential anabolic effect on atrophied muscle has not been investigated. We hypothesized that the mechanical activity associated with CCL induces an anabolic effect in skeletal muscle undergoing regrowth after a period of atrophy. Fischer-Brown Norway rats at 10 months of age were hindlimb unloaded for a period of 2 weeks. The rats were then allowed reambulation with CCL applied at a 4.5 N load at 0.5 Hz frequency for 30 min every other day for four bouts during a regrowth period of 8 days. Muscle fibre cross sectional area was enhanced by 18% with massage during regrowth compared to reloading alone, and this was accompanied by elevated myofibrillar and cytosolic protein as well as DNA synthesis. Focal adhesion kinase phosphorylation indicated that CCL increased mechanical stimulation, while a higher number of Pax7+ cells likely explains the elevated DNA synthesis. Surprisingly, the contralateral non-massaged limb exhibited a comparable 17% higher muscle fibre size compared to reloading alone, and myofibrillar protein synthesis, but not DNA synthesis, was also elevated. We conclude that massage in the form of CCL induces an anabolic response in muscles regrowing after an atrophy-inducing event. We suggest that massage can be used as an intervention to aid in the regrowth of muscle lost during immobilization.

Highly ordered square arrays of nanoscale pyramids produced by ion bombardment of a crystalline binary material.

A theory is developed for the nanoscale patterns formed when the (001) surface of a crystalline binary material with fourfold rotational symmetry is subjected to normal-incidence ion bombardment. The deterministic nonlinear continuum equations account for the Ehrlich-Schwoebel barrier, which produces uphill atomic currents on the crystal surface. We demonstrate that highly ordered square arrays of nanopyramids can form in a certain region of parameter space. An Ehrlich-Schwoebel barrier is required for patterns of this kind to develop. For another range of parameters, a disordered square array of nanodots forms and the pattern coarsens over time.

"Third-Generation"-Type Functional Tris(2-pyridyl)borate Ligands and Their Transition-Metal Complexes.

Phenyltris(2-pyridyl)borates (Tpyb) are a promising class of tripodal "scorpionate"-type ligands with potential utility in the development of transition-metal complexes with interesting optical, electronic, or magnetic properties and as building blocks to metallosupramolecular polymers. We report here a new class of "third-generation"-type Tpyb ligands that contain different functional groups attached to the boron-bound aryl moiety. The synthesis, characterization, and metal-ion complexation behavior of ligands with iodo and trimethylsilyl groups are discussed. The electrochemical and absorption characteristics of the corresponding low-spin iron(II) and ruthenium(II) complexes are compared. We demonstrate the further elaboration of iodo derivatives with alkynes via Sonogashira-Hagihara coupling, a process that proceeds with high yield for the iron(II) and ruthenium(II) complexes but not for the free ligand. Borylation of the silyl-substituted ruthenium(II) complex with BBr3 was also investigated. In addition to the expected borylation product Ru(Tpyb-Bpin)2, the replacement of one (major product) or two phenyl groups is observed, suggesting that electrophilic borylation occurs at both the C(Ph)-Si and the C(Ph)-B aromatic carbon atoms. The successful attachment of a range of different functional groups at the periphery of the Tpyb metal complexes is expected to provide opportunities to access new polymeric materials via C-C coupling or click-type reactions.

Modeling the contribution of individual proteins to mixed skeletal muscle protein synthetic rates over increasing periods of label incorporation.

Advances in stable isotope approaches, primarily the use of deuterium oxide ((2)H2O), allow for long-term measurements of protein synthesis, as well as the contribution of individual proteins to tissue measured protein synthesis rates. Here, we determined the influence of individual protein synthetic rates, individual protein content, and time of isotopic labeling on the measured synthesis rate of skeletal muscle proteins. To this end, we developed a mathematical model, applied the model to an established data set collected in vivo, and, to experimentally test the impact of different isotopic labeling periods, used (2)H2O to measure protein synthesis in cultured myotubes over periods of 2, 4, and 7 days. We first demonstrated the influence of both relative protein content and individual protein synthesis rates on measured synthesis rates over time. When expanded to include 286 individual proteins, the model closely approximated protein synthetic rates measured in vivo. The model revealed a 29% difference in measured synthesis rates from the slowest period of measurement (20 min) to the longest period of measurement (6 wk). In support of these findings, culturing of C2C12 myotubes with isotopic labeling periods of 2, 4, or 7 days revealed up to a doubling of the measured synthesis rate in the shorter labeling period compared with the longer period of labeling. From our model, we conclude that a 4-wk period of labeling is ideal for considering all proteins in a mixed-tissue fraction, while minimizing the slowing effect of fully turned-over proteins. In addition, we advocate that careful consideration must be paid to the period of isotopic labeling when comparing mixed protein synthetic rates between studies.

Producing nanodot arrays with improved hexagonal order by patterning surfaces before ion sputtering.

When the surface of a nominally flat binary material is bombarded with a broad, normally incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled dynamics of the height and composition of such a surface [Shipman and Bradley, Phys. Rev. B 84, 085420 (2011)]. We investigate the influence of initial conditions on the hexagonal order yielded by integration of those equations of motion. The initial conditions studied are hexagonal and sinusoidal templates, straight scratches, and nominally flat surfaces. Our simulations indicate that both kinds of templates lead to marked improvements in the hexagonal order if the initial wavelength is approximately equal to or double the linearly selected wavelength. Scratches enhance the hexagonal order in their vicinity if their width is close to or less than the linearly selected wavelength. Our results suggest that prepatterning a binary material can dramatically increase the hexagonal order achieved at large ion fluences.

Modeling the presence probability of invasive plant species with nonlocal dispersal.

Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.

Tris(2-pyridylborate) (Tpyb) metal complexes: synthesis, characterization, and formation of extrinsically porous materials with large cylindrical channels.

Sandwich-like metal complexes (Tpyb)2M (M = Mg, Fe, Mn) that are based on the novel t-butylphenyltris(2-pyridyl)borate ligand were prepared and fully characterized by multinuclear NMR spectroscopy, high-resolution matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, and single crystal X-ray crystallography. The unique steric and electronic nature of the Tpyb ligand led to structural parameters and properties that are quite different to those of previously reported tris(pyrazolyl)borate and tris(2-pyridyl)aluminate complexes. Most importantly, depending on the crystallization procedure, supramolecular structures could be generated with relatively smaller (ca. 4-5 Å) or larger (ca. 8 Å) diameter pores propagating throughout the crystal lattice. Although the supramolecular structures are held together only by weak intermolecular C-H···π interactions, the solvent in the larger channels could be completely removed without any loss of crystallinity or degradation of the framework. Surface area and gas uptake measurements on the Mg complex further confirmed the permanent porosity, while the calculated non-localized density functional theory (NLDFT) pore diameter of 8.6 Å proved to be in excellent agreement with that obtained from single crystal X-ray crystallography. Our new materials are remarkably thermally stable as degradation did not occur up to about 400 °C based on thermogravimetric analysis (TGA), and a sample of the Mg complex showed no loss of crystallinity even after heating to 140 °C under high vacuum for 72 h according to single crystal X-ray diffraction data.

Towards a continuous population model for natural language vowel shift.

The Great English Vowel Shift of 16th-19th centuries and the current Northern Cities Vowel Shift are two examples of collective language processes characterized by regular phonetic changes, that is, gradual changes in vowel pronunciation over time. Here we develop a structured population approach to modeling such regular changes in the vowel systems of natural languages, taking into account learning patterns and effects such as social trends. We treat vowel pronunciation as a continuous variable in vowel space and allow for a continuous dependence of vowel pronunciation in time and age of the speaker. The theory of mixtures with continuous diversity provides a framework for the model, which extends the McKendrick-von Foerster equation to populations with age and phonetic structures. We develop the general balance equations for such populations and propose explicit expressions for the factors that impact the evolution of the vowel pronunciation distribution. For illustration, we present two examples of numerical simulations. In the first one we study a stationary solution corresponding to a state of phonetic equilibrium, in which speakers of all ages share a similar phonetic profile. We characterize the variance of the phonetic distribution in terms of a parameter measuring a ratio of phonetic attraction to dispersion. In the second example we show how vowel shift occurs upon starting with an initial condition consisting of a majority pronunciation that is affected by an immigrant minority with a different vowel pronunciation distribution. The approach developed here for vowel systems may be applied also to other learning situations and other time-dependent processes of cognition in self-interacting populations, like opinions or perceptions.

Nitroxide-Mediated Controlled Free Radical Polymerization of the Chelate Monomer 4-Styryl-tris(2-pyridyl)borate (StTpyb) and Supramolecular Assembly via Metal Complexation.

The reaction of 4-(dibromoboryl)styrene with 2-pyridylmagnesium chloride resulted in the formation of 4-styryl-tris(2-pyridyl)borate free acid (StTypb), a new polymerizable nonpyrazolyl "scorpionate" ligand. StTypb did not undergo self-initiated polymerization under ambient conditions and proved to slowly polymerize through standard radical polymerization at 90 °C. Nitroxide-mediated polymerization (NMP) of StTypb at 135 °C proceeded with good control, resulting in a polymer of Mn = 27400 and PDI = 1.21. The TEMPO-terminated homopolymer successfully initiated the polymerization of styrene, generating an amphiphilic block copolymer with DPn of 1200 and 78 for the PS and the StTypb block, respectively. A similar block copolymer with DPn of 29 and 20 for the PS and the StTypb block respectively was obtained in a reverse polymerization procedure from a PS macroinitiator. The self-assembly of these block copolymers was examined in selective solvents and preliminary metal complexation studies were performed.

Self-assembly of borane end-functionalized polystyrene through tris(1-pyrazolyl)borate (Tp) iron(II) linkages.

Treatment of trimethylsilane-terminated polystyrenes with BBr(3) resulted in the formation of dibromoboryl-functionalized mono- or ditelechelic styrene polymers. Subsequently, the borane moieties were selectively converted to tris(1-pyrazolyl)borate (Tp) moieties capable of transition metal coordination. These novel telechelic polymers assemble into redox-active supramolecular polymer structures upon reaction with Fe(II) as indicated by GPC, UV-vis, and cyclic voltammetry studies.