Invariant cones of positive initial functions for delay differential equations

Consider the scalar delay differential equation x(t) + ∑ a_kx(t-r_k) = 0 (1) where a_k and r_k ≥ 0, (0 ≤k ≤ m), are real numbers.In this paper we show that there exists an invariant cone of the positive initial functions if and only if the characteristic equation of Eq. (1) has a real root. We also give the constraction of the maximal invariant cone among the positive initial functions with respect to Eq. (1). At the end of the paper we show the generalizations of these results for systems     

Erling Norrby,Nobel Prizes and Life Sciences

Structural Chemistry -     

Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, we describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “ensemble Kalman filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. We discuss both the mathematical basis of this approach and its implementation; our primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. We include some numerical results demonstrating the efficiency and accuracy of our implementation for assimilating real atmospheric data with the global forecast model used by the US National Weather Service.     

Integer-valued functions and increasing unions of first countable spaces

We determine those regular cardinals κ with the property that for each increasing κ-chain of first countable spaces there is a compatible first countable topology on the union of the chain. AssumingV=L any such κ must be weakly compact. It is relatively consistent with a supercompact cardinal that each κ>w ₁ has the property. The proofs exploit the connection with interesting families of integer-valued functions. Research of the second author supported by OTKA grant no. 1805. Research of the remaining authors partially supported by NSERC of Canada.     

Nanoscale probing of the enamel nanorod surface using polyamidoamine dendrimers

Although it is known that noncollagenous proteins of dental origin bind to the hydroxyapatite crystal surfaces, no measure of their binding strength has been calculated. This experiment used -COOH-capped generation 7 PAMAM dendrimers as nanoprobes of the biological hydroxyapatite nanorod surfaces. Dendrimer distribution was characterized using AFM. The results showed dendrimers to be spaced at intervals along the c-axis of the crystals. From these observations and assuming a fully ionized -COOH dendrimer, a mathematical model of the binding capacity of the crystal surface with the dendrimer was developed. The Monte Carlo method was used to simulate the binding process between the dendrimer and crystal surface, and the binding strength of the -COOH groups to the surface was calculated to be 90 +/- 20 kJ/mol. These results support the CFM studies which have described alternating bands of charge domains on the crystal surface and that the binding strength will be dependent on both the intensity of the charge on the protein and the crystal surface.     

Spatial bistability in a pH autocatalytic system: from long to short range activation

The acid-auto-activated chlorite-tetrathionate reaction is studied in a one-side-fed spatial reactor. It was previously shown that in these conditions the unstirred reaction-diffusion system can generate oscillatory and excitable states even though under well-stirred nonequilibrium conditions only steady-state bistability is observed. Numerical simulations suggest that these temporal reaction-diffusion instabilities result from long-range activation by rapidly diffusing protons. We study here experimentally and numerically the effect of introducing into this reaction-diffusion system macromolecular carboxylate species that reduce the effective diffusivity of protons. Consistent with the original assumption, the introduction of such slow mobility proton-binding species quenches both oscillatory and excitability dynamics. Within the bistability domain the direction of the propagation of an interface between the two steady states depends on control parameter value. We elaborate on the fact that beyond a low critical concentration of macromolecular carboxylate species, the stability limit of the "thermodynamic" branch of spatial steady state does not depend on this concentration. Despite the relative simplicity of the kinetic model used in the numerical simulations, the results are in quasi-quantitative agreement with the experimental observations.     

Effect of variation in the chain length and number in modulating the interaction of an immunogenic lipopeptide with biomembrane models

A differential scanning calorimetry study was carried out to investigate the effect exerted by immunogenic synthetic lipopeptides obtained by the conjugation of LCMV_33–41 peptide with lipoamino acids (Laas) bearing different alkyl chain lengths (C₁₂ and C₁₆) and number of chains (2 × C₁₂) on the thermotropic behaviour of dimyristoylphosphatidylcholine (DMPC) liposomes. The aim of this work was to study the ability of these compounds to be carried by a liposomal system and released to a biomembrane model.

The examined compounds caused variations of the thermotropic parameters that characterise the liposomal system (transition temperature, T_m and enthalpy variation, ΔH), and interacted with the biomembrane models in different way. The interaction was found to be modulated by the length and number of chains present in the examined compounds. In fact, the compounds with higher number of lipid chain showed a stronger interaction with the biomembrane models with respect to the pure peptide and the compounds with a single lipid chain. These results suggest that the lipoamino acid moiety could favour the peptide to be carried by the liposomal system and released to biomembrane.