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The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman-Bucy filter is consistent with the classic Kalman-Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.
The complex formation of the following diazaperylene ligands (L) 1,12-diazaperylene 1, 1,1-bisisoquinoline 2, 2,11-disubstituted 1,12-diazaperylenes (alkyl=methyl, ethyl, isopropyl, 3, 5, 7), 3,3-disubstituted 1,1-bisisoquinoline (alkyl=methyl, ethyl, isopropyl, 4, 6, 8 and with R=phenyl, 11 and with pyridine 12), and the 5,8-dimethoxy-substituted diazaperylene 9, 6,6-dimethoxy-substituted bisisoquinoline 10 with AgBF4 was investigated. Collision-induced dissociation measurements were used to evaluate the relative stabilities of the ligands themselves and for the [1:1](+) complexes as well as for the homoleptic and heteroleptic silver [1:2](+) complexes in the gas phase. This method is very useful in rapid screening of the stabilities of new complexes in the gas phase. The influence of the spatial arrangement of the ligands and the type of substituents employed for the complexation were examined. The effect of the preorganization of the diazaperylene on the threshold activation voltages and thus of the relative binding energies of the different complexes are discussed. Density functional theory calculations were used to calculate the optimized structures of the silver complexes and compared with the stabilities of the complexes in the gas phase for the first time.
The hydrolytic stability of polymers to be used for coatings in aqueous environments, for example, to confer anti-fouling properties, is crucial. However, long-term exposure studies on such polymers are virtually missing. In this context, we synthesized a set of nine polymers that are typically used for low-fouling coatings, comprising the well-established poly(oligoethylene glycol methylether methacrylate), poly(3-(N-2-methacryloylethyl-N,N-dimethyl) ammoniopropanesulfonate) (sulfobetaine methacrylate), and poly(3-(N-3-methacryamidopropyl-N,N-dimethyl)ammoniopropanesulfonate) (sulfobetaine methacrylamide) as well as a series of hitherto rarely studied polysulfabetaines, which had been suggested to be particularly hydrolysis-stable. Hydrolysis resistance upon extended storage in aqueous solution is followed by H-1 NMR at ambient temperature in various pH regimes. Whereas the monomers suffered slow (in PBS) to very fast hydrolysis (in 1 M NaOH), the polymers, including the polymethacrylates, proved to be highly stable. No degradation of the carboxyl ester or amide was observed after one year in PBS, 1 M HCl, or in sodium carbonate buffer of pH 10. This demonstrates their basic suitability for anti-fouling applications. Poly(sulfobetaine methacrylamide) proved even to be stable for one year in 1 M NaOH without any signs of degradation. The stability is ascribed to a steric shielding effect. The hemisulfate group in the polysulfabetaines, however, was found to be partially labile.
A notable uptick of interest in the stability of self-esteem has been observed over the past few years. Most researchers, however, have focused on unidimensional rather than multidimensional conceptualizations of self-esteem. The paucity of empirical research is surprising given conflicting theoretical perspectives on the stability of self-esteem. The goal of the present study was to thoroughly disentangle different conceptualizations of self-esteem and test opposing classical theories on (i) the stability and (ii) the direction of mutual influence of these different forms of self-esteem. We analysed two-year longitudinal data from participants (N=644 at T1, N=241 at T2) with an average age of 47.0years (SD=12.4). Analyses using a latent variable approach revealed that the domains of self-esteem were relatively stable in terms of rank order and mean levels. In fact, the size of the stability coefficients was comparable to that of other trait measures that have been reported in the literature and paralleled the stability observed for global self-esteem. Results did not provide support for either top-down or bottom-up effects between domain-specific and global self-esteem. These findings have important theoretical and practical implications regarding the stability and development of self-esteem in adulthood and advance the understanding of self-esteem in personality theory. (c) 2018 European Association of Personality Psychology
Phenotypic plasticity in prey can have a dramatic impact on predator-prey dynamics, e.g. by inducible defense against temporally varying levels of predation. Previous work has overwhelmingly shown that this effect is stabilizing: inducible defenses dampen the amplitudes of population oscillations or eliminate them altogether. However, such studies have neglected scenarios where being protected against one predator increases vulnerability to another (incompatible defense). Here we develop a model for such a scenario, using two distinct prey phenotypes and two predator species. Each prey phenotype is defended against one of the predators, and vulnerable to the other. In strong contrast with previous studies on the dynamic effects of plasticity involving a single predator, we find that increasing the level of plasticity consistently destabilizes the system, as measured by the amplitude of oscillations and the coefficients of variation of both total prey and total predator biomasses. We explain this unexpected and seemingly counterintuitive result by showing that plasticity causes synchronization between the two prey phenotypes (and, through this, between the predators), thus increasing the temporal variability in biomass dynamics. These results challenge the common view that plasticity should always have a stabilizing effect on biomass dynamics: adding a single predator-prey interaction to an established model structure gives rise to a system where different mechanisms may be at play, leading to dramatically different outcomes.