Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.Comment: to appear in Quarterly of Applied Mathematic

Spectroscopic Confirmation of the Cl 1604 Supercluster at z~0.9

We present spectroscopic confirmation of the Cl 1604 supercluster at z~0.9. Originally detected as two individual clusters, Cl 1604+4304 at z = 0.90 and Cl 1604+4321 at z = 0.92, which are closely separated in both redshift and sky position, subsequent imaging revealed a complex of red galaxies bridging the two clusters, suggesting that the region contained a large scale structure. We have carried out extensive multi-object spectroscopy, which, combined with previous measurements, provides ~600 redshifts in this area, including 230 confirmed supercluster members. We detect two additional clusters that are part of this structure, Cl 1604+4314 at z = 0.87 and Cl 1604+4316 at z = 0.94. All four have properties typical of local clusters, with line-of-sight velocity dispersions between 489 and 962 km/s. The structure is significantly extended in redshift space, which, if interpreted as a true elongation in real space, implies a depth of 93 Mpc. We examine the spatial and redshift distribution of the supercluster members.Comment: Accepted to ApJ Letters. 4 pages with 3 figure

Antikaon-nucleus dynamics: from quasibound states to kaon condensation

Coupled-channel Kbar-N dynamics near threshold and its repercussions in few-body Kbar-nuclear systems are briefly reviewed, highlighting studies of a K^-pp quasibound state. In heavier nuclei, the extension of mean-field calculations to multi-Kbar nuclear and hypernuclear quasibound states is discussed. It is concluded that strangeness in finite self-bound systems is realized through hyperons, with no room for kaon condensation.Comment: Proceedings version of plenary talk at Quark Nuclear Physics (QNP09) September 2009, Beijing; matches published versio

Abandon Statistical Significance

We discuss problems the null hypothesis significance testing (NHST) paradigm poses for replication and more broadly in the biomedical and social sciences as well as how these problems remain unresolved by proposals involving modified p-value thresholds, confidence intervals, and Bayes factors. We then discuss our own proposal, which is to abandon statistical significance. We recommend dropping the NHST paradigm--and the p-value thresholds intrinsic to it--as the default statistical paradigm for research, publication, and discovery in the biomedical and social sciences. Specifically, we propose that the p-value be demoted from its threshold screening role and instead, treated continuously, be considered along with currently subordinate factors (e.g., related prior evidence, plausibility of mechanism, study design and data quality, real world costs and benefits, novelty of finding, and other factors that vary by research domain) as just one among many pieces of evidence. We have no desire to "ban" p-values or other purely statistical measures. Rather, we believe that such measures should not be thresholded and that, thresholded or not, they should not take priority over the currently subordinate factors. We also argue that it seldom makes sense to calibrate evidence as a function of p-values or other purely statistical measures. We offer recommendations for how our proposal can be implemented in the scientific publication process as well as in statistical decision making more broadly

Some aspects of mathematical and chemical modeling of complex chemical processes

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra

RNA aptamers generated against oligomeric Abeta40 recognize common amyloid aptatopes with low specificity but high sensitivity.

Aptamers are useful molecular recognition tools in research, diagnostics, and therapy. Despite promising results in other fields, aptamer use has remained scarce in amyloid research, including Alzheimer's disease (AD). AD is a progressive neurodegenerative disease believed to be caused by neurotoxic amyloid beta-protein (Abeta) oligomers. Abeta oligomers therefore are an attractive target for development of diagnostic and therapeutic reagents. We used covalently-stabilized oligomers of the 40-residue form of Abeta (Abeta40) for aptamer selection. Despite gradually increasing the stringency of selection conditions, the selected aptamers did not recognize Abeta40 oligomers but reacted with fibrils of Abeta40, Abeta42, and several other amyloidogenic proteins. Aptamer reactivity with amyloid fibrils showed some degree of protein-sequence dependency. Significant fibril binding also was found for the naïve library and could not be eliminated by counter-selection using Abeta40 fibrils, suggesting that aptamer binding to amyloid fibrils was RNA-sequence-independent. Aptamer binding depended on fibrillogenesis and showed a lag phase. Interestingly, aptamers detected fibril formation with > or =15-fold higher sensitivity than thioflavin T (ThT), revealing substantial beta-sheet and fibril formation undetected by ThT. The data suggest that under physiologic conditions, aptamers for oligomeric forms of amyloidogenic proteins cannot be selected due to high, non-specific affinity of oligonucleotides for amyloid fibrils. Nevertheless, the high sensitivity, whereby aptamers detect beta-sheet formation, suggests that they can serve as superior amyloid recognition tools