Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new references added, fixed typo

Applying diagnosis and pharmacy-based risk models to predict pharmacy use in Aragon, Spain: The impact of a local calibration

<p>Abstract</p> <p>Background</p> <p>In the financing of a national health system, where pharmaceutical spending is one of the main cost containment targets, predicting pharmacy costs for individuals and populations is essential for budget planning and care management. Although most efforts have focused on risk adjustment applying diagnostic data, the reliability of this information source has been questioned in the primary care setting. We sought to assess the usefulness of incorporating pharmacy data into claims-based predictive models (PMs). Developed primarily for the U.S. health care setting, a secondary objective was to evaluate the benefit of a local calibration in order to adapt the PMs to the Spanish health care system.</p> <p>Methods</p> <p>The population was drawn from patients within the primary care setting of Aragon, Spain (n = 84,152). Diagnostic, medication and prior cost data were used to develop PMs based on the Johns Hopkins ACG methodology. Model performance was assessed through r-squared statistics and predictive ratios. The capacity to identify future high-cost patients was examined through c-statistic, sensitivity and specificity parameters.</p> <p>Results</p> <p>The PMs based on pharmacy data had a higher capacity to predict future pharmacy expenses and to identify potential high-cost patients than the models based on diagnostic data alone and a capacity almost as high as that of the combined diagnosis-pharmacy-based PM. PMs provided considerably better predictions when calibrated to Spanish data.</p> <p>Conclusion</p> <p>Understandably, pharmacy spending is more predictable using pharmacy-based risk markers compared with diagnosis-based risk markers. Pharmacy-based PMs can assist plan administrators and medical directors in planning the health budget and identifying high-cost-risk patients amenable to care management programs.</p

Modernization and Its Discontents

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67022/2/10.1177_000276427702100208.pd

Stability of domain structures in multi-domain proteins

Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR

Multi-Scaled Explorations of Binding-Induced Folding of Intrinsically Disordered Protein Inhibitor IA3 to its Target Enzyme

Biomolecular function is realized by recognition, and increasing evidence shows that recognition is determined not only by structure but also by flexibility and dynamics. We explored a biomolecular recognition process that involves a major conformational change – protein folding. In particular, we explore the binding-induced folding of IA3, an intrinsically disordered protein that blocks the active site cleft of the yeast aspartic proteinase saccharopepsin (YPrA) by folding its own N-terminal residues into an amphipathic alpha helix. We developed a multi-scaled approach that explores the underlying mechanism by combining structure-based molecular dynamics simulations at the residue level with a stochastic path method at the atomic level. Both the free energy profile and the associated kinetic paths reveal a common scheme whereby IA3 binds to its target enzyme prior to folding itself into a helix. This theoretical result is consistent with recent time-resolved experiments. Furthermore, exploration of the detailed trajectories reveals the important roles of non-native interactions in the initial binding that occurs prior to IA3 folding. In contrast to the common view that non-native interactions contribute only to the roughness of landscapes and impede binding, the non-native interactions here facilitate binding by reducing significantly the entropic search space in the landscape. The information gained from multi-scaled simulations of the folding of this intrinsically disordered protein in the presence of its binding target may prove useful in the design of novel inhibitors of aspartic proteinases

Chromosomal Inversions between Human and Chimpanzee Lineages Caused by Retrotransposons

The long interspersed element-1 (LINE-1 or L1) and Alu elements are the most abundant mobile elements comprising 21% and 11% of the human genome, respectively. Since the divergence of human and chimpanzee lineages, these elements have vigorously created chromosomal rearrangements causing genomic difference between humans and chimpanzees by either increasing or decreasing the size of genome. Here, we report an exotic mechanism, retrotransposon recombination-mediated inversion (RRMI), that usually does not alter the amount of genomic material present. Through the comparison of the human and chimpanzee draft genome sequences, we identified 252 inversions whose respective inversion junctions can clearly be characterized. Our results suggest that L1 and Alu elements cause chromosomal inversions by either forming a secondary structure or providing a fragile site for double-strand breaks. The detailed analysis of the inversion breakpoints showed that L1 and Alu elements are responsible for at least 44% of the 252 inversion loci between human and chimpanzee lineages, including 49 RRMI loci. Among them, three RRMI loci inverted exonic regions in known genes, which implicates this mechanism in generating the genomic and phenotypic differences between human and chimpanzee lineages. This study is the first comprehensive analysis of mobile element bases inversion breakpoints between human and chimpanzee lineages, and highlights their role in primate genome evolution

A network linking scene perception and spatial memory systems in posterior cerebral cortex

The neural systems supporting scene-perception and spatial-memory systems of the human brain are well-described. But how do these neural systems interact? Here, using fine-grained individual-subject fMRI, we report three cortical areas of the human brain, each lying immediately anterior to a region of the scene perception network in posterior cerebral cortex, that selectively activate when recalling familiar real-world locations. Despite their close proximity to the scene-perception areas, network analyses show that these regions constitute a distinct functional network that interfaces with spatial memory systems during naturalistic scene understanding. These “place-memory areas” offer a new framework for understanding how the brain implements memory-guided visual behaviors, including navigation

The Alzheimer's Disease Prediction Of Longitudinal Evolution (TADPOLE) Challenge: Results after 1 Year Follow-up

We present the findings of "The Alzheimer's Disease Prediction Of Longitudinal Evolution" (TADPOLE) Challenge, which compared the performance of 92 algorithms from 33 international teams at predicting the future trajectory of 219 individuals at risk of Alzheimer's disease. Challenge participants were required to make a prediction, for each month of a 5-year future time period, of three key outcomes: clinical diagnosis, Alzheimer's Disease Assessment Scale Cognitive Subdomain (ADAS-Cog13), and total volume of the ventricles. No single submission was best at predicting all three outcomes. For clinical diagnosis and ventricle volume prediction, the best algorithms strongly outperform simple baselines in predictive ability. However, for ADAS-Cog13 no single submitted prediction method was significantly better than random guessing. Two ensemble methods based on taking the mean and median over all predictions, obtained top scores on almost all tasks. Better than average performance at diagnosis prediction was generally associated with the additional inclusion of features from cerebrospinal fluid (CSF) samples and diffusion tensor imaging (DTI). On the other hand, better performance at ventricle volume prediction was associated with inclusion of summary statistics, such as patient-specific biomarker trends. The submission system remains open via the website https://tadpole.grand-challenge.org, while code for submissions is being collated by TADPOLE SHARE: https://tadpole-share.github.io/. Our work suggests that current prediction algorithms are accurate for biomarkers related to clinical diagnosis and ventricle volume, opening up the possibility of cohort refinement in clinical trials for Alzheimer's disease