Hexicon 2: Automated Processing of Hydrogen-Deuterium Exchange Mass Spectrometry Data with Improved Deuteration Distribution Estimation

Hydrogen–deuterium exchange (HDX) experiments analyzed by mass spectrometry (MS) provide information about the dynamics and the solvent accessibility of protein backbone amide hydrogen atoms. Continuous improvement of MS instrumentation has contributed to the increasing popularity of this method; however, comprehensive automated data analysis is only beginning to mature. We present Hexicon 2, an automated pipeline for data analysis and visualization based on the previously published program Hexicon (Lou et al. 2010). Hexicon 2 employs the sensitive NITPICK peak detection algorithm of its predecessor in a divide-and-conquer strategy and adds new features, such as chromatogram alignment and improved peptide sequence assignment. The unique feature of deuteration distribution estimation was retained in Hexicon 2 and improved using an iterative deconvolution algorithm that is robust even to noisy data. In addition, Hexicon 2 provides a data browser that facilitates quality control and provides convenient access to common data visualization tasks. Analysis of a benchmark dataset demonstrates superior performance of Hexicon 2 compared with its predecessor in terms of deuteration centroid recovery and deuteration distribution estimation. Hexicon 2 greatly reduces data analysis time compared with manual analysis, whereas the increased number of peptides provides redundant coverage of the entire protein sequence. Hexicon 2 is a standalone application available free of charge under http://hx2.mpimf-heidelberg.mpg.de.

Existence and stability of large scale nonlinear oscillations in suspension bridges

A nonlinear model of a suspension bridge is considered in which large-scale, stable oscillatory motions can be produced by constant loading and a small-scale, external oscillatory force. Loud's implicit-function theoretic method for determining existence and stability of periodic solutions or nonlinear differential equations is extended to a case of a non-differentiable nonlinearity.Author partially supported by NSF under Grant DMS 8318204 and AFOSR Grant 85-0330.Author partially supported by NSF under Grant DMS 9519882.Author partially supported by NSF under Grant DMS 8519776.     

On the Positivity of the Stochastic Heat Equation

We study the positivity preserving properties of the heat equation with a white noise potential and random initial condition. Moreover, we find a generalized Feynman--Kac formula for the solution of the problem using methods from the white noise analysis. The initial condition can anticipate the driving white noise. We show that the solution is positive, when the random initial condition is positive. For the case of a time-dependent white noise potential, we give a special representation of the solution together with regularity results.     

Polyhedral convexity cuts and negative edge extensions

This note shows that convexity cuts defined relative to polyhedral convex sets can utilize negative as well as positive edge extensions under appropriate circumstances, yielding stronger cuts than customarily available. We also show how to partially collapse the polyhedron to further improve these cuts.     

Development and Validation of a Computer‐Administered Number Sense Scale for Fifth‐Grade Children in Taiwan

To investigate the structure of number sense and then to assess its uses in fifth‐grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and substantially valid. It can be reliably used as a screening measure for a quick check of students' number sense development via online self‐assessment. Compared with our previous study, both qualitative and quantitative changes were detected in students' number sense development at different grades. The qualitative change in number sense development is manifested in different numbers of factor components produced at different grades. The quantitative change is manifested in different amounts of factor variance explained at different grades. Furthermore, among the four aspects of number sense, Taiwanese students perform best on recognizing the relative number size yet relatively worse on judging the reasonableness of computational results.     

Solving the maximum edge weight clique problem via unconstrained quadratic programming

The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more traditional methods. In this paper we report on the application of UQP to the maximum edge-weighted clique problem. Computational experience is reported illustrating the attractiveness of the approach.     

Unstable attractors induce perpetual synchronization and desynchronization

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.