Targeted analysis of glycomics liquid chromatography/mass spectrometry data

Hydrophilic interaction chromatography (HILIC) liquid chromatography/mass spectrometry (LC/MS) is appropriate for all native and reductively aminated glycan classes. HILIC carries the advantage that retention times vary predictably according to oligosaccharide composition. Chromatographic conditions are compatible with sensitive and reproducible glycomics analysis of large numbers of samples. The data are extremely useful for quantitative profiling of glycans expressed in biological tissues. With these analytical developments, the rate-limiting factor for widespread use of HILIC LC/MS in glycomics is the analysis of the data. In order to eliminate this problem, a Java-based open source software tool, Manatee, was developed for targeted analysis of HILIC LC/MS glycan datasets. This tool uses user-defined lists of compositions that specify the glycan chemical space in a given biological context. The program accepts high-resolution LC/MS data using the public mzXML format and is capable of processing a large data file in a few minutes on a standard desktop computer. The program allows mining of HILIC LC/MS data with an output compatible with multivariate statistical analysis. It is envisaged that the Manatee tool will complement more computationally intensive LC/MS processing tools based on deconvolution and deisotoping of LC/MS data. The capabilities of the tool were demonstrated using a set of HILIC LC/MS data on organ-specific heparan sulfates.     

On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems

It was recently proven in Case et al. (2010) [2] that, under mild restrictions, grad-div stabilized Taylor-Hood solutions of Navier-Stokes problems converge to the Scott-Vogelius solution of that same problem. However, even though the analytical rate was only shown to be (where γ is the stabilization parameter), the computational results suggest the rate may be improvable to γ−1. We prove herein the analytical rate is indeed γ−1, and extend the result to other incompressible flow problems including Leray-α and MHD. Numerical results are given that verify the theory.     

Regenerative cascade homotopies for solving polynomial systems

A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution set of a polynomial system, the witness superset contains all the needed information. Sommese and Wampler gave the first numerical method to compute witness supersets, based on dimension-by-dimension slicing of the solution set by generic linear spaces, followed later by the cascade homotopy of Sommese and Verschelde. Recently, the authors of this article introduced a new method, regeneration, to compute solution sets of polynomial systems. Tests showed that combining regeneration with the dimension-by-dimension algorithm was significantly faster than naively combining it with the cascade homotopy. However, in this article, we combine an appropriate randomization of the polynomial system with the regeneration technique to construct a new cascade of homotopies for computing witness supersets. Computational tests give strong evidence that regenerative cascade is superior in practice to previous methods.     

A three-dimensional steady-state tumor system

The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions. Linear and nonlinear stability for these solutions are determined numerically.     

A new infinite family of minimally nonideal matrices

Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on the possible cores of minimally nonideal matrices. This paper disproves their conjecture by constructing a new infinite family of square minimally nonideal matrices. In particular, we show that there exists a minimally nonideal matrix with r ones in each row and column for any r?3.     

On Quillen?s Theorem A for posets

A theorem of McCord of 1966 and Quillen?s Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We give an alternative elementary proof of this result and we deduce also a stronger statement: under the hypotheses of the theorem, the map is not only a homotopy equivalence but a simple homotopy equivalence. This leads then to stronger formulations of the simplicial version of Quillen?s Theorem A, the Nerve Lemma and other known results. In particular we establish a conjecture of Kozlov on the simple homotopy type of the crosscut complex and we improve a well-known result of Cohen on contractible mappings.     

Energy decay estimates for the dissipative wave equation with space–time dependent potential

We study the asymptotic behavior of solutions of dissipative wave equations with space–time‐dependent potential. When the potential is only time‐dependent, Fourier analysis is a useful tool to derive sharp decay estimates for solutions. When the potential is only space‐dependent, a powerful technique has been developed by Todorova and Yordanov to capture the exact decay of solutions. The presence of a space–time‐dependent potential, as in our case, requires modifications of this technique. We find the energy decay and decay of the L² norm of solutions in the case of space–time‐dependent potential. Copyright © 2010 John Wiley & Sons, Ltd.     

A sequential perspective on searching for static targets

We present a sequential approach to detect static targets with imperfect sensors, which range from tower-mounted cameras to satellites. The scenario is operationally relevant to many military, homeland security, search and rescue, environmental engineering, counter-narcotics, and law enforcement applications. The idea is to stop the search as soon as there is enough probabilistic evidence about the targets’ locations, given an operator-prescribed error tolerance, knowledge of the sensors’ parameters, and a sequence of detection signals from the sensors. By stopping the search as soon as possible, we promote efficiency by freeing up sensors and operators to perform other tasks. The model we develop has the added benefits of decreasing operator workload and providing negative information as a search progresses.