Traveling periodic waves of chemical activity

It is shown that within the manifold of exact solutions a system of reaction-diffusion equations admits only travelling waves with planar symmetry. A derivation of the generic form of approximate (asymptotic) cylindrical and spiral travelling periodic wave solutions is given. If an exact solution homogeneous in space and periodic in time is admitted by the system of reaction-diffusion equations, then travelling periodic spiral waves are admissble as approximate solutions. This is the theoretical explanation for the travelling periodic waves of chemical activity observed in recent experiments.     

Legendre transforms and r-particle irreducibility in quantum field theory: The formal power series framework

We study the higher Legendre transforms Γ^(r) {A } of the generating functional G for connected Green's functions in Euclidean boson field theories. To analyze Γ^(r) {A } rigorously even when it does not make sense as an ordinary functional, we develop the framework of formal power series in A. For r = 1, 2 we isolate regularity conditions on G that ensure the existence of Γ^(r) as a formal power series and we verify these conditions for the weakly coupled P(φ)₂ model. We also establish the improved regularity of the functional Φ^(r) obtained by subtracting from Γ^(r) its trivial singular part.     

Sufficient conditions for solving linearly constrained separable concave global minimization problems

A concave function defined on a polytope may have many local minima (in fact every extreme point may be a local minimum). Sufficient conditions are given such that if they are satisfied at a point, this point is known to be a global minimum. It is only required to solve a single linear program to test whether the sufficient conditions are satisfied. This test has been incorporated into an earlier algorithm to give improved performance. Computational results presented show that these sufficient conditions are satisfied for certain types of problems and may substantially reduce the effort needed to find and recognize a global minimum.     

Approximating Data in \mathfrak{R}^{n} by a Quadratic Underestimator with Specified Hessian Minimum and Maximum Eigenvalues

The problem of approximating m data points (x _i , y _i ) in , with a quadratic function q(x, p) with s parameters, m ≥ s, is considered. The parameter vector is to be determined so as to satisfy three conditions: (1) q(x, p) must underestimate all m data points, i.e. q(x _i , p) ≤ y _i , i=1,...,m. (2) The error of the approximation is to be minimized in the L1 norm. (3) The eigenvalues of H are to satisfy specified lower and upper bounds, where H is the Hessian of q(x, p) with respect to x. This is called the Quadratic Underestimator with Bounds on Eigenvalues (QUBE) problem. An algorithm for its solution (QUBE algorithm) is given and justified, and computational results presented. The QUBE algorithm has application to finding the global minimum of a basin (or funnel) shaped function with a large number of local minima. Such problems arise in computational biology where it is desired to find the global minimum of an energy surface, in order to predict native protein-ligand docking geometry (drug design) or protein structure. Computational results for a simulated docking energy surface, with n=15, are presented. It is shown that specifying a small condition number for H improves the ability of the underestimator to correctly predict the global minimum point.     

Neural correlates of intelligibility in speech investigated with noise vocoded speech--a positron emission tomography study

Functional imaging studies of speech perception in the human brain have identified a key role for auditory association areas in the temporal lobes (bilateral superior temporal gyri and sulci) in the perceptual processing of the speech signal. This is extended to suggest some functional specialization within this bilateral system, with a particular role for the left anterior superior temporal sulcus (STS) in processing intelligible speech. In the current study, noise-vocoded speech was used to vary the intelligibility of speech parametrically. This replicated the finding of a selective response to intelligibility in speech in the left anterior superior temporal sulcus, in contrast to the posterior superior temporal sulcus, which showed a response profile insensitive to the degree of intelligibility. These results are related to theories of functional organization in the human auditory system, which have indicated that there are separate processing streams, with different functional roles, running anterior and posterior to primary auditory cortex. Specifically, it is suggested that an anterior stream processing intelligibility can be distinguished from a posterior stream associated with transient representations, important in spoken repetition and working memory.     

An approximation theory for the identification of nonlinear volterra equations

An abstract approximation framework and convergence theory for Galerkin approximations to inverse problems involving nonlinear Volterra integral equations is developed. The approach relies on the theory of m-accretive operators in Banach spaces. An application to heat flow in materials with memory is also discussed.     

Charged condensation

We consider Bose–Einstein condensation of massive electrically charged scalars in a uniform background of charged fermions. We focus on the case when the scalar condensate screens the background charge, while the net charge of the system resides on its boundary surface. A distinctive signature of this substance is that the photon acquires a Lorentz-violating mass in the bulk of the condensate. Due to this mass, the transverse and longitudinal gauge modes propagate with different group velocities. We give qualitative arguments that at high enough densities and low temperatures a charged system of electrons and helium-4 nuclei, if held together by laboratory devices or by force of gravity, can form such a substance. We briefly discuss possible manifestations of the charged condensate in compact astrophysical objects.     

Automatic correction of in-plane bulk motion artifacts in self-navigated radial MRI

Radial MRI is typically used for scans that are sensitive to unavoidable motion. While the translational motion artifact can be easily removed from the radial trajectory data by phase correction, correction of rotational motion still remains a challenge in radial MRI. We present a novel method to refocus the image corrupted by view-to-view motion in the view-interleaved radial MRI data. In this method, the error in rotational view angles was modeled as a polynomial function of the view order and the model parameters were estimated by minimizing the self-navigator image metrics such as image entropy, gradient entropy, normalized gradient squared and mean square difference. Translational motion correction was conducted by aligning the projection profiles. Simulation studies were conducted to demonstrate the robustness of both translational and rotational motion correction methods in different noise levels. The proposed method was successfully applied to correct for motion of healthy subjects. Substantial motion correction with relative error of less than 5% was achieved by using either first- or second-order model with the image metrics. This study demonstrates the potential of the method for motion-sensitive applications.     

Combinatorics,graph theory,and computing

Journal of Algebraic Combinatorics -     

Block–Stereoblock Copolymers of Poly(ϵ‐Caprolactone) and Poly(Lactic Acid)

A magnesium complex of the type {ONNN}Mg‐HMDS wherein {ONNN} is a sequential tetradentate monoanionic ligand is introduced. In the presence of an alcohol initiator this complex catalyzes the living and immortal homopolymerization of the lactide enantiomers and ?‐caprolactone at room‐temperature with exceptionally high activities, as well as the precise block copolymerization of these monomers in a one‐pot synthesis by sequential monomer addition. Copolymers of unprecedented microstructures such as the PCL‐b‐PLLA‐b‐PDLA and PDLA‐b‐PLLA‐b‐PCL‐b‐PLLA‐b‐PDLA block–stereoblock microstructures that feature unique thermal properties are readily accessed.