In vivo 13C NMR spectroscopy and metabolic modeling in the brain: a practical perspective

In vivo 13C NMR spectroscopy has the unique capability to measure metabolic fluxes noninvasively in the brain. Quantitative measurements of metabolic fluxes require analysis of the 13C labeling time courses obtained experimentally with a metabolic model. The present work reviews the ingredients necessary for a dynamic metabolic modeling study, with particular emphasis on practical issues.     

Virtual retractions,conjugacy separability and omnipotence

We use wreath products to provide criteria for a group to be conjugacy separable or omnipotent. These criteria are in terms of virtual retractions onto cyclic subgroups. We give two applications: a straightforward topological proof of the theorem of Stebe that infinite-order elements of Fuchsian groups (of the first type) are conjugacy distinguished, and a proof that surface groups are omnipotent.     

Generating and measuring instances of hard semidefinite programs

Linear Programming, LP, problems with finite optimal value have a zero duality gap and a primal–dual strictly complementary optimal solution pair. On the other hand, there exist Semidefinite Programming, SDP, problems which have a nonzero duality gap (different primal and dual optimal values; not both infinite). The duality gap is assured to be zero if a constraint qualification, e.g., Slater’s condition (strict feasibility) holds. Measures of strict feasibility, also called distance to infeasibility, have been used in complexity analysis, and, it is known that (near) loss of strict feasibility results in numerical difficulties. In addition, there exist SDP problems which have a zero duality gap but no strict complementary primal–dual optimal solution. We refer to these problems as hard instances of SDP. The assumption of strict complementarity is essential for asymptotic superlinear and quadratic rate convergence proofs. In this paper, we introduce a procedure for generating hard instances of SDP with a specified complementarity nullity (the dimension of the common nullspace of primal–dual optimal pairs). We then show, empirically, that the complementarity nullity correlates well with the observed local convergence rate and the number of iterations required to obtain optimal solutions to a specified accuracy, i.e., we show, even when Slater’s condition holds, that the loss of strict complementarity results in numerical difficulties. We include two new measures of hardness that correlate well with the complementarity nullity.     

Numeric solution of advection–diffusion equations by a discrete time random walk scheme

Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups, and discontinuities. Here we present an explicit numerical scheme for solving nonlinear advection–diffusion equations admitting shock solutions that is both easy to implement and stable. The numerical scheme is obtained by considering the continuum limit of a discrete time and space stochastic process for nonlinear advection–diffusion. The stochastic process is well posed and this guarantees the stability of the scheme. Several examples are provided to highlight the importance of the formulation of the stochastic process in obtaining a stable and accurate numerical scheme.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.     

ADMM for the SDP relaxation of the QAP

Semidefinite programming, SDP, relaxations have proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem, QAP, arguably one of the hardest NP-hard discrete optimization problems. There are several difficulties that arise in efficiently solving the SDP relaxation, e.g., increased dimension; inefficiency of the current primal–dual interior point solvers in terms of both time and accuracy; and difficulty and high expense in adding cutting plane constraints. We propose using the alternating direction method of multipliers ADMM in combination with facial reduction, FR, to solve the SDP relaxation. This first order approach allows for: inexpensive iterations, a method of cheaply obtaining low rank solutions; and a trivial way of exploiting the FR for adding cutting plane inequalities. In fact, we solve the doubly nonnegative, DNN, relaxation that includes both the SDP and all the nonnegativity constraints. When compared to current approaches and current best available bounds we obtain robustness, efficiency and improved bounds.     

A magnetic bead‐based serum proteomic fingerprinting method for parallel analytical analysis and micropreparative purification

ProteinChip surface‐enhanced laser desorption/ionization technology and magnetic beads‐based ClinProt system are commonly used for semi‐quantitative profiling of plasma proteome in biomarker discovery. Unfortunately, the proteins/peptides detected by MS are non‐recoverable. To obtain the protein identity of a MS peak, additional time‐consuming and material‐consuming purification steps have to be done. In this study, we developed a magnetic beads‐based proteomic fingerprinting method that allowed semi‐quantitative proteomic profiling and micropreparative purification of the profiled proteins in parallel. The use of different chromatographic magnetic beads allowed us to obtain different proteomic profiles, which were comparable to those obtained by the ProteinChip surface‐enhanced laser desorption/ionization technology. Our assays were semi‐quantitative. The normalized peak intensity was proportional to concentration measured by immunoassay. Both intra‐assay and inter‐assay coefficients of variation of the normalized peak intensities were in the range of 4–30%. Our method only required 2 μL of serum or plasma for generating enough proteins for semi‐quantitative profiling by MALDI‐TOF‐MS as well as for gel electrophoresis and subsequent protein identification. The protein peaks and corresponding gel spots could be easily matched by comparing their intensities and masses. Because of its high efficiency and reproducibility, our method has great potentials in clinical research, especially in biomarker discovery.     

Enantioselective Brønsted base catalyzed [4+2] cycloaddition using novel amino-substituted tetraphenylene derivatives

This paper is concerned with the syntheses of 1,8,9,16-tetrahydroxytetraphenylene derivatives and their applications as Brønsted base organocatalysts for [4+2] cycloaddition between anthrone and maleimides. The structural modifications of the catalysts and their related catalytic properties are described and discussed in details.     

Halogenated catechols from cycloaddition reactions of η-(2-ethoxyvinylketene)iron(0) complexes with 1-haloalkynes

1-Chloroalkynes and 1-bromohexyne undergo cycloaddition reactions with ethoxyvinylketeneiron(0) complexes to form chloro and bromocatechols. With most substituents, the halogen is incorporated ortho to the phenolic hydroxyl group regioselectively. With chloroethyne, chlorohexyne, and methyl chloropropiolate, the reverse regioselection is observed. Ab initio calculations reveal that the products are, in most cases, nearly isoenergetic, which indicates that the intermediate ketene-alkyne adduct geometry must be important in determining the product distribution.     

Fundamental Measurements in Online Polymerization Reaction Monitoring and Control with a Focus on ACOMP

Fundamental measurements in online polymerization reaction monitoring and control seek to avoid empirical and inferential models in data interpretation. One such approach making use of multiple detectors is automatic continuous online monitoring of polymerization reactions (ACOMP), wherein a continuous reactor stream is automatically, continuously diluted and conditioned to where measurements reflect intrinsic particle properties and not the interactions that can dominate measurements in concentrated media. Examples where dilute regime measurements are needed include static and dynamic light scattering, and reduced viscosity. This review focuses on ACOMP to illustrate a number of reaction contexts where fundamental measurements are used to gain a comprehensive picture of reaction characteristics.