Two-dimensional ultrashort echo time imaging using a spiral trajectory

Tissues with very short transverse relaxation time (T2) cannot be detected using conventional magnetic resonance (MR) sequences due to the rapid decay of excited MR signals. In this work, a multiecho sequence employing half-pulse excitation and spiral sampling was developed for ultrashort echo time (UTE) imaging of tissues with short T2. Spiral readout gradients were measured and precompensated to reduce gradient distortions due to eddy currents and gradient anisotropy. The effects of spatial blurring due to fast signal decay were investigated experimentally through spiral UTE (SUTE) imaging of rubber bands with different spiral sampling duration. The unwanted long T2 signals were suppressed through the use of an inversion pulse and nulling, and/or subtraction of a later echo image from the initial one. This technique has been applied to imaging of the short T2 components in brain white matter, knee cartilage, bone and carotid vessel wall of normal volunteers at 1.5 T. Preliminary results show high spatial resolution and excellent image contrast for a variety of short T2 tissues in the human body under a relatively short scan time. A quantitative comparison was also made between radial UTE and SUTE in terms of signal-to-noise ratio efficiency.     

On the rate of convergence of solutions in free boundary problems via penalization

The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans.     

Numerical solution for the anisotropic Willmore flow of graphs

The Willmore flow is well known problem from the differential geometry. It minimizes the Willmore functional defined as integral of the mean-curvature square over given manifold. For the graph formulation, we derive modification of the Willmore flow with anisotropic mean curvature. We define the weak solution and we prove an energy equality. We approximate the solution numerically by the complementary finite volume method. To show the stability, we re-formulate the resulting scheme in terms of the finite difference method. By using simple framework of the finite difference method (FDM) we show discrete version of the energy equality. The time discretization is done by the method of lines and the resulting system of ODEs is solved by the Runge–Kutta–Merson solver with adaptive integration step. We also show experimental order of convergence as well as results of the numerical experiments, both for several different anisotropies.     

Harnack inequalities for SDEs driven by subordinate Brownian motions

By using regularization approximations of the underlying subordinator and a gradient estimate approach, the dimension-independent Harnack inequalities are established for the inhomogeneous semigroup associated with a class of SDEs with Lévy noise containing a subordinate Brownian motion. Our estimates in Harnack type inequalities improve the corresponding ones in the recent paper by Wang and Wang (2014) [10].     

Quantitative screening for steroids in animal feeding water using reversed phase LC with gradient elution

Several isocratic separations for the determination of 20 steroids (STER) in animal feeding water samples (AFWS) from drinking-trough by LC using a mobile phase ACN/H(2)O (35:65 v/v) and different RP columns (Hypersil C18, Gemini C18 (GM), Purospher Star C18, Synergi Max C12, and Synergi Fusion) and UV detection were obtained. The elution order was the same: a first group of corticoids (CC) was early eluted, a second group of CC and anabolics (AAS) exhibited intermediate retention, and a third group constituted by AAS was strongly retained. To improve the separation performances of the isocratic separations an ACN gradient elution optimization was carried out for each column. The most satisfactory results were obtained using a Purospher column which allowed the separation of 19 STER in an analysis time close to 26 min. After sample preparation using SPE, method validation was performed in an AFWS spiked with STER according to the EC decision criteria established for quantitative screening methods. For this purpose calibration graphs, extraction efficiencies, decision limits, detection capabilities, precision (repeatability and within-laboratory reproducibility), accuracy, selectivity, and robustness were evaluated. The proposed method was applied to other AFWS with satisfactory results.     

Measure-Valued Differentiation for Markov Chains

This paper addresses the problem of sensitivity analysis for finite-horizon performance measures of general Markov chains. We derive closed-form expressions and associated unbiased gradient estimators for the derivatives of finite products of Markov kernels by measure-valued differentiation (MVD). In the MVD setting, the derivatives of Markov kernels, called -derivatives, are defined with respect to a class of performance functions such that, for any performance measure , the derivative of the integral of g with respect to the one-step transition probability of the Markov chain exists. The MVD approach (i) yields results that can be applied to performance functions out of a predefined class, (ii) allows for a product rule of differentiation, that is, analyzing the derivative of the transition kernel immediately yields finite-horizon results, (iii) provides an operator language approach to the differentiation of Markov chains and (iv) clearly identifies the trade-off between the generality of the performance classes that can be analyzed and the generality of the classes of measures (Markov kernels). The -derivative of a measure can be interpreted in terms of various (unbiased) gradient estimators and the product rule for -differentiation yields a product-rule for various gradient estimators. Part of this work was done while the first author was with EURANDOM, Eindhoven, Netherlands, where he was supported by Deutsche Forschungsgemeinschaft under Grant He3139/1-1. The work of the second author was partially supported by NSERC and FCAR grants of the Government of Canada and Québec.     

Gradient estimates in Orlicz spaces for quasilinear elliptic equation

In this paper we generalize classical L^q$L^q$, q≥p$q\ge p$, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type.     

Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure

We consider nonlinear parabolic systems of the form ut=−∇V(u)+u_xx$u_t=-\mathrm{\nabla }V(u)+u_{xx}$, where u∈Rn$u\in {\mathbb{R}}^n$, n?1$n?1$, x∈R$x\in \mathbb{R}$, and the potential V   is coercive at infinity. For such systems, we prove a result of global convergence toward bistable fronts which states that invasion of a stable homogeneous equilibrium (a local minimum of the potential) necessarily occurs via a traveling front connecting to another (lower) equilibrium. This provides, for instance, a generalization of the global convergence result obtained by Fife and McLeod [P. Fife, J.B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335–361] in the case n=1$n=1$. The proof is based purely on energy methods, it does not make use of comparison principles, which do not hold any more when n>1$n>1$.     

Optimizing Membranes for Osmotic Power Generation

The design of ion-selective membranes is the key towards efficient reverse electrodialysis-based osmotic power conversion. The tradeoff between ion selectivity (output voltage) and ion permeability (output current) in existing porous membranes, however, limits the upgradation of power generation efficiency for practical applications. Thus, we provide the simple guidelines based on fundamentals of ion transport in nanofluidics for promoting osmotic power conversion. In addition, we discuss strategies for optimizing membrane performance through analysis of various material parameters in membrane design, such as pore size, surface charge, pore density, membrane thickness, ion pathway, pore order, and ionic diode effect. Lastly, a perspective on the future directions of membrane design to further maximize the efficiency of osmotic power conversion is outlined.