A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Mendacastrum n. gen. and Domuzdagia n. gen., two Jurassic spherical Spumellaria (Radiolaria) with hagiastrid medullary shell

Two new spumellarian radiolarian genera, Mendacastrum and Domuzdagia, are described from the lower Tithonian and lower Pliensbachian respectively. Both have a spherical cortical shell of actinommid type and a spherical or subspherical double medullary shell with the inner medullary shell of hagiastrid s.l. type. The inner medullary shell of Mendacastrum is of dactyliosphaerid or higumastrid s. sit. type, whereas that of Domuzdagia is of angulobracchiid type. Since they cannot be assigned to any described Mesozoic pyloniacean families, they are considered as type genera of two new families: Mendacastridae and Domuzdagiidae respectively.

Optimal asymptotic bounds for spherical designs

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In vitro Comparison of Disk Diffusion and Agar Dilution Antibiotic Susceptibility Test Methods for Neisseria gonorrhoeae

At present, most Neisseria gonorrhoeae testing is done with ß-lactamase and agar dilution tests with common therapeutic agents. Generally, in bacteriological diagnosis laboratories in Argentina, study of antibiotic susceptibility of N.gonorrhoeae is based on ß-lactamase determination and agar dilution method with common therapeutic agents. The National Committee for Clinical Laboratory Standards (NCCLS) has recently described a disk diffusion test that produces results comparable to the reference agar dilution method for antibiotic susceptibility of N.gonorrhoeae, using a dispersion diagram for analyzing the correlation between both techniques. We obtained 57 gonococcal isolates from patients attending a clinic for sexually transmitted diseases in Tucumán, Argentina. Antibiotic susceptibility tests using agar dilution and disk diffusion techniques were compared. The established NCCLS interpretive criteria for both susceptibility methods appeared to be applicable to domestic gonococcal strains. The correlation between the MIC's and the zones of inhibition was studied for penicillin, ampicillin, cefoxitin, spectinomycin, cefotaxime, cephaloridine, cephalexin, tetracycline, norfloxacin and kanamycin. Dispersion diagrams showed a high correlation between both methods.

An introduction to model-independent diffusion magnetic resonance imaging.

ABSTRACT: q-Space-based techniques such as diffusion spectrum imaging, q-ball imaging, and their variations have been used extensively in research for their desired capability to delineate complex neuronal architectures such as multiple fiber crossings in each of the image voxels. The purpose of this article was to provide an introduction to the q-space formalism and the principles of basic q-space techniques together with the discussion on the advantages as well as challenges in translating these techniques into the clinical environment. A review of the currently used q-space-based protocols in clinical research is also provided.

Anti-basal ganglia antibodies and Tourette's syndrome: a voxel-based morphometry and diffusion tensor imaging study in an adult population.

Anti-basal ganglia antibodies (ABGAs) have been suggested to be a hallmark of autoimmunity in Gilles de la Tourette's syndrome (GTS), possibly related to prior exposure to streptococcal infection. In order to detect whether the presence of ABGAs was associated with subtle structural changes in GTS, whole-brain analysis using independent sets of T(1) and diffusion tensor imaging MRI-based methods were performed on 22 adults with GTS with (n = 9) and without (n = 13) detectable ABGAs in the serum. Voxel-based morphometry analysis failed to detect any significant difference in grey matter density between ABGA-positive and ABGA-negative groups in caudate nuclei, putamina, thalami and frontal lobes. These results suggest that ABGA synthesis is not related to structural changes in grey and white matter (detectable with these methods) within frontostriatal circuits.

Microautophagy of the nucleus coincides with a vacuolar diffusion barrier at nuclear-vacuolar junctions.

Nuclei bind yeast vacuoles via nucleus-vacuole (NV) junctions. Under nutrient restriction, NV junctions invaginate and release vesicles filled with nuclear material into vacuoles, resulting in piecemeal microautophagy of the nucleus (PMN). We show that the electrochemical gradient across the vacuolar membrane promotes invagination of NV junctions. Existing invaginations persist independently of the gradient, but final release of PMN vesicles requires again V-ATPase activity. We find that NV junctions form a diffusion barrier on the vacuolar membrane that excludes V-ATPase but is enriched in the VTC complex and accessible to other membrane-integral proteins. V-ATPase exclusion depends on the NV junction proteins Nvj1p,Vac8p, and the electrochemical gradient. It also depends on factors of lipid metabolism, such as the oxysterol binding protein Osh1p and the enoyl-CoA reductase Tsc13p, which are enriched in NV junctions, and on Lag1p and Fen1p. Our observations suggest that NV junctions form in two separable steps: Nvj1p and Vac8p suffice to establish contact between the two membranes. The electrochemical potential and lipid-modifying enzymes are needed to establish the vacuolar diffusion barrier, invaginate NV junctions, and form PMN vesicles.

Confirmation of functional zones within the human subthalamic nucleus: patterns of connectivity and sub-parcellation using diffusion weighted imaging.

The subthalamic nucleus (STN) is a small, glutamatergic nucleus situated in the diencephalon. A critical component of normal motor function, it has become a key target for deep brain stimulation in the treatment of Parkinson's disease. Animal studies have demonstrated the existence of three functional sub-zones but these have never been shown conclusively in humans. In this work, a data driven method with diffusion weighted imaging demonstrated that three distinct clusters exist within the human STN based on brain connectivity profiles. The STN was successfully sub-parcellated into these regions, demonstrating good correspondence with that described in the animal literature. The local connectivity of each sub-region supported the hypothesis of bilateral limbic, associative and motor regions occupying the anterior, mid and posterior portions of the nucleus respectively. This study is the first to achieve in-vivo, non-invasive anatomical parcellation of the human STN into three anatomical zones within normal diagnostic scan times, which has important future implications for deep brain stimulation surgery.

Acute Damage to the Posterior Limb of the Internal Capsule on Diffusion Tensor Tractography as an Early Imaging Predictor of Motor Outcome after Stroke

Background and Purpose Early prediction of motor outcome is of interest in stroke management. We aimed to determine whether lesion location at DTT is predictive of motor outcome after acute stroke and whether this information improves the predictive accuracy of the clinical scores. Methods We evaluated 60 consecutive patients within 12 hours of MCA stroke onset. We used DTT to evaluate CST involvement in the MC and PMC, CS, CR, and PLIC and in combinations of these regions at admission, at day 3, and at day 30. Severity of limb weakness was assessed using the m-NIHSS (5a, 5b, 6a, 6b). We calculated volumes of infarct and FA values in the CST of the pons. Results Acute damage to the PLIC was the best predictor associated with poor motor outcome, axonal damage, and clinical severity at admission (P&.001). There was no significant correlation between acute infarct volume and motor outcome at day 90 (P=.176, r=0.485). The sensitivity, specificity, and positive and negative predictive values of acute CST involvement at the level of the PLIC for 4 motor outcome at day 90 were 73.7%, 100%, 100%, and 89.1%, respectively. In the acute stage, DTT predicted motor outcome at day 90 better than the clinical scores (R2=75.50, F=80.09, P&.001). Conclusions In the acute setting, DTT is promising for stroke mapping to predict motor outcome. Acute CST damage at the level of the PLIC is a significant predictor of unfavorable motor outcome.