Discrete Variational Derivative Methods for the EPDiff equation

The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational Derivative Method (DVDM) on a rectangular domain discretized with a regular, structured, orthogonal grid. We present numerical experiments to support our claims: we investigate the preservation of energy and linear momenta, the reversibility, and the empirical convergence of the schemes. The quality of our schemes is finally tested by simulating the interaction of singular wave fronts.Comment: 41 pages, 41 figure

The Medio-Ventral Muscles of the Abdomen in Macacus cyclopsis (M. rectus abdominis and M. pyramidalis)

There are very few reports concerning with anatomical study of M. rectus abdominis and M, pyramidalis on primates in large sample of one species. In this investigation, statistical study of M. rectus abdominis and M. pyramidalis were done on 50 Formosan monkey (Macacus cyclopsis) in order to accertain the standard type of origin, insertion and their relations to the nerves. In addition the finding were compared with the findings in other primates

Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind

AbstractIn this paper we propose new numerical methods for linear Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far

Mathematical analysis and numerical comparison of energy-conservative schemes for the Zakharov equations

Furihata and Matsuo proposed in 2010 an energy-conserving scheme for the Zakharov equations, as an application of the discrete variational derivative method (DVDM). This scheme is distinguished from conventional methods (in particular the one devised by Glassey in 1992) in that the invariants are consistent with respect to time, but it has not been sufficiently studied both theoretically and numerically. In this study, we theoretically prove the solvability under the loosest possible assumptions. We also prove the convergence of this DVDM scheme by improving the argument by Glassey. Furthermore, we perform intensive numerical experiments for comparing the above two schemes. It is found that the DVDM scheme is superior in terms of accuracy, but since it is fully-implicit, the linearly-implicit Glassey scheme is better for practical efficiency. In addition, we proposed a way to choose a solution for the first step that would allow Glassey's scheme to work more efficiently

A new unified framework for designing convex optimization methods with prescribed theoretical convergence estimates: A numerical analysis approach

We propose a new unified framework for describing and designing gradient-based convex optimization methods from a numerical analysis perspective. There the key is the new concept of weak discrete gradients (weak DGs), which is a generalization of DGs standard in numerical analysis. Via weak DG, we consider abstract optimization methods, and prove unified convergence rate estimates that hold independent of the choice of weak DGs except for some constants in the final estimate. With some choices of weak DGs, we can reproduce many popular existing methods, such as the steepest descent and Nesterov's accelerated gradient method, and also some recent variants from numerical analysis community. By considering new weak DGs, we can easily explore new theoretically-guaranteed optimization methods; we show some examples. We believe this work is the first attempt to fully integrate research branches in optimization and numerical analysis areas, so far independently developed

Effect of dietary fatty acid composition on Th1/Th2 polarization in lymphocytes.

BACKGROUND: It has become increasingly clear that polyunsaturated fatty acids (PUFAs) have immunomodulatory effects. However, the intake of these fatty acids used in animal studies often greatly exceeds dietary human intake. Whether differences in the composition of fatty acids that are consumed in amounts consistent with normal dietary intake can influence immune function remains uncertain. METHODS: We manufactured 3 types of liquid diet, related to modified fatty acid composition (omega-6/omega-3 = 0.25, 2.27 and 42.9), but excluding eicosapentaenoic acid and docosahexaenoic acid, based upon a liquid diet used clinically in humans. We assessed CD3-stimulated cytokine production of splenocytes in female BALB/c mice (n = 4 per group) fed 1 of 3 liquid diets for 4 weeks. We also measured the cytokine production of peripheral blood mononuclear cells stimulated with phorbol myristate acetate and ionomycin in humans at the end of a 4-week period of consumption of 2 different liquid diets (omega-6/omega-3 = 3 and 44). RESULTS: We found that the ratio of interfero omega-gamma (IFN-gamma) / interleukin-4 (IL-4) was significantly higher in mice fed the omega-3 rich diet than in others. In humans, IFN-gamma / IL-4 was significantly higher after the omega-3 versus the omega-6 enhanced diet. CONCLUSIONS: Differences in the composition of omega-3 and omega-6 PUFAs induces a shift in the Th1/Th2 balance in both mouse and human lymphocytes, even when ingested in normal dietary amounts. An omega-3 rich diet containing alpha-linolenic acid modulates immune function

Is the Importance of Achieving Stable Disease Different between Epidermal Growth Factor Receptor Tyrosine Kinase Inhibitors and Cytotoxic Agents in the Second-Line Setting for Advanced Non-small Cell Lung Cancer?

BackgroundIt is controversial whether achieving stable disease leads to a survival benefit and whether the importance of achieving stable disease differs between cytotoxic agents and molecular targeted agents. To examine these questions, the authors retrospectively reviewed phase II and III studies in the second-line setting for advanced non-small cell lung cancer using epidermal growth factor receptor (EGFR) tyrosine kinase inhibitors (TKIs) and cytotoxic agents separately.MethodsThe authors chose 45 trials for the chemotherapy group and nine for the EGFR TKI group by searching the PubMed database. All nine trials in the EGFR TKI group concern gefitinib and erlotinib.ResultsThe median survival time increased 0.0375 month with each 1% increase in stable disease rate (p = 0.039), and each 1% increase in response rate resulted in 0.0744 (p < 0.001) month of median survival time in the analysis combined with both cytotoxic agents and EGFR TKIs. Main and interaction terms for EGFR TKI treatment were not statistically significant. With respect to time to progression, only response rate showed a statistically significant relationship with survival.ConclusionsTo obtain response seems to be more important than to achieve stable disease for both cytotoxic agents and EGFR TKIs, although achieving stable disease is still valuable. The relationship between survival and response or stable disease appears similar for cytotoxic agents and EGFR TKIs

Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization

The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available from the author

A novel indole compound MA-35 attenuates renal fibrosis by inhibiting both TNF-α and TGF-β1 pathways

Renal fibrosis is closely related to chronic inflammation and is under the control of epigenetic regulations. Because the signaling of transforming growth factor-β1 (TGF-β1) and tumor necrosis factor-α (TNF-α) play key roles in progression of renal fibrosis, dual blockade of TGF-β1 and TNF-α is desired as its therapeutic approach. Here we screened small molecules showing anti-TNF-α activity in the compound library of indole derivatives. 11 out of 41 indole derivatives inhibited the TNF-α effect. Among them, Mitochonic Acid 35 (MA-35), 5-(3, 5-dimethoxybenzyloxy)-3-indoleacetic acid, showed the potent effect. The anti-TNF-α activity was mediated by inhibiting IκB kinase phosphorylation, which attenuated the LPS/GaIN-induced hepatic inflammation in the mice. Additionally, MA-35 concurrently showed an anti-TGF-β1 effect by inhibiting Smad3 phosphorylation, resulting in the downregulation of TGF-β1-induced fibrotic gene expression. In unilateral ureter obstructed mouse kidney, which is a renal fibrosis model, MA-35 attenuated renal inflammation and fibrosis with the downregulation of inflammatory cytokines and fibrotic gene expressions. Furthermore, MA-35 inhibited TGF-β1-induced H3K4me1 histone modification of the fibrotic gene promoter, leading to a decrease in the fibrotic gene expression. MA-35 affects multiple signaling pathways involved in the fibrosis and may recover epigenetic modification; therefore, it could possibly be a novel therapeutic drug for fibrosis