Aggregating Litigation

A comment on Judith Resnik\u27s article on the aggregation of civil cases is presented. The goals of aggregating litigation and the very circumstances in which aggregation works best in achieving those goals are discussed. The aggregation of personal injury cases is also discussed

Berkeley’s Arguments on Realism and Idealism

We analyse Berkeley's argument that realism cannot be defined, and show that his epistemological assumptions lead to the inevitable conclusion that solipsism is the only definable metaphysics. We conclude with a discussion of what this means for the realism/idealism debate, and also with a discussion of the possibility for apodictic evidence in this matter

Divisibility, Logic, Radical Empiricism, and Metaphysics

We will explore the problem of the manner in which the world may be divided into parts, and how this affects the application of logic. We will also consider how this affects the problem of knowing the world. Such considerations bring us to discuss how the divisibility of the world relates to idealism, realism, and the radical empiricist program of James. The epistemological difficulties sometimes associated with realism will in particular be shown to be in principle the result of misunderstanding the nature of the divisibility of the world. When such divisibility is properly understood, we claim that there is no epistemological dilemma, at least in principle, although of course in practice there may be other difficulties. We conclude by tentatively analyzing these practical difficulties

Differential inflammatory response to Helicobacter pylori infection: etiology and clinical outcomes

The bacterial pathogen Helicobacter pylori commonly colonizes the human gastric mucosa during early childhood and persists throughout life. The organism has evolved multiple mechanisms for evading clearance by the immune system and, despite inducing inflammation in the stomach, the majority of infections are asymptomatic. H. pylori is the leading cause of peptic ulcer disease and gastric cancer. However, disease outcomes are related to the pattern and severity of chronic inflammation in the gastric mucosa, which in turn is influenced by both bacterial and host factors. Despite over 2 decades of intensive research, there remains an incomplete understanding of the circumstances leading to disease development, due to the fascinating complexity of the host-pathogen interactions. There is accumulating data concerning the virulence factors associated with increased risk of disease, and the majority of these have pro-inflammatory activities. Despite this, only a small proportion of those infected with virulent strains develop disease. Several H. pylori virulence factors have multiple effects on different cell types, including the induction of pro- and anti-inflammatory, immune stimulatory, and immune modulatory responses. The expression of multiple virulence factors is also often linked, making it difficult to assess the meaning of their effects in isolation. Overall, H. pylori is thought to usually modulate inflammation and limit acute damage to the mucosa, enabling the bacteria to persist. If this delicate balance is disturbed, disease may then develop

A Higher-Order Energy Expansion to Two-Dimensional Singularly Neumann Problems

Of concern is the following singularly perturbed semilinear elliptic problem \begin{equation*} \left\{ \begin{array}{c} \mbox{${\epsilon}^2\Delta u -u+u^p =0$ in $\Omega$}\\ \mbox{$u>0$ in $\Omega$ and $\frac{\partial u}{\partial \nu}=0$ on $\partial \Omega$}, \end{array} \right. \end{equation*} where $\Omega$ is a bounded domain in ${\mathbf{R}}^N$ with smooth boundary $\partial \Omega$, $\epsilon>0$ is a small constant and $1< p<\left(\frac{N+2}{N-2}\right)_+$. Associated with the above problem is the energy functional $J_{\epsilon}$ defined by \begin{equation*} J_{\epsilon}[u]:=\int_{\Omega}\left(\frac{\epsilon^2}{2}{|\nabla u|}^2 +\frac{1}{2}u^2 -F(u)\right)dx \end{equation*} for $u\in H^1(\Omega)$, where $F(u)=\int_{0}^{u}s^p ds$. Ni and Takagi (\cite{nt1}, \cite{nt2}) proved that for a single boundary spike solution $u_{\epsilon}$, the following asymptotic expansion holds: \begin{equation*} (1) \ \ \ \ \ \ \ \ J_{\epsilon}[u_{\epsilon}]=\epsilon^{N} \left[\frac{1}{2}I[w]-c_1 \epsilon H(P_{\epsilon})+o(\epsilon)\right], \end{equation*} where $I[w]$ is the energy of the ground state, $c_1 >0$ is a generic constant, $P_{\epsilon}$ is the unique local maximum point of $u_{\epsilon}$ and $H(P_{\epsilon})$ is the boundary mean curvature function at $P_{\epsilon}\in \partial \Omega$. Later, Wei and Winter (\cite{ww3}, \cite{ww4}) improved the result and obtained a higher-order expansion of $J_{\epsilon}[u_{\epsilon}]$: \begin{equation*} (2) \ \ \ \ \ \ J_{\epsilon}[u_{\epsilon}]=\epsilon^{N} \left[\frac{1}{2}I[\omega]-c_{1} \epsilon H(P_{\epsilon})+\epsilon^2 [c_2(H(P_\epsilon))^2 +c_{3} R(P_\epsilon)]+o(\epsilon^2)\right], \end{equation*} where $c_2$ and $c_3>0$ are generic constants and $R(P_\epsilon)$ is the scalar curvature at $P_\epsilon$. However, if $N=2$, the scalar curvature is always zero. The expansion (2) is no longer sufficient to distinguish spike locations with same mean curvature. In this paper, we consider this case and assume that $2 \leq p <+\infty$. Without loss of generality, we may assume that the boundary near P\in\partial\Om is represented by the graph $\{ x_2 = \rho_{P} (x_1) \}$. Then we have the following higher order expansion of $J_\epsilon[u_\epsilon]:$ \begin{equation*} (3) \ \ \ \ \ J_\epsilon [u_\epsilon] =\epsilon^N \left[\frac{1}{2}I[w]-c_1 \epsilon H({P_\epsilon})+c_2 \epsilon^2(H({P_\epsilon}))^2 ] +\epsilon^3 [P(H({P_\epsilon}))+c_3S({P_\epsilon})]+o(\epsilon^3)\right], \end{equation*} where H(P_\ep)= \rho_{P_\ep}^{''} (0) is the curvature, $P(t)=A_1 t+A_2 t^2+A_3 t^3$ is a polynomial, $c_1$, $c_2$, $c_3$ and $A_1$, $A_2$,$A_3$ are generic real constants and S(P_\epsilon)= \rho_{P_\ep}^{(4)} (0). In particular $c_3<0$. Some applications of this expansion are given

Minimal Neutrino Beta Beam for Large theta_13

We discuss the minimum requirements for a neutrino beta beam if theta_13 is discovered by an upcoming reactor experiment, such as Double Chooz or Daya Bay. We require that both neutrino mass hierarchy and leptonic CP violation can be measured to competitive precisions with a single-baseline experiment in the entire remaining theta_13 range. We find that for very high isotope production rates, such as they might be possible using a production ring, a (B,Li) beta beam with a gamma as low as 60 could already be sufficient to perform all of these measurements. If only the often used nominal source luminosities can be achieved, for example, a (Ne,He) beta beam from Fermilab to a possibly existing water Cherenkov detector at Homestake with gamma \sim 190-350 (depending on the Double Chooz best-fit) could outperform practically any other beam technology including wide-band beam and neutrino factory.Comment: 11 pages, 2 figures, 1 tabl