Meaning, moral realism, and the importance of morality

Many philosophers have suspected that the normative importance of morality depends on moral realism. In this paper, I defend a version of this suspicion: I argue that if teleological forms of moral realism, those that posit an objective purpose to human life, are true, then we gain a distinctive kind of reason to do what is morally required. I argue for this by showing that if these forms of realism are true, then doing what is morally required can provide a life with meaning, which is a widespread human need. I also argue that rival meta-ethical views, like anti-realism or non-naturalist realism, cannot make morality meaning-conferring in this way

On martingale approximations

Consider additive functionals of a Markov chain $W_k$, with stationary (marginal) distribution and transition function denoted by $\pi$ and $Q$, say $S_n=g(W_1)+...+g(W_n)$, where $g$ is square integrable and has mean 0 with respect to $\pi$. If $S_n$ has the form $S_n=M_n+R_n$, where $M_n$ is a square integrable martingale with stationary increments and $E(R_n^2)=o(n)$, then $g$ is said to admit a martingale approximation. Necessary and sufficient conditions for such an approximation are developed. Two obvious necessary conditions are $E[E(S_n|W_1)^2]=o(n)$ and $\lim_{n\to \infty}E(S_n^2)/n<\infty$. Assuming the first of these, let $\Vert g\Vert^2_+=\limsup_{n\to \infty}E(S_n^2)/n$; then $\Vert\cdot\Vert_+$ defines a pseudo norm on the subspace of $L^2(\pi)$ where it is finite. In one main result, a simple necessary and sufficient condition for a martingale approximation is developed in terms of $\Vert\cdot\Vert_+$. Let $Q^*$ denote the adjoint operator to $Q$, regarded as a linear operator from $L^2(\pi)$ into itself, and consider co-isometries ($QQ^*=I$), an important special case that includes shift processes. In another main result a convenient orthonormal basis for $L_0^2(\pi)$ is identified along with a simple necessary and sufficient condition for the existence of a martingale approximation in terms of the coefficients of the expansion of $g$ with respect to this basis.Comment: Published in at http://dx.doi.org/10.1214/07-AAP505 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Law of the iterated logarithm for stationary processes

There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes $...,X_{-1},X_0,X_1,...$ whose partial sums $S_n=X_1+...+X_n$ are of the form $S_n=M_n+R_n$, where $M_n$ is a square integrable martingale with stationary increments and $R_n$ is a remainder term for which $E(R_n^2)=o(n)$. Here we explore the law of the iterated logarithm (LIL) for the same class of processes. Letting $\Vert\cdot\Vert$ denote the norm in $L^2(P)$, a sufficient condition for the partial sums of a stationary process to have the form $S_n=M_n+R_n$ is that $n^{-3/2}\Vert E(S_n|X_0,X_{-1},...)\Vert$ be summable. A sufficient condition for the LIL is only slightly stronger, requiring $n^{-3/2}\log^{3/2}(n)\Vert E(S_n|X_0,X_{-1},...)\Vert$ to be summable. As a by-product of our main result, we obtain an improved statement of the conditional central limit theorem. Invariance principles are obtained as well.Comment: Published in at http://dx.doi.org/10.1214/009117907000000079 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

MAVS expressed by hematopoietic cells is critical for control of West Nile virus infection and pathogenesis

West Nile virus (WNV) is the most important cause of epidemic encephalitis in North America. Innate immune responses, which are critical for control of WNV infection, are initiated by signaling through pathogen recognition receptors, RIG-I and MDA5, and their downstream adaptor molecule, MAVS. Here, we show that a deficiency of MAVS in hematopoietic cells resulted in increased mortality and delayed WNV clearance from the brain. In Mavs(−/−) mice, a dysregulated immune response was detected, characterized by a massive influx of macrophages and virus-specific T cells into the infected brain. These T cells were polyfunctional and lysed peptide-pulsed target cells in vitro. However, virus-specific T cells in the brains of infected Mavs(−/−) mice exhibited lower functional avidity than those in wild-type animals, and even virus-specific memory T cells generated by prior immunization could not protect Mavs(−/−) mice from WNV-induced lethal disease. Concomitant with ineffective virus clearance, macrophage numbers were increased in the Mavs(−/−) brain, and both macrophages and microglia exhibited an activated phenotype. Microarray analyses of leukocytes in the infected Mavs(−/−) brain showed a preferential expression of genes associated with activation and inflammation. Together, these results demonstrate a critical role for MAVS in hematopoietic cells in augmenting the kinetics of WNV clearance and thereby preventing a dysregulated and pathogenic immune response. IMPORTANCE West Nile virus (WNV) is the most important cause of mosquito-transmitted encephalitis in the United States. The innate immune response is known to be critical for protection in infected mice. Here, we show that expression of MAVS, a key adaptor molecule in the RIG-I-like receptor RNA-sensing pathway, in hematopoietic cells is critical for protection from lethal WNV infection. In the absence of MAVS, there is a massive infiltration of myeloid cells and virus-specific T cells into the brain and overexuberant production of proinflammatory cytokines. These results demonstrate the important role that MAVS expression in hematopoietic cells has in regulating the inflammatory response in the WNV-infected brain

Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems

In the post-Newtonian (PN) regime, the timescale on which the spins of binary black holes precess is much shorter than the radiation-reaction timescale on which the black holes inspiral to smaller separations. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period $\tau$, during which the orbital angular momentum precesses about the total angular momentum by an angle $\alpha$. This defines two distinct frequencies that vary on the radiation-reaction timescale: the nutation frequency $\omega \equiv 2\pi/\tau$ and the precession frequency $\Omega \equiv \alpha/\tau$. We use analytic solutions for generic spin precession at 2PN order to derive Fourier series for the total and orbital angular momenta in which each term is a sinusoid with frequency $\Omega - n\omega$ for integer $n$. As black holes inspiral, they can pass through nutational resonances ($\Omega = n\omega$) at which the total angular momentum tilts. We derive an approximate expression for this tilt angle and show that it is usually less than $10^{-3}$ radians for nutational resonances at binary separations $r > 10M$. The large tilts occurring during transitional precession (near zero total angular momentum) are a consequence of such states being approximate $n=0$ nutational resonances. Our new Fourier series for the total and orbital angular momenta converge rapidly with $n$ providing an intuitive and computationally efficient approach to understanding generic precession that may facilitate future calculations of gravitational waveforms in the PN regime.Comment: 18 pages, 9 figures, version published in PR