A Brief Rejoinder to Professor Mullock

Mullock on Summers on Hart is bad enough, but Summers on Mullock on Summers on Hart is worse. Fortunately or unfortunately, there is no rule (primary or secondary) entitling either of us to vouch Professor Hart into the proceedings. With all due respect to Professor Mullock (and to me, of course), I fear the two of us may be compounding erroneous interpretations of Professor Hart’s work. Sans Hart, I shall exercise admirable restraint and argue over the meaning of the scripture. Regrettably, Professor Mullock and I are both defenders of the faith; I had hoped to draw the fire of a non-Christian

On Deriving Space-Time From Quantum Observables and States

We prove that, under suitable assumptions, operationally motivated data completely determine a space-time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined. To minimize technical complications, this is done in the example of three-dimensional Minkowski space.Comment: 19 pages, to appear in Communications in Mathematical Physics; minor corrections mad

Comparative Energy Dependence of Proton and Pion Degradation in Diamond

A comparative theoretical study of the damages produced by protons and pions, in the energy range 50 MeV - 50 GeV, in diamond, is presented. The concentration of primary defects (CPD) induced by hadron irradiation is used to describe material degradation. The CPD has very different behaviours for protons and pions: the proton degradation is important at low energies and is higher than the pion one in the whole energy range investigated, with the exception of the Delta33 resonance region, where a large maximum of the degradation exists for pions. In comparison with silicon, the most investigated and the most studied material for detectors, diamond theoretically proves to be one order of magnitude more resistant, both to proton and pion irradiation.Comment: 7 pages, 5 figure

Remarks on Causality in Relativistic Quantum Field Theory

It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras \cA(V_1),\cA(V_2) associated with spacelike separated spacetime regions $V_1,V_2$ have a (Reichenbachian) common cause located in the union of the backward light cones of $V_1$ and $V_2$. Further comments on causality and independence in quantum field theory are made.Comment: 10 pages, Latex, Quantum Structures 2002 Conference Proceedings submission. Minor revision of the order of definitions on p.

Performance guarantees for greedy maximization of non-submodular controllability metrics

A key problem in emerging complex cyber-physical networks is the design of information and control topologies, including sensor and actuator selection and communication network design. These problems can be posed as combinatorial set function optimization problems to maximize a dynamic performance metric for the network. Some systems and control metrics feature a property called submodularity, which allows simple greedy algorithms to obtain provably near-optimal topology designs. However, many important metrics lack submodularity and therefore lack provable guarantees for using a greedy optimization approach. Here we show that performance guarantees can be obtained for greedy maximization of certain non-submodular functions of the controllability and observability Gramians. Our results are based on two key quantities: the submodularity ratio, which quantifies how far a set function is from being submodular, and the curvature, which quantifies how far a set function is from being supermodular

GALAXY DYNAMICS IN CLUSTERS

We use high resolution simulations to study the formation and distribution of galaxies within a cluster which forms hierarchically. We follow both dark matter and baryonic gas which is subject to thermal pressure, shocks and radiative cooling. Galaxy formation is identified with the dissipative collapse of the gas into cold, compact knots. We examine two extreme representations of galaxies during subsequent cluster evolution --- one purely gaseous and the other purely stellar. The results are quite sensitive to this choice. Gas-galaxies merge efficiently with a dominant central object while star-galaxies merge less frequently. Thus, simulations in which galaxies remain gaseous appear to suffer an ``overmerging'' problem, but this problem is much less severe if the gas is allowed to turn into stars. We compare the kinematics of the galaxy population in these two representations to that of dark halos and of the underlying dark matter distribution. Galaxies in the stellar representation are positively biased (\ie over-represented in the cluster) both by number and by mass fraction. Both representations predict the galaxies to be more centrally concentrated than the dark matter, whereas the dark halo population is more extended. A modest velocity bias also exists in both representations, with the largest effect, $\sigma_{gal}/\sigma_{DM} \simeq 0.7$, found for the more massive star-galaxies. Phase diagrams show that the galaxy population has a substantial net inflow in the gas representation, while in the stellar case it is roughly in hydrostatic equilibrium. Virial mass estimators can underestimate the true cluster mass by up to a factor of 5. The discrepancy is largest if only the most massive galaxies are used, reflecting significant mass segregation.Comment: 30 pages, self-unpacking (via uufiles) postscript file without figures. Eighteen figures (and slick color version of figure 3) and entire paper available at ftp://oahu.physics.lsa.umich.edu/groups/astro/fews Total size of paper with figures is ~9.0 Mb uncompressed. Submitted to Ap.J