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

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

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.

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

Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B

Resolution of Nearly Mass Degenerate Higgs Bosons and Production of Black Hole Systems of Known Mass at a Muon Collider

The direct s-channel coupling to Higgs bosons is 40000 times greater for muons than electrons; the coupling goes as mass squared. High precision scanning of the lighter $h^0$ and the higher mass $H^0$ and $A^0$ is thus possible with a muon collider. The $H^0$ and $A^0$ are expected to be nearly mass degenerate and to be CP even and odd, respectively. A muon collider could resolve the mass degeneracy and make CP measurements. The origin of CP violation in the $K^{0}$ and $B^{0}$ meson systems might lie in the the $H^0/A^0$ Higgs bosons. If large extra dimensions exist, black holes with lifetimes of $\sim 10^{-26}$ seconds could be created and observed via Hawking radiation at the LHC. Unlike proton or electron colliders, muon colliders can produce black hole systems of known mass. This opens the possibilities of measuring quantum remnants, gravitons as missing energy, and scanning production turn on. Proton colliders are hampered by parton distributions and CLIC by beamstrahlung. The ILC lacks the energy reach.Comment: Latex, 5 pages, 2 figures, proceedings to the DPF 2004: Annual Meeting of the Division of Particles and Fields of APS, 26 August-31 August 2004, Riverside, CA, US

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