Group Cohomology, Modular Theory and Space-time Symmetries

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for the existence of a covariant action of the (universal covering of) the Poincar\'e group. In particular this gives, together with our previous results, an intrinsic characterization of positive-energy conformal pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore theory of central extensions of locally compact groups by polish groups, selecting and making an analysis of a wider class of extensions with natural measurable properties and showing henceforth that the universal covering of the Poincar\'e group has only trivial central extensions (vanishing of the first and second order cohomology) within our class.Comment: 18 pages, plain TeX, preprint Roma Tor vergata n. 20 dec. 9

The Impact of Alternative Grade Configurations on Student Outcomes through Middle and High School

We use statewide administrative data from Florida to estimate the impact of attending public schools with different grade configurations on student achievement through grade 10. Based on an instrumental variable estimation strategy, we find that students moving from elementary to middle school suffer a sharp drop in student achievement in the transition year. These achievement drops persist through grade 10. We also find that middle school entry increases student absences and is associated with higher grade 10 dropout rates. Transitions to high school in grade nine cause a smaller one-time drop in achievement but do not alter students' performance trajectories.educational production, public schools, grade configuration, middle schools, high schools

The Impact of Alternative Grade Configurations on Student Outcomes through Middle and High School

We use statewide administrative data from Florida to estimate the impact of attending public schools with different grade configurations on student achievement through grade 10. To identify the causal effect of structural school transitions, we use student fixed effects and instrument for middle and high school attendance based on the terminal grade of the school attended in grades 3 and 6, respectively. Consistent with recent evidence from other settings, we find that students moving from elementary to middle school in grade 6 or 7 suffer a sharp drop in student achievement in the transition year. We confirm that these achievement drops occur in nonurban areas and persist through grade 10, by which time most students have transitioned into high school. We also find that middle school entry increases student absences and is associated with higher grade 10 dropout rates. Transitions to high school in grade nine cause a smaller one-time drop in achievement but do not alter students’ performance trajectories.educational production, public schools, grade configuration, middle schools, high schools

Modular localization and Wigner particles

We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare' group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh-Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and de Sitter spacetime.Comment: 22 pages, LaTeX. Some errors have been corrected. To appear on Rev. Math. Phy

Ratcheted molecular-dynamics simulations identify efficiently the transition state of protein folding

The atomistic characterization of the transition state is a fundamental step to improve the understanding of the folding mechanism and the function of proteins. From a computational point of view, the identification of the conformations that build out the transition state is particularly cumbersome, mainly because of the large computational cost of generating a statistically-sound set of folding trajectories. Here we show that a biasing algorithm, based on the physics of the ratchet-and-pawl, can be used to identify efficiently the transition state. The basic idea is that the algorithmic ratchet exerts a force on the protein when it is climbing the free-energy barrier, while it is inactive when it is descending. The transition state can be identified as the point of the trajectory where the ratchet changes regime. Besides discussing this strategy in general terms, we test it within a protein model whose transition state can be studied independently by plain molecular dynamics simulations. Finally, we show its power in explicit-solvent simulations, obtaining and characterizing a set of transition--state conformations for ACBP and CI2

On a conjecture regarding Fisher information

Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product of them has been conjectured to exhibit a non trivial lower bound in [Phys. Rev. A (2000) 62 012107]. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schr\"odinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schr\"odinger equation. We also give a new conjecture regarding any normalizable time-dependent solution of this equation.Comment: 4 pages; revised equations, results unchange