Modal dynamics for positive operator measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how {\em deterministic} dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e. the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state $\ket{n}$. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.Comment: 14 page

Lusztig Induction, Unipotent Supports, and Character Bounds

Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in a $(\mathbf{G},F)$-split Levi subgroup $\mathbf{M}$ of $\mathbf{G}$ and that $\mathbf{G}$ is defined over a field of good characteristic. In this paper, assuming a weak version of Lusztig's conjecture relating irreducible characters and characteristic functions of character sheaves holds, we considerably generalize this result by removing the condition that $\mathbf{M}$ is split. This assumption is known to hold whenever $Z(\mathbf{G})$ is connected or when $\mathbf{G}$ is a special linear or symplectic group and $\mathbf{G}$ is defined over a sufficiently large finite field.Comment: 35 pages; v2. minor improvements to abstract and introduction; v3. further improvements to the exposition; v4. significant changes. Main result now works for special linear and symplectic groups. Added results on groups of type A generalising results of Hildebrand; v5. post referee repor

Non-Measles Hemadsorption in a Cell Line Persistently Infected with Measles Virus (BGM/MV)

Adsorption of Rhesus monkey erythrocytes to the plasma membranes of measles virus infected cells is frequently carried out to detect the presence of plasma membrane-associated measles virus hemagglutinin. The hemagglutinin is a viral genome-coded structural glycoprotein of the measles virion that is associated with the plasma membrane of the host cell during measles virus replication. BGM/MV, anon-virogenic line of African green monkey kidney cells persistently-infected with measles virus, adsorbed Rhesus monkey erythrocytes in an inverse fashion relative to the number of cells present in the culture and the time post-seeding. Serological studies employing the hemadsorption-inhibition and membrane immunofluorescence assay procedures, suggested that this phenomenon was not mediated by the viral hemagglutinin. Assays for Simian virus-5 and mycoplasma, contaminating agents that induce erythrocyte adsorption, were negative. Incubation of BGM/MV cells at 33°C or with graded concentrations of fetal calf serum, to stimulate the metabolism of resting (Go) cells, suggested that adsorption was related to a phase(s) of the cell growth cycle other than Go₁, for adsorption was prolonged and stimulated in a dose-response fashion, respectively. Comparative adsorption studies employing the parent cell line (BGM), not infected with measles virus, were performed using various species of erythrocytes. While both cell lines adsorbed Rhesus monkey erythrocytes in an inverse fashion relative to cell density, differences were noted in the adsorption of some of the other species of erythrocytes. These data suggest that Rhesus monkey erythrocyte adsorption to BGM/MV cells was mediated by a receptor(s) of cellular origin

Invariance of generalized wordlength patterns

The generalized wordlength pattern (GWLP) introduced by Xu and Wu (2001) for an arbitrary fractional factorial design allows one to extend the use of the minimum aberration criterion to such designs. Ai and Zhang (2004) defined the $J$-characteristics of a design and showed that they uniquely determine the design. While both the GWLP and the $J$-characteristics require indexing the levels of each factor by a cyclic group, we see that the definitions carry over with appropriate changes if instead one uses an arbitrary abelian group. This means that the original definitions rest on an arbitrary choice of group structure. We show that the GWLP of a design is independent of this choice, but that the $J$-characteristics are not. We briefly discuss some implications of these results.Comment: To appear in: Journal of Statistical Planning and Inferenc

The Effect of Milwaukee’s Parental Choice Program on Student Achievement in Milwaukee Public Schools

This paper examines evidence on the “systemic effects” of expanding school choice in Milwaukee, Wisconsin. Milwaukee is home to one of the nation’s largest and longest-running school choice programs. If there are systemic effects from expanding school choice we should be able to see them in Milwaukee. This paper also introduces a novel method for analyzing systemic effects. Taking full advantage of student-level data, we develop a new measure of those effects based on the extent of voucher options that each student has each year. The idea behind this measure is that school systems face greater competitive pressure to serve students well when students have more options to leave. This type of measure might be useful for future analyses of systemic effects. Using this new approach, we find that students fare better academically when they have more options from Milwaukee’s voucher program. The effects are modest in magnitude, but they are robust to multiple specifications of the model

On the Employment Effect of Technology: Evidence from US Manufacturing for 1958-1996

Recently, Gali and others find that technological progress may be contractionary: a favorable technology shock reduces hours worked in the short run. We ask whether this observation is robust in disaggregate data. According to our VAR analysis of 458 four-digit U.S. manufacturing industries for 1958-1996, some industries do exhibit temporary reduction in hours in response to a permanent increase in TFP. However, there are far more industries in which technological progress significantly increases hours. Using micro data on average price duration, we ask whether the difference across industries is related to the stickiness of industry-output prices. Among 87 manufacturing goods, we do not find such a relation.Technology Shocks, Hours Fluctuations, Sticky Prices

On the Employment Effect of Technology: Evidence from US Manufacturing for 1958-1996

Recently, Galí and others find that technological progress may be contractionary: a favorable technology shock reduces hours worked in the short run. We ask whether this observation is robust in disaggregate data. According to our VAR analysis of 458 four-digit U.S. manufacturing industries for 1958-1996, some industries do exhibit temporary reduction in hours in response to a permanent increase in TFP. However, there are far more industries in which technological progress significantly increases hours. Using micro data on average price duration, we ask whether the difference across industries is related to the stickiness of industry-output prices. Among 87 manufacturing goods, we do not find such a relation.Technology Shocks, Hours Fluctuations, Sticky Prices