Uncertainty Relations for Positive Operator Valued Measures

How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this context we introduce an uncertainty operator which measures how much additional noise is introduced by carrying out a POVM rather than a von Neumann measurement. We illustrate this first approach by studying the variances of joint estimates of \sigma_x and \sigma_z for spin 1/2 particles. We show that for unbiased measurements the sum of these variances is lower bounded by 1. In our second approach we study the entropy of the POVM outcomes. In particular we try to establish lower bounds on the entropy of the POVM outcomes. We illustrate this second approach by examples.Comment: 5 pages, minor modifications and clarification

A model for alignment between microscopic rods and vorticity

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the product of the strain relaxation time $\tau_{\rm s}$ and the angular velocity $\omega$ about the vorticity axis. We find that when $\omega\tau_{\rm s}\gg 1$, the rods are predominantly either perpendicular or parallel to the vorticity

Curable polyphosphazene copolymers and terpolymers

Copolymers and terpolymers comprising randomly repeating units represented by the general formulae ##EQU1## wherein the R' radicals contain OH functionality and R being at least one member of the group of monovalent radicals selected from alkyl, substituted alkyl, aryl, substituted aryl and arylalkyl, and R' is represented by ##EQU2## wherein Q represents either --(CH.sub.2).sub. n or --C.sub.6 H.sub.4 X(CH.sub.2).sub. m, the --X(CH.sub.2).sub. m group being either meta or para and n is an integer from 1 to 6, m is an integer from 1 to 3, X is O or CH.sub.2, and R is H or a lower alkyl radical with up to four carbon atoms (methyl, ethyl, etc.). The ratio of R to R' is between 99.5 to 0.5 and 65 to 35

Historic Professions: Stabilizing the Reified Image of the Law and Other Historic Professions

Social institutions are commonly said to evolve. Yet there may be good reason why some institutions and some concepts are reified advantageously limiting any free-wheeling evolution over time. This is certainly true concepts like currency which stabilizes social ontology as much as concepts like rock stabilize natural kinds ontology. Important institutions such as the four historic professions moor civilization by being continually reified over generations aligning with sustainable public expectation. When a profession such as law is weaned from reified expectations of the public the effect is likely to be de-stabilizing of both the profession’s membership and the public the membership is meant to serve. The reified image of the bar, those entitled to the honor “esquire” following their name, assures society that a social ontology designates this group of professionals as leaders in forwarding society’s civilizing expectations. De-stabilizing this reification is not only self-destructive to the historic professions but to the societies they were intended to lead as well

Age Sensitivity of Behavioral Tests and Brain Substrates of Normal Aging in Mice

Knowledge of age sensitivity, the capacity of a behavioral test to reliably detect age-related changes, has utility in the design of experiments to elucidate processes of normal aging. We review the application of these tests in studies of normal aging and compare and contrast the age sensitivity of the Barnes maze, eyeblink classical conditioning, fear conditioning, Morris water maze, and rotorod. These tests have all been implemented to assess normal age-related changes in learning and memory in rodents, which generalize in many cases to age-related changes in learning and memory in all mammals, including humans. Behavioral assessments are a valuable means to measure functional outcomes of neuroscientific studies of aging. Highlighted in this review are the attributes and limitations of these measures in mice in the context of age sensitivity and processes of brain aging. Attributes of these tests include reliability and validity as assessments of learning and memory, well-defined neural substrates, and sensitivity to neural and pharmacological manipulations and disruptions. These tests engage the hippocampus and/or the cerebellum, two structures centrally involved in learning and memory that undergo functional and anatomical changes in normal aging. A test that is less well represented in studies of normal aging, the context pre-exposure facilitation effect (CPFE) in fear conditioning, is described as a method to increase sensitivity of contextual fear conditioning to changes in the hippocampus. Recommendations for increasing the age sensitivity of all measures of normal aging in mice are included, as well as a discussion of the potential of the under-studied CPFE to advance understanding of subtle hippocampus-mediated phenomena