Comment on "A note on the construction of the Ermakov-Lewis invariant"

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new

Differences in the weighting and choice of evidence for plausible versus implausible causes.

Individuals have difficulty changing their causal beliefs in light of contradictory evidence. We hypothesized that this difficulty arises because people facing implausible causes give greater consideration to causal alternatives, which, because of their use of a positive test strategy, leads to differential weighting of contingency evidence. Across 4 experiments, participants learned about plausible or implausible causes of outcomes. Additionally, we assessed the effects of participants' ability to think of alternative causes of the outcomes. Participants either saw complete frequency information (Experiments 1 and 2) or chose what information to see (Experiments 3 and 4). Consistent with the positive test account, participants given implausible causes were more likely to inquire about the occurrence of the outcome in the absence of the cause (Experiments 3 and 4) than those given plausible causes. Furthermore, they gave less weight to Cells A and B in a 2 × 2 contingency table and gave either equal or less weight to Cells C and D (Experiments 1 and 2). These effects were inconsistently modified by participants' ability to consider alternative causes of the outcome. The total of the observed effects are not predicted by either dominant models of normative causal inference or by the particular positive test account proposed here, but they may be commensurate with a more broadly construed positive test account.This is the author accepted manuscript. The final version is available from the American Psychological Association via http://dx.doi.org/10.1037/a003554

Noether symmetries for two-dimensional charged particle motion

We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The associated electromagnetic field satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding three classes of electromagnetic fields compatible with Noether point symmetries. The corresponding Noether invariants are derived and interpreted

Novel tau filament fold in chronic traumatic encephalopathy encloses hydrophobic molecules

Chronic traumatic encephalopathy (CTE) is a neurodegenerative tauopathy that is associated with repetitive head impacts or exposure to blast waves. First described as punch-drunk syndrome and dementia pugilistica in retired boxers1-3, CTE has since been identified in former participants of other contact sports, ex-military personnel and after physical abuse4-7. No disease-modifying therapies currently exist, and diagnosis requires an autopsy. CTE is defined by an abundance of hyperphosphorylated tau protein in neurons, astrocytes and cell processes around blood vessels8,9. This, together with the accumulation of tau inclusions in cortical layers II and III, distinguishes CTE from Alzheimer's disease and other tauopathies10,11. However, the morphologies of tau filaments in CTE and the mechanisms by which brain trauma can lead to their formation are unknown. Here we determine the structures of tau filaments from the brains of three individuals with CTE at resolutions down to 2.3 Å, using cryo-electron microscopy. We show that filament structures are identical in the three cases but are distinct from those of Alzheimer's and Pick's diseases, and from those formed in vitro12-15. Similar to Alzheimer's disease12,14,16-18, all six brain tau isoforms assemble into filaments in CTE, and residues K274-R379 of three-repeat tau and S305-R379 of four-repeat tau form the ordered core of two identical C-shaped protofilaments. However, a different conformation of the β-helix region creates a hydrophobic cavity that is absent in tau filaments from the brains of patients with Alzheimer's disease. This cavity encloses an additional density that is not connected to tau, which suggests that the incorporation of cofactors may have a role in tau aggregation in CTE. Moreover, filaments in CTE have distinct protofilament interfaces to those of Alzheimer's disease. Our structures provide a unifying neuropathological criterion for CTE, and support the hypothesis that the formation and propagation of distinct conformers of assembled tau underlie different neurodegenerative diseases

Numerical simulation of a negative ion plasma expansion into vacuum

The expansion into vacuum of a one-dimensional, collisionless, negative ion plasma is investigated in the framework of the Vlasov–Poisson model. The basic equations are written in a ‘‘new time space’’ by use of a rescaling transformation and, subsequently, solved numerically through a fully Eulerian code. As in the case of a two species plasma, the time-asymptotic regime is found to be self-similar with the temperature decreasing as t22. The numerical results exhibit clearly the physically expected effects produced by the variation of parameters such as initial temperatures, mass ratios and charge of the negative ions

On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

Modified Zakharov equations for plasmas with a quantum correction

Quantum Zakharov equations are obtained to describe the nonlinear interaction between quantum Langmuir waves and quantum ion-acoustic waves. These quantum Zakharov equations are applied to two model cases, namely the four-wave interaction and the decay instability. In the case of the four-wave instability, sufficiently large quantum effects tend to suppress the instability. For the decay instability, the quantum Zakharov equations lead to results similar to those of the classical decay instability except for quantum correction terms in the dispersion relations. Some considerations regarding the nonlinear aspects of the quantum Zakharov equations are also offered.Comment: 4 figures. Accepted for publication in Physics of Plasmas (2004

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries