Stereological analysis of hippocampus in rat treated with chemotherapeutic agent oxaliplatin

Background: Oxaliplatin (OX) has been widely used for treatment of colorectal and other cancers. Adverse effect of OX and other anticancer agents on cognition have been reported, but studies on the effects of chemotherapy on brain structure are scarce. This study describes the morphometrical features of the hippocampus structures in rat following OX treatment using design-based stereological methods. Materials and methods: Ten male Wistar rats were randomised into two groups. The rats from OX group received 2.4 mg/kg OX in vehicle for 5 consecutive days every week for 2 weeks intraperitoneally. Controls received vehicle only. Cavalieri’s method and the optical fractionator method were used for volume and neuron estimation, respectively. Results: Cavalieri’s method was used to estimate volume and showed that the volume of the hippocampus was significantly decreased in OX group (31.84 ± ± 1.24 mm3) compared with the vehicle control group (36.95 ± 3.48 mm3). The optical fractionator method was used to estimate neuron number and showed that the number of neurons in dentate gyrus, cornu ammonis 1 and 3 in OX group (8.147 ± 2.84 × 105, 4.257 ± 0.59 × 105 and 2.133 ± 0.22 × 105, respectively) did not differ from those of vehicle control group (7.36 ± 1.42 × 105, 3.521 ± ± 0.54 × 105 and 1.989 ± 0.46 × 105, respectively). Conclusions: These findings suggested that OX treatment induces loss of hippocampal volume without neuronal loss which might help to clarify the mechanism by which OX affects cognition and to improve preventive treatment strategies

Photon position measure

The positive operator valued measure (POVM) for a photon counting array detector is derived and found to equal photon flux density integrated over pixel area and measurement time. Since photon flux density equals number density multiplied by the speed of light, this justifies theoretically the observation that a photon counting array provides a coarse grained measurement of photon position. The POVM obtained here can be written as a set of projectors onto a basis of localized states, consistent with the description of photon position in a recent quantum imaging proposal [M. Tsang, Phys. Rev. Lett. \textbf{102}, 253601 (2009)]. The wave function that describes a photon counting experiment is the projection of the photon state vector onto this localized basis. Collapse is to the electromagnetic vacuum and not to a localized state, thus violating the text book rules of quantum mechanics but compatible with the theory of generalized observables and the nonlocalizability of an incoming photon

Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is $\frak{so}(3,1)$ and the SGA is $\frak{so}(4,2)$. We start with a representation of $\frak{so}(4,2)$ by functions on a realization of the Lobachevski space given by a two sheeted hyperboloid, where the Lie algebra commutators are the usual Poisson-Dirac brackets. Then, introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and "naive" ladder operators are identified. The previously defined "naive" ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non self-adjoint function of a linear combination of the ladder operators which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of two sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.Comment: 23 page

The various power decays of the survival probability at long times for free quantum particle

The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator at long times, in terms of the integral operators. This enables us to obtain the asymptotic formula for the survival probability of the initial state $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

Lorentz invariant photon number density

A Lorentz invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization sensitive position eigenvector and the photon wave function. It is found that this scalar product is independent of the form chosen for the wave function and that the normalized positive frequency vector potential-electric field pair is a convenient choice of wave function in the presence of matter. The number amplitude describing a localized state is a delta-function at the instant at which localization and detection are seen as simultaneous.Comment: As published in Phys. Rev. A 78, 012111 (2008). Two sentences following Eq. (19) delete

Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.Comment: 40 page

INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION

It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at [email protected] (internet)

Secondary literacy across the curriculum: Challenges and possibilities

This paper discusses the challenges and possibilities attendant upon successfully implementing literacy across the curriculum initiatives – or ‘school language policies’ as they have come to be known - particularly at the secondary or high school level. It provides a theoretical background to these issues, exploring previous academic discussions of school language policies, and highlights key areas of concern as well as opportunity with respect to school implementation of such policies. As such, it provides a necessary conceptual background to the subsequent papers in this special issue, which focus upon the Secondary Schools’ Literacy Initiative (SSLI) – a New Zealand funded programme that aims to establish cross-curricular language and literacy policies in secondary schools

The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I

We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann-Schwinger equation--and therefore for scattering theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur

The Role of Additive Neurogenesis and Synaptic Plasticity in a Hippocampal Memory Model with Grid-Cell Like Input

Recently, we presented a study of adult neurogenesis in a simplified hippocampal memory model. The network was required to encode and decode memory patterns despite changing input statistics. We showed that additive neurogenesis was a more effective adaptation strategy compared to neuronal turnover and conventional synaptic plasticity as it allowed the network to respond to changes in the input statistics while preserving representations of earlier environments. Here we extend our model to include realistic, spatially driven input firing patterns in the form of grid cells in the entorhinal cortex. We compare network performance across a sequence of spatial environments using three distinct adaptation strategies: conventional synaptic plasticity, where the network is of fixed size but the connectivity is plastic; neuronal turnover, where the network is of fixed size but units in the network may die and be replaced; and additive neurogenesis, where the network starts out with fewer initial units but grows over time. We confirm that additive neurogenesis is a superior adaptation strategy when using realistic, spatially structured input patterns. We then show that a more biologically plausible neurogenesis rule that incorporates cell death and enhanced plasticity of new granule cells has an overall performance significantly better than any one of the three individual strategies operating alone. This adaptation rule can be tailored to maximise performance of the network when operating as either a short- or long-term memory store. We also examine the time course of adult neurogenesis over the lifetime of an animal raised under different hypothetical rearing conditions. These growth profiles have several distinct features that form a theoretical prediction that could be tested experimentally. Finally, we show that place cells can emerge and refine in a realistic manner in our model as a direct result of the sparsification performed by the dentate gyrus layer