Position and momentum tomography

We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related, models; the sequential measurement model, the Arthurs-Kelly model and the eight-port homodyne detection model. In each case, the method of moments gives the position and momentum distribution for a large class of initial states, the relevant condition being the exponential boundedness of the distributions.Comment: 15 pages, 1 figur

Einstein energy associated with the Friedmann -Robertson -Walker metric

Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general formula for the total matter plus gravitational field energy ($P_0$) of an arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C., {\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962)); Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in quasi-Cartesian coordinates, this formula leads to the well known result $P_0 = \int \sqrt{-g} (T_0^0 - T_1^1 -T_2^2 -T_3^3) ~d^3 x$, where $g$ is the determinant of the metric tensor and $T^a_b$ is the energy momentum tensor of the {\em matter}. Though in the literature, this is known as "Tolman Mass", it must be realized that this is essentially "Einstein Mass" because the underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz obtained the same expression for the "inertial mass" of a static isolated system without using any pseudo-tensor at all and which points to physical significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz, E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed., 1962)! For the first time we apply this general formula to find an expression for $P_0$ for the Friedmann- Robertson -Walker (FRW) metric by using the same quasi-Cartesian basis. As we analyze this new result, physically, a spatially flat model having no cosmological constant is suggested. Eventually, it is seen that conservation of $P_0$ is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the journal version is uploade

IL-7 and IL-15 independently program the differentiation of intestinal CD3−NKp46+ cell subsets from Id2-dependent precursors

The natural cytotoxicity receptor NKp46 (encoded by Ncr1) was recently shown to identify a subset of noncytotoxic, Rag-independent gut lymphocytes that express the transcription factor Rorc, produce interleukin (IL)-22, and provide innate immune protection at the intestinal mucosa. Intestinal CD3−NKp46+ cells are phenotypically heterogeneous, comprising a minority subset that resembles classical mature splenic natural killer (NK) cells (NK1.1+, Ly49+) but also a large CD127+NK1.1− subset of lymphoid tissue inducer (LTi)–like Rorc+ cells that has been proposed to include NK cell precursors. We investigated the developmental relationships between these intestinal CD3−NKp46+ subsets. Gut CD3−NKp46+ cells were related to LTi and NK cells in requiring the transcriptional inhibitor Id2 for normal development. Overexpression of IL-15 in intestinal epithelial cells expanded NK1.1+ cells within the gut but had no effect on absolute numbers of the CD127+NK1.1−Rorc+ subset of CD3−NKp46+ cells. In contrast, IL-7 deficiency strongly reduced the overall numbers of CD3−NKp46+NK1.1− cells that express Rorc and produce IL-22 but failed to restrict homeostasis of classical intestinal NK1.1+ cells. Finally, in vivo fate-mapping experiments demonstrated that intestinal NK1.1+CD127− cells are not the progeny of Rorc-expressing progenitors, indicating that CD127+NK1.1−Rorc+ cells are not canonical NK cell precursors. These studies highlight the independent cytokine regulation of functionally diverse intestinal NKp46+ cell subsets

Affine Gravity, Palatini Formalism and Charges

Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge-Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein's theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized methods. As a novel application we calculate the Bondi energy loss in five dimensional gravity, based on the asymptotic solution given by Tanabe, Tanahashi and Shiromizu, and obtain, as expected, the same result. We also give the superpotential for Einstein-Gauss-Bonnet gravity and find the superpotential for Lovelock theories of gravity when the number of dimensions tends to infinity with maximally symmetrical boundaries. The paper is written in standard component formalism.Comment: The work is dedicated to Joshua Goldberg from whom I learned and got interested in conservation laws in General Relativity (J.K

A case study of a mother's intertwining experiences with incest and postpartum depression

The association between childhood sexual abuse (CSA) and major depression disorder (MDD) gives reason to suspect that many mothers with postpartum depression (PPD) have a history of CSA. However, few studies have investigated how CSA and PPD are related. In this case study we explore how the experience of incest intertwines with the experience of postpartum depression. We focus on participant subject “Nina,” who has experienced both. We interviewed her three times and we analysed the interviews with Giorgi's phenomenological descriptive method to arrive at a contextualised meaning structure. Nina's intruding fantasies of men who abuse her children merge with her recollections of her own incest experiences. She may succeed in forcing these fantasies out of her consciousness, but they still alter her perceptions, thoughts, and emotions. She feels overwhelmed and succumbs to sadness, while she also is drawn towards information about CSA, which in turn feeds her fantasies. The psychodynamic concepts of repetition compulsion, transference, and projection may provide some explanation of Nina's actions, thoughts, and emotions through her past experiences. With our phenomenological stance, we aim to acknowledge Nina's descriptions of her everyday life here and now. With reference to Husserl, Heidegger, Merleau-Ponty, and Minkowski, we show that Nina's past is not a dated memory; rather it determines the structure of her consciousness that constitutes her past as her true present and future. Incest dominates Nina's world, and her possibilities for action are restricted by this perceived world. Any suspension of action implies anguish, and she resolves this by incest-structured action that in turn feeds and colours her expectations. Thus anxiety and depression are intertwined in the structure of this experience