The joint moment generating function of quadratic forms in multivariate autoregressive series - The case with deterministic components

Let {X-t} follow a discrete Gaussian vector autoregression with deterministic components. We derive the exact finite-sample joint moment generating function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of functionals involving multivariate and univariate Ornstein–Uhlenbeck processes, drifts, and time trends. Such processes arise asymptotically from more general non-Gaussian processes and also from the Gaussian {X-t} and have also been used in areas other than time series,such as the “goodness of fit” literature

The ISO-LWS map of the Serpens cloud core. II. The line spectra

We present spectrophotometric ISO imaging with the LWS and the CAM-CVF of the Serpens molecular cloud core. The LWS map is centred on the far infrared and submillimetre source SMM1 and its size is 8' x 8'. The fine structure line emission in [OI] and [CII] is extended and can be successfully modelled to originate in a PDR with G_0 = 15 and n(H2) about 10^4 - 10^5 cm^-3. Extended emission is also observed in the rotational line emission of H2O and high-J CO. However, lack of sufficient angular resolution prevents us from excluding the possibility that the emssion regions of these lines are point like, which could be linked to the embedded objects SMM9 and SMM4. Toward the Class0 source SMM1, the LWS observations reveal, in addition to fine structure line emission, a rich spectrum of molecular lines. The sub-thermally excited and optically thick CO, H2O and OH lines are tracing an about 10^3 AU source with temperatures higher than 300 K and densities above 10^6 cm^-3. We show that geometry is of concern for the correct interpretation of the data and based on 2D-radiative transfer modelling of the disk/torus around SMM1, which successfully reproduces the entire observed SED and the observed line profiles of CO isotopomers, we can exclude the disk to be the source of the LWS-molecular line emission. The CAM-CVF permits us to see a region of rotational H2 emission. This H2 gas has a temperature of 10^3 K, which suggests that the heating of the gas is achieved through relatively slow shocks. Although we are not able to establish any firm conclusion regarding the detailed nature of the shock waves, our observations of the molecular line emission from SMM1 can be explainable in terms of an admixture of J-shocks and of C-shocks.Comment: 20 pages, 20 figures, accepted for publication in A&

Memory cost of quantum contextuality

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimal amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information carrying capacity of the system.Comment: 18 pages, no figures, v2: revised for clarit

Minority Economic Development: The Problem of Business Failures

Inflammatory pseudotumour is a rare condition that can affect various organs. The clinical and histologic appearance of the pseudotumour may mimic haematological, lymphoproliferative, paraneoplastic or malignant processes. A previously healthy 39-year-old man presented with nephrotic syndrome. He had a history of headaches, nausea and swollen ankles. Computed tomography of the abdomen revealed a 6-cm mass in the spleen. Following a renal biopsy, a diagnosis of membranoproliferative glomerulonephritis (MPGN) type I was made. Splenectomy was performed and the examination revealed a mixed population of lymphocytes with predominantly T-cells, B-cells and lymphoplasmacytoid cells. Immunostaining confirmed that the small cells were mostly T-cells positive for all T-cell markers including CD2, CD3, CD4, CD5, CD7 and CD8. A diagnosis of inflammatory pseudotumour was established. The removal of the spleen was followed by remission of glomerulonephritis, but it was complicated by a subphrenic abscess and pneumonia. This association between an inflammatory pseudotumour of the spleen and MPGN has not been previously described. Abnormal immune response due to the inflammation leading to secondary glomerulonephritis might be the main pathogenic mechanism