A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator

Robust Quantum Communication Using A Polarization-Entangled Photon Pair

Noise and imperfection of realistic devices are major obstacles for implementing quantum cryptography. In particular birefringence in optical fibers leads to decoherence of qubits encoded in polarization of photon. We show how to overcome this problem by doing single qubit quantum communication without a shared spatial reference frame and precise timing. Quantum information will be encoded in pair of photons using ``tag'' operations which corresponds to the time delay of one of the polarization modes. This method is robust against the phase instability of the interferometers despite the use of time-bins. Moreover synchronized clocks are not required in the ideal situation no photon loss case as they are only necessary to label the different encoded qubits.Comment: 4 pages, 2 figure

Mechanisms for error propagation and cancellation in Glimm’s scheme without rarefactions

Abstract. We derive an a posteriori error bound for Glimm's approximate solutions to convex scalar conservation laws containing only shock waves. Using Liu's wave-tracing method, we show that the L 1 norm of the error is bounded by a sum of residuals containing independent contributions from each wave in the approximate solution. We introduce a framework, similar to the method of characteristics, for the analysis of the local errors generated by wave interactions. The analysis allows for explicit cancellation among the errors created by a single wave and for error propagation along discontinuities

Effect of nucleon exchange on projectile multifragmentation in the reactions of 28Si + 112Sn and 124Sn at 30 and 50 MeV/nucleon

Multifragmentation of quasiprojectiles was studied in reactions of 28Si beam with 112Sn and 124Sn targets at projectile energies 30 and 50 MeV/nucleon. The quasiprojectile observables were reconstructed using isotopically identified charged particles with Z_f <= 5 detected at forward angles. The nucleon exchange between projectile and target was investigated using isospin and excitation energy of reconstructed quasiprojectile. For events with total reconstructed charge equal to the charge of the beam (Z_tot = 14) the influence of beam energy and target isospin on neutron transfer was studied in detail. Simulations employing subsequently model of deep inelastic transfer, statistical model of multifragmentation and software replica of FAUST detector array were carried out. A concept of deep inelastic transfer provides good description of production of highly excited quasiprojectiles. The isospin and excitation energy of quasiprojectile were described with good overall agreement. The fragment multiplicity, charge and isospin were reproduced satisfactorily. The range of contributing impact parameters was determined using backtracing procedure.Comment: 11 pages, 8 Postscript figures, LaTeX, to appear in Phys. Rev. C ( Dec 2000

PET/MRI of Hepatic 90Y Microsphere Deposition Determines Individual Tumor Response.

PurposeThe purpose of our study is to determine if there is a relationship between dose deposition measured by PET/MRI and individual lesion response to yttrium-90 ((90)Y) microsphere radioembolization.Materials and methods26 patients undergoing lobar treatment with (90)Y microspheres underwent PET/MRI within 66 h of treatment and had follow-up imaging available. Adequate visualization of tumor was available in 24 patients, and contours were drawn on simultaneously acquired PET/MRI data. Dose volume histograms (DVHs) were extracted from dose maps, which were generated using a voxelized dose kernel. Similar contours to capture dimensional and volumetric change of tumors were drawn on follow-up imaging. Response was analyzed using both RECIST and volumetric RECIST (vRECIST) criteria.ResultsA total of 8 hepatocellular carcinoma (HCC), 4 neuroendocrine tumor (NET), 9 colorectal metastases (CRC) patients, and 3 patients with other metastatic disease met inclusion criteria. Average dose was useful in predicting response between responders and non-responders for all lesion types and for CRC lesions alone using both response criteria (p &lt; 0.05). D70 (minimum dose to 70 % of volume) was also useful in predicting response when using vRECIST. No significant trend was seen in the other tumor types. For CRC lesions, an average dose of 29.8 Gy offered 76.9 % sensitivity and 75.9 % specificity for response.ConclusionsPET/MRI of (90)Y microsphere distribution showed significantly higher DVH values for responders than non-responders in patients with CRC. DVH analysis of (90)Y microsphere distribution following treatment may be an important predictor of response and could be used to guide future adaptive therapy trials

Absorbed radiation dosimetry of the D3-specific PET radioligand [18F]FluorTriopride estimated using rodent and nonhuman primate

[(18)F]FluorTriopride ([(18)F]FTP) is a dopamine D(3)-receptor preferring radioligand with potential for investigation of neuropsychiatric disorders including Parkinson disease, dystonia and schizophrenia. Here we estimate human radiation dosimetry for [(18)F]FTP based on the ex-vivo biodistribution in rodents and in vivo distribution in nonhuman primates. Biodistribution data were generated using male and female Sprague-Dawley rats injected with ~370 KBq of [(18)F]FTP and euthanized at 5, 30, 60, 120, and 240 min. Organs of interest were dissected, weighed and assayed for radioactivity content. PET imaging studies were performed in two male and one female macaque fascicularis administered 143-190 MBq of [(18)F]FTP and scanned whole-body in sequential sections. Organ residence times were calculated based on organ time activity curves (TAC) created from regions of Interest. OLINDA/EXM 1.1 was used to estimate human radiation dosimetry based on scaled organ residence times. In the rodent, the highest absorbed radiation dose was the upper large intestines (0.32-0.49 mGy/MBq), with an effective dose of 0.07 mSv/MBq in males and 0.1 mSv/MBq in females. For the nonhuman primate, however, the gallbladder wall was the critical organ (1.81 mGy/MBq), and the effective dose was 0.02 mSv/MBq. The species discrepancy in dosimetry estimates for [(18)F]FTP based on rat and primate data can be attributed to the slower transit of tracer through the hepatobiliary track of the primate compared to the rat, which lacks a gallbladder. Out findings demonstrate that the nonhuman primate model is more appropriate model for estimating human absorbed radiation dosimetry when hepatobiliary excretion plays a major role in radiotracer elimination

Adipocyte size as a determinant of metabolic disease and adipose tissue dysfunction

Obesity is a heterogeneous disease and is associated with comorbidities such as type 2 diabetes mellitus, cardiovascular disease and cancer. Several studies have examined the role of dysfunctional adipose tissue in the pathogenesis of obesity, highlighting the contrasting properties and impact of distinct fat compartments, sometimes with contradictory results. Dysfunctional adipose tissue involves enlargement, or hypertrophy, of pre-existing fat cells, which is thought to confer increases in cardiometabolic risk, independent of the level of obesity per se . In this article, we critically analyze available literature that examined the ability of adipocyte cell size to predict metabolic disease and adipose tissue dysfunction in humans. Many studies demonstrate that increased fat cell size is a significant predictor of altered blood lipid profiles and glucose–insulin homeostasis independent of adiposity indices. The contri- bution of visceral adiposity to these associations appears to be of particular importance. However, available studies are not unanimous and many fat depot-specific aspects of the relationship between increased fat cell size and cardiometabolic risk or parameters of adipose tissue dysfunction are still unresolved. Methodological factors such as the approach used to express the data may represent significant confounders in these studies. Additional studies should consider the fact that the relationship between fat cell size and common adiposity indices is non-linear, particularly when reaching the obese range. In conclusion, our analysis demonstrates that fat cell size is a significant predictor of the cardiometabolic alterations related to obesity. We propose that adipocyte hypertrophy, especially in the visceral fat compartment, may represent a strong marker of limited hyperplasic capacity in subcutaneous adipose tissues, which in turn is associated with the presence of numerous cardiometabolic alterations