Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C^n tensor C^n whose operator-Schmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number S for every S in {1,...,9}. This corollary was unexpected, since it contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003) 052301] based on intuition from a striking result in the two-qubit case. By the results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901 quant-ph/0112124], who also considered the two-qubit case, our result implies that there are nine equivalence classes of unitaries on C^3 tensor C^3 which are probabilistically interconvertible by (stochastic) local operations and classical communication. As another corollary, a prescription is produced for constructing maximally-entangled operators from biunimodular functions. Reversing tact, we state a generalized operator-Schmidt decomposition of the quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 --> C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by Nielsen's bound) that the communication cost of the QFT remains maximal when a net transfer of qudits is permitted. In an appendix, a canonical procedure is given for removing basis-dependence for results and proofs depending on the "magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum and Reversible Computation at Stony Brook May 31, 2003. The talk slides and audio are available at http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos and minor cosmetic

Incidence of Acute Thrombo-Embolic Occlusion of the Superior Mesenteric Artery—A Population-based Study

AbstractObjective. To determine the incidence of acute thrombo-embolic occlusion of the superior mesenteric artery (AOSMA) in a population-based study.Material. All clinical (n=23,446) and forensic (n=7569) autopsies performed in the city of Malmö between 1970 and 1982 (population 264,000–230,000 inhabitants). The autopsy rate was 87%.Methods. Calculation of the incidence of AOSMA with intestinal gangrene in those autopsies coded for bowel ischaemia (997/23,446 clinical and 9/7569 forensic autopsies). The operative procedures performed in 1970, 1976 and 1982 were also analysed.Results. Two forensic and 211 clinical autopsies demonstrated AOSMA with intestinal gangrene. Previous suspicion of intestinal ischaemia was noted in only 33%. Sixteen patients were operated. The cause-specific mortality was 6.0/1000 deaths. The incidence was 8.6/100,000 person years, increasing exponentially with age (p<0.001). Mortality was 93%.Conclusions. The incidence and mortality of AOSMA is higher than previously reported from clinical series. There is seldom any suspicion of the diagnosis prior to death

Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and Theoretical (2007

When the optimal is not the best: parameter estimation in complex biological models

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results: We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions: The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system, and point to the need of a theory that addresses this problem more generally

Effects of cereal breakfasts on postprandial glucose, appetite regulation and voluntary energy intake at a subsequent standardized lunch; focusing on rye products

<p>Abstract</p> <p>Background</p> <p>Rye products have been demonstrated to lower the acute insulin demand, induce a low and prolonged blood glucose response (high Glycemic Profile, GP) and reduce subclinical inflammation. These products may therefore contribute to a lowered risk of obesity, type 2 diabetes and cardio vascular disease. The objective of the present paper was to evaluate the mechanism for a reduced postprandial insulin demand with rye products, and to explore possible appetite regulating properties.</p> <p>Methods</p> <p>10 healthy subjects were served breakfast meals (50 g of available starch) with endosperm- or whole grain rye breads, with and without lactic acid, boiled whole grain rye- (RK) or wheat (WK) kernels, or white wheat bread reference (WWB) in random order in a cross-over design. Plasma concentrations of glucose, ghrelin, serum insulin, free fatty acids, adiponectin, breath hydrogen excretion (H₂), and subjective satiety was evaluated during the postprandial phase. 270 min after the breakfast, an ad lib lunch buffet was served and the voluntary energy intake (EI) was registered.</p> <p>Results</p> <p>All rye products and WK induced lower insulinemic indices (II) than WWB. A lower incremental insulin peak following breakfast correlated with a lower EI at lunch (r = 0.38). A low II was related to improved satiety in the early postprandial phase (fullness AUC 0-60 min, r = -0.36). RK induced a higher GP compared to WWB and WK. A higher GP was related to a lowered <it>desire to eat </it>before lunch (AUC 210-270) and to a lower concentration of ghrelin in the late postprandial phase after breakfast (270 min), r = -0.29 and -0.29), which in turn was related to a lower voluntary EI (r = 0.43 and 0.33). The RK breakfast improved satiety in the early postprandial phase (0-60 min) compared to WWB, and induced a lower EI at lunch (-16%). A high content of indigestible carbohydrates in the breakfast products was related to improved satiety (0-60 min, r = 0.68 for fullness), and a higher breath H₂in the late postprandial phase (120-270 and 270-390 min, r = 0.46 and 0.70). High H₂(AUC 120-270 min) also correlated with lower EI (r = -0.34).</p> <p>Conclusions</p> <p>Rye products, rich in indigestible carbohydrates, induce colonic fermentation already post the breakfast meal, and lowers acute insulin responses. A high excretion of breath H2 also correlated with a higher GP. Especially, rye kernels induced a high GP which was associated with a 16% lowering of energy intake at a subsequent lunch meal. The bulking effect of rye fiber, colonically derived fermentation metabolites, a high GP and a low insulin response possibly all contributes to the benefits on glucose- and appetite regulation seen in an acute and semi-acute perspective.</p

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Acute thrombosis of the superior mesenteric artery in a 39-year-old woman with protein-S deficiency: a case report

<p>Abstract</p> <p>Introduction</p> <p>Acute thromboembolic occlusion of the superior mesenteric artery is a condition with an unfavorable prognosis. Treatment of this condition is focused on early diagnosis, surgical or intravascular restoration of blood flow to the ischemic intestine, surgical resection of the necrotic bowel and supportive intensive care. In this report, we describe a case of a 39-year-old woman who developed a small bowel infarct because of an acute thrombotic occlusion of the superior mesenteric artery, also involving the splenic artery.</p> <p>Case presentation</p> <p>A 39-year-old Caucasian woman presented with acute abdominal pain and signs of intestinal occlusion. The patient was given an abdominal computed tomography scan and ultrasonography in association with Doppler ultrasonography, highlighting a thrombosis of the celiac trunk, of the superior mesenteric artery, and of the splenic artery. She immediately underwent an explorative laparotomy, and revascularization was performed by thromboendarterectomy with a Fogarty catheter. In the following postoperative days, she was given a scheduled second and third look, evidencing necrotic jejunal and ileal handles. During all the surgical procedures, we performed intraoperative Doppler ultrasound of the superior mesenteric artery and celiac trunk to control the arterial flow without evidence of a new thrombosis.</p> <p>Conclusion</p> <p>Acute mesenteric ischemia is a rare abdominal emergency that is characterized by a high mortality rate. Generally, acute mesenteric ischemia is due to an impaired blood supply to the intestine caused by thromboembolic phenomena. These phenomena may be associated with a variety of congenital prothrombotic disorders. A prompt diagnosis is a prerequisite for successful treatment. The treatment of choice remains laparotomy and thromboendarterectomy, although some prefer an endovascular approach. A second-look laparotomy could be required to evaluate viable intestinal handles. Some authors support a laparoscopic second-look. The possibility of evaluating the arteriotomy, during a repeated laparotomy with a Doppler ultrasound, is crucial to show a new thrombosis. Although the prognosis of acute mesenteric ischemia due to an acute arterial mesenteric thrombosis remains poor, a prompt diagnosis, aggressive surgical treatment and supportive intensive care unit could improve the outcome for patients with this condition.</p

Modelled glacier response to centennial temperature and precipitation trends on the Antarctic Peninsula

The northern Antarctic Peninsula is currently undergoing rapid atmospheric warming. Increased glacier-surface melt during the twentieth century has contributed to ice-shelf collapse and the widespread acceleration, thinning and recession of glaciers. Therefore, glaciers peripheral to the Antarctic Ice Sheet currently make a large contribution to eustatic sea-level rise, but future melting may be offset by increased precipitation. Here we assess glacier-climate relationships both during the past and into the future, using ice-core and geological data and glacier and climate numerical model simulations. Focusing on Glacier IJR45 on James Ross Island, northeast Antarctic Peninsula, our modelling experiments show that this representative glacier is most sensitive to temperature change, not precipitation change. We determine that its most recent expansion occurred during the late Holocene a Little Ice Age' and not during the warmer mid-Holocene, as previously proposed. Simulations using a range of future Intergovernmental Panel on Climate Change climate scenarios indicate that future increases in precipitation are unlikely to offset atmospheric-warming-induced melt of peripheral Antarctic Peninsula glaciers

Editor's Choice – European Society for Vascular Surgery (ESVS) 2023 Clinical Practice Guidelines on Radiation Safety

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