The CONEstrip algorithm

Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs

The Effect of High Dose Total Body Irradiation on ACTH, Corticosterone, and Catecholamines in the Rat

Total body irradiation (TBI) or partial body irradiation is a distinct risk of accidental, wartime, or terrorist events. Total body irradiation is also used as conditioning therapy before hematopoietic stem cell transplantation. This therapy can result in injury to multiple tissues and might result in death as a result of multiorgan failure. The hypothalamic–pituitary–adrenal (HPA) axis could play a causative role in those injuries, in addition to being activated under conditions of stress. In a rat model of TBI, we have established that radiation nephropathy is a significant lethal complication, which is caused by hypertension and uremia. The current study assessed HPA axis function in rats undergoing TBI. Using a head-shielded model of TBI, we found an enhanced response to corticotropin-releasing hormone (CRH) in vitro in pituitaries from irradiated compared with nonirradiated rats at both 8 and 70 days after 10-Gy single fraction TBI. At 70, but not 8 days, plasma adrenocorticotrophic hormone (ACTH) and corticosterone levels were increased significantly in irradiated compared with nonirradiated rats. Plasma aldosterone was not affected by TBI at either time point, whereas plasma renin activity was decreased in irradiated rats at 8 days. Basal and stimulated adrenal steroid synthesis in vitro was not affected by TBI. In addition, plasma epinephrine was decreased at 70 days after TBI. The hypothalamic expression of CRH messenger RNA (mRNA) and hippocampal expression of glucocorticoid receptor mRNA were unchanged by irradiation. We conclude that the hypertension of radiation nephropathy is not aldosterone or catecholamine-dependent but that there is an abscopal activation of the HPA axis after 10 Gy TBI. This activation was attributable at least partially to enhanced pituitary ACTH production

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14

Quantum Monte Carlo study of a nonmagnetic impurity in the two-dimensional Hubbard model

In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, Quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a bare impurity potential which is onsite and attractive, magnetic and single-particle properties have been calculated. The QMC results show that giant oscillations develop in the Knight shift response around the impurity site due to the short-range antiferromagnetic correlations. These results are useful for interpreting the NMR data on Li and Zn substituted layered cuprates.Comment: 10 pages, 7 figure

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

Complementary vertices and adjacency testing in polytopes

Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent. For simple polytopes this test is perfect; for non-simple polytopes it may be indeterminate, and instead acts as a filter to identify non-adjacent pairs. Our test requires an O(n^2 V + n V^2) precomputation, which is acceptable in settings such as all-pairs adjacency testing. These results improve upon the more general O(nV) combinatorial and O(n^3) algebraic adjacency tests from the literature.Comment: 14 pages, 5 figures. v1: published in COCOON 2012. v2: full journal version, which strengthens and extends the results in Section 2 (see p1 of the paper for details

Friedel oscillations induced by non-magnetic impurities in the two-dimensional Hubbard model

We study the interplay of correlations and disorder using an unrestricted Slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.Comment: 9 pages, RevTeX, includes 8 figure