186 research outputs found
On the Regularity of Optimal Transportation Potentials on Round Spheres
In this paper the regularity of optimal transportation potentials defined on
round spheres is investigated. Specifically, this research generalises the
calculations done by Loeper, where he showed that the strong (A3) condition of
Trudinger and Wang is satisfied on the round sphere, when the cost-function is
the geodesic distance squared. In order to generalise Loeper's calculation to a
broader class of cost-functions, the (A3) condition is reformulated via a
stereographic projection that maps charts of the sphere into Euclidean space.
This reformulation subsequently allows one to verify the (A3) condition for any
case where the cost-fuction of the associated optimal transportation problem
can be expressed as a function of the geodesic distance between points on a
round sphere. With this, several examples of such cost-functions are then
analysed to see whether or not they satisfy this (A3) condition.Comment: 24 pages, 4 figure
A glimpse into the differential topology and geometry of optimal transport
This note exposes the differential topology and geometry underlying some of
the basic phenomena of optimal transportation. It surveys basic questions
concerning Monge maps and Kantorovich measures: existence and regularity of the
former, uniqueness of the latter, and estimates for the dimension of its
support, as well as the associated linear programming duality. It shows the
answers to these questions concern the differential geometry and topology of
the chosen transportation cost. It also establishes new connections --- some
heuristic and others rigorous --- based on the properties of the
cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page
Efficacy and complications of neurosurgical treatment of acromegaly
The aim of the study was to evaluate the frequency of occurrence of pituitary failure following neurosurgery and the efficacy of transsphenoidal tumour resection in acromegalic patients. We retrospectively evaluated 85 patients (60 female and 25 male), of mean age 43.9 ± 13.2 years, treated by transsphenoidal neurosurgery. Macroadenoma and microadenoma of pituitary were found in 66 (77.6%) and 19 (22.4%) of these patients, respectively. Criteria of cure following neurosurgery were: basal GH < 2.5 μg/l, GH at 120 min in OGTT < 1.0 μg/l and serum concentration of IGF-1 within normal ranges for age and sex. After surgery 32 patients (37.6%) were cured and 53 patients (62.4%) required somatostatin analogue treatment. In patients cured by surgery, lower levels of basal GH (P < 0.05), IGF-1 (P < 0.001), GH at 120 min in OGTT and smaller size of pituitary tumour (P < 0.05) were found at diagnosis, as compared to patients in whom surgery was unsuccessful. Significant correlation between basal serum level of GH at diagnosis and size of pituitary tumour was found (P < 0.001). Invasive tumours were found in 45 of 53 (84.9%) patients not cured and in only 8 of 32 (25.0%) patients cured (P < 0.001). Impaired function of pituitary anterior lobe after surgery was observed in 30% and 4% of patients with macro- and microadenoma, respectively (P < 0.05). The efficacy of neurosurgery is affected by concentration of basal serum GH and IGF-1, GH at 120 min in OGTT, tumour size and invasiveness. Hypopituitarism after surgery is more frequent in patients with macroadenoma. Pituitary insufficiency, as a consequence of surgery, was found in 21% of patients with normal pituitary function prior to operation
The Structure of Hyperalkaline Aqueous Solutions Containing High Concentrations of Gallium - a Solution X-ray Diffraction and Computational Study
Highly concentrated alkaline NaOH/Ga(OH)3 solutions with 1.18 M Ga(III)T 2.32 M and 2.4 M NaOHT 4.9 M (where the subscript T denotes total or analytical concentrations) have been prepared and investigated by solution X-ray diffraction and also by ab initio quantum chemical calculations. The data obtained are consistent with the presence of only one predominant Ga(III)-bearing species in these solutions, that is the tetrahedral hydroxo complex Ga(OH)4–. This finding is in stark contrast to that found for Al(III)-containing solutions of similar concentrations, in which, besides the monomeric complex, an oxo-bridged dimer was also found to form. From the solution X-ray diffraction measurements, the formation of the dimeric (OH)3Ga–O–Ga(OH)32– could not unambiguously be shown, however, from the comparison of experimental IR, Raman and 71Ga NMR spectra with calculated ones, its formation can be safely excluded. Moreover, higher mononuclear stepwise hydroxo complexes, like Ga(OH)63–, that have been claimed to exist by others in the literature, was not possible to experimentally detect in these solutions with any of the spectroscopic techniques used
Oxidant-NO dependent gene regulation in dogs with type I diabetes: impact on cardiac function and metabolism
<p>Abstract</p> <p>Background</p> <p>The mechanisms responsible for the cardiovascular mortality in type I diabetes (DM) have not been defined completely. We have shown in conscious dogs with DM that: <it>1</it>) baseline coronary blood flow (CBF) was significantly decreased, <it>2</it>) endothelium-dependent (ACh) coronary vasodilation was impaired, and <it>3</it>) reflex cholinergic NO-dependent coronary vasodilation was selectively depressed. The most likely mechanism responsible for the depressed reflex cholinergic NO-dependent coronary vasodilation was the decreased bioactivity of NO from the vascular endothelium. The goal of this study was to investigate changes in cardiac gene expression in a canine model of alloxan-induced type 1 diabetes.</p> <p>Methods</p> <p>Mongrel dogs were chronically instrumented and the dogs were divided into two groups: one normal and the other diabetic. In the diabetic group, the dogs were injected with alloxan monohydrate (40-60 mg/kg iv) over 1 min. The global changes in cardiac gene expression in dogs with alloxan-induced diabetes were studied using Affymetrix Canine Array. Cardiac RNA was extracted from the control and DM (n = 4).</p> <p>Results</p> <p>The array data revealed that 797 genes were differentially expressed (P < 0.01; fold change of at least ±2). 150 genes were expressed at significantly greater levels in diabetic dogs and 647 were significantly reduced. There was no change in eNOS mRNA. There was up regulation of some components of the NADPH oxidase subunits (gp91 by 2.2 fold, P < 0.03), and down-regulation of SOD1 (3 fold, P < 0.001) and decrease (4 - 40 fold) in a large number of genes encoding mitochondrial enzymes. In addition, there was down-regulation of Ca<sup>2+ </sup>cycling genes (ryanodine receptor; SERCA2 Calcium ATPase), structural proteins (actin alpha). Of particular interests are genes involved in glutathione metabolism (glutathione peroxidase 1, glutathione reductase and glutathione S-transferase), which were markedly down regulated.</p> <p>Conclusion</p> <p>our findings suggest that type I diabetes might have a direct effect on the heart by impairing NO bioavailability through oxidative stress and perhaps lipid peroxidases.</p
A user's guide to optimal transport
This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below
Reconstruction of the early Universe as a convex optimization problem
We show that the deterministic past history of the Universe can be uniquely
reconstructed from the knowledge of the present mass density field, the latter
being inferred from the 3D distribution of luminous matter, assumed to be
tracing the distribution of dark matter up to a known bias. Reconstruction
ceases to be unique below those scales -- a few Mpc -- where multi-streaming
becomes significant. Above 6 Mpc/h we propose and implement an effective
Monge-Ampere-Kantorovich method of unique reconstruction. At such scales the
Zel'dovich approximation is well satisfied and reconstruction becomes an
instance of optimal mass transportation, a problem which goes back to Monge
(1781). After discretization into N point masses one obtains an assignment
problem that can be handled by effective algorithms with not more than cubic
time complexity in N and reasonable CPU time requirements. Testing against
N-body cosmological simulations gives over 60% of exactly reconstructed points.
We apply several interrelated tools from optimization theory that were not
used in cosmological reconstruction before, such as the Monge-Ampere equation,
its relation to the mass transportation problem, the Kantorovich duality and
the auction algorithm for optimal assignment. Self-contained discussion of
relevant notions and techniques is provided.Comment: 26 pages, 14 figures; accepted to MNRAS. Version 2: numerous minour
clarifications in the text, additional material on the history of the
Monge-Ampere equation, improved description of the auction algorithm, updated
bibliography. Version 3: several misprints correcte
A male patient with acromegaly and breast cancer: treating acromegaly to control tumor progression
Remote limb ischemic post-conditioning attenuates ischemia-reperfusion injury in rat skin flapby limiting oxidative stress
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