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Tatonnement is a simple and natural rule for updating prices in Exchange (Arrow-Debreu) markets. In this paper we define a class of markets for which tatonnement is equivalent to gradient descent. This is the class of markets for which there is a convex potential function whose gradient is always equal to the negative of the excess demand and we call it(More)
This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities. The current work(More)
This paper studies two functions arising separately in the analysis of algorithms. The first function is the solution to the Multidimensional Divide-And-Conquer (MDC) Recurrence that arises when solving problems involving points in d-dimensional space. The second function concerns weighted digital sums. Let n = (bibi−1 · · · b1b0)2 and SM (n) = i t=0 t(t +(More)
We examined nine patients with histologically proven nasopharyngeal carcinoma (NPC), treated with radiotherapy, using dynamic susceptibility contrast MRI (DSC-MRI). In eight there was clinical evidence of radionecrosis of the temporal lobe, and one was examined for local recurrence in the nasopharynx. All patients had either high-signal finger-like or(More)
Given a graph where vertices are partitioned into k terminals and non-terminals, the goal is to compress the graph (i.e., reduce the number of non-terminals) using minor operations while preserving terminal distances approximately. The distortion of a compressed graph is the maximum multiplicative blow-up of distances between all pairs of terminals. We(More)
In a prospective study using CT as the initial means of radiologic evaluation in 262 patients with proved nasopharyngeal carcinoma, the paranasopharyngeal space was found to be the most commonly involved region (84.4%), both uni- and bilaterally. Unilateral involvement was found in 44.3% of patients (116/262) and bilateral involvement in 40.1% (105/262).(More)
BACKGROUND AND PURPOSE This clinical trial investigates the effectiveness of intravenous glycerol therapy in patients with acute cortical infarction in whom intracerebral hemorrhage was rigorously excluded. METHODS Within 48 hours of symptoms from their first ischemic stroke, 113 hospital inpatients were randomized into the trial, provided that hemorrhage(More)
A case of central neurocytoma occurring in the thalamus, confirmed by electron microscopy and immunohistochemistry, is reported. Computed tomography demonstrated a hypodense mass with an irregular margin arising from the right thalamus, extending into the lateral ventricle and crossing the midline. It contained areas of calcification and showed slight(More)
Hypertrophic olivary degeneration (HOD) is a rare type of neuronal degeneration involving the dento-rubo-olivary pathway. It is distinguished from other types of neuronal degeneration in that hypertrophy, rather than atrophy, takes place in the neurons in the inferior olivary nucleus. Prior to the invention of Magnetic Resonance Imaging (MRI), HOD was(More)