Uniform, Equal Division, and Other Envy-Free Rules between The Two

This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two

A comparative study on the efficacy of 10% hypertonic saline and equal volume of 20% mannitol in the treatment of experimentally induced cerebral edema in adult rats

<p>Abstract</p> <p>Background</p> <p>Hypertonic saline and mannitol are commonly used in the treatment of cerebral edema and elevated intracranial pressure (ICP) at present. In this connection, 10% hypertonic saline (HS) alleviates cerebral edema more effectively than the equal volume of 20% mannitol. However, the exact underlying mechanism for this remains obscure. This study aimed to explore the possible mechanism whereby 10% hypertonic saline can ameliorate cerebral edema more effectively than mannitol.</p> <p>Results</p> <p>Adult male Sprague-Dawley (SD) rats were subjected to permanent right-sided middle cerebral artery occlusion (MCAO) and treated with a continuous intravenous infusion of 10% HS, 20% mannitol or D-[1-³H(N)]-mannitol. Brain water content (BWC) as analyzed by wet-to-dry ratios in the ischemic hemisphere of SD rats decreased more significantly after 10% HS treatment compared with 20% mannitol. Concentration of serum Na⁺and plasma crystal osmotic pressure of the 10% HS group at 2, 6, 12 and 18 h following permanent MCAO increased significantly when compared with 20% mannitol treated group. Moreover, there was negative correlation between the BWC of the ipsilateral ischemic hemisphere and concentration of serum Na⁺, plasma crystal osmotic pressure and difference value of concentration of serum Na⁺and concentration of brain Na⁺in ipsilateral ischemic hemisphere in the 10% HS group at the various time points after MCAO. A remarkable finding was the progressive accumulation of mannitol in the ischemic brain tissue.</p> <p>Conclusions</p> <p>We conclude that 10% HS is more effective in alleviating cerebral edema than the equal volume of 20% mannitol. This is because 10% HS contributes to establish a higher osmotic gradient across BBB and, furthermore, the progressive accumulation of mannitol in the ischemic brain tissue counteracts its therapeutic efficacy on cerebral edema.</p

Maximal Domain for Strategy-Proof Rules in Allotment Economies

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric, and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: There is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaued domain

Strategy-Proofness on Bankruptcy Problems with an Indivisible Object

We analyze bankruptcy problems with an indivisible object, where real owners and outside traders want to allocate an indivisible object among them with monetary compensation. The object might be a company that has gone bankrupt or a house left by a parent who has died, and so on. We show that there exists no rule satisfying strategyproofness and the ownership lower bound on any domains that include at least three common preferences