Asymptotic behavior of the order parameter in a stochastic sandpile

We derive the first four terms in a series for the order paramater (the stationary activity density rho) in the supercritical regime of a one-dimensional stochastic sandpile; in the two-dimensional case the first three terms are reported. We reorganize the pertubation theory for the model, recently derived using a path-integral formalism [R. Dickman e R. Vidigal, J. Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties. Since the process has a strictly conserved particle density p, the Fourier mode N^{-1} psi_{k=0} -> p, when the number of sites N -> infinity, and so is not a random variable. Isolating this mode, we obtain a new effective action leading to an expansion for rho in the parameter kappa = 1/(1+4p). This requires enumeration and numerical evaluation of more than 200 000 diagrams, for which task we develop a computational algorithm. Predictions derived from this series are in good accord with simulation results. We also discuss the nature of correlation functions and one-site reduced densities in the small-kappa (large-p) limit.Comment: 18 pages, 5 figure

No Exit? Withdrawal Rights and the Law of Corporate Reorganizations

Bankruptcy scholarship is largely a debate about the comparative merits of a mandatory regime on one hand and bankruptcy by free design on the other. By the standard account, the current law of corporate reorganization is mandatory. Various rules that cannot be avoided ensure that investors’ actions are limited and they do not exercise their rights against specialized assets in a way that destroys the value of a business as a whole. These rules solve collective action problems and reduce the risk of bargaining failure. But there are costs to a mandatory regime. In particular, investors cannot design their rights to achieve optimal monitoring as they could in a system of bankruptcy by free design. This Article suggests that the academic debate has missed a fundamental feature of the law. Bankruptcy operates on legal entities, not on firms in the economic sense. For this reason, sophisticated investors do not face a mandatory regime at all. The ability of investors to place assets in separate entities gives them the ability to create specific withdrawal rights in the event the firm encounters financial distress. There is nothing mandatory about rules like the automatic stay when assets can be partitioned off into legal entities that are beyond the reach of the bankruptcy judge. Thus, by partitioning assets of one economic enterprise into different legal entities, investors can create a tailored bankruptcy regime. In this way, legal entities serve as building blocks that can be combined to create specific and varied but transparent investor withdrawal rights. This regime of tailored bankruptcy has been unrecognized and underappreciated and may be preferable to both mandatory and free design regimes. By allowing a limited number of investors to opt out of bankruptcy in a particular, discrete, and visible way, investors as a group may be able to both limit the risk of bargaining failure and at the same time enjoy the disciplining effect that a withdrawal right brings with it

Differential Patterns of Synaptotagmin7 mRNA Expression in Rats with Kainate- and Pilocarpine-Induced Seizures

Previous studies in rat models of neurodegenerative disorders have shown disregulation of striatal synaptotagmin7 mRNA. Here we explored the expression of synaptotagmin7 mRNA in the brains of rats with seizures triggered by the glutamatergic agonist kainate (10 mg/kg) or by the muscarinic agonist pilocarpine (30 mg/kg) in LiCl (3 mEq/kg) pre-treated (24 h) rats, in a time-course experiment (30 min - 1 day). After kainate-induced seizures, synaptotagmin7 mRNA levels were transiently and uniformly increased throughout the dorsal and ventral striatum (accumbens) at 8 and 12 h, but not at 24 h, followed at 24 h by somewhat variable upregulation within different parts of the cerebral cortex, amigdala and thalamic nuclei, the hippocampus and the lateral septum. By contrast, after LiCl/pilocarpine-induced seizures, there was a more prolonged increase of striatal Synaptotagmin7 mRNA levels (at 8, 12 and 24 h), but only in the ventromedial striatum, while in some other of the aforementioned brain regions there was a decline to below the basal levels. After systemic post-treatment with muscarinic antagonist scopolamine in a dose of 2 mg/kg the seizures were either extinguished or attenuated. In scopolamine post-treated animals with extinguished seizures the striatal synaptotagmin7 mRNA levels (at 12 h after the onset of seizures) were not different from the levels in control animals without seizures, while in rats with attenuated seizures, the upregulation closely resembled kainate seizures-like pattern of striatal upregulation. In the dose of 1 mg/kg, scopolamine did not significantly affect the progression of pilocarpine-induced seizures or pilocarpine seizures-like pattern of striatal upregulation of synaptotagmin7 mRNA. In control experiments, equivalent doses of scopolamine per se did not affect the expression of synaptotagmin7 mRNA. We conclude that here described differential time course and pattern of synaptotagmin7 mRNA expression imply regional differences of pathophysiological brain activation and plasticity in these two models of seizures

Noncomparabilities & Non Standard Logics

Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims