A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents

We consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer science, mathematics, and economics. Although, the elegant Selfridge-Conway envy-free protocol for three agents has been known since 1960, it has been a major open problem for the last fifty years to obtain a bounded envy-free protocol for more than three agents. We propose a discrete and bounded envy-free protocol for four agents

Chronic orthostatic and antiorthostatic restraint induce neuroendocrine, immune and neurophysiologial disorders in rats.

International audienceThe tail-cast suspension rat model has been developed in ground laboratories interested in space physiology for extensive study of mechanisms causing the pathophysiological syndrome associated with space flights. We used individually-caged male rats to explore the effects of acute and chronic (7d) orthostatic restraint (OR) and head-down anti-orthostatic restraint (AOR) on a series of physiological variables. The acute restraint study showed that (1) the installation of the OR device induced an acute reaction for 2 days, with a substantial rise in ACTH (x2) and CORT (x6), and that (2) the head-down tilt from OR to AOR induced (i) within 10 min and lasting 60 min a 2-fold rise in the intra-cerebro-ventricular pressure (Picv) monitored with an icv telemetric recording system, which receded to normal between 60 and 120 min; and (ii) within 30 min a short-lived 4-fold rise in plasma ACTH and CORT levels. Chronic OR induced (1) the suppression of the diurnal ACTH/CORT rhythm, with increased mean levels, especially for ACTH, (2) a degraded circadian locomotor activity rhythm manifested by a significant reduction in the spectral power of the 24h periodicity and a concomitant emergence of shorter (ultradian) periodicities, (3) an associated, but less pronounced alteration of the diurnal rhythm in body temperature; and (4) a marked increase in baseline plasma levels of IL-1 beta and an increased reactivity in cytokine release following an E. coli endotoxin (LPS) challenge. AOR induced (1) a similar obliteration of the circadian ACTH/CORT rhythm, (2) the loss of close correlation between ACTH and CORT, (3) a generalized increase in baseline plasma IL-1 beta levels and (4) more extensive degradation of the circadian periodicity for both locomotor activity and, to a lesser extent, body temperature, replaced by dominant spectral powers for ultradian periodicities (3 to 10h). In conclusion, both experimental paradigms--but AOR more than OR--caused a blockade of the circadian rhythmicity of major physiological variables, the loss of normal correlations between ACTH and CORT, and inflammatory-immune hyperreactivity. These pathophysiological disorders may all be parts of a complex chronic stress syndrome

Different responses of plasma ACTH and corticosterone and of plasma interleukin-1 beta to single and recurrent endotoxin challenges.

International audienceIn a parallel study in 10 individual rats, three time series of plasma concentrations of ACTH, corticosterone (CORT), and interleukin-1 beta (IL-1 beta) were measured before (time 0) and at intervals between 15 and 480 min following intra-arterial (i.a.) infusions of 25 microgram/kg lipopolysaccharide (LPS). All LPS injections were given at 9 AM. The first time series was performed on naive rats (day 1). A sequence of six daily injections (days 3-8) of the same dose of LPS followed. The post-LPS time course of the plasma ACTH, CORT and IL-1 beta levels were studies on days 3 (second injection) and 8 (seventh injection). The first LPS injection induced a rapid (30 min) eightfold rise in plasma ACTH and CORT, culminating in concentrations 30 times the baseline at 60 min (ACTH) and 15 times baseline at 120 min (CORT). Both hormones receded back to the initial basal level at 480 min. On the other hand, IL-1 beta increased slowly to peak at 13 times baseline 120 min before declining to minimal seven- to ninefold basal levels, 480 min and even 48 h post-LPS. During the second phase of the experiment starting 48 h after the initial LPS priming sequence, the ACTH and CORT responses to daily recurrent LPS injections again differed from those of IL-1 beta. The post-LPS time courses of the ACTH and CORT reaction displayed a typical pattern of a progressive attenuation studied at days 3 and 8. The peak amplitudes at days 3 and 8 were reduced to 60 and 10%, respectively, for ACTH, and to 85 and 45% for CORT of those observed at the first LPS test. The duration of the response (both) was also shortened from 480 min (first LPS test) to 300 min at days 3 and 8. The post-LPS patterns of the IL-1 beta responses were characterized, first by basal levels seven to nine times higher than the initial baseline values (day 1), and by a rapid suppression of the post-LPS response, with only a slight (30%) increase at day 3 and no increase at day 8. Thus, after both acute and recurrent LPS administration, ACTH/CORT and IL-1 beta reacted differently to the endotoxin challenge. The two LPS reactive systems were not correlated. This is inconsistent with the often proposed role of increased plasma IL-1 beta release as an intermediary factor in the LPS-induced recruitment of the corticotropic axis in general infections