No abstract

We generalize the multiparty communication model of Chandra, Furst, and Lipton (1983) to functions with b-bit output (b = 1 in the CFL model). We allow the players to receive up to b−1 bits of information from an all-powerful benevolent Helper who can see all the input. Extending results of Babai, Nisan, and Szegedy (1992) to this model, we construct families of explicit functions for which Ω(n/c k ) bits of communication are required to find the "missing bit," where n is the length of each player's input and k is the number of players. As a consequence we settle the problem of separating the one-way vs. multiround communication complexities (in the CFL sense) for k ≤ (1 − ) log n players, extending a result of Nisan and Wigderson (1991) who demonstrated this separation for k = 3 players. As a by-product we obtain Ω(n/c k ) lower bounds for the multiparty complexity (in the CFL sense) of new families of explicit boolean functions (not derivable from BNS). The proofs exploit the interplay between two concepts of multicolor discrepancy; discrete Fourier analysis is the basic tool. We also include an unpublished lower bound by A. Wigderson regarding the one-way complexity of the 3-party pointer jumping function.

In the multiparty communication game (CFL-game) of Chandra, Furst, and Lipton (Proc. 15th ACM STOC, 1983, 94-99) k players collaboratively evaluate a function f (x 0 , . . . , x k−1 ) in which player i knows all inputs except x i . The players have unlimited computational power. The objective is to minimize communication.In this paper, we study the Simultaneous Messages (SM) model of multiparty communication complexity. The SM model is a restricted version of the CFL-game in which the players are not allowed to communicate with each other. Instead, each of the k players simultaneously sends a message to a referee, who sees none of the inputs. The referee then announces the function value.We prove lower and upper bounds on the SM-complexity of several classes of explicit functions. Our lower bounds extend to randomized SM complexity via an entropy argument. A lemma establishing a tradeoff between average Hamming distance and range size for transformations of the Boolean cube might be of independent interest.Our lower bounds on SM-complexity imply an exponential gap between the SM-model and the CFL-model for up to (log n) 1− players, for any > 0. This separation is obtained by comparing the respective complexities of the generalized addressing function, GAF G,k , where G is a group of order n. We also combine our lower bounds on SM complexity with ideas of Håstad and Goldmann (Computational Complexity 1 (1991), 113-129) to derive superpolynomial lower bounds for certain depth-2 circuits computing a function related to the GAF function.We prove some counter-intuitive upper bounds on SM-complexity. We show that GAF Z t 2 ,3has SM-complexity O(n 0.92 ). When the number of players is at least c log n, for some constant c > 0, our SM protocol for GAF Z t 2 ,k has polylog(n) complexity. We also examine a class of functions defined by certain depth-2 circuits. This class includes the "Generalized Inner Product" function and "Majority of Majorities." When the number of players is at least 2+log n, we obtain polylog(n) upper bounds for this class of functions.

No abstract

The concentrations of plasma epinephrine (E) and norepinephrin (N) measured at rest in bullfrogs (Rana catesbeiana) were 12.0 and 8.2 nmol liter-1 respectively: the ratio of [E]/[N] was 1.33 (+/- SE 0.35). Adrenal glands contained high concentrations of epinephrine (2,923 nmole g wet weight-1) and norepinephrine (6,194), at a ratio of 0.46 (+/- SE 0.04) [E]/[N]. This differs from the measured plasma ratio and endogenous release ratios of about 2 for [E]/[N] reported for other Rana species, although the 95% confidence interval of our plasma ratio (0.97) spans the range of values from 0.36 to 2.3, including the observed plasma ratio of 0.46. Therefore, resting plasma catecholamine levels generally reflect the proportional adrenal content of catecholamines. Plasma epinephrine and norepinephrine concentrations significantly increased after activity to 50.4 and 18.1 nmol liter-1, respectively. The ratio of epinephrine to norepinephrine ([E]/[N]) also increased (but not significantly) to 8.53 (+/- SE 4.23), suggesting a shift away from some adrenal tone at rest to sympathetic nerve dominance with activity. Graded hemorrhage led to further increases in plasma epinephrine concentration and [E]/[N] but not norepinephrine, indicating sympathetic but not adrenal involvement. The in vitro epinephrine sensitivity of vascular beds indicates recruitment of the dorsal aorta vascular beds before the pulmocutaneous vascular bed. The minimum sensitivity of vascular beds to perfused epinephrine (10(4) nmol liter-1) was at higher concentrations than maximal plasma concentrations measured during hemorrhage. The bullfrog is less tolerant of hemorrhage than the cane toad Bufo marinus. The major difference in the catecholamine response of these two species was the massive contribution of adrenal catecholamines with severe hemorrhage in toads, which is absent in bullfrogs. This suggests that the enhanced hemorrhage and dehydration tolerance of toads may in part be the result of their greater adrenal gland development and activity.