Almost Budget Balanced Mechanisms with Scalar Bids For Allocation of a Divisible Good

This paper is about allocation of an infinitely divisible good to several rational and strategic agents. The allocation is done by a social planner who has limited information because the agents' valuation functions are taken to be private information known only to the respective agents. We allow only a scalar signal, called a bid, from each agent to the social planner. Yang and Hajek [Jour. on Selected Areas in Comm., 2007] as well as Johari and Tsitsiklis [Jour. of Oper. Res., 2009] proposed a scalar strategy Vickrey-Clarke-Groves (SSVCG) mechanism with efficient Nash equilibria. We consider a setting where the social planner desires minimal budget surplus. Example situations include fair sharing of Internet resources and auctioning of certain public goods where revenue maximization is not a consideration. Under the SSVCG framework, we propose a mechanism that is efficient and comes close to budget balance by returning much of the payments back to the agents in the form of rebates. We identify a design criterion for {\em almost budget balance}, impose feasibility and voluntary participation constraints, simplify the constraints, and arrive at a convex optimization problem to identify the parameters of the rebate functions. The convex optimization problem has a linear objective function and a continuum of linear constraints. We propose a solution method that involves a finite number of constraints, and identify the number of samples sufficient for a good approximation.Comment: Accepted for publication in the European Journal of Operational Research (EJOR

A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks

We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on factored-out, partial reaction propensities. This novel exact SSA, called the partial propensity direct method (PDM), is highly efficient and has a computational cost that scales at most linearly with the number of chemical species, irrespective of the degree of coupling of the reaction network. In addition, we propose a sorting variant, SPDM, which is especially efficient for multiscale reaction networks.Comment: 23 pages, 3 figures, 4 tables; accepted by J. Chem. Phy

Nonequilibrium phase transitions in models of adsorption and desorption

The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of particles is finite to one in which it grows linearly in time. The exponents characterizing the mass distribution near the critical point are calculated in all dimensions.Comment: 10 pages, 2 figures (To appear in Phys. Rev. E

Who is Afraid of the Friedman Rule?

In this paper, we explore the connection between optimal monetary policy and heterogeneity among agents. We study a standard monetary economy with two types of agents in which the stationary distribution of money holdings is non-degenerate. Sans type-specific fiscal policy, we show that the zero-nominal-interest rate policy (the Friedman rule) does not maximize type-specific welfare; it may not maximize aggregate social welfare either. Indeed, one or, more surprisingly, both types may benefit if the central bank deviates from the Friedman rule. Our results suggest a positive explanation for why central banks around the world do not implement the Friedman rule.Friedman rule, monetary policy, money-in-the-utility-function

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady states, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite size system, however, continues to show a signature of the original transition, and we characterize the finite size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte

Amenorrhea Due to Defects in Steroid Biosynthesis

Amenorrhea as the first manifestation of a steroid biosynthetic defect is rather unusual. The common forms of congenital adrenal hyperplasia are classic examples of steroid biosynthetic defects. Yet in genotypic females, this disorder is usually evident from birth because of virilization. Effective treatment usually ensues and amenorrhea is only a problem when control is inadequate. However, there are individuals whose disorder will be manifest for the first time in the postnatal or adult period. In addition, multiple other steroid defects have now been clearly delineated. Many of these individuals will have amenorrhea, virilization, or sexual ambiguities as part of the clinical picture. The paper will describe some of the more clearly delineated steroidal biosynthetic defects. Also the clinical management of patients with postnatal onset of 21-hydroxylase deficiency form of congenital adrenal hyperplasia will be discussed