The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

All assignment games with the same core have the same nucleolus

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representative

Getting down to the core of homologous recombination.

In a paper in this week's issue of Science, Voloshin et al. (p. 868) show that a 20-amino acid peptide from RecA, a bacterial protein that repairs and recombines DNA, can mediate DNA strand exchange--one of the functions of the RecA protein. Stasiak discusses why this result is surprising and what the rest of the RecA protein is for.

Microscopic origin of exchange bias in core/shell nanoparticles

We report the results of Monte Carlo simulations with the aim to clarify the microscopic origin of exchange bias in the magnetization hysteresis loops of a model of individual core/shell nanoparticles. Increase of the exchange coupling across the core/shell interface leads to an enhancement of exchange bias and to an increasing asymmetry between the two branches of the loops which is due to different reversal mechanisms. A detailed study of the magnetic order of the interfacial spins shows compelling evidence that the existence of a net magnetization due to uncompensated spins at the shell interface is responsible for both phenomena and allows to quantify the loop shifts directly in terms of microscopic parameters with striking agreement with the macroscopic observed values.

Liquid-liquid phase transition for soft-core attractive potential

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential¿s parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Fine structure of the vaccinia virus gene encoding the precursor of the major core protein 4 a.

A 6008 base pair fragment of the vaccinia virus DNA containing the gene for the precursor of the major core protein 4 a, which has been designated P4 a, was sequenced. A long open reading frame (ORF) encoding a protein of molecular weight 102,157 started close to the position where the P4 a mRNA had been mapped. Analysis of the mRNA by S1 nuclease mapping and primer extension indicated that the 5' end defined by the former method is not the true 5' end. This suggests that the P4 a coding region is preceded by leader sequences that are not derived from the immediate vicinity of the gene, similar to what has been reported for another late vaccinia virus mRNA. The sequenced DNA contained several further ORFs on the same, or opposite DNA strand, providing further evidence for the close spacing of protein-coding sequences in the viral genome.

Molecular basis of leukocyte rolling on PSGL-1. Predominant role of core-2 O-glycans and of tyrosine sulfate residue 51.

Interactions between the leukocyte adhesion receptor L-selectin and P-selectin glycoprotein ligand-1 play an important role in regulating the inflammatory response by mediating leukocyte tethering and rolling on adherent leukocytes. In this study, we have examined the effect of post-translational modifications of PSGL-1 including Tyr sulfation and presentation of sialylated and fucosylated O-glycans for L-selectin binding. The functional importance of these modifications was determined by analyzing soluble L-selectin binding and leukocyte rolling on CHO cells expressing various glycoforms of PSGL-1 or mutant PSGL-1 targeted at N-terminal Thr or Tyr residues. Simultaneous expression of core-2 beta1,6-N-acetylglucosaminyltransferase and fucosyltransferase VII was required for optimal L-selectin binding to PSGL-1. Substitution of Thr-57 by Ala but not of Thr-44, strongly decreased L-selectin binding and leukocyte rolling on PSGL-1. Substitution of Tyr by Phe revealed that PSGL-1 Tyr-51 plays a predominant role in mediating L-selectin binding and leukocyte rolling whereas Tyr-48 has a minor role, an observation that contrasts with the pattern seen for the interactions between PSGL-1 and P-selectin where Tyr-48 plays a key role. Molecular modeling analysis of L-selectin and P-selectin interactions with PSGL-1 further supported these observations. Additional experiments showed that core-2 O-glycans attached to Thr-57 were also of critical importance in regulating the velocity and stability of leukocyte rolling. These observations pinpoint the structural characteristics of PSGL-1 that are required for optimal interactions with L-selectin and may be responsible for the specific kinetic and mechanical bond properties of the L-selectin-PSGL-1 adhesion receptor-counterreceptor pair.

Regular population monotonic allocation schemes and the core

A subclass of games with population monotonic allocation schemes is studied, namelygames with regular population monotonic allocation schemes (rpmas). We focus on theproperties of these games and we prove the coincidence between the core and both theDavis-Maschler bargaining set and the Mas-Colell bargaining set

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

All assignment games with the same core have the same nucleolus

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representative

On the monotonic core

The monotonic core of a cooperative game with transferable utility (T.U.-game) is the set formed by all its Population Monotonic Allocation Schemes. In this paper we show that this set always coincides with the core of a certain game associated to the initial game.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.