Collaborative effects in polymer translocation and the appearance of fictitious free-energy barriers.

The translocation time of a polymer through a pore under the influence of an external field depends on a number of parameters, the most important of which are the field strength, the interaction with the pore, and the confinement entropy. Experimentally, the translocation is dominated either by the driving force (electrophoretic regime) or by the entropy of confinement or pore interaction (barrier dominated regime). In this Rapid Communication we study a simple model for polymer translocation, loosely based on the asymmetric exclusion process, which shows that it is possible to have what experimentally would be interpreted as barrier dominated, even where there is no barrier to translocation. This effective barrier is interpreted as being due to collaborative effects between the monomers forming the polymer chain.

Single polymer gating of channels under a solvent gradient.

We study the effect of a gradient of solvent quality on the coil-globule transition for a polymer in a narrow pore. A simple self-attracting, self-avoiding walk model of a polymer in solution shows that the variation in the strength of the interaction across the pore leads the system to go from one regime (good solvent) to the other (poor solvent) across the channel. This may be thought to be analogous to thermophoresis, where the polymer goes from the hot region to the cold region under the temperature gradient. The behavior of short chains is studied using exact enumeration while the behavior of long chains is studied using transfer matrix techniques. The distribution of the monomer density across the layer suggests that a gatelike effect can be created, with potential applications as a sensor.

Translocation of short and long polymers through an interacting pore.

We perform two-dimensional Langevin dynamics simulations of electric-field driven polymer translocation through an attractive nanopore. We investigate the effect of the location of the attractive region using different pore patterns. This is found to have an impact on both the translocation time as a function of the chain length and on the polymer entry frequency. We qualitatively compare our results to available experimental data.

Generalized interacting self-avoiding trails on the square lattice: phase diagram and critical behavior.

A generalized model for interacting self-avoiding trails on a square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and crossings. Rigidity is also included in the model. The model includes the Nienhuis O(n=0) model and the interacting self-avoiding trail model as special cases. It is shown that the generic type of collapse found is the same as in the pure interacting self-avoiding trail model.

Bethe approximation for a DNA-like self-avoiding walk model with variable solvent quality.

The phase diagram and critical behavior of a simple toy model for DNA zipping/unzipping are examined in the framework of the Bethe approximation. The effects of solvent quality are included and found to lead to a variety of different thermodynamic behaviors.

Bethe approximation for the hydrogen-bonding self-avoiding walk in a solvent.

A square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, extended to include the effects of solvent quality, is examined in the framework of the Bethe approximation.

Statistical mechanics of the two-dimensional hydrogen-bonding self-avoiding walk including solvent effects.

A two-dimensional square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, is extended to include the effects of solvent quality. This is achieved by allowing configuration-dependent nearest-neighbor interactions. The phase diagram is presented and found to have a much richer variety of phases than either the pure hydrogen-bonding self-avoiding walk model or the standard Theta-point model.

Corner-transfer-matrix renormalization-group method for two-dimensional self-avoiding walks and other O(n) models.

We present an extension of the corner-transfer-matrix renormalization-group (CTMRG) method to O(n) invariant models, with particular interest in the self-avoiding walk class of models [O(n=0)]. The method is illustrated using an interacting self-avoiding walk model. Based on the efficiency and versatility, when compared to other available numerical methods, we present the CTMRG as the method of choice for two-dimensional self-avoiding walk problems.

On the impossibility of predicting the behavior of rational agents.

A foundational assumption in economics is that people are rational: they choose optimal plans of action given their predictions about future states of the world. In games of strategy this means that each player's strategy should be optimal given his or her prediction of the opponents' strategies. We demonstrate that there is an inherent tension between rationality and prediction when players are uncertain about their opponents' payoff functions. Specifically, there are games in which it is impossible for perfectly rational players to learn to predict the future behavior of their opponents (even approximately) no matter what learning rule they use. The reason is that in trying to predict the next-period behavior of an opponent, a rational player must take an action this period that the opponent can observe. This observation may cause the opponent to alter his next-period behavior, thus invalidating the first player's prediction. The resulting feedback loop has the property that, a positive fraction of the time, the predicted probability of some action next period differs substantially from the actual probability with which the action is going to occur. We conclude that there are strategic situations in which it is impossible in principle for perfectly rational agents to learn to predict the future behavior of other perfectly rational agents based solely on their observed actions.

Met and unmet demand for hospital beds. Some recent evidence.

Many commentators have noted the interrelation of demand and supply of hospital beds and have suggested that an increase in the supply of hospital beds tends to generate additional demand either in the form of more patients admitted or patients treated for longer periods of time or some combination of the two. We can report that the bed use rate can be predicted more accurately in terms of the five-seventh rule, that is if a National Health Service bed is made available for an additional week, then for five out of seven days it will be occupied. This rule was found to apply at both regional and district level. Variation in admission rates was also investigated and it was found that a large proportion of the observed variation could be explained in terms of one variable--bed supply. In view of the Resource Allocation Working Party's proposals, the relationship between the overall standardized mortality ratio and bed supply, admissions rate and bed use rate was investigated. No significant effect, however, was discovered. In other words, it is bed supply which strongly influences the demand for hospital care and not the overall standardized mortality ratio.