Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

Dynamic surface tension measurements of surfactant solutions using the maximum bubble pressure method – limits of applicability

One of the essential differences in the design of bubble pressure tensiometers consists in the geometry of the measuring capillaries. To reach extremely short adsorption times of milliseconds and below, the so-called deadtime of the capillaries must be of the order of some 10 ms. In particular, for concentrated surfactant solutions, such as micellar solutions, short deadtimes are needed to minimize the initial surfactant load of the generated bubbles. A theoretical model is derived and confirmed by experiments performed for a wide range of experimental conditions, mainly in respect to variations in deadtime and bubble volume.     

Topics in data assimilation: Stochastic processes

Stochastic models with varying degrees of complexity are increasingly widespread in the oceanic and atmospheric sciences. One application is data assimilation, i.e., the combination of model output with observations to form the best picture of the system under study. For any given quantity to be estimated, the relative weights of the model and the data will be adjusted according to estimated model and data error statistics, so implementation of any data assimilation scheme will require some assumption about errors, which are considered to be random. For dynamical models, some assumption about the evolution of errors will be needed. Stochastic models are also applied in studies of predictability.

The formal theory of stochastic processes was well developed in the last half of the twentieth century. One consequence of this theory is that methods of simulation of deterministic processes cannot be applied to random processes without some modification. In some cases the rules of ordinary calculus must be modified.

The formal theory was developed in terms of mathematical formalism that may be unfamiliar to many oceanic and atmospheric scientists. The purpose of this article is to provide an informal introduction to the relevant theory, and to point out those situations in which that theory must be applied in order to model random processes correctly.     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Reaction field model with free volume for the NMR chemical shift of129Xe dissolved in organic solvents

The temperature dependence of the NMR chemical shift of¹²⁹Xe dissolved in liquid alkanes is examined in the context of the reaction field model. An essential feature of the theory is the inclusion of the temperature dependence of the density of thesolvent. The theory of free volume for liquids is incorporated into the reaction field model to account for this temperature dependence. Comparison of the theory with previously reported measurements indicates the sensitivity of the¹²⁹Xe chemical shift to the free volume of liquids. Incorporation of free volume improves the agreement between measurement and theory for branched alkane solvents, and resolves the origin of the 62 ppm intercept in the plot of reaction field as a function of¹²⁹Xe chemical shift for the n-alkanes.