Isomorphism and embedding of Borel systems on full sets

A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure. For every t>0 we show that in this category there exists a unique free Borel system (Y,S) which is strictly t-universal in the sense that all invariant measures on Y have entropy <t, and if (X,T) is another free system obeying the same entropy condition then X embeds into Y off a null set. One gets a strictly t-universal system from mixing shifts of finite type of entropy at least t by removing the periodic points and "restricting" to the part of the system of entropy <t. As a consequence, after removing their periodic points the systems in the following classes are completely classified by entropy up to Borel isomorphism off null sets: mixing shifts of finite type, mixing positive-recurrent countable state Markov chains, mixing sofic shifts, beta shifts, synchronized subshifts, and axiom-A diffeomorphisms. In particular any two equal-entropy systems from these classes are entropy conjugate in the sense of Buzzi, answering a question of Boyle, Buzzi and Gomez.Comment: 17 pages, v2: correction to bibliograph

Advertising Versus Sales In Demand Creation

Using an analytical model, we investigate the dynamics of a firm with market power whose advertisements and sales contribute to its customers’ stock of goodwill. An advertising campaign precedes the firm’s sales when customers are not familiar with its product, (e.g., movies), whereas sales of a new brand of a familiar product may start without advertising (e.g. Crocs shoes). For constant demand elasticity, both advertising and sales take place from the start. Two different types of solutions then emerge: one for low demand elasticity and one for high demand elasticity. These solutions are analyzed by phase diagrams. We also perform a numerical sensitivity analysis.Dynemic Advertisement, Diffusion, Adoption, Goodwill, Learning by Buying, Phase Diagram

Recent Results on Charm Photoproduction

Photoproduction of $D_s^{\pm}$ mesons has been measured in the ZEUS detector at HERA and compared with predictions of NLO pQCD calculations. The ratio of $D_s^{*\pm}$ to $D^{*\pm}$ cross sections has been compared to results from $e^{+}e^{-}$ experiments. Orbitally excited P-wave charm mesons have been observed in the $D^{*\pm}\pi^{\mp}$ final state. The fraction of $D^{*\pm}$ 's originating from these mesons has been calculated and compared with that from $e^{+}e^{-}$ interactions. No evidence for radially excited mesons decaying to $D^{*\pm}\pi^{+}\pi^{-}$ was found. The inelastic production of J/$\psi$ mesons has been measured and compared to LO and NLO pQCD predictions.Comment: 7 pages, 4 figures, Talk given at the PHOTON 2000 Conference, Ambleside, UK, August 26-31,200

A ratio ergodic theorem for multiparameter non-singular actions

We prove a ratio ergodic theorem for non-singular free $Z^d$ and $R^d$ actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in $R^d$. The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general group actions, the Besicovitch covering property not only implies the maximal inequality, but is equivalent to it, implying that further generalization may require new methods.Comment: 21 pages, to appear in JEM

Is “Race” Modern? Disambiguating the Question

Race theorists have been unable to reach a consensus regarding the basic historical question, “is ‘race’ modern?” I argue that this is partly because the question itself is ambiguous. There is not really one question that race scholars are answering, but at least six. First, is the concept of race modern? Second, is there a modern concept of race that is distinct from earlier race concepts? Third, are “races” themselves modern? Fourth, are racialized groups modern? Fifth, are the means and methods associated with racialization modern? And sixth, are the meanings attached to racialized traits modern? Because these questions have different answers, the debate about the historical origins of “race” cannot be resolved unless they are distinguished. I will explain the ways in which “race” is and is not modern by answering these questions, thereby offering a resolution to a seemingly intractable problem

Upcrossing inequalities for stationary sequences and applications

For arrays $(S_{i,j})_{1\leq i\leq j}$ of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process $(S_{1,n})_{n=1}^{\infty}$ can be bounded in terms of a measure of the ``mean subadditivity'' of the process $(S_{i,j})_{1\leq i\leq j}$. We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon--MacMillan--Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.Comment: Published in at http://dx.doi.org/10.1214/09-AOP460 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org