Social differences in women's use of personal care products: A study of magazine advertisements, 1950 - 1994

This study examined advertising for women's personal care products from 1950 through 1994 in widely read, long-lived magazines whose audience have different demographic profiles: Ladies' Home Journal, Mademoiselle, and Essence

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Martingale Models for Quantum State Reduction

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations experienced by the expectation of the observable during the course of the reduction process and an upper bound is established for the ensemble average of the greatest fluctuations incurred. We consider the general projection postulate of L\"uders applicable in the case of a possibly degenerate eigenvalue spectrum, and derive this result rigorously from the underlying stochastic dynamics for state reduction in the case of both a pure and a mixed initial state. We also analyse the associated Lindblad equation for the evolution of the density matrix, and obtain an exact time-dependent solution for the state reduction that explicitly exhibits the transition from a general initial density matrix to the L\"uders density matrix. Finally, we apply Girsanov's theorem to derive a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.Comment: 30 pages LaTeX. Submitted to Journal of Physics

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Inferring Networks of Substitutable and Complementary Products

In a modern recommender system, it is important to understand how products relate to each other. For example, while a user is looking for mobile phones, it might make sense to recommend other phones, but once they buy a phone, we might instead want to recommend batteries, cases, or chargers. These two types of recommendations are referred to as substitutes and complements: substitutes are products that can be purchased instead of each other, while complements are products that can be purchased in addition to each other. Here we develop a method to infer networks of substitutable and complementary products. We formulate this as a supervised link prediction task, where we learn the semantics of substitutes and complements from data associated with products. The primary source of data we use is the text of product reviews, though our method also makes use of features such as ratings, specifications, prices, and brands. Methodologically, we build topic models that are trained to automatically discover topics from text that are successful at predicting and explaining such relationships. Experimentally, we evaluate our system on the Amazon product catalog, a large dataset consisting of 9 million products, 237 million links, and 144 million reviews.Comment: 12 pages, 6 figure

Quantum noise and stochastic reduction

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schrodinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this article, two such models are investigated: one that achieves state reduction in infinite time, and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions--algebraic in character and involving no integration--are obtained for both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system, and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems.Comment: 50 page

Separable approximation to two-body matrix elements

Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the transformation to center of mass and relative coordinate (in the spirit of Talmi's method) and therefore it is only useful (finite number of expansion terms) for harmonic oscillator single particle states. The converge of the expansion with the number of terms retained is studied for a Gaussian two body interaction. The limit of a contact (delta) force is also considered. Ways to handle the general case are also discussed.Comment: 10 pages, 5 figures (for high resolution versions of some of the figures contact the author

Generalized seniority from random Hamiltonians

We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J=0 ground states and an energy gap, but the relationship between ground state wave functions of neighboring nuclei show signatures of pairing as well. Matrix elements of pair creation/annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required.Comment: 10 pages, 7 figure

REACTIVITY OF CHLOROPHYLL a/b-PROTEINS AND MICELLAR TRITON X-100 COMPLEXES OF CHLOROPHYLLS a OR b WITH BOROHYDRIDE

The reaction of several plant chlorophyll-protein complexes with NaBH4 has been studied by absorption spectroscopy. In all the complexes studied, chlorophyll b is more reactive than Chi a, due to preferential reaction of its formyl substituent at C-7. The complexes also show large variations in reactivity towards NaBH4 and the order of reactivity is: LHCI > PSII complex > LHCII > PSI > P700 (investigated as a component of PSI). Differential pools of the same type of chlorophyll have been observed in several complexes. Parallel work was undertaken on the reactivity of micellar complexes of chlorophyll a and of chlorophyll b with NaBH4 to study the effect of aggregation state on this reactivity. In these complexes, both chlorophyll a and b show large variations in reactivity in the order monomer > oligomer > polymer with chlorophyll b generally being more reactive than chlorophyll a. It is concluded that aggregation decreases the reactivity of chlorophylls towards NaBH4 in vitro, and may similarly decrease reactivity in naturally-occurring chlorophyll-protein complexes