Extending the Generalized Multinomial Logit Model: Error Scale and Decision-Maker Characteristics

This essay contributes to the development of models that allow for heterogeneity across respondents in the error scale of the multinomial logit model. The potential to explain respondent heterogeneity by differences in error scale has been recognized for some time (Louviere 2001), but models that allow for continuous error scale heterogeneity have only recently been developed (Sonnier, Ainslie and Otter 2007, Keane et al. 2009). The most general of these models is the “Generalized Multinomial Logit Model” (G-MNL), which allows for heterogeneity both in error scale and all attribute preferences, including the price attribute (Keane et al. 2009). We further develop the G-MNL by proposing a Bayesian estimation strategy, allowing for straightforward incorporation of decision-maker characteristics as covariates to individual-level error scale, in a way that is computationally tractable. In a data set on personal computer (PC) choices in a survey setting (Lenk et al. 1996), we find that respondents who are older have higher average error scale indicating that they make less reliable decisions than those who are younger. Respondents who perceive themselves to be expert when it comes to making PC choices have lower average error scale, indicating that they make more reliable choices. These findings are consistent with recent theorizing on the relationship between cognitive resources and error scale (Swait and Adamowicz 2001). We also facilitate the use of G-MNL in practice by empirically exploring the data requirements for obtaining accurate estimates of the G-MNL and find that estimating this model requires a somewhat larger number of respondents and a larger number of observed choices per respondent than is typical in commercial market research

Selective amplification of scars in a chaotic optical fiber

In this letter we propose an original mechanism to select scar modes through coherent gain amplification in a multimode D-shaped fiber. More precisely, we numerically demonstrate how scar modes can be amplified by positioning a gain region in the vicinity of specific points of a short periodic orbit known to give rise to scar modes

Efficient evaluation of accuracy of molecular quantum dynamics using dephasing representation

Ab initio methods for electronic structure of molecules have reached a satisfactory accuracy for calculation of static properties, but remain too expensive for quantum dynamical calculations. We propose an efficient semiclassical method for evaluating the accuracy of a lower level quantum dynamics, as compared to a higher level quantum dynamics, without having to perform any quantum dynamics. The method is based on dephasing representation of quantum fidelity and its feasibility is demonstrated on the photodissociation dynamics of CO2. We suggest how to implement the method in existing molecular dynamics codes and describe a simple test of its applicability.Comment: 5 pages, 2 figure

Ultrahigh harmonics from laser-assisted ion-atom collisions

We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.Comment: 5 pages, 4 figure

Quaternionic Madelung Transformation and Non-Abelian Fluid Dynamics

In the 1920's, Madelung noticed that if the complex Schroedinger wavefunction is expressed in polar form, then its modulus squared and the gradient of its phase may be interpreted as the hydrodynamic density and velocity, respectively, of a compressible fluid. In this paper, we generalize Madelung's transformation to the quaternionic Schroedinger equation. The non-abelian nature of the full SU(2) gauge group of this equation leads to a richer, more intricate set of fluid equations than those arising from complex quantum mechanics. We begin by describing the quaternionic version of Madelung's transformation, and identifying its ``hydrodynamic'' variables. In order to find Hamiltonian equations of motion for these, we first develop the canonical Poisson bracket and Hamiltonian for the quaternionic Schroedinger equation, and then apply Madelung's transformation to derive non-canonical Poisson brackets yielding the desired equations of motion. These are a particularly natural set of equations for a non-abelian fluid, and differ from those obtained by Bistrovic et al. only by a global gauge transformation. Because we have obtained these equations by a transformation of the quaternionic Schroedinger equation, and because many techniques for simulating complex quantum mechanics generalize straightforwardly to the quaternionic case, our observation leads to simple algorithms for the computer simulation of non-abelian fluids.Comment: 15 page

Archeological Investigations At The Old Pecos Cemetery (41RV127), Reeves County, Texas

This report summarizes the results of archeological and historical investigations for the Old Pecos Cemetery in Pecos City, Reeves County, Texas. Colgate Energy plans to purchase the area around the cemetery and construct oil and gas facilities on that property. The Old Pecos Cemetery contains graves interred from 1881 to around 1910. It occupies an area of about 0.33 acres and is known to contain many unmarked burials. Colgate Energy hired AmaTerra in August 2017 to investigate outside the fenced limits of the cemetery, to determine whether any unmarked graves are located outside it, and if so, determine the extent of the graves so that they can be avoided. The land is currently owned by Reeves County, a political subdivision of the State of Texas. Therefore, an Antiquities Permit was required under the Antiquities Code of Texas. Work was conducted under Permit No. 8138 and consisted of visual inspection, mechanical scraping using a road grader, and archival research. The survey documented 51 unmarked grave shafts and 10 surface features that likely represent graves within an area encompassing approximately 4.2 acres. AmaTerra documented the expanded cemetery as site 41RV127, and has recorded the new boundary at the Reeves County Clerk’s Office, as required under Chapter 711.011 of the Texas Health and Safety Code. This report recommends that the cemetery 41RV127 is of undetermined eligibility as a State Antiquities Landmark; and further recommends fencing the new cemetery boundary to avoid impacts to marked and unmarked graves within it. No artifacts were collected during the survey, but all notes and records from field investigation will be curated the Center for Archaeological Studies at Texas State University in San Marcos

Improved Semiclassical Approximation for Bose-Einstein Condensates: Application to a BEC in an Optical Potential

We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in the sense that one only needs to solve an effective 1D nonlinear Schrodinger equation, but the solution incorporates correct 3D aspects of the problem. The solution in classically allowed regions is matched onto that in classically forbidden regions by a connection formula that properly accounts for the nonlinear mean-field interaction. Special cases for vortex solutions are treated too. Comparisons of the Q1D solution with full 3D and Thomas-Fermi ones are presented.Comment: 14 pages, 5 figure

Time evolution for quantum systems at finite temperature

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check selfconsistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable.Comment: uuencoded, 14 pp in Latex, 8 ps Fig

Reality Check: Combining Survey and Market Data to Estimate the Importance of Product Attributes

Discrete choice models estimated using hypothetical choices made in a survey setting (i.e., choice experiments) are widely used to estimate the importance of product attributes in order to make product design and marketing mix decisions. Choice experiments allow the researcher to estimate preferences for product features that do not yet exist in the market. However, parameters estimated from experimental data often show marked inconsistencies with those inferred from the market, reducing their usefulness in forecasting and decision making. We propose an approach for combining choice-based conjoint data with individual-level purchase data to produce estimates that are more consistent with the market. Unlike prior approaches for calibrating conjoint models so that they correctly predict aggregate market shares for a “baseline” market, the proposed approach is designed to produce parameters that are more consistent with those that can be inferred from individual-level market data. The proposed method relies on a new general framework for combining two or more sources of individual-level choice data to estimate a hierarchical discrete choice model. Past approaches to combining choice data assume that the population mean for the parameters is the same across both data sets and require that data sets are sampled from the same population. In contrast, we incorporate in the model individual characteristic variables, and assert only that the mapping between individuals\u27 characteristics and their preferences is the same across the data sets. This allows the model to be applied even if the sample of individuals observed in each data set is not representative of the population as a whole, so long as appropriate product-use variables are collected that can explain the systematic deviations between them. The framework also explicitly incorporates a model for the individual characteristics, which allows us to use Bayesian missing-data techniques to handle the situation where each data set contains different demographic variables. This makes the method useful in practice for a wide range of existing market and conjoint data sets. We apply the method to a set of conjoint and market data for minivan choice and find that the proposed method predicts holdout market choices better than a model estimated from conjoint data alone or a model that does not include demographic variables

Measuring Multi-Channel Advertising Effectiveness Using Consumer-Level Advertising Response Data

Advances in data collection have made it increasingly easy to collect information on advertising exposures. However, translating this seemingly rich data into measures of advertising response has proven difficult, largely because of concerns that advertisers target customers with a higher propensity to buy or increase advertising during periods of peak demand. We show how this problem can be addressed by studying a setting where a firm randomly held out customers from each campaign, creating a sequence of randomized field experiments that mitigates (many) potential endogeneity problems. Exploratory analysis of individual holdout experiments shows positive effects for both email and catalog; however, the estimated effect for any individual campaign is imprecise, because of the small size of the holdout. To pool data across campaigns, we develop a hierarchical Bayesian model for advertising response that allows us to account for individual differences in purchase propensity and marketing response. Building on the traditional ad-stock framework, we are able to estimate separate decay rates for each advertising medium, allowing us to predict channel-specific short- and long-term effects of advertising and use these predictions to inform marketing strategy. We find that catalogs have substantially longer-lasting impact on customer purchase than emails. We show how the model can be used to score and target individual customers based on their advertising responsiveness, and we find that targeting the most responsive customers increases the predicted returns on advertising by approximately 70% versus traditional recency, frequency, and monetary value-based targeting