Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Modelització de les propietats òptiques de partícules metàl•liques en matriu dielèctrica

En el marc del projecte "Modelització de les propietats òptiques de partícules metàl•liques en matriu dielèctrica" s'han desenvolupat un conjunt d'eines numèriques que permeten avançar en l'ús de l'espectroscòpia òptica per a l'obtenció d'informació morfològica de materials compostos consistents en partícules metàl•liques en matriu dielèctrica. S'han implementat esquemes numèrics per a calcular les propietats òptiques de materials compostos on les partícules poden presentar una distribució de mides i formes i diferent graus d'ordenament espacial. Les simulacions s'han realitzat a dos nivells: i) amb l’aproximació quasi-estàtica, que permet descriure el comportament d'aquests materials en termes de constants òptiques efectives i ii) amb càlculs electrodinàmics exactes, que han servit per avaluar la validesa de l’aproximació anterior i que han permès d'estudiar la interacció de partícules amb feixos de llum focalitzats o amb polarització no homogènia. A través de l’anàlisi d'aquestes simulacions, s'han desenvolupat models senzills que permeten parametritzar la influència de diferents quantitats físiques en el comportament òptic del material. Aquests models s'han implementat en un programari de càlcul que permeten trobar el valor òptim dels paràmetres físics d'interès mitjançant l'ajust d'espectres òptics. Els models s'han avaluat amb l'anàlisi de dades experimentals subministrades per altres laboratoris.

Quantifying urban attractiveness from the distribution and density of digital footprints

In the past, sensors networks in cities have been limited to fixed sensors, embedded in particular locations, under centralised control. Today, new applications can leverage wireless devices and use them as sensors to create aggregated information. In this paper, we show that the emerging patterns unveiled through the analysis of large sets of aggregated digital footprints can provide novel insights into how people experience the city and into some of the drivers behind these emerging patterns. We particularly explore the capacity to quantify the evolution of the attractiveness of urban space with a case study of in the area of the New York City Waterfalls, a public art project of four man-made waterfalls rising from the New York Harbor. Methods to study the impact of an event of this nature are traditionally based on the collection of static information such as surveys and ticket-based people counts, which allow to generate estimates about visitors’ presence in specific areas over time. In contrast, our contribution makes use of the dynamic data that visitors generate, such as the density and distribution of aggregate phone calls and photos taken in different areas of interest and over time. Our analysis provides novel ways to quantify the impact of a public event on the distribution of visitors and on the evolution of the attractiveness of the points of interest in proximity. This information has potential uses for local authorities, researchers, as well as service providers such as mobile network operators.

On prediction of individual sequences

Sequential randomized prediction of an arbitrary binary sequence isinvestigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

Intellectual property rights and efficient firm organization

I show that intellectual property rights yield static efficiency gains, irrespective oftheir dynamic role in fostering innovation. I develop a property-rights model of firmorganization with two dimensions of non-contractible investment. In equilibrium, thefirst best is attained if and only if ownership of tangible and intangible assets is equallyprotected. If IP rights are weaker, firm structure is distorted and efficiency declines:the entrepreneur must either integrate her suppliers, which prompts a decline in theirinvestment; or else risk their defection, which entails a waste of her human capital. Mymodel predicts greater prevalence of vertical integration where IP rights are weaker,and a switch from integration to outsourcing over the product cycle. Both empiricalpredictions are consistent with evidence on multinational companies. As a normativeimplication, I find that IP rights should be strong but narrowly defined, to protect abusiness without holding up its potential spin-offs.

A comparison of stock market mechanisms

This paper studies the relationship between the amount of publicinformation that stock market prices incorporate and the equilibriumbehavior of market participants. The analysis is framed in a static, NREEsetup where traders exchange vectors of assets accessing multidimensionalinformation under two alternative market structures. In the first(the unrestricted system), both informed and uninformed speculators cancondition their demands for each traded asset on all equilibrium prices;in the second (the restricted system), they are restricted to conditiontheir demand on the price of the asset they want to trade. I show thatinformed traders incentives to exploit multidimensional privateinformation depend on the number of prices they can condition upon whensubmitting their demand schedules, and on the specific price formationprocess one considers. Building on this insight, I then give conditionsunder which the restricted system is more efficient than the unrestrictedsystem.

Dynamic perceptual mapping

Perceptual maps have been used for decades by market researchers to illuminatethem about the similarity between brands in terms of a set of attributes, to position consumersrelative to brands in terms of their preferences, or to study how demographic and psychometricvariables relate to consumer choice. Invariably these maps are two-dimensional and static. Aswe enter the era of electronic publishing, the possibilities for dynamic graphics are opening up.We demonstrate the usefulness of introducing motion into perceptual maps through fourexamples. The first example shows how a perceptual map can be viewed in three dimensions,and the second one moves between two analyses of the data that were collected according todifferent protocols. In a third example we move from the best view of the data at the individuallevel to one which focuses on between-group differences in aggregated data. A final exampleconsiders the case when several demographic variables or market segments are available foreach respondent, showing an animation with increasingly detailed demographic comparisons.These examples of dynamic maps use several data sets from marketing and social scienceresearch.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Wage inequality in a frictional labor market

Wage inequality in the United States has grown substantially in thepast two decades. Standard supply-demand analysis in the empiricsof inequality (e.g.Katz and Murphy (1992)) indicates that we mayattribute some of this trend to an outward shift in the demand forhigh skilled labor. In this paper we examine a simple static channelin which the wage premium for skill may grow -increased firm entry.We consider a model of wage dispersion where there are two types ofworkers and homogeneous firms must set wages and preferences forwhat type of worker they would like to hire. We find that both thewage differential and the demand for high skill workers can increasewith the proportion of high skill workers -these high skill workerstherefore 'create' their own demand without exogenous factors. Inaddition, within group wage inequality can increase in step with thebetween group wage inequality. Simulations of the model are providedin order to compare the findings with empirical results.