Speed of convergence of recursive least squares learning with ARMA perceptions

This paper fills a gap in the existing literature on least squareslearning in linear rational expectations models by studying a setup inwhich agents learn by fitting ARMA models to a subset of the statevariables. This is a natural specification in models with privateinformation because in the presence of hidden state variables, agentshave an incentive to condition forecasts on the infinite past recordsof observables. We study a particular setting in which it sufficesfor agents to fit a first order ARMA process, which preserves thetractability of a finite dimensional parameterization, while permittingconditioning on the infinite past record. We describe how previousresults (Marcet and Sargent [1989a, 1989b] can be adapted to handlethe convergence of estimators of an ARMA process in our self--referentialenvironment. We also study ``rates'' of convergence analytically and viacomputer simulation.

Country asymmetries, endogenous product choice and the speed of trade liberalization

In a world with two countries which differ in size, we study theimpact of (the speed of) trade liberalization on firms' profitsand total welfare of the countries involved. Firms correctlyanticipate the pace of trade liberalization and take it intoaccount when deciding on their product choices, which areendogenously determined at the beginning of the game. Competitionin the marketplace then occurs either on quantities or on prices.As long as the autarkic phase continues, local firms are nationalmonopolists. When trade liberalization occurs, firms compete in aninternational duopoly. We analyze trade effects by using twodifferent models of product differentiation. Across all thespecifications adopted (and independently of the price v. quantitycompetition hypothesis), total welfare always unambiguously riseswith the speed of trade liberalization: Possible losses by firmsare always outweighed by consumers' gains, which come under theform of lower prices, enlarged variety of higher average qualitiesavailable. The effect on profits depends on the type of industryanalyzed. Two results in particular seem to be worth of mention.With vertical product differentiation and fixed costs of qualityimprovements, the expected size of the market faced by the firmsdetermines the incentive to invest in quality. The longer the periodof autarky, the lower the possibility that the firm from the smallcountry would be producing the high quality and be the leader in theinternational market when it opens. On the contrary, when trade opensimmediately, national markets do not play any role and firms fromdifferent countries have the same opportunity to become the leader.Hence, immediate trade liberalization might be in the interest ofproducers in the small country. In general, the lower the size of thesmall country, the more likely its firm will gain from tradeliberalization. Losses from the small country firm can arise when itis relegated to low quality good production and the domestic marketsize is not very small. With horizontal product differentiation (thehomogeneous good case being a limit case of it when costs ofdifferentiation tend to infinity), investments in differentiationbenefit both firms in equal manner. Firms from the small country do notrun the risk of being relegated to a lower competitive position undertrade. As a result, they would never lose from it. Instead, firms fromthe large country may still incur losses from the opening of trade whenthe market expansion effect is low (i.e. when the country is very largerelative to the other).

Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

Assessment of speed of human locomotion using a differential satellite global positioning system.

PURPOSE: The objective was to explore whether a satellite-based navigation system, global positioning system used in differential mode (DGPS), could accurately assess the speed of running in humans. METHODS: A subject was equipped with a portable GPS receptor coupled to a receiver for differential corrections, while running outdoors on a straight asphalt road at 27 different speeds. Actual speed (reference method) was assessed by chronometry. RESULTS: The accuracy of speed prediction had a standard deviation (SD) of 0.08 km x h(-1) for walking, 0.11 km x h(-1) for running, yielding a coefficient of variation (SD/mean) of 1.38% and 0.82%, respectively. There was a highly significant linear relationship between actual and DGPS speed assessment (r2 = 0.999) with little bias in the prediction equation, because the slope of the regression line was close to unity (0.997). CONCLUSION: the DGPS technique appears to be a valid and inconspicuous tool for "on line" monitoring of the speed of displacement of individuals located on any field on earth, for prolonged periods of time and unlimited distance, but only in specific environmental conditions ("open sky"). Furthermore, the accuracy of speed assessment using the differential GPS mode was improved by a factor of 10 as compared to non-differential GPS.

Food's visually perceived fat content affects discrimination speed in an orthogonal spatial task.

Choosing what to eat is a complex activity for humans. Determining a food's pleasantness requires us to combine information about what is available at a given time with knowledge of the food's palatability, texture, fat content, and other nutritional information. It has been suggested that humans may have an implicit knowledge of a food's fat content based on its appearance; Toepel et al. (Neuroimage 44:967-974, 2009) reported visual-evoked potential modulations after participants viewed images of high-energy, high-fat food (HF), as compared to viewing low-fat food (LF). In the present study, we investigated whether there are any immediate behavioural consequences of these modulations for human performance. HF, LF, or non-food (NF) images were used to exogenously direct participants' attention to either the left or the right. Next, participants made speeded elevation discrimination responses (up vs. down) to visual targets presented either above or below the midline (and at one of three stimulus onset asynchronies: 150, 300, or 450 ms). Participants responded significantly more rapidly following the presentation of a HF image than following the presentation of either LF or NF images, despite the fact that the identity of the images was entirely task-irrelevant. Similar results were found when comparing response speeds following images of high-carbohydrate (HC) food items to low-carbohydrate (LC) food items. These results support the view that people rapidly process (i.e. within a few hundred milliseconds) the fat/carbohydrate/energy value or, perhaps more generally, the pleasantness of food. Potentially as a result of HF/HC food items being more pleasant and thus having a higher incentive value, it seems as though seeing these foods results in a response readiness, or an overall alerting effect, in the human brain.

Variation in performance across Swiss mammography screening programmes: the influence of reading strategy and experience.

[Abstract] Reading volume and mammography screening performance appear positively correlated. Performance was compared across organised Swiss screening programmes, which target relatively small populations. Except for accreditation of 2nd readers radiologists (restrictive vs non-restrictive strategy), Swiss programmes have similar screening regimen/procedures and duration, which maximises comparability. Variation in performance was explored in order to improve mammography practice and optimise screening performance. Indicators of quality and effectiveness were evaluated for about 200,000 screens performed over 4 screening rounds in the 3 longest-standing Swiss cantonal programmes (of Vaud, Geneva and Valais). Interval cancers were identified by linkage with cancer registries records. Most European standards of performance were met with a favourable cancer stage shift. Several performance indicators showed substantial variation across programmes. In subsequent rounds, compared with programmes (Vaud and Geneva) which accredited few 2nd readers to increase their individual reading volume, proportions of in situ lesions and of small cancers (? 1cm) were one third lower and halved, respectively, and the proportion of advanced lesions (stage II+) nearly 50% higher in the programme without a restrictive selection strategy. Discrepancy in second-year proportional incidence of interval cancers appears to be multicausal. Differences in performance could partly be explained by a selective strategy for 2nd readers and a prior experience in service screening, but not by the levels of opportunistic screening and programme attendance. This study provides clues for enhancing mammography screening performance in low-volume Swiss programmes.

Speed Limit Questions? Here’s Your Answer, July 6, 2005

Iowa’s speed regulations are based on the same basic speed law that is used in all 50 states: “Any person driving a motor vehicle on a highway shall drive the same at a careful and prudent speed not greater than nor less than is reasonable and proper, having due regard to the traffic, surface, and width of the highway and of any other conditions then existing, and no person shall drive any vehicle upon a highway at a speed greater than will permit the person to bring it to a stop within the assured clear distance ahead, such driver having the right to assume, however, that all persons using said highway will observe the law.” Statutory limits are based on the concept that uniform categories of highways can be traveled safely at certain preset maximum speeds under ideal conditions. Whether the speed limit is posted or unposted, drivers should reduce their speed below these values in poor weather, heavy traffic, and under other potentially hazardous conditions.

Determination of sea surface salinity and wind speed by L-band microwave radiometry from a fixed platform

The European Space Agency Soil Moisture andOcean Salinity (SMOS) mission aims at obtaining global maps ofsoil moisture and sea surface salinity from space for large-scale andclimatic studies. It uses an L-band (1400–1427 MHz) MicrowaveInterferometric Radiometer by Aperture Synthesis to measurebrightness temperature of the earth’s surface at horizontal andvertical polarizations ( h and v). These two parameters will beused together to retrieve the geophysical parameters. The retrievalof salinity is a complex process that requires the knowledge ofother environmental information and an accurate processing ofthe radiometer measurements. Here, we present recent resultsobtained from several studies and field experiments that were partof the SMOS mission, and highlight the issues still to be solved.

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

The prediction of speed and incline in outdoor running in humans using accelerometry.

PURPOSE: To explore whether triaxial accelerometric measurements can be utilized to accurately assess speed and incline of running in free-living conditions. METHODS: Body accelerations during running were recorded at the lower back and at the heel by a portable data logger in 20 human subjects, 10 men, and 10 women. After parameterizing body accelerations, two neural networks were designed to recognize each running pattern and calculate speed and incline. Each subject ran 18 times on outdoor roads at various speeds and inclines; 12 runs were used to calibrate the neural networks whereas the 6 other runs were used to validate the model. RESULTS: A small difference between the estimated and the actual values was observed: the square root of the mean square error (RMSE) was 0.12 m x s(-1) for speed and 0.014 radiant (rad) (or 1.4% in absolute value) for incline. Multiple regression analysis allowed accurate prediction of speed (RMSE = 0.14 m x s(-1)) but not of incline (RMSE = 0.026 rad or 2.6% slope). CONCLUSION: Triaxial accelerometric measurements allows an accurate estimation of speed of running and incline of terrain (the latter with more uncertainty). This will permit the validation of the energetic results generated on the treadmill as applied to more physiological unconstrained running conditions.

Assessing High-Speed Internet Access in the State of Iowa: Sixth Assessment, January 2008

This Assessment gauges the availability of highspeed Internet access to both rural and non-rural Iowans. The Board continues to evaluate the progress in the deployment of high-speed Internet access through this Sixth Assessment, including information related to Internet speeds available to consumers and pricing of high-speed Internet services. Comparison of this Assessment with the earlier efforts is critical if a clear perspective on the developing availability of high-speed Internet access to all residents of the State of Iowa is desired.