When “Close Enough” is Not Enough: Accommodating the Religiously Devout

Title VII of the Civil Rights Act of 1964 requires employers to “reasonably accommodate” employees’ religious practices that conflict with work requirements unless doing so would cause undue hardship to their business operations. Can an accommodation be reasonable if it only partially removes the conflict between an employee’s job and their religious beliefs? For instance, if a Christian employee requests Sundays off because he believes working on his Sabbath is a sin, and his employer responds by giving him Sunday mornings off to attend church services but requires him to work in the afternoon, has the employer provided a reasonable accommodation? The federal courts of appeals are divided. For some, the answer is no because the proposed accommodation does not eliminate the conflict; the employee still must choose between his job and his religion—the precise dilemma Title VII seeks to avoid. For others, the answer could be yes. These courts take the view that because the statute requires only “reasonable” accommodation, rather than “full,” “total,” or “complete,” an accommodation that lessens, but does not eliminate, the conflict may nonetheless be reasonable depending on the circumstances. This Article argues that an accommodation is reasonable only if it fully eliminates the conflict between an employee’s job and religion. Several tools of statutory interpretation support this position, including textualism, legislative history, Supreme Court precedent, and agency guidance. Additionally, and perhaps even more importantly, a full-accommodation rule reflects the reality of religious devotion for the millions of American workers who believe in full obedience to the tenets of their faiths. For these individuals, religious observance is not something that can or should be done partway. If an employee believes it is sinful to work on Sundays, the ability to attend church in the morning hardly mitigates the sin of working in the afternoon. Thus, a partial accommodation is not just unreasonable—it is no accommodation at all

Estimating multivariate ARIMA models: when is close not good enough?

The purpose of this study is to examine the forecasting abilities of the same multivariate autoregressive model estimated using two methods. The first method is the "exact method" used by the SCA System from Scientific Computing Associates. The second method is an approximation method as implemented in the MTS system by Automatic Forecasting Systems, Inc. ; The two methods were used to estimate a five-series multivariate autoregressive model for the Quenouille series on hog numbers, hog prices, corn prices, corn supply, and farm wage rates. The 82 observations were arbitrarily divided into two periods: the first 60 observations were used to estimate the models; then forecasts for one through eight years ahead were calculated for each possible point in the remaining 22 observations. The root mean square error (RMSE) using the SCA-estimated parameters was smaller than the RMSE using the MTS-estimated parameters for 38 of the 40 possible values (five variables by eight forecast horizons) and tied for one point. The average increase in the RMSE when using the MTS parameters was approximately 9 percent. Using the SCA parameters for forecasting provided smaller mean absolute error (MAE) for 35 of the 40 values, with the average increase from using the MTS parameters being approximately 5.6 percent. Using the SCA parameters provided smaller mean errors (ME) for 39 of the 40 values, with the average increase from using the MTS parameters being approximately .023. Thus, the SCA estimation method is shown to provide better forecasts than the MTS method for this one example.Forecasting ; Time-series analysis

Exponential times in the one-dimensional Gross--Petaevskii equation with multiple well potential

We consider the Gross-Petaevskii equation in 1 space dimension with a $n$-well trapping potential. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest n eigenvalues of the linear operator is slightly deformed by the nonlinear term into an almost invariant manifold M. Precisely, one has that solutions starting on M, or close to it, will remain close to M for times exponentially long with the inverse of the size of the nonlinearity. As heuristically expected the effective equation on M is a perturbation of a discrete nonlinear Schroedinger equation. We deduce that when the size of the nonlinearity is large enough then tunneling among the wells essentially disappears: that is for almost all solutions starting close to M their restriction to each of the wells has norm approximatively constant over the considered time scale. In the particular case of a double well potential we give a more precise result showing persistence or destruction of the beating motions over exponentially long times. The proof is based on canonical perturbation theory; surprisingly enough, due to the Gauge invariance of the system, no non-resonance condition is required

On the Origin of Risk Sensitivity: the Energy Budget Rule Revisited

The risk-sensitive foraging theory formulated in terms of the (daily) energy budget rule has been influential in behavioural ecology as well as other disciplines. Predicting risk-aversion on positive budgets and risk-proneness on negative budgets, however, the budget rule has recently been challenged both empirically and theoretically. In this paper, we critically review these challenges as well as the original derivation of the budget rule and propose a `gradual' budget rule, which is normatively derived from a gradual nature of risk sensitivity and encompasses the conventional budget rule as a special case. The gradual budget rule shows that the conventional budget rule holds when the expected reserve is close enough to a threshold for overnight survival, selection pressure being significant. The gradual view also reveals that the conventional budget rule does not need to hold when the expected reserve is not close enough to the threshold, selection pressure being insignificant. The proposed gradual budget rule better fits the empirical findings including those that used to challenge the conventional budget rule.Comment: 13 pages, 4 figure

Induced scattering of short radio pulses

Effect of the induced Compton and Raman scattering on short, bright radio pulses is investigated. It is shown that when a single pulse propagates through the scattering medium, the effective optical depth is determined by the duration of the pulse but not by the scale of the medium. The induced scattering could hinder propagation of the radio pulse only if close enough to the source a dense enough plasma is presented. The induced scattering within the relativistically moving source places lower limits on the Lorentz factor of the source. The results are applied to the recently discovered short extragalactic radio pulse.Comment: submitted to Ap

Direct Detection of Giant Close-In Planets Around the Source Stars of Caustic-Crossing Microlensing Events

We propose a direct method to detect close-in giant planets orbiting stars in the Galactic bulge. This method uses caustic-crossing binary microlensing events discovered by survey teams monitoring the bulge to measure light from a planet orbiting the source star. When the planet crosses the caustic, it is more magnified than the source star; its light is magnified by two orders of magnitude for Jupiter size planets. If the planet is a giant close to the star, it may be bright enough to make a significant deviation in the light curve of the star. Detection of this deviation requires intensive monitoring of the microlensing light curve using a 10-meter class telescope for a few hours after the caustic. This is the only method yet proposed to directly detect close-in planets around stars outside the solar neighborhood.Comment: 4 pages, 2 figures. Submitted to ApJ Letter