How biased are maximum entropy models?

Maximum entropy models have become popular statistical models in neuroscience and other areas in biology, and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias; i.e. the true entropy of the data can be severely underestimated. Here we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We show that if the data is generated by a distribution that lies in the model class, the bias is equal to the number of parameters divided by twice the number of observations. However, in practice, the true distribution is usually outside the model class, and we show here that this misspecification can lead to much larger bias. We provide a perturbative approximation of the maximally expected bias when the true model is out of model class, and we illustrate our results using numerical simulations of an Ising model; i.e. the second-order maximum entropy distribution on binary data.

Polarization Structures in the Thomson-Scattered Emission Lines in Active Galactic Nuclei

A line photon incident in an electron-scattering medium is transferred in a diffusive way both in real space and in frequency space, and the mean number of scatterings changes as the wavelength shifts from the line center. This leads to the profile broadening and polarization dependence on the wavelength shift as a function of the Thomson optical depth $\tau_T$. We find that the polarization of the Thomson-scattered emission lines has a dip around the line center when $\tau_T$ does not exceed a few. Various structures such as the polarization flip are also seen. An application to an ionized halo component surrounding the broad emission line region in active galactic nuclei is considered and it is found that the polarization structures may still persist. Brief discussions on observational implications are given.Comment: 14 pages, 3 figures, accepted for publication in ApJ Letter

INTERACTION EFFECTS OF PROMOTION, RESEARCH, AND PRICE SUPPORT PROGRAMS FOR U.S. COTTON

Many agricultural commodities have industry-funded generic promotion and/or research ("checkoff") programs designed to improve the economic performance of producers. To determine the effectiveness of these programs, the net benefits to producers attributable to activities funded by the checkoff must be separated from those due to other factors influencing commodity markets. One such factor that is very important in many agricultural commodity markets is the effect of government programs. However, studies evaluating the returns to checkoff programs often do not explicitly discuss the impact of pre-existing distortions caused by federal farm programs. Because the distortions caused by farm programs can be quite large, this omission can lead to seriously biased estimates of the returns to the checkoff programs. In this study, we develop a model that captures the influence of two Federal programs (loan deficiency payments to farmers and subsidies to consuming mills) on the estimated returns to the Cotton Research and Promotion Program. Using an econometrically estimated model of the U.S. cotton market, we find that the program interaction effects have a large impact on checkoff program returns.Agricultural and Food Policy, Crop Production/Industries,

Spatial synchronization and extinction of species under external forcing

We study the interplay between synchronization and extinction of a species. Using a general model we show that under a common external forcing, the species with a quadratic saturation term in the population dynamics first undergoes spatial synchronization and then extinction, thereby avoiding the rescue effect. This is because the saturation term reduces the synchronization time scale but not the extinction time scale. The effect can be observed even when the external forcing acts only on some locations provided there is a synchronizing term in the dynamics. Absence of the quadratic saturation term can help the species to avoid extinction.Comment: 4 pages, 2 figure

The RHIC Zero Degree Calorimeter

High Energy collisions of nuclei usually lead to the emission of evaporation neutrons from both ``beam'' and ``target'' nuclei. At the RHIC heavy ion collider with 100GeV/u beam energy, evaporation neutrons diverge by less than $~2$ milliradians from the beam axis Neutral beam fragments can be detected downstream of RHIC ion collisions (and a large aperture Accelerator dipole magnet) if $\theta\leq$ 4 mr but charged fragments in the same angular range are usually too close to the beam trajectory. In this 'zero degree' region produced particles and other secondaries deposit negligible energy when compared with that of beam fragmentation neutrons. The purpose of the RHIC zero degree calorimeters (ZDC's) is to detect neutrons emitted within this cone along both beam directions and measure their total energy (from which we calculate multiplicity). The ZDC coincidence of the 2 beam directions is a minimal bias selection of heavy ion collisions. This makes it useful as an event trigger and a luminosity monitor\cite{baltz} and for this reason we built identical detectors for all 4 RHIC experiments. The neutron multiplicity is also known to be correlated with event geometry \cite{appel} and will be used to measure collision centrality in mutual beam int eractions.Comment: 18 pages, 12 figure

Relativistic theory of tidal Love numbers

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.Comment: 25 pages, 8 figures, many tables; final version to be published in Physical Review

Dynamical Effects from Asteroid Belts for Planetary Systems

The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.Comment: accepted by International Journal of Bifurcation and Chaos in Aug. 2003, AAS Latex, 27 pages with 6 color figure

Quantifying Liability Under the Architect\u27s Standard of Care

In recent years, architects and other design professionals have become the targets of claims arising from problems encountered in construction projects. In addition to incurring the costs of defending such claims, these design professionals (or their insurers) have often found themselves absorbing the liability for many errors and omissions that are difficult to defend when individually excerpted from a substantial project. This treatment of claims for defective design reflects a distortion of the architect\u27s professional standard of care that is justified neither by the contractual liability assumed by the architect nor by the economic balance among the parties involved in a construction project