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.

“Que(e)rying Religious Activism: Culture, Identity, and the Politics of Family in Unitarian Universalist Churches”

Despite the longstanding debate about religion’s role in social movements, conservative religious opposition to lesbian, gay, bisexual, transgender, and queer (LGBTQ) social movement in the United States has limited sociological research in this area to questions of individual identity or the oppositional strategies used by religious and LGTBQ groups to sway public opinion and policy decisions. This dissertation addresses the less well-understood dynamics of mainstream religious group participation in LGBTQ social movement. Through frameworks of social movement theory, organizational culture, and queer theory, it explores the organizational elements shaping congregants’ practices in two Unitarian Universalist (UU) churches considered “Welcoming Congregations”. Analysis of data generated from participant observations, in-depth interviews, and church and denominational texts highlight how structures of church governance, materiality, and history intersected with embedded discourses of gender and sexuality to promote “closeting” and “covering” repertoires of discourse and action on behalf of marriage equality. Findings underscore the value of continued research on the specific ways in which specific elements of organizational culture can shape local group discourses and practices at varying depths, degrees, and dimensions of organizational embeddedness

Measurement of solid precipitation with an optical disdrometer

A study about measurements of solid precipitation using an optical disdrometer is presented. The optical disdrometer is an improved version of the ODM 470 disdrometer. It allows to measure hydrometeors within a size range of 0.4 to 22 mm in diameter. <br><br> The main advantage of this instrument is its ability to estimate accurately precipitation even under strong wind conditions (Großklaus, 1996). To measure solid precipitation a geometrical model was developed to determine the mean cross-sectional area of snow crystals for different predefined shapes and sizes. It serves to develop an algorithm, which relates the mean cross sectional area of snow crystals to their maximum dimension, liquid water content, and terminal velocity. The algorithm was applied to disdrometer measurements during winter 1999/2000 in Uppsala/Sweden. Resulting precipitation was compared to independent measurements of a Geonor gauge and to manual measurements. In terms of daily precipitation the disdrometer shows a reliable performance

Measurements of solid precipitation with an optical disdrometer

A study about measurements of solid precipitation using an optical disdrometer is presented. The optical disdrometer is an improved version of the ODM 470 disdrometer. It allows to measure hydrometeors within a size range of 0.4 to 22 mm in diameter. The main advantage of this instrument is its ability to estimate accurately precipitation even under strong wind conditions (Großklaus, 1996). To measure solid precipitation a geometrical model was developed to determine the mean cross-sectional area of snow crystals for different predefined shapes and sizes. It serves to develop an algorithm, which relates the mean cross sectional area of snow crystals to their maximum dimension, liquid water content, and terminal velocity. The algorithm was applied to disdrometer measurements during winter 1999/2000 in Uppsala/Sweden. Resulting precipitation was compared to independent measurements of a Geonor gauge and to manual measurements. In terms of daily precipitation the disdrometer shows a reliable performance

Coupled Cluster Channels in the Homogeneous Electron Gas

We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD are determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Gr\"uneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner Hamltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely ladder-only CCD, ring-only CCD and crossed-ring-only CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.Comment: 9 pages, 4 figures, 1 table. Comments welcome: [email protected]

Electronic depth profiles with atomic layer resolution from resonant soft x-ray reflectivity

The analysis of x-ray reflectivity data from artificial heterostructures usually relies on the homogeneity of optical properties of the constituent materials. However, when the x-ray energy is tuned to an absorption edge, this homogeneity no longer exists. Within the same material, spatial regions containing elements at resonance will have optical properties very different from regions without resonating sites. In this situation, models assuming homogeneous optical properties throughout the material can fail to describe the reflectivity adequately. As we show here, resonant soft x-ray reflectivity is sensitive to these variations, even though the wavelength is typically large as compared to the atomic distances over which the optical properties vary. We have therefore developed a scheme for analyzing resonant soft x-ray reflectivity data, which takes the atomic structure of a material into account by "slicing" it into atomic planes with characteristic optical properties. Using LaSrMnO4 as an example, we discuss both the theoretical and experimental implications of this approach. Our analysis not only allows to determine important structural information such as interface terminations and stacking of atomic layers, but also enables to extract depth-resolved spectroscopic information with atomic resolution, thus enhancing the capability of the technique to study emergent phenomena at surfaces and interfaces.Comment: Completely overhauled with respect to the previous version due to peer revie

Quantitative determination of bond order and lattice distortions in nickel oxide heterostructures by resonant x-ray scattering

We present a combined study of Ni $K$-edge resonant x-ray scattering and density functional calculations to probe and distinguish electronically driven ordering and lattice distortions in nickelate heterostructures. We demonstrate that due to the low crystal symmetry, contributions from structural distortions can contribute significantly to the energy-dependent Bragg peak intensities of a bond-ordered NdNiO$_3$ reference film. For a LaNiO$_3$-LaAlO$_3$ superlattice that exhibits magnetic order, we establish a rigorous upper bound on the bond-order parameter. We thus conclusively confirm predictions of a dominant spin density wave order parameter in metallic nickelates with a quasi-two-dimensional electronic structure

Optical precursors in transparent media

We theoretically study the linear propagation of a stepwise pulse through a dilute dispersive medium when the frequency of the optical carrier coincides with the center of a natural or electromagnetically induced transparency window of the medium (slow-light systems). We obtain fully analytical expressions of the entirety of the step response and show that, for parameters representative of real experiments, Sommerfeld-Brillouin precursors, main field and second precursors "postcursors" can be distinctly observed, all with amplitudes comparable to that of the incident step. This behavior strongly contrasts with that of the systems generally considered up to now