Expectation-maximization for logistic regression

We present a family of expectation-maximization (EM) algorithms for binary and negative-binomial logistic regression, drawing a sharp connection with the variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results allow a version of this variational-Bayes approach to be re-interpreted as a true EM algorithm. We study several interesting features of the algorithm, and of this previously unrecognized connection with variational Bayes. We also generalize the approach to sparsity-promoting priors, and to an online method whose convergence properties are easily established. This latter method compares favorably with stochastic-gradient descent in situations with marked collinearity

The Changing Nature of Faculty Employment

[Excerpt] The last two decades of the twentieth century saw a significant growth in the shares of faculty members in American colleges and universities that are part-time or are full-time without tenure-track status. Growing student enrollments faced by academic institutions during tight financial times and growing differentials between the salaries of part-time and full-time non-tenure track faculty on the one hand, and tenured and tenure-track faculty on the other hand are among the explanations given for these trends. However, there have been few econometric studies that seek to test these hypotheses. Our paper begins by presenting information, broken down by form of control (public/private) and 1994 Carnegie Category, on how the proportions of full-time faculty at 4-year American colleges and universities that are tenured and on tenure tracks and that are not on tenure tracks have changed since 1989, using information for a consistent sample of institutions from the annual IPEDS Faculty Salary Surveysand the biennial IPEDS Fall Staff Surveys. The latter source also permits us to present similar estimates of the proportions of faculty that are employed part-time and the share of new full-time faculty appointments that are not on tenure tracks. To analyze the role that economic variables play in causing changes in faculty employment across categories, we conduct two types of econometric analyses. First, in section III, we use panel data to estimate demand functions for tenure and tenure-track faculty on the one hand and full-time non tenure-track faculty on the other hand to learn how changes in revenues per student and the average salaries of different types of full-time faculty influence the distribution of faculty across categories of full-time faculty. We do this using both equilibrium models that assume instantaneous adjustments to changes in revenues and faculty salaries and lagged adjustment models that permit partial adjustments to equilibrium each year. Second, in section IV, we estimate models that seek to explain the flow of new hires of each type of faculty member (rather than the levels of faculty employment) using data on new hires that are available from the IPEDS Fall Staff Surveys. To explain new hires, in addition to information on changes in revenues per student, changes in enrollment, and the levels of faculty salaries, we require information on the number of vacant positions that are available to be potentially filled. We construct information on the latter using data on the number of continuing full-time faculty members at an institution each year that the American Association of University Professors (AAUP) collects (but does not publish) as part of its annual salary survey. Continuing faculty members in a rank are defined as the number of faculty members in a rank one year, who also are on the payroll of the institution in the next year, regardless of their rank in the second year. Summing up an institution’s continuing faculty members across ranks in a year and subtracting that number from the institution’s total faculty employment in the previous year provides us with an estimate of the number of full-time faculty vacancies that an institution could have filled in a year if it had replaced each of its departing full-time faculty members. A brief concluding section summarizes our findings and discusses their implications for American colleges and universities and their students

Uniform Semiclassical Approximation for the Wigner 6j6j Symbol in Terms of Rotation Matrices

A new uniform asymptotic approximation for the Wigner $6j$ symbol is given in terms of Wigner rotation matrices ($d$-matrices). The approximation is uniform in the sense that it applies for all values of the quantum numbers, even those near caustics. The derivation of the new approximation is not given, but the geometrical ideas supporting it are discussed and numerical tests are presented, including comparisons with the exact $6j$-symbol and with the Ponzano-Regge approximation.Comment: 44 pages plus 20 figure

Do Tenured and Tenure-Track Faculty Matter?

During the last two decades, there has been a significant growth in the share of faculty members at American colleges and universities that are employed in part-time or full-time non tenure-track positions. Our study is the first to address whether the increased usage of such faculty adversely affects undergraduate students’ graduation rates. Using institutional level panel data from the College Board and other sources, our econometric analyses suggest that the increased usage of these faculty types does adversely affect graduation rates at 4-year colleges, with the largest impact on students being felt at the public master’s level institutions

Faculty Employment and R&D Expenditures at Research Universities

This study uses panel data to examine the relationship between faculty employment and external R&D expenditures at research and doctoral institutions over a 15-year period of time. Not surprisingly, full-time faculty that are tenured or on tenure-tracks is the main category of faculty that generates external R&D funding. On the other hand, our results suggest that an increasing usage of part-time faculty, holding constant the institution’s full-time faculty size boosts an institution’s external R&D expenditures, probably through reducing teaching responsibilities for the full-time faculty. Increases in graduate student enrollments are associated with increases in external R&D expenditures. Finally, an institution’s external R&D expenditures are significantly influenced by both the amount of its own institutionally financed research expenditures and the level of federal funding for research

Optical Resonator Analog of a Two-Dimensional Topological Insulator

A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes.Comment: 10 pages, 9 figure

Controllable Persistent Atom Current of Bose-Einstein Condensates in an Optical Lattice Ring

In this paper the macroscopic quantum states of Bose-Einstein condensates in optical lattices is studied by solving the periodic Gross-Pitaevskii equation in one-dimensional geometry. It is shown that an exact solution seen to be a travelling wave of excited macroscopic quantum states resultes in a persistent atom current which can be controlled by adjusting of the barrier height of the optical periodic potential. A critical condition to generate the travelling wave is demonstrated and we moreover propose a practical experiment to realize the persistent atom current in a toroidal atom waveguide.Comment: 9 pages, 1 figure

A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page