Umbral Moonshine and the Niemeier Lattices

In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally defined quotient of the lattice automorphism group, and for each conjugacy class of each of these groups we identify a vector-valued mock modular form whose components coincide with mock theta functions of Ramanujan in many cases. This leads to the umbral moonshine conjecture, stating that an infinite-dimensional module is assigned to each of the Niemeier lattices in such a way that the associated graded trace functions are mock modular forms of a distinguished nature. These constructions and conjectures extend those of our earlier paper, and in particular include the Mathieu moonshine observed by Eguchi-Ooguri-Tachikawa as a special case. Our analysis also highlights a correspondence between genus zero groups and Niemeier lattices. As a part of this relation we recognise the Coxeter numbers of Niemeier root systems with a type A component as exactly those levels for which the corresponding classical modular curve has genus zero.Comment: 181 pages including 95 pages of Appendices; journal version, minor typos corrected, Research in the Mathematical Sciences, 2014, vol.

A Glass Half Full

Presents a vision for remaking ourselves as a society by addressing the basic needs of all children and defining, assessing, and developing high quality teaching

Moving At-Risk Teenagers Out of High-Risk Neighborhoods: Why Girls Fare Better Than Boys

neighborhood effects; social experiment; mixed methods; youth risk behavior

Mathieu Moonshine and N=2 String Compactifications

There is a `Mathieu moonshine' relating the elliptic genus of K3 to the sporadic group M_{24}. Here, we give evidence that this moonshine extends to part of the web of dualities connecting heterotic strings compactified on K3 \times T^2 to type IIA strings compactified on Calabi-Yau threefolds. We demonstrate that dimensions of M_{24} representations govern the new supersymmetric index of the heterotic compactifications, and appear in the Gromov--Witten invariants of the dual Calabi-Yau threefolds, which are elliptic fibrations over the Hirzebruch surfaces F_n.Comment: 28 pages; v2: minor changes, published versio

Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine

We show that certain BPS counting functions for both fundamental strings and strings arising from fivebranes wrapping divisors in Calabi--Yau threefolds naturally give rise to skew-holomorphic Jacobi forms at rational and attractor points in the moduli space of string compactifications. For M5-branes wrapping divisors these are forms of weight negative one, and in the case of multiple M5-branes skew-holomorphic mock Jacobi forms arise. We further find that in simple examples these forms are related to skew-holomorphic (mock) Jacobi forms of weight two that play starring roles in moonshine. We discuss examples involving M5-branes on the complex projective plane, del Pezzo surfaces of degree one, and half-K3 surfaces. For del Pezzo surfaces of degree one and certain half-K3 surfaces we find a corresponding graded (virtual) module for the degree twelve Mathieu group. This suggests a more extensive relationship between Mathieu groups and complex surfaces, and a broader role for M5-branes in the theory of Jacobi forms and moonshine.Comment: 36 pages, LaTeX; minor typos corrected, footnote added at bottom of page 9 to accommodate JHEP editor's suggestio

Do Physician-based or Hospital-based Provider Service Networks Better Control Medicaid Expenditures?

In a recent demonstration project, Florida Medicaid enrollees were required to pick a managed care plan that was either a Health Maintenance Organization (HMO) or a Provider Service Network (PSN). PSNs are a form of managed care very similar to Accountable Care Organizations (ACOs) that provides health care services directly through a provider or network of organizations to a defined population without a “middle man” such as a third party insurance company and health plan. There are two types of PSNs: Physician-based PSNs and Healthcare system-based PSNs. Physician-based PSNs are created and controlled by physicians groups. Healthcare system-based PSNs are based on safety net hospitals and their outpatient clinics. Health system-based PSNs are integrated delivery systems, which are organizations that combine healthcare providers into one organization and may provide more efficient care with lower cost of care due to economies of scale. The objective of this study was to examine the differences in healthcare expenditures by enrollees in physician-based and health system-based PSNs. Using a difference in difference approach our study found that compared to enrollees in physician-based PSNs, enrollees in health system-based PSNs lowered expenditures to a greater extent over time compared to physician-based PSNs. Findings from this study provide important information to states considering implementing alternative delivery models to control Medicaid costs

What Can We Learn about Neighborhood Effects from the Moving to Opportunity Experiment?

Experimental estimates from Moving to Opportunity (MTO) show no significant impacts of moves to lower‐poverty neighborhoods on adult economic self‐sufficiency four to seven years after random assignment. The authors disagree with Clampet‐Lundquist and Massey's claim that MTO was a weak intervention and therefore uninformative about neighborhood effects. MTO produced large changes in neighborhood environments that improved adult mental health and many outcomes for young females. Clampet‐Lundquist and Massey's claim that MTO experimental estimates are plagued by selection bias is erroneous. Their new nonexperimental estimates are uninformative because they add back the selection problems that MTO's experimental design was intended to overcome.Economic