Estimation of subgraph density in noisy networks

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version of some underlying network as data. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. Accordingly, we develop method-of-moment estimators of network subgraph densities and error rates for the case where a minimal number of network replicates are available. These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates based on the asymptotic normality. To construct the confidence intervals, a new and non-standard bootstrap method is proposed to compute asymptotic variances, which is infeasible otherwise. We illustrate the proposed methods in the context of gene coexpression networks

Supporting graduate teaching assistants in two STEM areas

No abstract available

Fourier relationship between angular position and optical orbital angular momentum

We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.Comment: 4 pages, 4 figure

The Role of market returns in retirement decision-making

Abstract only.Abstract only. Abstract: This study utilizes nine interview waves of the Health and Retirement Study and a multilevel discrete-time survival analysis to investigate the effect of market returns on individual elective retirement decisions. Individuals who retire at a market peak have an increased risk of shortening the longevity of their retirement income. Unfortunately, they were found to be more likely to retire when market returns are high, indicating the influence of a projection bias on the timing of elective retirement. Having experienced the recent market crash and the housing slump and facing the uncertain future of Social Security, baby boomers are starting to exit the workforce. Acting on projection bias would expose their retirement portfolio to a higher probability of experiencing an early negative hit and outliving their retirement resources. Researchers, employers, financial educators and financial practitioners should help pre-retirees overcome the stock market's influence on their decision-making to avoid the negative effect of market sequencing on their retirement wealth.Includes bibliographical references

Experimental design laboratories in introductory physics courses: enhancing cognitive tasks and deep conceptual learning

Being able to contextualise and solve complex problems is a highly valued skill in STEM graduates—a skill which we strive to nurture in our students. Since its introduction into undergraduate teaching, laboratory teaching has been used to consolidate students conceptual understanding, develop their practical skills and inculcate an evidence based problem solving approach. Much work has been done to achieve these goals with varying degrees of success. Here we present an alternative to the regular introductory level physics laboratory experiments which enhances students learning by focusing on problem solving rather than simply following detailed instructions. Working in small groups, students were able to achieve the aims of the experiment through self and peer-instruction. Similar experiments can be easily and cost effectively implemented in any standard secondary school and undergraduate teaching laboratory. These can be adjusted to target the development of a wide range of specific skill sets as well as deepen students understanding of different physics principles and concepts. Our approach will enable the teaching laboratory to truly fulfil the function with which it was originally conceived