Induced Distributions from Generalized Unfair Dice

In this paper we analyze the probability distributions associated with rolling (possibly unfair) dice infinitely often. Specifically, given a $q$-sided die, if $x_i\in\{0,\ldots,q-1\}$ denotes the outcome of the $i^{\text{th}}$ toss, then the distribution function is $F(x)=\mathbb{P}[X\leq x]$, where $X = \sum_{i=1}^\infty x_i q^{-i}$. We show that $F$ is singular and establish a piecewise linear, iterative construction for it. We investigate two ways of comparing $F$ to the fair distribution -- one using supremum norms and another using arclength. In the case of coin flips, we also address the case where each independent flip could come from a different distribution. In part, this work aims to address outstanding claims in the literature on Bernoulli schemes. The results herein are motivated by emerging needs, desires, and opportunities in computation to leverage physical stochasticity in microelectronic devices for random number generation.Comment: 18 pages, 1 figur

From Mirrors to Wallpapers: A Virtual Math Circle Module on Symmetry

Symmetry is a natural property that children see in their everyday lives; it also has deep mathematical connections to areas like tiling and objects like wallpaper groups. The Tucson Math Circle (TMC) presents a 7-part module on symmetry that starts with reflective symmetry and culminates in the deconstruction of wallpapers into their ‘generating tiles’. This module utilizes a scaffolded, hands-on approach to cover old and new mathematical topics with various interactive activities; all activities are made available through free web-based platforms. In this paper, we provide lesson plans for the various activities used, and discuss their online implementation with Zoom, Miro, and the TMC Widget. We touch on the benefits and disadvantages of the online environment, and provide suggestions for moving these activities to an in-person format. We also include links to files in our Google Drive, where members of the Math Circle community can download our worksheets and Miro board templates

An inhibitory pull-push circuit in frontal cortex.

Push-pull is a canonical computation of excitatory cortical circuits. By contrast, we identify a pull-push inhibitory circuit in frontal cortex that originates in vasoactive intestinal polypeptide (VIP)-expressing interneurons. During arousal, VIP cells rapidly and directly inhibit pyramidal neurons; VIP cells also indirectly excite these pyramidal neurons via parallel disinhibition. Thus, arousal exerts a feedback pull-push influence on excitatory neurons-an inversion of the canonical push-pull of feedforward input

What Is a Representative Brain? Neuroscience Meets Population Science

The last decades of neuroscience research have produced immense progress in the methods available to understand brain structure and function. Social, cognitive, clinical, affective, economic, communication, and developmental neurosciences have begun to map the relationships between neuro-psychological processes and behavioral outcomes, yielding a new understanding of human behavior and promising interventions. However, a limitation of this fast moving research is that most findings are based on small samples of convenience. Furthermore, our understanding of individual differences may be distorted by unrepresentative samples, undermining findings regarding brain–behavior mechanisms. These limitations are issues that social demographers, epidemiologists, and other population scientists have tackled, with solutions that can be applied to neuroscience. By contrast, nearly all social science disciplines, including social demography, sociology, political science, economics, communication science, and psychology, make assumptions about processes that involve the brain, but have incorporated neural measures to differing, and often limited, degrees; many still treat the brain as a black box. In this article, we describe and promote a perspective—population neuroscience—that leverages interdisciplinary expertise to (i) emphasize the importance of sampling to more clearly define the relevant populations and sampling strategies needed when using neuroscience methods to address such questions; and (ii) deepen understanding of mechanisms within population science by providing insight regarding underlying neural mechanisms. Doing so will increase our confidence in the generalizability of the findings. We provide examples to illustrate the population neuroscience approach for specific types of research questions and discuss the potential for theoretical and applied advances from this approach across areas

Characteristics of the National Applicant Pool for Clinical Informatics Fellowships (2016-2017)

We conducted a national study to assess the numbers and diversity of applicants for 2016 and 2017 clinical informatics fellowship positions. In each year, we collected data on the number of applications that programs received from candidates who were ultimately successful vs. unsuccessful. In 2017, we also conducted an anonymous applicant survey. Successful candidates applied to an average of 4.2 and 5.5 programs for 2016 and 2017, respectively. In the survey, unsuccessful candidates reported applying to fewer programs. Assuming unsuccessful candidates submitted between 2-5 applications each, the total applicant pool numbered 42-69 for 2016 (competing for 24 positions) and 52-85 for 2017 (competing for 30 positions). Among survey respondents (n=33), 24% were female, 1 was black and none were Hispanic. We conclude that greater efforts are needed to enhance interest in clinical informatics among medical students and residents, particularly among women and members of underrepresented minority groups

Structure at Work: Organizational Forms and the Division of Labor in U.S. Wineries

We show how organizational forms shape job structures, specifically the variety and types of jobs employees hold, extending previous research on job structures in four ways. First, the social codes associated with wineries' generalist and specialist forms constrain the number of jobs and functional areas delineated by job titles. Second, form-based constraints are weakened by institutional rules that impose categorical distinctions on organizations. Third, these constraints are stronger when there is more consensus around forms. Fourth, these constraints are contingent on the legitimacy and resources of organizations of varying ages and sizes

A Bayesian network to predict coastal vulnerability to sea level rise

This paper is not subject to U.S. copyright. The definitive version was published in Journal of Geophysical Research 116 (2011): F02009, doi:10.1029/2010JF001891.Sea level rise during the 21st century will have a wide range of effects on coastal environments, human development, and infrastructure in coastal areas. The broad range of complex factors influencing coastal systems contributes to large uncertainties in predicting long-term sea level rise impacts. Here we explore and demonstrate the capabilities of a Bayesian network (BN) to predict long-term shoreline change associated with sea level rise and make quantitative assessments of prediction uncertainty. A BN is used to define relationships between driving forces, geologic constraints, and coastal response for the U.S. Atlantic coast that include observations of local rates of relative sea level rise, wave height, tide range, geomorphic classification, coastal slope, and shoreline change rate. The BN is used to make probabilistic predictions of shoreline retreat in response to different future sea level rise rates. Results demonstrate that the probability of shoreline retreat increases with higher rates of sea level rise. Where more specific information is included, the probability of shoreline change increases in a number of cases, indicating more confident predictions. A hindcast evaluation of the BN indicates that the network correctly predicts 71% of the cases. Evaluation of the results using Brier skill and log likelihood ratio scores indicates that the network provides shoreline change predictions that are better than the prior probability. Shoreline change outcomes indicating stability (−1 1 m/yr) was not well predicted. We find that BNs can assimilate important factors contributing to coastal change in response to sea level rise and can make quantitative, probabilistic predictions that can be applied to coastal management decisions.Funding for this work was provided by the USGS Coastal and Marine Geology and Global Change Research programs

Rab7A Is Required for Efficient Production of Infectious HIV-1

Retroviruses take advantage of cellular trafficking machineries to assemble and release new infectious particles. Rab proteins regulate specific steps in intracellular membrane trafficking by recruiting tethering, docking and fusion factors, as well as the actin- and microtubule-based motor proteins that facilitate vesicle traffic. Using virological tests and RNA interference targeting Rab proteins, we demonstrate that the late endosome-associated Rab7A is required for HIV-1 propagation. Analysis of the late steps of the HIV infection cycle shows that Rab7A regulates Env processing, the incorporation of mature Env glycoproteins into viral particles and HIV-1 infectivity. We also show that siRNA-mediated Rab7A depletion induces a BST2/Tetherin phenotype on HIV-1 release. BST2/Tetherin is a restriction factor that impedes HIV-1 release by tethering mature virus particles to the plasma membrane. Our results suggest that Rab7A contributes to the mechanism by which Vpu counteracts the restriction factor BST2/Tetherin and rescues HIV-1 release. Altogether, our results highlight new roles for a major regulator of the late endocytic pathway, Rab7A, in the late stages of the HIV-1 replication cycle

High-Performance Work Systems and Organizational Performance in Emerging Economies: Evidence from MNEs in Turkey

This study examines the association between the usage of high-performance work systems (HPWS) by subsidiaries of multinational enterprises (MNEs) in Turkey and employee and subsidiary level outcomes. The study is based on a survey of 148 MNE subsidiaries operating in Turkey. The results show that the usage of HPWS has a significant positive impact on employee effectiveness. However, their impact on employee skills and development, and organizational financial performance are far less clear. Our findings highlight the extent to which HWPS need to be adapted to take account of context-specific institutional realities. © 2014 Springer-Verlag Berlin Heidelberg