On the Speed of an Excited Asymmetric Random Walk

An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to investigate than those of a simple random walk. For example, the limiting speed of an excited random walk is either zero or unknown depending on its initial conditions. While its limiting speed is unknown in most cases, the qualitative behavior of an excited random walk is largely determined by a parameter $\delta$ which can be computed explicitly. Despite this, it is known that the limiting speed cannot be written as a function of $\delta$. We offer a new proof of this fact, and use techniques from this proof to further investigate the relationship between $\delta$ and speed. We also generalize the standard excited random walk by introducing a "bias" to the right, and call this generalization an excited asymmetric random walk. Under certain initial conditions we are able to compute an explicit formula for the limiting speed of an excited asymmetric random walk.Comment: 22 pages, 4 figures, presented at 2017 MAA MathFes

Existence and uniqueness for non-Markovian triangular quadratic BSDEs

We prove the existence and uniqueness of solutions to a class of quadratic BSDE systems which we call triangular quadratic. Our results generalize several existing results about diagonally quadratic BSDEs in the non-Markovian setting. As part of our analysis, we obtain new results about linear BSDEs with unbounded coefficients, which may be of independent interest. Through a non-uniqueness example, we answer a "crucial open question" raised by Harter and Richou by showing that the stochastic exponential of an n x n matrix-valued BMO martingale need not satisfy a reverse H\"older inequality

Quantitative convergence for displacement monotone mean field games with controlled volatility

We study the convergence problem for mean field games with common noise and controlled volatility. We adopt the strategy recently put forth by Lauri\`ere and the second author, using the maximum principle to recast the convergence problem as a question of ``forward-backward propagation of chaos", i.e (conditional) propagation of chaos for systems of particles evolving forward and backward in time. Our main results show that displacement monotonicity can be used to obtain this propagation of chaos, which leads to quantitative convergence results for open-loop Nash equilibria for a class of mean field games. Our results seem to be the first (quantitative or qualitative) which apply to games in which the common noise is controlled. The proofs are relatively simple, and rely on a well-known technique for proving well-posedness of FBSDEs which is combined with displacement monotonicity in a novel way. To demonstrate the flexibility of the approach, we also use the same arguments to obtain convergence results for a class of infinite horizon discounted mean field games

Chapter 20 The Hybrid Course: Facilitating Learning through Social Interaction Technologies

This chapter surveys the benefits and challenges of hybrid courses, which blend face-to-face instruction with online learning, and opportunities provided by the introduction of Web-based social interaction technologies. It discusses the pedagogical implications of various Web 2.0 tools: that is, asynchronous discussion boards, blogs, wikis, podcasts, RSS, e-portfolios, folksonomies, educational gaming, data mashups, and simulations. The authors argue that as hybrid courses continue to evolve to meet the needs of students, instructors, and institutions of higher learning, the integration of Web 2.0 applications in a hybrid model requires thoughtful course design, clear educational objectives, and carefully planned activities

A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R

Roles of Cross-Membrane Transport and Signaling in the Maintenance of Cellular Homeostasis

Organelles allow specialized functions within cells to be localized, contained and independently regulated. This separation is oftentimes achieved by selectively permeable membranes, which enable control of molecular transport, signaling between compartments and containment of stress-inducing factors. Here we consider the role of a number of membrane systems within the cell: the plasma membrane, that of the endoplasmic reticulum, and then focusing on the nucleus, depository for chromatin and regulatory centre of the cell. Nuclear pores allow shuttling of ions, metabolites, proteins and mRNA to and from the nucleus. The activity of transcription factors and signaling molecules is also modulated by translocation across the nuclear envelope. Many of these processes require 'active transportation' against a concentration gradient and may be regulated by the nuclear pores, Ran-GTP activity and the nuclear lamina. Cells must respond to a combination of biochemical and physical inputs and we discuss too how mechanical signals are carried from outside the cell into the nucleus through integrins, the cytoskeleton and the 'linker of nucleo- and cyto-skeletal' (LINC) complex which spans the nuclear envelope. Regulation and response to signals and stresses, both internal and external, allow cells to maintain homeostasis within functional tissue

Searching for Soul, Reframing the Pursuit of Capital: A Comparison of Kahlil Joseph’s and Derek Pike’s ‘I Need A Dollar’ Music Videos

Two music videos were commissioned for Aloe Blacc’s breakthrough song ‘I Need A Dollar’ (2010). The Harlem, New York version directed by Kahlil Joseph adopts a split-screen technique, depicting an unnamed man negotiating the city’s busy streets while, at the same time, framing Blacc as a directionless musician singing wistfully at the window of a dilapidated flat. Derek Pike’s Las Vegas, Nevada version, on the other hand, portrays the singer as a struggling musician traversing the desert before – unexpectedly – winning the jackpot at a casino. This article explores two main lines of argument. Firstly, I explore how institutional and industrial contexts result in two distinguishable music videos, suggesting that although both versions are created in similarly professional and commercialised settings one video is produced within a more ‘independent’ environment. Secondly, I explore how two different music videos can emphasise or de-emphasise certain elements of a song’s content and meaning, drawing from Emily J. Lordi’s theorisation of ‘soul’ to suggest that the ‘soul music’ qualities of Blacc’s ‘I Need A Dollar’ record are emphasised when practitioners adopt a more ‘soulful’ approach to music video creation (Lordi, 2020)

Kahlil Joseph, New Media, and the New Black Cinema: A Case for Situating Kahlil Joseph's Audiovisual Work Within the Theoretical Frameworks of African Film

This article explores the various ways that African American filmmaker Kahlil Joseph represents contemporary experiences of the African diaspora in his new media work, Belhaven Meridian (2010). Reflecting the present world system's complex network environment, Joseph's screen text is a node within numerous theoretical networks, oscillating within disparate conceptual frameworks concurrently. Weaving the strands of these divergent theories together with the "crossroads" concepts from Harry J. Elam Jr., Kennell Jackson's Black Cultural Traffic (2005), and Akin Adesokan's Postcolonial Artists and Global Aesthetics (2011), this article scrutinizes Joseph's work through intersections of emergent music video and new media theories, as well as film theories from African, American, and European perspectives. The article argues that such an approach enriches the didactic possibilities of their respective and, simultaneously, entwined theoretical branches