Effect of Addiction Modeling Reinforcement Schedules on Delay Discounting

Elevated delay discounting, in which delayed rewards quickly lose value as a function of time, is associated with substance use and abuse. Currently, the direction of causation is unclear: while some research indicates that elevated delay discounting leads to future substance use, it is also possible that chronic substance use and specifically the rate of reinforcement associated with drug use, leads to elevated delay discounting. This project aims to examine the latter possibility. 47 participants completed ten 30-minute daily sessions of a visual attention task, and were reinforced at a rate intended to model drug use (fixed ratio 1) or drug abstinence (fixed ratio 10). Baseline and post-training rates of delay discounting were assessed for hypothetical $50 and $1000. Area under the curve of the indifference points as a function of delay was calculated. A greater area under the curve suggests more self-control, whereas a lower value represents more impulsiveness. Results at the monetary value of both $50 and $1000 showed increased impulsivity in relation to the control for both the FR1 and FR10 groups indicating that the two schedules may both model drug use.

Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

The Relation between Substance Use and Medication Adherence among HIV Positive Substance Users in Residential Treatment

Poor medication adherence is problematic among HIV positive, low-income African-American substance users. Substance use has been shown to be associated with poor medication adherence, though we do not know the mechanism that underlies this relationship. Lack of positive environmental rewards and the propensity to discount delayed rewards may be possible mechanisms to explain this relationship. Using baseline data from a randomized controlled trial, we examined the relationships between substance use and medication adherence, testing both environmental rewards and delay discounting as independent mediators. There was a main effect of substance use on adherence, such that high frequency of substance use predicted poor adherence. There was also a main effect of environmental rewards on adherence, such that a lack of environmental reinforcement predicted poor adherence. This study shed light on the processes that contribute to low adherence, namely substance use and lack of environmental contingencies, and suggests important targets for intervention.

ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.