Bounds for graph regularity and removal lemmas

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemer\'edi's regularity lemma. In order to gain some control over irregular pairs, another regularity lemma, known as the strong regularity lemma, was developed by Alon, Fischer, Krivelevich, and Szegedy. For this lemma, we prove a lower bound of wowzer-type, which is one level higher in the Ackermann hierarchy than the tower function, on the number of parts in the strong regularity lemma, essentially matching the upper bound. On the other hand, for the induced graph removal lemma, the standard application of the strong regularity lemma, we find a different proof which yields a tower-type bound. We also discuss bounds on several related regularity lemmas, including the weak regularity lemma of Frieze and Kannan and the recently established regular approximation theorem. In particular, we show that a weak partition with approximation parameter \epsilon may require as many as 2^{\Omega(\epsilon^{-2})} parts. This is tight up to the implied constant and solves a problem studied by Lov\'asz and Szegedy.Comment: 62 page

Dialectic tensions in the financial markets: a longitudinal study of pre- and post-crisis regulatory technology

This article presents the findings from a longitudinal research study on regulatory technology in the UK financial services industry. The financial crisis with serious corporate and mutual fund scandals raised the profile of compliance as governmental bodies, institutional and private investors introduced a ‘tsunami’ of financial regulations. Adopting a multi-level analysis, this study examines how regulatory technology was used by financial firms to meet their compliance obligations, pre- and post-crisis. Empirical data collected over 12 years examine the deployment of an investment management system in eight financial firms. Interviews with public regulatory bodies, financial institutions and technology providers reveal a culture of compliance with increased transparency, surveillance and accountability. Findings show that dialectic tensions arise as the pursuit of transparency, surveillance and accountability in compliance mandates is simultaneously rationalized, facilitated and obscured by regulatory technology. Responding to these challenges, regulatory bodies continue to impose revised compliance mandates on financial firms to force them to adapt their financial technologies in an ever-changing multi-jurisdictional regulatory landscape

Rho GTPase function in flies: insights from a developmental and organismal perspective.

Morphogenesis is a key event in the development of a multicellular organism and is reliant on coordinated transcriptional and signal transduction events. To establish the segmented body plan that underlies much of metazoan development, individual cells and groups of cells must respond to exogenous signals with complex movements and shape changes. One class of proteins that plays a pivotal role in the interpretation of extracellular cues into cellular behavior is the Rho family of small GTPases. These molecular switches are essential components of a growing number of signaling pathways, many of which regulate actin cytoskeletal remodeling. Much of our understanding of Rho biology has come from work done in cell culture. More recently, the fruit fly Drosophila melanogaster has emerged as an excellent genetic system for the study of these proteins in a developmental and organismal context. Studies in flies have greatly enhanced our understanding of pathways involving Rho GTPases and their roles in development

Mapping HIV prevalence in sub-Saharan Africa between 2000 and 2017

HIV/AIDS is a leading cause of disease burden in sub-Saharan Africa. Existing evidence has demonstrated that there is substantial local variation in the prevalence of HIV; however, subnational variation has not been investigated at a high spatial resolution across the continent. Here we explore within-country variation at a 5 × 5-km resolution in sub-Saharan Africa by estimating the prevalence of HIV among adults (aged 15–49 years) and the corresponding number of people living with HIV from 2000 to 2017. Our analysis reveals substantial within-country variation in the prevalence of HIV throughout sub-Saharan Africa and local differences in both the direction and rate of change in HIV prevalence between 2000 and 2017, highlighting the degree to which important local differences are masked when examining trends at the country level. These fine-scale estimates of HIV prevalence across space and time provide an important tool for precisely targeting the interventions that are necessary to bringing HIV infections under control in sub-Saharan Africa