Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods

In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring logarithmic factors involving the dimension of the input matrix and the size of its entries, both run in time $\widetilde{O}\left(m\log \kappa \log^2 (1/\epsilon)\right)$ where $\epsilon$ is the amount of error we are willing to tolerate. Here, $\kappa$ represents the ratio between the largest and the smallest entries of the optimal scalings. This implies that our algorithms run in nearly-linear time whenever $\kappa$ is quasi-polynomial, which includes, in particular, the case of strictly positive matrices. We complement our results by providing a separate algorithm that uses an interior-point method and runs in time $\widetilde{O}(m^{3/2} \log (1/\epsilon))$. In order to establish these results, we develop a new second-order optimization framework that enables us to treat both problems in a unified and principled manner. This framework identifies a certain generalization of linear system solving that we can use to efficiently minimize a broad class of functions, which we call second-order robust. We then show that in the context of the specific functions capturing matrix scaling and balancing, we can leverage and generalize the work on Laplacian system solving to make the algorithms obtained via this framework very efficient.Comment: To appear in FOCS 201

Corticotropin-releasing hormone interacts with interleukin-1 to regulate prostaglandin H synthase-2 expression in human myometrium during pregnancy and labor

Context: The onset of labor appears to involve the activation of myometrial inflammatory pathways, and transcription factors such as nuclear factor-κB (NF-κB) control expression of the contraction-associated proteins required to induce a procontractile phenotype. These responses might involve CRH, which integrates immune and neuroendocrine systems. Objectives: In human myometrium we investigated cyclooxygenase 2 (PGHS2) expression and regulation by CRH and the proinflammatory cytokine IL-1β before and after labor. Design: Myometrial tissues obtained from pregnant women at term before (n = 12) or during labor (n = 10) and pathological cases of choriamnionitis-associated term labor (n = 5) were used to isolate primary myocytes and investigate in vitro, CRH effects on basal and IL-1β regulated p65 activation and PGHS2 expression. Results: In nonlaboring myometrial cells, CRH was unable to induce NF-κB nuclear translocation; however, it altered the temporal dynamics of IL-1β-driven NF-κB nuclear entry by initially delaying entry and subsequently prolonging retention. These CRH-R1-driven effects were associated with a modest inhibitory action in the early phase (within 2 hours) of IL-1β stimulated PGHS2 mRNA expression, whereas prolonged stimulation for 6–18 hours augmented the IL-1β effects. The early-phase effect required intact protein kinase A activity and was diminished after the onset of labor. The presence of chorioamnionitis led to exaggerated PGHS2 mRNA responses to IL-1β but diminished effects of CRH. Conclusions: CRH is involved in the inflammatory regulation of PGHS2 expression before and during labor; these actions might be important in priming and preparing the myometrium for labor and cellular adaptive responses to inflammatory mediator

The binding constraint on firms'growth in developing countries

Firms in developing countries face numerous and serious constraints on their growth, ranging from corruption to lack of infrastructure to inability to access finance. Countries lack the resources to remove all the constraints at once and so would be better off removing the most binding one first. This paper uses data from World Bank Enterprise Surveys in 2006-10 to identify the most binding constraints on firm operations in developing countries. While each country faces a different set of constraints, these constraints also vary by firm characteristics, especially firm size. Across all countries, access to finance is among the most binding constraints; other obstacles appear to matter much less. This result is robust for all regions. Smaller firms must rely more on their own funds to invest and would grow significantly faster if they had greater access to external funds. As a result, a low level of financial development skews the firm size distribution by increasing the relative share of small firms. The results suggest that financing constraints play a significant part in explaining the"missing middle"-- the failure of small firms in developing countries to grow into medium-size or large firms.Access to Finance,Environmental Economics&Policies,Microfinance,Debt Markets,Banks&Banking Reform