The Accuracy of Interpolation by Finite Differences

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Quantitative characterization and analysis of the dynamic NF-κB response in microglia

<p>Abstract</p> <p>Background</p> <p>Activation of the NF-κB transcription factor and its associated gene expression in microglia is a key component in the response to brain injury. Its activation is dynamic and is part of a network of biochemical species with multiple feedback regulatory mechanisms. Mathematical modeling, which has been instrumental for understanding the NF-κB response in other cell types, offers a valuable tool to investigate the regulation of NF-κB activation in microglia at a systems level.</p> <p>Results</p> <p>We quantify the dynamic response of NF-κB activation and activation of the upstream kinase IKK using ELISA measurements of a microglial cell line following treatment with the pro-inflammatory cytokine TNFα. A new mathematical model is developed based on these data sets using a modular procedure that exploits the feedback structure of the network. We show that the new model requires previously unmodeled dynamics involved in the stimulus-induced degradation of the inhibitor IκBα in order to properly describe microglial NF-κB activation in a statistically consistent manner. This suggests a more prominent role for the ubiquitin-proteasome system in regulating the activation of NF-κB to inflammatory stimuli. We also find that the introduction of nonlinearities in the kinetics of IKK activation and inactivation is essential for proper characterization of transient IKK activity and corresponds to known biological mechanisms. Numerical analyses of the model highlight key regulators of the microglial NF-κB response, as well as those governing IKK activation. Results illustrate the dynamic regulatory mechanisms and the robust yet fragile nature of the negative feedback regulated network.</p> <p>Conclusions</p> <p>We have developed a new mathematical model that incorporates previously unmodeled dynamics to characterize the dynamic response of the NF-κB signaling network in microglia. This model is the first of its kind for microglia and provides a tool for the quantitative, systems level study the dynamic cellular response to inflammatory stimuli.</p

Perfect Reflection of Light by an Oscillating Dipole

We show theoretically that a directional dipole wave can be perfectly reflected by a single point-like oscillating dipole. Furthermore, we find that in the case of a strongly focused plane wave up to 85 % of the incident light can be reflected by the dipole. Our results hold for the full spectrum of the electromagnetic interactions and have immediate implications for achieving strong coupling between a single propagating photon and a single quantum emitter.Comment: 3 figure

Masculinity as Governance: police, public service and the embodiment of authority, c. 1700-1850

About the book: Public Men offers an introduction to an exciting new field: the history of masculinities in the political domain and will be essential reading for students and specialists alike with interests in gender or political culture. By building upon new work on gender and political culture, these new case studies explore the gendering of the political domain and the masculinities of the men who have historically dominated it. As such, Public Men is a major contribution to our understanding of the history of Britain between the Eighteenth and the Twentieth centuries

Banking from Leeds, not London: regional strategy and structure at the Yorkshire Bank, 1859–1952

Industrial philanthropist Edward Akroyd created the Yorkshire Penny Savings Bank in 1859. Despite competition from the Post Office Savings Bank after 1861 and a serious reserve problem in 1911, it sustained his overall strategy to become a successful regional bank. Using archival and contemporary sources to build on recent scholarship illustrating how savings banks were integrated into local economies and the complementary roles of philanthropy and paternalism, we analyse an English regional bank's strategy, including an assessment of strategic innovation, ownership changes and management structure. This will demonstrate that the founder's vision continued, even though the 1911 crisis radically altered both strategy and structure

Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure

The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page