Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras

We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the short distance expansion for the duals of the Virasoro algebra, affine Lie Algebras and the geometrically realized N-extended supersymmetric GR Virasoro algebra.Comment: 19 pages, LaTeX twice, no figure, replacement has corrected Lie algebr

High performance, accelerometer-based control of the Mini-MAST structure at Langley Research Center

Many large space system concepts will require active vibration control to satisfy critical performance requirements such as line of sight pointing accuracy and constraints on rms surface roughness. In order for these concepts to become operational, it is imperative that the benefits of active vibration control be shown to be practical in ground based experiments. The results of an experiment shows the successful application of the Maximum Entropy/Optimal Projection control design methodology to active vibration control for a flexible structure. The testbed is the Mini-Mast structure at NASA-Langley and has features dynamically traceable to future space systems. To maximize traceability to real flight systems, the controllers were designed and implemented using sensors (four accelerometers and one rate gyro) that are actually mounted to the structure. Ground mounted displacement sensors that could greatly ease the control design task were available but were used only for performance evaluation. The use of the accelerometers increased the potential of destabilizing the system due to spillover effects and motivated the use of precompensation strategy to achieve sufficient compensator roll-off

Operator Sequence Alters Gene Expression Independently of Transcription Factor Occupancy in Bacteria

A canonical quantitative view of transcriptional regulation holds that the only role of operator sequence is to set the probability of transcription factor binding, with operator occupancy determining the level of gene expression. In this work, we test this idea by characterizing repression in vivo and the binding of RNA polymerase in vitro in experiments where operators of various sequences were placed either upstream or downstream from the promoter in Escherichia coli. Surprisingly, we find that operators with a weaker binding affinity can yield higher repression levels than stronger operators. Repressor bound to upstream operators modulates promoter escape, and the magnitude of this modulation is not correlated with the repressor-operator binding affinity. This suggests that operator sequences may modulate transcription by altering the nature of the interaction of the bound transcription factor with the transcriptional machinery, implying a new layer of sequence dependence that must be confronted in the quantitative understanding of gene expression

Misleading Betas: An Educational Example

The dual-beta model is a generalization of the CAPM model. In the dual-beta model, separate beta estimates are provided for up-market and down-market days. This paper uses the historical “Anscombe quartet” results which illustrated how very different datasets can produce the same regression coefficients to motivate a discussion of the dual-beta model. Using data from 39 mutual funds, it is shown how very different dual-beta models can lead to the same CAPM beta estimates, much like the Anscombe quartet scenarios

Theoretical and Experimental Dissection of DNA Loop-Mediated Repression

Transcriptional networks across all domains of life feature a wide range of regulatory architectures. Theoretical models now make clear predictions about how key parameters describing those architectures modulate gene expression, and the ability to construct genetic circuits with tunable parameters enables precise tests of such models. We dissect gene regulation through DNA looping by tuning network parameters such as repressor copy number, DNA binding strengths, and loop length in both thermodynamic models and experiments. Our results help clarify the short-length mechanical properties of DNA

Finding The Beta For A Portfolio Isn't Obvious: An Educational Example

When a portfolio is not actively managed to maintain a fixed investment percentage in each asset but rather maintains a fixed number of shares for each asset, the portfolio weights will change over time because the market returns of the different assets will not be the same.  Consequently, portfolio betas computed as a linear combination of asset betas, which is the usual practice, will be different from betas computed using regression techniques on portfolio returns as is done when evaluating individual assets and mutual funds.  The alternative approaches can result in quite different beta statistics and, consequently, inconsistent decisions depending on which method is used.&nbsp

An Overview Of Fiduciary Standards And Suitability For Financial Planning Students

Financial planning is an interdisciplinary field including finance and business law topics. Consequently, standard pedagogical resources often omit topics that fall between these fields. To address a key gap in educational materials for financial planning students and faculty, this article reviews recent regulatory developments for financial planning students, including strengthened fiduciary standards and FINRA suitability requirements. The discussion introduces FINRA 2090, FINRA 2111, the Uniform Prudent Investor Act, and other widely adopted fiduciary-oriented model laws. The article concludes with a discussion of implications for financial planning professors and students

Raising Cash Under Duress And The Role Of Cash Value Life Insurance: An Educational Example

Consumers face hard choices when they need cash quickly. Hard choices can lead to emotional or economically unsound decisions. Traditional classroom discussions of raising funds to pay for expenses usually focus on generating income, borrowing, or the sale of real and financial assets, if hardship is discussed at all. However, many families have additional “non-traditional” sources of cash. This article examines the use of life insurance surrenders and policy loans as a source of funds for both routine funding needs as well as a source of emergency financing. The article concludes with a review of the economic considerations of life insurance for Insurance and Financial Planning educators and students

Why Downside Beta Is Better: An Educational Example

An educational example is presented that is an effective teaching illustration to help students understand the difference between traditional CAPM beta and downside (or down-market) beta and why downside beta is a superior measure for use in personal financial planning investment policy statements