Dual Polar Graphs, a nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials

Let $\Gamma$ be a dual polar graph with diameter $D \geqslant 3$, having as vertices the maximal isotropic subspaces of a finite-dimensional vector space over the finite field $\mathbb{F}_q$ equipped with a non-degenerate form (alternating, quadratic, or Hermitian) with Witt index $D$. From a pair of a vertex $x$ of $\Gamma$ and a maximal clique $C$ containing $x$, we construct a $2D$-dimensional irreducible module for a nil-DAHA of type $(C^{\vee}_1, C_1)$, and establish its connection to the generalized Terwilliger algebra with respect to $x$, $C$. Using this module, we then define the non-symmetric dual $q$-Krawtchouk polynomials and derive their recurrence and orthogonality relations from the combinatorial points of view. We note that our results do not depend essentially on the particular choice of the pair $x$, $C$, and that all the formulas are described in terms of $q$, $D$, and one other scalar which we assign to $\Gamma$ based on the type of the form.Comment: an extended abstract of this work appeared in proceedings for FPSAC 201

Systematic Procedures to Determine Incentive / Disincentive Dollar Amounts for Highway Transportation Construction Projects, Research Report 11-22

The Federal Highway Administration has encouraged state transportation agencies to implement Incentive/Disincentive (I/D) contracting provisions for early project completion. Although general guidelines to determine the I/D dollar amount for a project are available, there is no systematic and practical tool in use to determine optimum I/D dollar amounts for I/D projects considering road user cost, agency cost, contractor’s acceleration cost, and contractor’s cost savings. Therefore, systematic procedures and models to assist project planners and engineers in determining an appropriate I/D dollar amount are essential to optimizing the use of I/D contracting techniques. This research performed a literature review related to the determination of daily I/D dollar amounts. Caltrans I/D project data were then collected and evaluated. Project performance data were analyzed with regard to project outcomes in two key areas: project time and project cost. Statistical analyses were performed to identify the impact of I/D dollar amount on project time and cost performance. Using Construction Analysis for Pavement Rehabilitation Strategies (CA4PRS) software, Caltrans I/D projects were analyzed to introduce three different levels of CA4PRS implementations for the I/D dollar amounts calculation. Based on the results of the I/D project case studies, the systematic procedures to determine appropriate I/D dollar amounts were developed using the CA4PRS schedule-traffic-cost integration process for the new I-5 rehabilitation project in LA. The proposed procedures were applied to a typical highway pavement rehabilitation project using HMA (hot mix asphalt) materials. Further research is needed to apply the proposed model to other types of highway projects, with adjustment for the type of project

Does Source of Income Affect Risk and Intertemporal Choices?

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