Interactive decision software and computer graphics for architectural and space planning

We describe the development and successful implementation of a decision support system now being used by several leading firms in the architecture and space planning industries. The system, which we call SPDS (spatial programming design system) has the following characteristics: (i) user-friendly convenience features permitting architects and space planners to operate the system without being experienced programmers; (ii) interactive capabilities allowing the user to control and to manipulate relevant parameters, orchestrating conditions to which his or her intuition provides valuable input; (iii) informative and understandable graphics, providing visual displays of interconnections that the computer itself treats in a more abstract methematical form; (iv) convenient ways to change configurations, and to carry out ‘what if’ analyses calling on the system’s decision support capabilities; (v) a collection of new methods, invisible to the user, capable of generating good solutions to the mathematical programming problems that underlie each major design component. These new methods succeed in generating high quality solutions to a collection of complex discrete, highly nonlinear problems. While these problems could only be solved in hours, or not at all, with previously existing software, the new methods obtain answers in seconds to minutes on a minicomputer. Major users, including Dalton, Dalton, Newport, and Marshal Erdwin, report numerous advantages of the system over traditional architectural design methods.     

Directly testing the linearity assumption for assay validation

The ICH Q2(R1) (International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use) guideline for testing linearity in validation of analytical procedures suggests that “linearity should be evaluated by visual inspection of a plot of signals as a function of analyte concentration or content.” The EP6‐A guideline recommends more quantitative methods that compare straight‐line and higher‐order polynomial curve fits. In this paper, a new equivalence test is proposed to compare the quality of a straight‐line fit to that of a higher‐order polynomial. By using orthogonal polynomials and generalized pivotal quantity analysis, one may estimate the probability of equivalence between a straight line and a polynomial curve fit either in the assay signal space (the Y values) or in the concentration space (the X values). In the special case of the linear‐to‐quadratic polynomial comparison, an equivalence test may be constructed via a two one‐sided T test. Copyright © 2013 John Wiley & Sons, Ltd.     

Rotational Spectra of Argon Acetone: A Two-Top Internally Rotating Complex

The rotational spectra of the argon acetone weakly bound complex was studied by pulsed jet Fabry-Perot Fourier transform microwave spectroscopy. Over 500 transitions of the complex were measured between 5.5 and 26 GHz from J=2-1 to J=12-11. The two methyl groups undergo hindered internal rotation resulting in four or five internal rotation states. The microwave transitions are within these states, resulting in a splitting of each rotational transition into four and sometimes five distinct transitions. The three-fold barrier to internal rotation is determined to be 260 cm⁻¹, 2% less than the 266 cm⁻¹ barrier in acetone itself. The structure of the complex has the argon atom above the heavy atom plane of the acetone, 3.52 Å from the CO bond and approximately in the C_s plane, which is perpendicular to the CCC plane of acetone.     

The Worpitzky identity for the groups of signed and even-signed permutations

Journal of Algebraic Combinatorics - The well-known Worpitzky identity $$\begin{aligned} (x+1)^n = \sum \limits _{k=0}^{n-1} A_{n,k} {{x+n-k} \atopwithdelims (){n}} \end{aligned}$$ provides a...     

Diagram Literacy in Preservice Math Teachers, Computer Science Majors, and Typical Undergraduates: The Case of Matrices, Networks, and Hierarchies

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence - implicit, construction, similarity, structural, metacognitive, and translational. A study is reported that examined college students' diagram literacy for three interrelated mathematical diagrams - matrices, networks, and hierarchies. Three groups of students participated: preservice, secondary-level, math teachers; computer science majors; and typical undergraduates. The results of the study are reassuring in some ways concerning the level of diagram literacy possessed by students at the culmination of current K through 12 instruction and by teachers of future secondary students. However, the results also point to areas in which preservice math teachers should be better prepared if the goals for students' diagram literacy are to be met.     

Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

HDX Workbench: Software for the Analysis of H/D Exchange MS Data

Hydrogen/deuterium exchange mass spectrometry (HDX-MS) is an established method for the interrogation of protein conformation and dynamics. While the data analysis challenge of HDX-MS has been addressed by a number of software packages, new computational tools are needed to keep pace with the improved methods and throughput of this technique. To address these needs, we report an integrated desktop program titled HDX Workbench, which facilitates automation, management, visualization, and statistical cross-comparison of large HDX data sets. Using the software, validated data analysis can be achieved at the rate of generation. The application is available at the project home page http://hdx.florida.scripps.edu .