A model to set measurement quality objectives and to establish measurement uncertainty expectations in analytical chemistry laboratories using ASTM proficiency test data

A model is presented that correlates historical proficiency test data as the log of interlaboratory standard deviations versus the log of analyte concentrations, independent of analyte (measurand) or matrix. Analytical chemistry laboratories can use this model to set their internal measurement quality objectives and to apply the uncertainty budget process to assign the maximum allowable variation in each major step in their bias-free measurement systems. Laboratories that are compliant with this model are able to pass future proficiency tests and demonstrate competence to laboratory clients and ISO 17025 accreditation bodies. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/ 10.1007/s007690100398-y. Received: 31 March 2001 Accepted: 11 September 2001     

Excited-state properties of Rh(2)(O(2)CCH(3))(4)(L)(2) (L = CH(3)OH, THF, PPh(3), py)

The photophysical properties of Rh(2)(O(2)CCH(3))(4)(L)(2) (L = CH(3)OH, THF = tetrahydrofuran, PPh(3) = triphenylphosphine, py = pyridine) were explored upon excitation with visible light. Time-resolved absorption shows that all the complexes possess a long-lived transient (3.5-5.0 micros) assigned as an electronic excited state of the molecules, and they exhibit an optical transition at approximately 760 nm whose position is independent of axial ligand. No emission from the Rh(2)(O(2)CCH(3))(4)(L)(2) (L = CH(3)OH, THF, PPh(3), py) systems was detected, but energy transfer from Rh(2)(O(2)CCH(3))(4)(PPh(3))(2) to the (3)pipi excited state of perylene is observed. Electron transfer from Rh(2)(O(2)CCH(3))(4)(PPh(3))(2) to 4,4'-dimethyl viologen (MV(2+)) and chloro-p-benzoquinone (Cl-BQ) takes place with quenching rate constants (k(q)) of 8.0 x 10(6) and 1.2 x 10(6) M(-1) s(-1) in methanol, respectively. A k(q) value of 2 x 10(8) M(-1) s(-1) was measured for the quenching of the excited state of Rh(2)(O(2)CCH(3))(4)(PPh(3))(2) by O(2) in methanol. The observations are consistent with the production of an excited state with excited-state energy, E(00), between 1.34 and 1.77 eV.     

Multilinear forms and measures of dependence between random variables

Based on an idea of Rosenblatt, the methods of interpolation theory are used to establish moment inequalities and equivalence relations for measures of dependence between two or more families of random variables. A couple of “interpolation” theorems proved here appear to be new.     

From image processing to topological modelling with <Emphasis Type="Italic">p</Emphasis>-adic numbers

Encoding the hierarchical structure of images by p-adic numbers allows for image processing and computer vision methods motivated from arithmetic physics. The p-adic Polyakov action leads to the p-adic diffusion equation in low level vision. Hierarchical segmentation provides another way of p-adic encoding. Then a topology on that finite set of p-adic numbers yields a hierarchy of topological models underlying the image. In the case of chain complexes, the chain maps yield conditions for the existence of a hierarchy, and these can be expressed in terms of p-adic integrals. Such a chain complex hierarchy is a special case of a persistence complex from computational topology, where it is used for computing persistence barcodes for shapes. The approach is motivated by the observation that using p-adic numbers often leads to more efficient algorithms than their real or complex counterparts.     

On some results of M. I. Gordin: A clarification of a misunderstanding

M. I. Gordin proved a central limit theorem for some strictly stationary strongly mixing random sequences without the assumption of finite second moments. Because of a series of misunderstandings, his own correct formulation of the theorem has been essentially ignored, while an incorrect formulation has been discussed extensively and attributed to him in many references. This note explains in detail what has happened, in the hope of clearing up the misunderstandings.     

Embedding hypertrees into steiner triple systems

In this paper, we are interested in the following question: given an arbitrary Steiner triple system on vertices and any 3‐uniform hypertree on vertices, is it necessary that contains as a subgraph provided ? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.     

Ultrametricity indices for the Euclidean and Boolean hypercubes

Motivated by Murtagh’s experimental observation that sparse random samples of the hypercube become more and more ultrametric as the dimension increases, we consider a strict version of his ultrametricity coefficient, an index derived from Rammal’s degree of ultrametricity, and a topological ultrametricity index. First, we prove that the three ultrametricity indices converge in probability to one as dimension increases, if the sample size remains fixed. This is done for uniformly and normally distributed samples in the Euclidean hypercube, and for uniformly distributed samples in F₂ ^N with Hamming distance, as well as for very general probability distributions. Further, this holds true for random categorial data in complete disjunctive form. A second result is that the ultrametricity indices vanish in the limit for the full hypercube F₂ ^N as dimensionN increases,whereby Murtagh’s ultrametricity index is largest, and the topological ultrametricity index smallest, if N is large.     

Parametric Euler sum identities

We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums.     

Inducing models of behavior from expert task performance in virtual environments

We developed an end-to-end process for inducing models of behavior from expert task performance through in-depth case study. A subject matter expert (SME) performed navigational and adversarial tasks in a virtual tank combat simulation, using the dTank and Unreal platforms. Using eye tracking and Cognitive Task Analysis, we identified the key goals pursued by and attributes used by the SME, including reliance on an egocentric spatial representation, and on the fly re-representation of terrain in qualitative terms such as “safe” and “risky”. We demonstrated methods for automatic extraction of these qualitative higher-order features from combinations of surface features present in the simulation, producing a terrain map that was visually similar to the SME annotated map. The application of decision-tree and instance-based machine learning methods to the transformed task data supported prediction of SME task selection with greater than 95 % accuracy, and SME action selection at a frequency of 10 Hz with greater than 63 % accuracy, with real time constraints placing limits on algorithm selection. A complete processing model is presented for a path driving task, with the induced generative model deviating from the SME chosen path by less than 2 meters on average. The derived attributes also enabled environment portability, with path driving models induced from dTank performance and deployed in Unreal demonstrating equivalent accuracy to those induced and deployed completely within Unreal.