Multiple robots formation manoeuvring and collision avoidance strategy

This paper presents a multiple robots formation manoeuvring and its collision avoidance strategy. The direction priority sequential selection algorithm is employed to achieve the raw path, and a new algorithm is then proposed to calculate the turning compliant waypoints supporting the multi-robot formation manoeuvre. The collision avoidance strategy based on the formation control is presented to translate the collision avoidance problem into the stability problem of the formation. The extension-decomposition-aggregation scheme is next applied to solve the formation control problem and subsequently achieve the collision avoidance during the formation manoeuvre. Simulation study finally shows that the collision avoidance problem can be conveniently solved if the stability of the constructed formation including unidentified objects can be satisfied.

Heteroduplex PCR analysis of rearranged immunoglobulin genes for clonality assessment in multiple myeloma.

BACKGROUND AND OBJECTIVE: Molecular analysis by PCR of monoclonally rearranged immunoglobulin (Ig) genes can be used for diagnosis in B-cell lymphoproliferative disorders (LPD), as well as for monitoring minimal residual disease (MRD) after treatment. This technique has the risk of false-positive results due to the "background" amplification of similar rearrangements derived from polyclonal B-cells. This problem can be resolved in advance by additional analyses that discern between polyclonal and monoclonal PCR products, such as the heteroduplex analysis. A second problem is that PCR frequently fails to amplify the junction regions, mainly due to somatic mutations frequently present in mature (post-follicular) B-cell lymphoproliferations. The use of additional targets (e.g. Ig light chain genes) can avoid this problem. DESIGN AND METHODS: We studied the specificity of heteroduplex PCR analysis of several Ig junction regions to detect monoclonal products in samples from 84 MM patients and 24 patients with B cell polyclonal disorders. RESULTS: Using two distinct VH consensus primers (FR3 and FR2) in combination with one JH primer, 79% of the MM displayed monoclonal products. The percentage of positive cases was increased by amplification of the Vlamda-Jlamda junction regions or kappa(de) rearrangements, using two or five pairs of consensus primers, respectively. After including these targets in the heteroduplex PCR analysis, 93% of MM cases displayed monoclonal products. None of the polyclonal samples analyzed resulted in monoclonal products. Dilution experiments showed that monoclonal rearrangements could be detected with a sensitivity of at least 10(-2) in a background with >30% polyclonal B-cells, the sensitivity increasing up to 10(-3) when the polyclonal background was

Joint Analysis of Multiple Algorithms and Performance Measures

There has been an increasing interest in the development of new methods using Pareto optimality to deal with multi-objective criteria (for example, accuracy and time complexity). Once one has developed an approach to a problem of interest, the problem is then how to compare it with the state of art. In machine learning, algorithms are typically evaluated by comparing their performance on different data sets by means of statistical tests. Standard tests used for this purpose are able to consider jointly neither performance measures nor multiple competitors at once. The aim of this paper is to resolve these issues by developing statistical procedures that are able to account for multiple competing measures at the same time and to compare multiple algorithms altogether. In particular, we develop two tests: a frequentist procedure based on the generalized likelihood-ratio test and a Bayesian procedure based on a multinomial-Dirichlet conjugate model. We further extend them by discovering conditional independences among measures to reduce the number of parameters of such models, as usually the number of studied cases is very reduced in such comparisons. Data from a comparison among general purpose classifiers is used to show a practical application of our tests.

Two problems from the Polishchuk and Positselski book on Quadratic algebras

In the book ’Quadratic algebras’ by Polishchuk and Positselski [23] algebras with a small number of generators (n = 2, 3) are considered. For some number r of relations possible Hilbert series are listed, and those appearing as series of Koszul algebras are specified. The first case, where it was not possible to do, namely the case of three generators n = 3 and six relations r = 6 is formulated as an open problem. We give here a complete answer to this question, namely for quadratic algebras with dimA_1 = dimA_2 = 3, we list all possible Hilbert series, and find out which of them can come from Koszul algebras, and which can not. As a consequence of this classification, we found an algebra, which serves as a counterexample to another problem from the same book [23] (Chapter 7, Sec. 1, Conjecture 2), saying that Koszul algebra of finite global homological dimension d has dimA_1 > d. Namely, the 3-generated algebra A given by relations xx + yx = xz = zy = 0 is Koszul and its Koszul dual algebra A^! has Hilbert series of degree 4: HA! (t) = 1 + 3t + 3t^2 + 2t^3 + t^4, hence A has global homological dimension 4.