The orientation-preserving diffeomorphism group of S^2 deforms to SO(3) smoothly

Smale proved that the orientation-preserving diffeomorphism group of S^2 has a continuous strong deformation retraction to SO(3). In this paper, we construct such a strong deformation retraction which is diffeologically smooth.Comment: 16 page

Log-Periodic Dipole Array Antenna as Chipless RFID Tag

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Dynamic consolidation problems in saturated soils solved through u-w formulation in a LME meshfree framework

A meshfree numerical model, based on the principle of Local Maximum Entropy (LME), including a B-bar algorithm to avoid instabilities, is applied to solve axisymmetric consolidation problems in elastic saturated soils. This numerical scheme has been previously validated for purely elastic problems without water (mono phase), as well as for steady seepage in elastic porous media. Hereinafter, an implementation of the novel numerical method in the axisymmetric configuration is proposed, and the model is validated for well known theoretical problems of consolidation in saturated soils, under both static and dynamic conditions with available analytical solutions. The solutions obtained with the new methodology are compared with a finite element commercial software for a set of examples. After validated, solutions for dynamic radial consolidation and sinks, which have not been found elsewhere in the literature, are presented as a novelty. This new numerical approach is demonstrated to be feasible for this kind of problems in porous media, particularly for high frequency, dynamic problems, for which very few results have been found in the literature in spite of their high practical importance

Computational algebraic methods in efficient estimation

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed, such as bias corrected Maximum Likelihood and more general estimators, and for which the estimating equations are purely algebraic. In addition it is shown how Gr\"obner basis technology, which is at the heart of algebraic statistics, can be used to reduce the degrees of the terms in the estimating equations. This points the way to the feasible use, to find the estimators, of special methods for solving polynomial equations, such as homotopy continuation methods. Simple examples are given showing both equations and computations. *** The proof of Theorem 2 was corrected by the latest version. Some minor errors were also corrected.Comment: 21 pages, 5 figure

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.Comment: 19 pages, 4 figure

Inkjet printed multimetal microelectrodes on PDMS for functionalized microfluidic systems

A novel direct method of metal microelectrode patterning on polydimethylsiloxane (PDMS) using inkjet printed gold and silver nanoparticles to form electrochemical sensors is presented. Inkjet printing is an additive microfabrication technique enabling microelectrode patterning directly over large areas at low-temperatures. (3-mercaptopropyl) trimethoxysilane (MPTMS) to promote PDMS surface wettability and improve metal adhesion and a pixel-printing subsampling method to overcome surface tension driven ink-droplet coalescence, are then employed to form a robust fabrication process. The resulting printed gold and silver microelectrodes exhibit good compactness, continuity and conductivity, and are used to manufacture functionalized microfluidic systems with in-situ three-electrode electrochemical sensors.published_or_final_versio

An interstitial fluid transdermal extraction system for continuous glucose monitoring

A novel microfluidic system which is fabricated with five polydimethylsiloxane layers for interstitial fluid (ISF) extraction, collection, and measurement toward the application of continuous and real-time glucose monitoring is presented in this paper. The system consists of a micro vacuum generator for ISF transdermal extraction and fluid manipulation, micro chambers for the collection of ISF, micro pneumatic valves for fluid management, and a micro flow sensor for ISF volume measurement. Sequentially controlled by the pneumatic valves, the ISF extraction, collection, and volumetric measurement functions of the system were demonstrated using the stable vacuum generated by the integrated vacuum generator. Through low-frequency ultrasound pretreated full-thickness pig skin, the normal saline solution with different glucose concentrations was transdermally extracted, collected, and measured. The absolute error in the volume measurement of the transdermally extracted ISF analog was less than 0.05 μ L. The microfluidic system makes it possible to realize the clinical application of continuous glucose monitoring based on ISF transdermal extraction technology. © 2012 IEEE.published_or_final_versio