I address the historical emergence of the mathematical infinite, and how we are to take the infinite in and out of mathematics. The thesis is that the mathematical infinite in mathematics is a matter of method. The infinite, of course, is a large topic. At the outset, one can historically discern two overlapping clusters of concepts: (1) wholeness, completeness, universality, absoluteness. (2) ...

This paper presents an automatic method to assess telangiectasia degreeing, by estimating the reduction of the varicose area from pre to post-treatment using digital image analysis techniques. First both images are geometrically transformed and color space reduced, in order to make them suitable for processing. Next, the varicose veins are segmented via watershed transform and the varicose area...

BACKGROUND Vital capacity is a key parameter in the determination of lung function, usually assessed by means of a forced expiration maneuver. This maneuver can be exhausting, and patients often cannot complete it. OBJECTIVES This study evaluates a method to estimate forced vital capacity (FVC) based on the extrapolation of volume-time curves from forced expiration. METHODS The algorithm wa...

A mathematical analysis of serological data has provided the basis for a new serotyping routine. This paper describes the process whereby the results of agglutination reactions between the standard O antigens of Escherichia coli and rabbit antisera raised against them were used to produce a much simpler, faster, and cheaper method of serotyping. This new method for serotyping E. coli requires o...

Mathematical expressions exist in all kinds of documents. The automatic location , recognition, analysis and understanding of mathematical expressions are important. Recognition of mathematical expressions has been an attractive problem for the pattern recognition community. When we meet the mathematical expressions we can’t recognize them like the way of ordinary text recognitions. We are in u...

In this thesis, a new smoothing penalty algorithm is introduced to solve a mathematical program with equilibrium constraints (MPEC). By smoothing the exact penalty function, an MPEC is reformulated as a series of subprograms which belong to a class of MPECs with simple linear complementarity constraints. To deal with the subproblems, a hybrid algorithm is proposed, which combines the active set...

This paper discusses dimensional manipulation, essentially a problem requiring symbolic mathematics techniques, using a numerical approach. The numerical method obeys the laws of dimensional arithmetic. This is achieved by specifying an encoding of units of measurement as prime numbers, and manipulating the resulting expressions numerically. The unique factorization theorem is applied to show t...

The mathematical structures of loopy belief propagation are reviewed for graphical models in probabilistic information processing in the stand point of cluster variation method. An extension of adaptive TAP approaches is given by introducing a generalized scheme of the cluster variation method. Moreover the practical message update rules in loopy belief propagation are summarized also for quant...

S. Tang LTCS, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China fluid–structure boundaries, the arbitrary Lagrangian Eulerian 26 (ALE) techniques (see [9,11,15,16,18,33,34]) and space27 time methods (see [28,29]) are typically used. Recently, such 28 approaches have also been adopted by [8] in the modeling of 29 fluid–particle (rigid) systems. Nevertheles...