scholarly journals A polynomial-time test for total dual integrality in fixed dimension

Author(s):  
W. Cook ◽  
L. Lovász ◽  
A. Schrijver
Author(s):  
Ryan Carpenter ◽  
Charles L. Samuels

For each algebraic number [Formula: see text] and each positive real number [Formula: see text], the [Formula: see text]-metric Mahler measure [Formula: see text] creates an extremal problem whose solution varies depending on the value of [Formula: see text]. The second author studied the points [Formula: see text] at which the solution changes, called exceptional points for[Formula: see text] . Although each algebraic number has only finitely many exceptional points, it is conjectured that, for every [Formula: see text], there exists a number having at least [Formula: see text] exceptional points. In this paper, we describe a polynomial time algorithm for establishing the existence of numbers with at least [Formula: see text] exceptional points. Our work constitutes an improvement over the best known existing algorithm which requires exponential time. We apply our main result to show that there exist numbers with at least [Formula: see text] exceptional points, another improvement over previous work which was only able to reach [Formula: see text] exceptional points.


2014 ◽  
Vol 43 (5) ◽  
pp. 1728-1780 ◽  
Author(s):  
Martin Čadek ◽  
Marek Krčál ◽  
Jiří Matoušek ◽  
Lukáš Vokřínek ◽  
Uli Wagner

1991 ◽  
Vol 153 ◽  
pp. 183-192 ◽  
Author(s):  
H. Väliaho
Keyword(s):  

1954 ◽  
Vol 26 (5) ◽  
pp. 781-788 ◽  
Author(s):  
Sheldon S. Waldstein ◽  
Bruce T. Forsyth ◽  
Edward J. Jahnke

2010 ◽  
Vol 30 (04) ◽  
pp. 212-216 ◽  
Author(s):  
R. Jovic ◽  
M. Hollenstein ◽  
P. Degiacomi ◽  
M. Gautschi ◽  
A. Ferrández ◽  
...  

SummaryThe activated partial thromboplastin time test (aPTT) represents one of the most commonly used diagnostic tools in order to monitor patients undergoing heparin therapy. Expression of aPTT coagulation time in seconds represents common practice in order to evaluate the integrity of the coagulation cascade. The prolongation of the aPTT thus can indicate whether or not the heparin level is likely to be within therapeutic range. Unfortunately aPTT results are highly variable depending on patient properties, manufacturer, different reagents and instruments among others but most importantly aPTT’s dose response curve to heparin often lacks linearity. Furthermore, aPTT assays are insensitive to drugs such as, for example, low molecular weight heparin (LMWH) and direct factor Xa (FXa) inhibitors among others. On the other hand, the protrombinase-induced clotting time assay (PiCT®) has been show to be a reliable functional assay sensitive to all heparinoids as well as direct thrombin inhibitors (DTIs). So far, the commercially available PiCT assay (Pefakit®-PiCT®, DSM Nutritional Products Ltd. Branch Pentapharm, Basel, Switzerland) is designed to express results in terms of units with the help of specific calibrators, while aPTT results are most commonly expressed as coagulation time in seconds. In this report, we describe the results of a pilot study indicating that the Pefakit PiCT UC assay is superior to the aPTT for the efficient monitoring of patients undergoing UFH therapy; it is also suitable to determine and quantitate the effect of LMWH therapy. This indicates a distinct benefit when using this new approach over the use of aPPT for heparin monitoring.


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