On average case complexity

The airn of this talk is to give an introduction to the notion of Levin's average case complexity and then show sorne of the fields were recent research in this area is focused on. The first part is motivated by the struggle to find a precise and generally accepted definition of what is an efficient time on the average algorithm, given some distribution on the input. The definition should be easy (to use) and of course be machine independent and should posses properties like being closed under composition of algorithms. A reduction of a problem A to another problem which is efficiently solvable on average should give an efficient on average procedure to solve A. We then look in more detail at DistNP the class of problems in NP with polynomial time distributions on the inputs. This class has complete and self-reducible problems

Average-case intractability vs. worst-case intractability

AbstractWe show that not all sets in NP (or other levels of the polynomial-time hierarchy) have efficient average-case algorithms unless the Arthur-Merlin classes MA and AM can be derandomized to NP and various subclasses of P/poly collapse to P. Furthermore, other complexity classes like P(PP) and PSPACE are shown to be intractable on average unless they are easy in the worst case

Structural Average Case Complexity

AbstractLevin introduced an average-case complexity measure, based on a notion of “polynomial on average,” and defined “average-case polynomial-time many-one reducibility” among randomized decision problems. We generalize his notions of average-case complexity classes, Random-NP and Average-P. Ben-Davidet al. use the notation of 〈C, F〉 to denote the set of randomized decision problems (L, μ) such thatLis a set in C andμis a probability density function in F. This paper introduces Aver〈C, F〉 as the class of randomized decision problems (L, μ) such thatLis computed by a type-C machine onμ-average andμis a density function in F. These notations capture all known average-case complexity classes as, for example, Random-NP= 〈NP, P-comp〉 and Average-P=Aver〈P, ∗〉, where P-comp denotes the set of density functions whose distributions are computable in polynomial time, and ∗ denotes the set of all density functions. Mainly studied are polynomial-time reductions between randomized decision problems: many–one, deterministic Turing and nondeterministic Turing reductions and the average-case versions of them. Based on these reducibilities, structural properties of average-case complexity classes are discussed. We give average-case analogues of concepts in worst-case complexity theory; in particular, the polynomial time hierarchy and Turing self-reducibility, and we show that all known complete sets for Random-NP are Turing self-reducible. A new notion of “real polynomial-time computations” is introduced based on average polynomial-time computations for arbitrary distributions from a fixed set, and it is used to characterize the worst-case complexity classesΔpkandΣpkof the polynomial-time hierarchy

Randomized QuickSort and the Entropy of the Random Source

The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from $nlog n$ to $n^2$, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution

Is the Stack Distance Between Test Case and Method Correlated With Test Effectiveness?

Mutation testing is a means to assess the effectiveness of a test suite and its outcome is considered more meaningful than code coverage metrics. However, despite several optimizations, mutation testing requires a significant computational effort and has not been widely adopted in industry. Therefore, we study in this paper whether test effectiveness can be approximated using a more light-weight approach. We hypothesize that a test case is more likely to detect faults in methods that are close to the test case on the call stack than in methods that the test case accesses indirectly through many other methods. Based on this hypothesis, we propose the minimal stack distance between test case and method as a new test measure, which expresses how close any test case comes to a given method, and study its correlation with test effectiveness. We conducted an empirical study with 21 open-source projects, which comprise in total 1.8 million LOC, and show that a correlation exists between stack distance and test effectiveness. The correlation reaches a strength up to 0.58. We further show that a classifier using the minimal stack distance along with additional easily computable measures can predict the mutation testing result of a method with 92.9% precision and 93.4% recall. Hence, such a classifier can be taken into consideration as a light-weight alternative to mutation testing or as a preceding, less costly step to that.Comment: EASE 201

Correction of endothelial dysfunction in chronic heart failure: additional effects of exercise training and oral L-arginine supplementation

AbstractOBJECTIVESThe aim of this study was to analyze whether L-arginine (L-arg.) has comparable or additive effects to physical exercise regarding endothelium-dependent vasodilation in patients with chronic heart failure (CHF).BACKGROUNDEndothelial dysfunction in patients with CHF can be corrected by both dietary supplementation with L-arg. and regular physical exercise.METHODSForty patients with severe CHF (left ventricular ejection fraction 19 ± 9%) were randomized to an L-arg. group (8 g/day), a training group (T) with daily handgrip training, L-arg. and T (L-arg. + T) or an inactive control group (C). The mean internal radial artery diameter was determined at the beginning and after four weeks in response to brachial arterial administration of acetylcholine (ACh) (7.5, 15, 30 μg/min) and nitroglycerin (0.2 mg/min) with a transcutaneous high-resolution 10 MHz A-mode echo tracking system coupled with a Doppler device. The power of the study to detect clinically significant differences in endothelium-dependent vasodilation was 96.6%.RESULTSAt the beginning, the mean endothelium-dependent vasodilation in response to ACh, 30 μg/min was 2.54 ± 0.09% (p = NS between groups). After four weeks, internal radial artery diameter increased by 8.8 ± 0.9% after ACh 30 μg/min in L-arg. (p < 0.001 vs. C), by 8.6 ± 0.9% in T (p < 0.001 vs. C) and by 12.0 ± 0.3% in L-arg. + T (p < 0.005 vs. C, L-arg. and T). Endothelium-independent vasodilation as assessed by infusion of nitroglycerin was similar in all groups at the beginning and at the end of the study.CONCLUSIONSDietary supplementation of L-arg. as well as regular physical exercise improved agonist-mediated, endothelium-dependent vasodilation to a similar extent. Both interventions together seem to produce additive effects with respect to endothelium-dependent vasodilation

Myocardial perfusion and regression of coronary artery disease in patients on a regimen of intensive physical exercise and low fat diet

AbstractThis intervention program tested the applicability and effects of intensive physical exercise and a low fat diet on progression of coronary atherosclerotic lesions and stress-induced myocardial ischemia in patients with stable angina pectoris. Eighteen patients participated in this program for 1 year; they consumed a low fat, low cholesterol diet (< 20 energy % fat, cholesterol < 200 mg/day) and exercised for >3 h/week. Change in coronary morphology was assessed by angiography and digital image processing; stress-induced myocardial ischemia was measured by thallium-201 scintigraphy. Results were compared with those in patients receiving “usual care.”In the intervention group, significant regression of coronary atherosclerotic lesions was noted in 7 of the 18 patients: no change or progression was present in 11 patients. In patients receiving usual care, regression was detected in only 1, with no change or progression in 11 patients (different from intervention, p < 0.05). There was a significant reduction in stress-induced myocardial ischemia, which was not limited to patients with regression of coronary atherosclerotic lesions. Thus, regular physical exercise and a low fat diet may retard progression of coronary artery disease; however, improvement of myocardial perfusion may be achieved independently from regression of stenotic lesions

Internationale Klassifikation von Gesteinen nach pedologischen Gesichtspunkten

Im Rahmen des europäischen eSOTER Projekts (www.esoter.net) werden neue Me-thoden für die bodenkundlich ausgerichtete Abgrenzung von Landschaften mit GIS-Mo¬dellen entwickelt. Diese basieren im Wesentlichen auf digitalen Relief- und Lithologiedaten. Der Schwerpunkt der BGR-Arbeiten liegt auf der einheitlichen Erfas-sung und Darstellung von Gesteinsinforma¬tionen nach pedologischen Aspekten. Mit diesen Aktivitäten unterstützt die BGR auch ein Projekt des globalen Umweltüberwa-chungssystems GEOSS (Task „Global Soil Data“). Die BGR stellt nunmehr eine Über-arbeitung der FAO-Ausgangsgesteinsklassi¬fikation zur Diskussion

Reliefanalyse als Mittel für eine objektivere Abgrenzung von Bodengroßlandschaften

Bodengroßlandschaften (BGL) und Bodenregionen (BR) sind als hierarchische Gliederungsebene für die Erstellung klein- und mittelmaßstäbiger Bodenkarten von Bedeutung. Dabei sind BGL und BR wichtige Hilfsmittel für eine systematische Integration von Bodendaten unterschiedlicher Herkunft, z.B. aus verschiedenen Bundesländern oder bei der Erstellung einer Europaweit einheitlichen Bodenübersichtskarte. Zunehmend wichtig werden Grenzen von BGL und BR auch bei der Kopplung von Bodeninformationen aus Karten und Inventurdaten mit Modellszenarien, wie sie z.B. bei der Bewertung von Kohlenstoffvorräten in Waldböden (ZIRLEWAGEN & VON WILPERT 2010) oder bei der Abschätzung von Folgen des Klimawandels benötigt werden. Solche Modelle liefern häufig bessere Ergebnisse, wenn eine landschaftsspezifische Eichung erfolgen kann. Die Definitionen von BGL, wie sie gegenwärtig in der Bodenkundlichen Kartieranleitung (KA5) zu finden sind, werden diesen Anforderungen nicht gerecht. Zum einen sind die Definitionen häufig nicht eindeutig und lassen dem Bearbeiter bei der Abgrenzung viel Spielraum. Zum anderen ist der methodische Ansatz problematisch, BGL zunächst "aus kleinmaßstäbigen Grundlagendaten "top-down" abzugrenzen. Gegenwärtig werden daher bei der BGR Vorschläge für eine verbesserte Definierung und Abgrenzung der BGL als Diskussionsgrundlage entworfen. Dabei werden u.a. auch Möglichkeiten der GIS-gestützten Analyse von digitalen Höhenmodelldaten untersucht, um den reliefbezogenen Anteil der BGL-Grenzen zu modellieren

Safety and Efficacy of Itraconazole Compared to Amphotericin B as Empirical Antifungal Therapy for Neutropenic Fever in Patients with Haematological Malignancy

Safety, tolerability and efficacy of itraconazole and amphotericin B (AMB) were compared for empirical antifungal treatment of febrile neutropenic cancer patients. Patients and Methods: In an open, randomised study, 162 patients with at least 72 h of antimicrobial treatment received either intravenous followed by oral itraconazole suspension or intravenous AMB for a maximum of 28 days. Permanent discontinuation of study medication due to any adverse event was the primary safety parameter. Efficacy parameters included response and success rate for both treatment groups. Results: Significantly fewer itraconazole patients discontinued treatment due to any adverse event (22.2 vs. 56.8% AMB; p < 0.0001). The main reason for discontinuation was a rise in serum creatinine (1.2% itraconazole vs. 23.5% AMB). Renal toxicity was significantly higher and more drug-related adverse events occurred in the AMB group. Intention-to-treat (ITT) analysis showed favourable efficacy for itraconazole: response and success rate were both significantly higher than for AMB (61.7 vs. 42% and 70.4 vs. 49.3%, both p < 0.0001). Treatment failure was markedly reduced in itraconazole patients (25.9 vs. 43.2%), largely due to the better tolerability. Conclusions: Itraconazole was tolerated significantly better than conventional AMB and also showed advantages regarding efficacy. This study confirms the role of itraconazole as a useful and safe agent in empirical antifungal therapy of febrile neutropenic cancer patients.Hintergrund: Es wurden die Sicherheit, Verträglichkeit und Wirksamkeit von Itraconazol und Amphotericin B (AMB) in der antimykotischen Therapie der persistierend febrilen Neutropenie verglichen. Patienten und Methoden: In einer offenen, randomisierten Studie erhielten 162 Patienten mit mindestens 72-stündiger antibiotischer Therapie entweder Itraconazol (erst intravenös, dann oral) oder AMB (intravenös) für maximal 28 Tage. Primärer Sicherheitsparameter war die dauerhafte Unterbrechung der Studienmedikation aufgrund von Nebenwirkungen. Die Wirksamkeitsparameter umfassten die Ansprech- und Erfolgsrate für beide Behandlungsgruppen. Ergebnisse: Signifikant weniger Itraconazol-Patienten brachen die Behandlung wegen Nebenwirkungen ab (22,2 vs. 56,8% AMB; p < 0,0001). Hauptursache für Studienabbrüche war der Anstieg des Serum-Kreatinin-Spiegels (1,2% Itraconazol vs. 23,5% AMB). Nephrotoxische und weitere Nebenwirkungen traten im AMB-Studienarm signifikant häufiger auf. Intention-to-Treat (ITT)-Analysen zeigten eine bessere Wirksamkeit von Itraconazol: Ansprech- und Erfolgsrate waren signifikant höher als unter AMB (61,7 vs. 42% und 70,4 vs. 49,3%, beide p < 0,0001). Behandlungsversagen trat bei Itraconazol-Patienten merklich weniger auf (25,9 vs. 43,2%). Schlussfolgerungen: Die Verträglichkeit von Itraconazol war signifikant höher als beim herkömmlichen AMB. Itraconazol zeigte ebenfalls Vorteile in der Wirksamkeit. Diese Studie bestätigt die Rolle von Itraconazol als sinnvolles und sicheres Medikament in der empirischen antimykotischen Therapie von fiebrigen neutropenischen Tumorpatienten.Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich