The complexity of Boolean formula minimization

The Minimum Equivalent Expression problem is a natural optimization problem in the second level of the Polynomial-Time Hierarchy. It has long been conjectured to be Σ^P_2-complete and indeed appears as an open problem in Garey and Johnson (1979) [5]. The depth-2 variant was only shown to be Σ^P_2-complete in 1998 (Umans (1998) [13], Umans (2001) [15]) and even resolving the complexity of the depth-3 version has been mentioned as a challenging open problem. We prove that the depth-k version is Σ^P_2-complete under Turing reductions for all k ≥ 3. We also settle the complexity of the original, unbounded depth Minimum Equivalent Expression problem, by showing that it too is Σ^P_2-complete under Turing reductions

Inapproximability of Truthful Mechanisms via Generalizations of the VC Dimension

Algorithmic mechanism design (AMD) studies the delicate interplay between computational efficiency, truthfulness, and optimality. We focus on AMD's paradigmatic problem: combinatorial auctions. We present a new generalization of the VC dimension to multivalued collections of functions, which encompasses the classical VC dimension, Natarajan dimension, and Steele dimension. We present a corresponding generalization of the Sauer-Shelah Lemma and harness this VC machinery to establish inapproximability results for deterministic truthful mechanisms. Our results essentially unify all inapproximability results for deterministic truthful mechanisms for combinatorial auctions to date and establish new separation gaps between truthful and non-truthful algorithms

Progress on pricing with peering

This paper examines a simple model of how a provider ISP charges customer ISPs by assuming the provider ISP wants to maximize its revenue when customer ISPs have the possibility of setting up peering connections. It is shown that finding the optimal pricing is NP-complete, and APX-complete. Customers can respond to price in many ways, including throttling traffic as well as peering. An algorithm is studied which obtains a 1/4 approximation for a wide range of customer responses

Methods and protocols for incremental exercise testing in tetraplegia, using arm-crank ergometry assisted by Functional Electrical Stimulation

Cervical spinal cord injury (SCI) leads to tetraplegia, with paralysis and loss of sensation in the upper and lower limbs. The associated sedentary lifestyle results in an increased risk of cardiovascular disease. To address this, we require the design of exercise modalities aimed specifically at tetraplegia and methods to assess their efficacy. This paper describes methods for arm-crank ergometry (ACE) assisted by Functional Electrical Stimulation (FES) applied to the biceps and triceps. The instrumented ergometer enables work-rate control during exercise, implemented here for incremental exercise testing during FES-ACE. Detailed protocols for the tests are given. Experimental data collected during exercise tests with tetraplegic volunteers are provided to illustrate the feasibility of the proposed approach to testing and data analysis. Incremental tests enabled calculation of peak power output and peak oxygen uptake. We propose that the high-precision exercise testing protocols described here are appropriate to assess the efficacy of the novel exercise modality, FES-ACE, in tetraplegia

Reference values for and cross-validation of time to exhaustion on a modified Balke protocol in Norwegian men and women

acceptedVersio

Influence of the incremental step size in work rate on exercise response and gas exchange in patients with pulmonary hypertension

<p>Abstract</p> <p>Background</p> <p>Cardiopulmonary exercise testing (CPET) has become increasingly important as a routine procedure in daily clinical work. So far, it is generally accepted that an individualized exercise protocol with exercise duration of 6 to 12 minutes is preferable to assess maximal exercise performance. The aim of this study was to compare an individualized NYHA adapted exercise protocol with a fixed standard protocol in patients with severe pulmonary arterial hypertension.</p> <p>Methods</p> <p>Twenty-two patients (17 female, 5 male; mean age 49 ± 14 yrs) underwent symptom limited CPET on a bicycle. On two consecutive days each subject performed a stepwise CPET according to a modified Jones protocol (16 Watt per minute stages) as well as an individualized NYHA adapted protocol with 5 or 10 Watt/min stages in a randomized order. Oxygen uptake at peak exercise (peakVO₂) and anaerobic threshold (VO₂AT), maximal ventilation (VE), breathing reserve (VE/MVV), ventilatory efficiency (VE vs. VCO₂slope), exercise time, maximal power and work rate were assessed and compared between both protocols.</p> <p>Results</p> <p>Comparing both, adapted NYHA protocol and standardized Jones protocol, we found significant differences in maximal power (56.7 ± 19 W vs. 74 ± 18 W; p < 0.001) and exercise time (332 ± 107 sec. vs. 248 ± 72 sec.; p < 0.001). In contrast, no significant differences were obvious comparing both protocols concerning work rate, VE, VE/MVV, peakVO₂, VO₂AT and VE vs. VCO₂slope.</p> <p>Conclusion</p> <p>Variations of incremental step size during CPET significantly affect exercise time and maximal power, whereas relevant parameters for clinical judgement and prognosis such as oxygen uptake, ventilation and ventilatory efficiency remain unchanged. These findings have practical implications for the exercise evaluation of patients with pulmonary hypertension. To reach maximal results for ventilation, oxygen uptake and gas exchange an individualization of incremental step size appears not to be mandatory.</p

Handcycling: training effects of a specific dose of upper body endurance training in females

Purpose: This study aims to evaluate a handcycling training protocol based on ACSM guidelines in a well-controlled laboratory setting. Training responses of a specific dose of handcycling training were quantified in a homogeneous female subject population to obtain a more in depth understanding of physiological mechanisms underlying adaptations in upper body training. Methods: 22 female able-bodied participants were randomly divided in a training (T) and control group (C). T received 7-weeks of handcycling training, 3 × 30 min/week at 65 % heart rate reserve (HRR). An incremental handcycling test was used to determine local, exercise-specific adaptations. An incremental cycling test was performed to determine non-exercise-specific central/cardiovascular adaptations. Peak oxygen uptake (peakVO2), heart rate (peakHR) and power output (peakPO) were compared between T and C before and after training. Results: T completed the training sessions at 65 ± 3 % HRR, at increasing power output (59.4 ± 8.2 to 69.5 ± 8.9 W) over the training program. T improved on handcycling peakVO2 (+18.1 %), peakPO (+31.9 %), and peakHR (+4.0 %). No improvements were found in cycling parameters. Conclusion: Handcycling training led to local, exercise-specific improvements in upper body parameters. Results could provide input for the design of effective evidence-based training programs specifically aimed at upper body endurance exercise in females