Generation problems

AbstractGiven a fixed computable binary operation f, we study the complexity of the following generation problem: the input consists of strings a1,…,an,b. The question is whether b is in the closure of {a1,…,an} under operation f.For several subclasses of operations we prove tight upper and lower bounds for the generation problems. For example, we prove exponential-time upper and lower bounds for generation problems of length-monotonic polynomial-time computable operations. Other bounds involve classes like NP and PSPACE.Here, the class of bivariate polynomials with positive coefficients turns out to be the most interesting class of operations. We show that many of the corresponding generation problems belong to NP. However, we do not know this for all of them, e.g., for x2+2y this is an open question. We prove NP-completeness for polynomials xaybc where a,b,c⩾1. Also, we show NP-hardness for polynomials like x2+2y. As a by-product we obtain NP-completeness of the extended sum-of-subset problem SOSc={(w1,…,wn,z):∃I⊆{1,…,n}(∑i∈Iwic=z)} for any c⩾1

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

Immune Reconstitution During the First Year of Antiretroviral Therapy of HIV-1-Infected Adults in Rural Burkina Faso

There are no data on the outcome of highly active antiretroviral therapy (HAART) in HIV-infected adults in rural Burkina Faso. We therefore assessed CD4+ T-cell counts and HIV-1 plasma viral load (VL), the proportion of naive T-cells (co-expressing CCR7 and CD45RA) and T-cell activation (expression of CD95 or CD38) in 61 previously untreated adult patients from Nouna, Burkina Faso, at baseline and 2 weeks, 1, 3, 6, 9 and 12 months after starting therapy. Median CD4+ T-cell counts increased from 174 (10th-90th percentile: 33-314) cells/µl at baseline to 300 (114- 505) cells/µl after 3 months and 360 (169-562) cells/µl after 12 months of HAART. Median VL decreased from 5.8 (4.6- 6.6) log10 copies/ml at baseline to 1.6 (1.6-2.3) log10 copies/ml after 12 months. Early CD4+ T-cell recovery was accompanied by a reduction of the expression levels of CD95 and CD38 on T-cells. Out of 42 patients with complete virological follow-up under HAART, 19 (45%) achieved concordant good immunological (gain of ≥100 CD4+ T-cells/µl above baseline) and virological (undetectable VL) responses after 12 months of treatment (intention-to-treat analysis). Neither a decreased expression of the T-cell activation markers CD38 and CD95, nor an increase in the percentage of naive T-cells reliably predicted good virological treatment responses in patients with good CD4+ T-cell reconstitution. Repeated measurement of CD4+ T-cell counts during HAART remains the most important parameter for immunologic monitoring. Substitution of repeated VL testing by determination of T-cell activation levels (e.g., CD38 expression on CD8+ T-cells) should be applied with caution

Switchable zero-bias anomaly in individual C₆₀ molecules contacted with tunable aluminum electrodes

We report the observation of strong resonances at zero bias in the differential conductance through Al–C₆₀–Al junctions with tunable electrode distance, measured above T = 10 K. The conductance value at resonance ranges from a few percent up to eighty percent of the quantum of conductance. The resonances may disappear or reoccur completely and discontinuously upon very small changes of the electrode distance. However, once they are formed they are very robust with respect to changes of the electrode distance. We discuss similarities and differences to the common theories of the Kondo screening of a spontaneous spin polarization of the C₆₀ molecule. We deduce Kondo temperatures in the range from 35 to 160 K and demonstrate that the temperature dependence is in agreement with the scaling behavior of the Kondo effect in the temperature range of our experiment

Branched Chain Amino Acids are associated with Metabolic Complications in Liver Transplant Recipients

BACKGROUND: Obesity, dyslipidemia and type 2 diabetes (T2D) contribute substantially to increased cardiovascular morbidity and mortality in patients after orthotopic liver transplantation (OLTx). Elevated plasma branched chain amino acids (BCAA) are linked to metabolic disturbances and cardiovascular disease (CVD) risk profiles in several non-OLTx populations. METHODS: Cross-sectional analysis of liver transplant recipients from TransplantLines, a single-center biobank and cohort study. BCAA plasma levels were measured by means of nuclear-magnetic resonance spectroscopy. CVD and cardiometabolic factors were collected by using data from electronic patient records. Associations were determined between BCAA plasma levels and T2D, Metabolic Syndrome (MetS), CVD as well as mTOR inhibition in liver transplant recipients. RESULTS: 336 Patients were divided into sex-stratified tertiles of total BCAA. MetS (P<0.001) and T2D (P=0.002) were significantly more frequent in subjects in the highest BCAA tertile. In logistic regression analyses, the multivariable adjusted odds ratio (OR) per 1 standard deviation increase in BCAA was 1.68 (95%CI: 1.18-2.20, P=0.003) for MetS and 1.60 (95%CI: 1.14-2.23, P=0.006) for T2D. Use of Sirolimus (mTOR inhibitor) was significantly associated with higher BCAA plasma levels, independent of age, sex, time after OLTx, MetS and other immunosuppressive medication (adjusted P=0.002). CONCLUSION: Elevated BCAA plasma levels are associated with T2D, MetS and use of Sirolimus in liver transplant recipients. BCAA plasma levels may represent a valuable biomarker for cardiometabolic complications after OLTx

Query Answering in Normal Logic Programs under Uncertainty

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively