The Complexity of the List Partition Problem for Graphs

The k-partition problem is as follows: Given a graph G and a positive integer k, partition the vertices of G into at most k parts A1, A2, . . . , Ak, where it may be specified that Ai induces a stable set, a clique, or an arbitrary subgraph, and pairs Ai, Aj (i≠j) be completely nonadjacent, completely adjacent, or arbitrarily adjacent. The list k-partition problem generalizes the k-partition problem by specifying for each vertex x, a list L(x) of parts in which it is allowed to be placed. Many well-known graph problems can be formulated as list k-partition problems: e.g., 3-colorability, clique cutset, stable cutset, homogeneous set, skew partition, and 2-clique cutset. We classify, with the exception of two polynomially equivalent problems, each list 4-partition problem as either solvable in polynomial time or NP-complete. In doing so, we provide polynomial-time algorithms for many problems whose polynomial-time solvability was open, including the list 2-clique cutset problem. This also allows us to classify each list generalized 2-clique cutset problem and list generalized skew partition problem as solvable in polynomial time or NP-complete

Recognition of some perfectly orderable graph classes

AbstractThis paper presents new algorithms for recognizing several classes of perfectly orderable graphs. Bipolarizable and P4-simplicial graphs are recognized in O(n3.376) time, improving the previous bounds of O(n4) and O(n5), respectively. Brittle and semi-simplicial graphs are recognized in O(n3) time using a randomized algorithm, and O(n3log2n) time if a deterministic algorithm is required. The best previous time bound for recognizing these classes of graphs is O(m2). Welsh–Powell opposition graphs are recognized in O(n3) time, improving the previous bound of O(n4). HHP-free graphs and maxibrittle graphs are recognized in O(mn) and O(n3.376) time, respectively

Prevalence of non-motor symptoms in Parkinson’s disease

Background: Parkinson’s disease is a common neurodegenerative movement disorder characterised by motor symptoms of rest tremor, bradykinesia, rigidity and postural instability and non-motor symptoms (NMS) which include neuropsychiatric symptoms, sleep disturbances, autonomic symptoms, sensory symptoms and symptoms of mixed aetiology. Parkinson’s Disease Non Motor Group (PD-NMG) devised a comprehensive clinic-based self-completed NMS questionnaire that allows easy identification of NMS by the physician. Most NMS have a poor response to dopaminergic therapy as it is due to dysfunction of the serotonergic and noradrenergic pathways. Treatment of these nonmotor symptoms help in improving the quality of life in patients with Parkinson’s disease.Methods: There were 100 patients with Parkinson’s disease who had presented to our neuromedicine movement clinic were included in the study. Patients were diagnosed as PD based on UK Parkinson’s disease brain bank criteria. The inclusion criteria were diagnosis as PD, age >18 yrs, inclusion of both males and females and consent for the study. Patients with atypical parkinsonism and secondary parkinsonism, stroke, intake of antipsychotics were excluded from the study. Non motor symptom questionnaire was given to the study group and frequency of occurrence of each non motor symptoms and their predominance in both males and females were studied. The frequency of each NMS was calculated by computing the number of yes response and calculating the percentage related to the number of patients in the sample. Analysis was done to calculate the frequency of all NMS among the enrolled patient.Results: Nocturnal sleep disturbances (43%) were most common followed by constipation (29%).The most common non motor symptoms in males were constipation (20%), urinary urgency (18%) and nocturia (11%).The most common non motor symptoms in females were nocturnal sleep disturbance (25%), feeling sad (19%), unexplained pains (17%) and being anxious (13%).Conclusions: Non motor symptom questionnaire helps in screening patients with Parkinson’s disease of non-motor symptoms and aims at providing holistic treatment improving the quality of life

Investigation into Shrinkage of High-Performance Concrete Used for Iowa Bridge Decks and Overlays

High-performance concrete (HPC) overlays have been used increasingly as an effective and economical method for bridge decks in Iowa and other states. However, due to its high cementitious material content, HPC often displays high shrinkage cracking potential. This study investigated the shrinkage behavior and cracking potential of the HPC overlay mixes commonly used in Iowa. In the study, 11 HPC overlay mixes were studied. These mixes consisted of three types of cements (Type I, I/II, and IP) and various supplementary cementitious materials (Class C fly ash, slag and metakaolin). Limestone with two different gradations was used as coarse aggregates in 10 mixes and quartzite was used in one mix. Chemical shrinkage of pastes, free drying shrinkage, autogenous shrinkage of mortar and concrete, and restrained ring shrinkage of concrete were monitored over time. Mechanical properties (such as elastic modulus and compressive and splitting tensile strength) of these concrete mixes were measured at different ages. Creep coefficients of these concrete mixes were estimated using the RILEM B3 and NCHRP Report 496 models. Cracking potential of the concrete mixes was assessed based on both ASTM C 1581 and simple stress-to-strength ratio methods. The results indicate that among the 11 mixes studied, three mixes (4, 5, and 6) cracked at the age of 15, 11, and 17 days, respectively. Autogenous shrinkage of the HPC mixes ranges from 150 to 250 microstrain and free dying shrinkage of the concrete ranges from 700 to 1,200 microstrain at 56 days. Different concrete materials (cementitious type and admixtures) and mix proportions (cementitious material content) affect concrete shrinkage in different ways. Not all mixes having a high shrinkage value cracked first. The stresses in the concrete are associated primarily with the concrete shrinkage, elastic modulus, tensile strength, and creep. However, a good relationship is found between cementitious material content and total (autogenous and free drying) shrinkage of concrete

Agricultural bio-waste recycling through efficient microbial consortia

In India and other countries, rice straw, a byproduct of rice production, is burned in enormous amounts, which contributes to environmental pollution and climate change by releasing greenhouse gases viz., CO2, N2O, CH4, into the atmosphere. This study aimed to accelerate the degradation of this enormous amount of agricultural biomass via microbial inoculants. Four treatments—rice straw (RS), rice straw plus water (RSW), rice straw plus water plus Pusa decomposer (RSWF), and rice straw plus water plus Tamil Nadu Agricultural University (TNAU) biomineralizer (RSWB) were used in the current investigation. The study's findings demonstrated that rice straw treated with microorganisms decomposed more quickly than RS and RSW treatments. According to EDAX spectra of elemental composition, the carbon content of rice straw in the RS, RSW, RSWF, and RSWB treatments was 33.66%, 29.75%, 13.33%, and 20.65% w/w, respectively. The RSWF treatment of rice straw was found to have the highest nitrogen concentration (0.64% w/w), followed by RSWB (0.61% w/w), RSW (0.45%) w/w, and RS (0.43% w/w). Treatments RSWF and RSWB had lower C/N ratios 20.83, and 33.85, respectively, than that RSW (66.11) and RS (78.28). The RSWF and RSWB treatments' porous, distorted, and rough surface structures provided further evidence that both microbial consortia could decompose rice straw more quickly than the RSW and RS treatments. Therefore, the results of this study imply that rice straw could be added to the soil to improve soil fertility for sustainable crop production rather than being burned

A multi-centre randomised controlled trial comparing radiofrequency and mechanical occlusion chemically assisted ablation of varicose veins - final results of the Venefit versus Clarivein for varicose veins trial

BACKGROUND: Endovenous thermal ablation has revolutionised varicose vein treatment. New non-thermal techniques such as mechanical occlusion chemically assisted endovenous ablation (MOCA) allow treatment of entire trunks with single anaesthetic injections. Previous non-randomised work has shown reduced pain post-operatively with MOCA. This study presents a multi-centre randomised controlled trial assessing the difference in pain during truncal ablation using MOCA and radiofrequency endovenous ablation (RFA) with six months' follow-up. METHODS: Patients undergoing local anaesthetic endovenous ablation for primary varicose veins were randomised to either MOCA or RFA. Pain scores using Visual Analogue Scale and number scale (0-10) during truncal ablation were recorded. Adjunctive procedures were completed subsequently. Pain after phlebectomy was not assessed. Patients were reviewed at one and six months with clinical scores, quality of life scores and duplex ultrasound assessment of the treated leg. RESULTS: A total of 170 patients were recruited over a 21-month period from 240 screened. Patients in the MOCA group experienced significantly less maximum pain during the procedure by Visual Analogue Scale (MOCA median 15 mm (interquartile range 7-36 mm) versus RFA 34 mm (interquartile range 16-53 mm), p = 0.003) and number scale (MOCA median 3 (interquartile range 1-5) versus RFA 4 mm (interquartile range 3-6.5), p = 0.002). 'Average' pain scores were also significantly less in the MOCA group; 74% underwent simultaneous phlebectomy. Occlusion rates, clinical severity scores, disease specific and generic quality of life scores were similar between groups at one and six months. There were two deep vein thromboses, one in each group. CONCLUSION: Pain secondary to truncal ablation is less painful with MOCA than RFA with similar short-term technical, quality of life and safety outcomes