Counting Popular Matchings in House Allocation Problems

We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem. We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard

Heavy landings of juveniles of Indian scad, Decapterus russelli at Munambam Fisheries Harbour

Among the carangid fishes, the Indian scad, Decapterus russelli is an important pelagic fish and a major commercial species contributing to the marine fisheries of Kerala. The fish is locally called “kozhuchala” and it forms a regular fishery. The species is often caught as by-catch in shrimp trawl nets having cod-end mesh sizes ranging from 15 mm to 20 mm that is operated in the depth range of 55- 90 m almost throughout the year. They are consumed fresh as well as sun dried form

Comparison of Partial Recording Protocols in Disease Assessment among Periodontitis Patients in a Central Indian Population

Objectives: Partial recording protocols may be used for the purpose of assessing periodontal disease extent and severity in epidemiological studies. As there is very little data at present regarding the reliability of any partial examination methods among Indian populations, as an initial study, an attempt was made to determine the reliability of 9 different protocols in estimating the extent and severity of periodontal disease among periodontitis patients in a central Indian population. Study Design: Probing depths (PD) and clinical attachment levels (CAL) were recorded in 85 periodontitis patients on 6 sites on all the teeth excluding the third molars. Nine partial recording protocols (PRP) were compared with the full-mouth examination. Intra-class correlation coefficients (ICC) were calculated for mean PD, mean CAL, and percentage of sites with various thresholds of PD and CAL to determine the agreement between the PRP and the full-mouth examination. The sensitivity of different PRP for defining prevalence of sites with PD ≥6 and ≥7 mm and CAL ≥7 and ≥8 mm was also determined. Results: For all the tested PRP, the ICCs were consistently >0.9. The methods involving examination of 4 sites/ tooth slightly over-estimated the disease extent and severity in comparison with the full-mouth examination as well as PRP involving examination of 6 sites/tooth. Conclusions: The findings of the present study suggest that the tested PRP are in good agreement with the fullmouth examination. However, further studies need to be conducted with an improved methodology in a larger sample of subjects from the general population

Copepod Abundance and Diversity from Offshore Region of Tuticorin, South East Coast of India

A detailed study had been carried out on species abundance, biomass and composition of copepod in four different offshore stations namely, Station I: Vembar, II: Keelavaipar, III: Punnaikayal and IV: Thiruchendhur in Gulf of Mannar region from October 2011 to April 2012. A total of 56 copepod species belongs to 20 families under 4 orders have been encountered during the period. The percentage composition of different groups of copepod species was composed of Calanoida (35 numbers) 62.5%, Cyclopoida (4 numbers) 7.14%, Harpacticoida (8 numbers) 14.3% and Poecilostomatoida (9 numbers) 16.1%. The percentage of biomass composition of different groups of copepods during the study was in the order of Calanoida 38.99%, Harpacticoida 32.56%, Cyclopoida 15.22% and Poecilostomatoida 13.23%. In the case of species composition, Euterpina acutifrons (28.61%) was the most abundant species followed by Acrocalanus gracilis (17.68%), Corycaeus crassiusculus (12.33%), Oithona brevicornis (12.03%) and Temora turbinata (4.25%) were the other dominant species in observation. The copepod density in different stations were in the range of 8600–39900, 3900–64600, 3800–24800 and 5000–22500 numbers m-3 at station I, II, II and IV respectively. The lowest biomass of copepod was observed at station III and highest biomass was found at station II. The copepod species richness ranged from 0.48 to 2.72 and species diversity was in the range of 0.87 to 1.98 in the study areas. Species evenness was varied from 0.24 – 0.51 during the observation period

The estimation of economic benefits of urban trees using contingent valuation method in Tasik Perdana, Kuala Lumpur

Urban trees provide a multitude of tangible and intangible services which include provisionary, regulatory, as well as cultural and support services to the community. Unfortunately, to set a monetary value on these said services is challenging to say the least. Ignorance of such monetary value is unintentional and this is mainly due to the lack of awareness and the absence of monetary value of the services itself. Hence, the quality of these urban trees degrades over time as no one appreciates its monetary value. In light of this situation, a study was initiated to determine the economic benefits of the urban trees that were planted surrounding Tasik Perdana (TP) area. For this purpose, a total of 313 respondents were interviewed in the TP area using the contingent valuation method (CVM). The objective of this study was to elicit willingness to pay (WTP) for these urban trees. WTP represents the willingness of a person to pay in monetary terms to secure and sustain these urban trees. Hence, seven bid prices were used and distributed to the respondents: RM1.00, RM5.00, RM10.00, RM15.00, RM20.00, RM25.00 and RM30.00. Logit and linear regression models were applied to predict the maximum, mean, and median WTP. The study concludes that the estimated mean WTP is RM10.32 per visit and the estimated median WTP is RM10.08 per visit

Adoption of Sea Cage, Culture Practices in Thoothukudi District Tamil Nadu: An Eye Opener for Income Generation

Adoption of Sea Cage, Culture Practices in Thoothukudi District Tamil Nadu: An Eye Opener for Income Generatio

Manipulation Strategies for the Rank Maximal Matching Problem

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each applicant $a \in A$ has a preference list over the set of his neighbours in $G$, possibly involving ties. Preference lists are represented by ranks on the edges - an edge $(a,p)$ has rank $i$, denoted as $rank(a,p)=i$, if post $p$ belongs to one of $a$'s $i$-th choices. A rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching can be computed in $O(\min(c \sqrt{n},n) m)$ time, where $n$ denotes the number of applicants, $m$ the number of edges and $c$ the maximum rank of an edge in an optimal solution. A central authority matches applicants to posts. It does so using one of the rank-maximal matchings. Since there may be more than one rank- maximal matching of $G$, we assume that the central authority chooses any one of them randomly. Let $a_1$ be a manipulative applicant, who knows the preference lists of all the other applicants and wants to falsify his preference list so that he has a chance of getting better posts than if he were truthful. In the first problem addressed in this paper the manipulative applicant $a_1$ wants to ensure that he is never matched to any post worse than the most preferred among those of rank greater than one and obtainable when he is truthful. In the second problem the manipulator wants to construct such a preference list that the worst post he can become matched to by the central authority is best possible or in other words, $a_1$ wants to minimize the maximal rank of a post he can become matched to