Popular matchings with two-sided preferences and one-sided ties

We are given a bipartite graph $G = (A \cup B, E)$ where each vertex has a preference list ranking its neighbors: in particular, every $a \in A$ ranks its neighbors in a strict order of preference, whereas the preference lists of $b \in B$ may contain ties. A matching $M$ is popular if there is no matching $M'$ such that the number of vertices that prefer $M'$ to $M$ exceeds the number of vertices that prefer $M$ to~$M'$. We show that the problem of deciding whether $G$ admits a popular matching or not is NP-hard. This is the case even when every $b \in B$ either has a strict preference list or puts all its neighbors into a single tie. In contrast, we show that the problem becomes polynomially solvable in the case when each $b \in B$ puts all its neighbors into a single tie. That is, all neighbors of $b$ are tied in $b$'s list and $b$ desires to be matched to any of them. Our main result is an $O(n^2)$ algorithm (where $n = |A \cup B|$) for the popular matching problem in this model. Note that this model is quite different from the model where vertices in $B$ have no preferences and do not care whether they are matched or not.Comment: A shortened version of this paper has appeared at ICALP 201

Rank Maximal Matchings -- Structure and Algorithms

Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of applicants to their top-rank post, subject to this, the maximum number of applicants to their second rank post and so on. In this paper, we develop a switching graph characterization of rank-maximal matchings, which is a useful tool that encodes all rank-maximal matchings in an instance. The characterization leads to simple and efficient algorithms for several interesting problems. In particular, we give an efficient algorithm to compute the set of rank-maximal pairs in an instance. We show that the problem of counting the number of rank-maximal matchings is #P-Complete and also give an FPRAS for the problem. Finally, we consider the problem of deciding whether a rank-maximal matching is popular among all the rank-maximal matchings in a given instance, and give an efficient algorithm for the problem

A STUDY ON POSITIVE ATTITUDE TOWARDS CONTRIBUTION IN INSTITUTIONAL REPOSITORY SYSTEM AMONG THE FACULTY MEMBERS

Each educational institution will define which their potential authors are, depending on the documents that it decides to include in the repository. The study aimed to study the perception on various factors of academic parameters to deposit in the Institutional Repositories System. Majorities of the institutions had institutional repositories and three fourth of the respondents were depositing their works in their institutional repositories. The study noticed that there is a significant difference between experienced in depositing in IR and their willingness factor of advocacy, accessibility, altruistic intention and positive impact of self-archiving. It is inferred that among the professional recognition factors, Majorities (36%) of the respondents were depositing in IR which help to establish priority or prove their ownership of their ideas. Majorities (46%) of the respondents were depositing in IR for retaining their IPR for their works. More number of faculty members were willingness to deposit their works in IR for professional recognition, pre-print culture, university or department action and grant awarding body. It is also noticed that faculty members were depositing their work for their support (Additional time & effort) and monetary incentive

Anti-diabetic potential and safety profiles of Tephrosia purpurea on streptozotocin-nicotinamide induced diabetes in rats

Background: Tephrosia purpurea was traditionally used for the management of diabetes mellitus. Since this claim has not been investigated scientifically, the aim of this study was to evaluate the antidiabetic activity of Tephrosia purpurea extracts against STZ-Nicotinamide induced diabetes in rat. Methods: This preclinical study was done to evaluate the anti-hyperglycaemic activity of whole plant extract of Tephrosia purpurea in STZ- Nicotinamide induced diabetic rats, which produced a significant difference in blood glucose, lipid profile, renal and liver profile in comparison to untreated rats. In this study, the animals were divided into five groups and diabetes was induced by administering STZ-Nicotinamide and animals with blood sugar level >200 were enrolled in the study. Further the animals are grouped into Group I control (0.1% CMC), Group II, diabetic control and Group III reference control received glibenclamide. Group IV and V, diabetic rats treated with Tephrosia purpurea extract 200 mg/kg and 400 mg/kg respectively. All the test drugs were administered for 30 days. Results: In diabetic rats, treated with 200 and 400 mg/kg of Tephrosia purpurea blood glucose level significantly lowered on 10th day (p<0.05) and 5th day (p<0.01) respectively as compared to untreated rats. At the end of 30th day there is significant reduction in blood glucose treated with TP 400 mg/kg (p<0.001). Safety assessment shows the protective effect of TP (400 mg/kg) on lipid profile TC, TG (p<0.001), HDL (p<0.001), LDL (p<0.001) and VLDL (p<0.01). It also shows protective activity against AST (p<0.001), ALT (p<0.01), ALP (p<0.001) and Renal functions BUN (p<0.001), Creatinine (p<0.001). Conclusion: The anti-hyperglycaemic activity of Tephrosia purpurea is brought out in the study by its significant reduction in the blood glucose level. The safety and efficacy is established based on the protective effect of Tephrosia purpurea in lipid profile, renal and hepatic function of diabetic rats

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

Analysis of Variability for Qualitative and Quantitative Traits in Coleus forskohlii Briq.

Thirty seven Coleus forskohlii genotypes collected from different regions of Tamil Nadu and Karnataka were subjected to diversity analysis based on NBPGR descriptors. Eleven qualitative and fourteen quantitative traits of C. forskohlii were evaluated to assess the morphological variations available among the collected genotypes. For qualitative traits, a large number of genotypes out of 37 clustered together at 74 % similarity in four different groups. The dendrogram contract based on fourteen quantitative traits for the same set of genotypes did not reveal a clear pattern in grouping and the genotypes were grouped into ten different clusters. Cluster analysis of various sets of data revealed different groups of genotypes for each of the data set. A poor congruence observed among data sets of qualitative and quantitative traits in the comparison indicated that the morphological traits are not suitable for precise discrimination of closely related genotypes in C. forskohlii

Analyzing Variability in Coleus forskohlii Briq. Using RAPD Markers

Coleus forskohlii Briq. is an indigenous medicinal plant with high traditional use in India. Genetic analysis of 37 diverse C. forskohlii genotypes was performed using 25 RAPD primers, which yielded 117 bands, of which 60 (51.28%) were polymorphic providing an average of 3.75 bands per primer. There were no genotype-specific products. The number of bands per primer varied from 1 (OPZ 8&16) to 7 (OPZ 11). Similarity matrix was constructed using Jaccard's Coefficient and the data matrix of coefficient of similarity was subjected to cluster analysis using unweighted pair group methodology with arithmetic average (UPGMA). Cluster analysis resulted in grouping of 37 genotypes into two major clusters. The results indicated that RAPD could be used for genetic diversity analysis in C. forskohlii using higher number of primers as it is reliable, easy, rapid and cost-effective

ELECTROANALYSIS OF IBUPROFEN ON CONDUCTING POLYANILINE NANOFIBER COATED GLASSY CARBON SURFACE

Objective: Voltammetric procedure for analysis of pharmaceutical formulation of ibuprofen on conducting polyaniline nanofiber modified glassy carbon electrode was explored.Methods: The effect of pH was studied at different medium such as acidic, neutral and basic. The cyclic voltammetric behavior of ibuprofen was studied between−0.5 V and 1.8 V versus Ag/AgCl at modified glassy carbon surface.Results: The electroanalytical parameters of the detection are highly dependent on their configuration and dimensions of the electrode. The scan rate and concentration effect of ibuprofen were studied. The best limit of detection was 100 ppb and the linear range from 200 to 400 ppb on the modified electrode surface. The determination was successfully applied for the detection of drugs in several pharmaceutical drug formulations. The Atomic force microscopic (AFM) image shows the surface morphologies of polymer modified surface; compound adsorbed surface, particle distribution graphs and surface roughness values, which are in good agreement.Conclusion: The anodic peak was observed at 1.63 V, assigned for the oxidation of ibuprofen, which is not accompanied by corresponding cathodic reduction. This behavior suggested that the irreversibility of the electrode process