A Statistical Evaluation of The Depth of Inheritance Tree Metric for Open-Source Applications Developed in Java

The Depth of Inheritance Tree (DIT) metric, along with other ones, is used for estimating some quality indicators of software systems, including open-source applications (apps). In cases involving multiple inheritances, at a class level, the DIT metric is the maximum length from the node to the root of the tree. At an application (app) level, this metric defines the corresponding average length per class. It is known, at a class level, a DIT value between 2 and 5 is good. At an app level, similar recommended values for the DIT metric are not known. To find the recommended values for the DIT mean of an app we have proposed to use the confidence and prediction intervals. A DIT mean value of an app from the confidence interval is good since this interval indicates how reliable the estimate is for the DIT mean values of all apps used for estimating the interval. A DIT mean value higher than an upper bound of prediction interval may indicate that some classes have a large number of the inheritance levels from the object hierarchy top. What constitutes greater app design complexity as more classes are involved. We have estimated the confidence and prediction intervals of the DIT mean using normalizing transformations for the data sample from 101 open-source apps developed in Java hosted on GitHub for the 0.05 significance level.

Computational Aspects of Equilibria in Discrete Preference Games

We study the complexity of equilibrium computation in discrete preference games. These games were introduced by Chierichetti, Kleinberg, and Oren (EC '13, JCSS '18) to model decision-making by agents in a social network that choose a strategy from a finite, discrete set, balancing between their intrinsic preferences for the strategies and their desire to choose a strategy that is `similar' to their neighbours. There are thus two components: a social network with the agents as vertices, and a metric space of strategies. These games are potential games, and hence pure Nash equilibria exist. Since their introduction, a number of papers have studied various aspects of this model, including the social cost at equilibria, and arrival at a consensus. We show that in general, equilibrium computation in discrete preference games is PLS-complete, even in the simple case where each agent has a constant number of neighbours. If the edges in the social network are weighted, then the problem is PLS-complete even if each agent has a constant number of neighbours, the metric space has constant size, and every pair of strategies is at distance 1 or 2. Further, if the social network is directed, modelling asymmetric influence, an equilibrium may not even exist. On the positive side, we show that if the metric space is a tree metric, or is the product of path metrics, then the equilibrium can be computed in polynomial time.

A new efficient algorithm for inferring explicit hybridization networks following the Neighbor-Joining principle

Several algorithms and software have been developed for inferring phylogenetic trees. However, there exist some biological phenomena such as hybridization, recombination, or horizontal gene transfer which cannot be represented by a tree topology. We need to use phylogenetic networks to adequately represent these important evolutionary mechanisms. In this article, we present a new efficient heuristic algorithm for inferring hybridization networks from evolutionary distance matrices between species. The famous Neighbor-Joining concept and the least-squares criterion are used for building networks. At each step of the algorithm, before joining two given nodes, we check if a hybridization event could be related to one of them or to both of them. The proposed algorithm finds the exact tree solution when the considered distance matrix is a tree metric (i.e. it is representable by a unique phylogenetic tree). It also provides very good hybrids recovery rates for large trees (with 32 and 64 leaves in our simulations) for both distance and sequence types of data. The results yielded by the new algorithm for real and simulated datasets are illustrated and discussed in detail.

A matroid associated with a phylogenetic tree

Special issue PRIMA 2013 International audience A (pseudo-)metric D on a finite set X is said to be a \textquotelefttree metric\textquoteright if there is a finite tree with leaf set X and non-negative edge weights so that, for all x,y ∈X, D(x,y) is the path distance in the tree between x and y. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is – up to canonical isomorphism – uniquely determined by D, and one does not even need all of the distances in order to fully (re-)construct the tree\textquoterights edge weights in this case. Thus, it seems of some interest to investigate which subsets of X, 2 suffice to determine (\textquoteleftlasso\textquoteright) these edge weights. In this paper, we use the results of a previous paper to discuss the structure of a matroid that can be associated with an (unweighted) X-tree T defined by the requirement that its bases are exactly the \textquotelefttight edge-weight lassos\textquoteright for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T.