Computing unique maximum matchings in $$$$ time for König–Egerváry graphs and unicyclic graphs

Let \(\alpha \left( G\right) \) denote the maximum size of an independent set of vertices and \(\mu \left( G\right) \) be the cardinality of a maximum matching in a graph \(G\). A matching saturating all the vertices is a perfect matching. If \(\alpha \left( G\right) +\mu \left( G\right) =\left| V(G)\right| \), then \(G\) is called a König–Egerváry graph. A graph is unicyclic if it is connected and has a unique cycle. It is known that a maximum matching can be found in \(O(m\cdot \sqrt{n})\) time for a graph with \(n\) vertices and \(m\) edges. Bartha (Proceedings of the 8th joint conference on mathematics and computer science, Komárno, Slovakia, 2010) conjectured that a unique perfect matching, if it exists, can be found in \(O(m)\) time. In this paper we validate this conjecture for König–Egerváry graphs and unicylic graphs. We propose a variation of Karp–Sipser leaf-removal algorithm (Karp and Sipser in Proceedings of the 22nd annual IEEE symposium on foundations of computer science, 364–375, 1981) , which ends with an empty graph if and only if the original graph is a König–Egerváry graph with a unique perfect matching (obtained as an output as well). We also show that a unicyclic non-bipartite graph \(G\) may have at most one perfect matching, and this is the case where \(G\) is a König–Egerváry graph.     

Efficient Institutions and Effective Deterrence: On Timing and Uncertainty of Formal Sanctions

Journal of Risk and Uncertainty - Economic theory suggests that the deterrence of deviant behavior is driven by a combination of severity and certainty of punishment. This paper presents the first...     

Ordering Properties of Convolutions of Exponential Random Variables

Convolutions of independent random variables are usually compared. In this paper, after a synthetic comparison with respect to hazard rate ordering between sums of independent exponential random variables, we focus on the special case where one sum is identically distributed. So, for a given sum of n independent exponential random variables, we deduce the "best" Erlang-n bounds, with respect to each of the usual orderings: mean ordering, stochastic ordering, hazard rate ordering and likelihood ratio ordering.     

Copula directed acyclic graphs

A new methodology for selecting a Bayesian network for continuous data outside the widely used class of multivariate normal distributions is developed. The ‘copula DAGs’ combine directed acyclic graphs and their associated probability models with copula C/D-vines. Bivariate copula densities introduce flexibility in the joint distributions of pairs of nodes in the network. An information criterion is studied for graph selection tailored to the joint modeling of data based on graphs and copulas. Examples and simulation studies show the flexibility and properties of the method.     

Status and Career Decision: An Analysis of the Time Dimension*

This paper reports on a study which examined the input parental status has on the timing of career decision. Data for this study were collected by means of questionnaire from graduating seniors from 24 colleges and universities. It was hypothesized that students from upper-status parents would choose their future career later in their life than would students with lower-status parents. Although the data tend to support the hypothesis, it seems to hold more true for females than for males. This difference was attributed to the varying emphasis placed upon the responsibility for the achievement of success.     

The use of conditional cutoffs in a forward selection procedure

Using a forward selection procedure for selecting the best subset of regression variables involves the calculation of critical values (cutoffs) for an F-ratio at each step of a multistep search process. On dropping the restrictive (unrealistic) assumptions used in previous works, the null distribution of the F-ratio depends on unknown regression parameters for the variables already included in the subset. For the case of known σ, by conditioning the F-ratio on the set of regressors included so far and also on the observed (estimated) values of their regression coefficients, we obtain a forward selection procedure whose stepwise type I error does not depend on the unknown (nuisance) parameters. A numerical example with an orthogonal design matrix illustrates the difference between conditional cutoffs, cutoffs for the centralF-distribution, and cutoffs suggested by Pope and Webster.     

法社会学方法--关于"活法"的研究

法律发展的重心不在于国家的活动,而在于社会本身,必须从社会中寻找。我们发现,简单陈旧的奥地利法典在现实生活中,尤其是私法领域中,是完全被漠视的,代之发挥作用的是大量习惯法。以此为起点,就逐渐发展出“活法”学说。活法是和那些被法庭和其他裁判所强制实施的法律相对而言的,是那些支配着社会生活本身的规则;活法观具有独立的价值,活法构成了人类社会法律秩序的基础。从这一意义上讲,法社会学必须从探察发现活法开始。