We show that a wide variety of generalized increasing subsequence problems admit a one parameter family of extensions for which we can exactly compute the mean length of the longest increasing subsequence. By the nature of the extension, this gives upper bounds on the mean in the unextended model, which turn out to be asymptotically tight for all of the models that have so far been analyzed. A ...

Context. According to Swedish National Council for Crime Prevention, there is an increase of 19% in residential burglary crimes in Sweden over the last decade and only 5% of the total crimes reported were actually solved by the law enforcement agencies. In order to solve these cases quickly and efficiently, the law enforcement agencies has to look into the possible linked serial crimes. Many st...

This article examines the complexity of street gang homicides and focuses on situational factors that lead to gang members' susceptibility to this violent behavior within the context of a disadvantaged minority community. This study is based on an analysis of 28 homicides involving Mexican American gang members. The absence of immigrant youth involvement in these types of violent crimes is disc...

This paper is concerned with certain connections between the ensemble of n × n unitary matrices—specifically the characteristic function of the random variable tr(U)—and combinatorics—specifically Ulam’s problem concerning the distribution of the length of the longest increasing subsequence in permutation groups—and the appearance of Painlevé functions in the answers to apparently unrelated que...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or ti...

Rural migrants have suffered from serious social exclusion in the Chinese urban society. However, since the early 2000s, the Chinese government emphasizes social harmony as an important national development goal. Together with the reorientation of development goals, the livelihood of rural migrants has received unprecedented State attention. This paper studies the policy changes and examines wh...

Most crimes in America require that the defendant have mens rea, Latin for "guilty mind." However, mens rea is not legally required for strict liability crimes, such as speeding, for which someone is guilty even if ignorant or deceived about her speed. In 3 experiments involving participants responding to descriptive vignettes, we investigated whether the division of strict liability crimes in ...

There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety ...

The objective of this article is to identify the interpersonal factors that explain narratives of desistance among offenders who have been sentenced to prison. Through narrative interviews, we have studied a purposeful age-graded sample of men convicted of acquisitive crimes. Although the results confirm the leading research of Laub and Sampson (2003) about the importance of social bonds as a c...