The mechanics of Arabidopsis seed germination

Germination is defined as the protrusion of the embryonic radicle through the seed coat layers (endosperm and testa). As the radicle elongates, the testa ruptures, followed by rupture of the endosperm. Arabidopsis seeds exhibit a two-step germination process with sequential rupture of the testa and endosperm. We are interested in exploring the physical process of germination. Whilst much effort has previously been placed on genetic networks, a mathematical approach for furthering the understanding of the physical/mechanical properties of germination has not yet been described. The Mathematics in Plant Sciences Study Group helped us to develop a better understanding of the problem. Several different mathematical models were generated for radicle growth and endosperm stretching. These models were developed on multiscale dimensions – looking at the organ, tissue and cellular levels. The outcomes of the study group have heightened our interest in the mechanical aspects of germination, and we are currently progressing with a grant proposal – a collaboration between the Schools of Biosciences and Engineering at the University of Nottingham, and a group from the Department of Biology at the University of Freiburg, Germany

Elemental Tests of the Traditional Rational Voting Model

A simple, robust, quasi-linear, structural general equilibrium rational voting model indicates turnout by voters motivated by the possibility of deciding the outcome is bellcurved in the ex-post winning margin and inversely proportional to electorate size. Applying this model to a large set of union certification elections, which often end in ties, yields exacting, lucid tests of the theory. Voter turnout is strongly related to election closeness, but not in the way predicted by the theory. Thus, this relation is generated by some other mechanism, which is indeterminate, as no existing theory explains the nonlinear patterns of turnout in the data.

Imprisonment Inertia and Public Attitudes Toward Truth in Sentencing

In the space of a few short years in the 1990s, forty-two states adopted truth in sentencing (“TIS”) laws, which eliminated or greatly curtailed opportunities for criminal defendants to obtain parole release from prison. In the following decade, the pendulum seemingly swung in the opposite direction, with thirty-six states adopting new early release opportunities for prisoners. However, few of these initiatives had much impact, and prison populations continued to rise. The TIS ideal remained strong. In the hope of developing a better understanding of these trends and of the prospects for more robust early release reforms in the future, the authors conducted public opinion surveys of hundreds of Wisconsin voters in 2012 and 2013 and report the results here. Notable findings include the following: (1) public support for TIS is strong and stable; (2) support for TIS results less from fear of crime than from a dislike of the parole decisionmaking process (which helps to explain why support for TIS has remained strong even as crime rates have fallen sharply); (3) support for TIS is not absolute and inflexible, but is balanced against such competing objectives as cost-reduction and offender rehabilitation, (4) a majority of the public would favor release as early as the halfway point in a prison sentence if public safety would not be threatened, and (5) a majority would prefer to have release decisions made by a commission of experts instead of a judge

Public Attitudes Toward Punishment, Rehabilitation, and Reform: Lessons from the Marquette Law School Poll

Since the late 1990s, many opinion surveys have suggested that the American public may be growing somewhat less punitive and more open to reforms that emphasize rehabilitation over incarceration. In order to assess current attitudes toward punishment, rehabilitation, and the criminal justice system, we collected survey data of 804 registered voters in Wisconsin. Among other notable results, we found strong support for rehabilitation and for the early release of prisoners who no longer pose a threat to public safety. However, we also found significant divisions in public opinion. For instance, while black and white respondents largely shared the same priorities for the criminal justice system, black respondents tended to see the system as less successful in achieving those priorities. Additionally, we found significant differences in the views of Democrats and Republicans, with Republicans more likely to favor punishment as a top priority and Democrats more likely to support rehabilitation. Finally, we found that survey respondents that hold negative views of African Americans are significantly less likely to support rehabilitation, even after statistically controlling for the other variables in the model

Simultaneous Representation of Proper and Unit Interval Graphs

In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where all objects share the same common structure. While the recognition problem for general simultaneous interval graphs - the simultaneous version of arguably one of the most well-studied graph classes - is NP-complete, the complexity of the sunflower case for three or more simultaneous interval graphs is currently open. In this work we settle this question for proper interval graphs. We give an algorithm to recognize simultaneous proper interval graphs in linear time in the sunflower case where we allow any number of simultaneous graphs. Simultaneous unit interval graphs are much more "rigid" and therefore have less freedom in their representation. We show they can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G=(V,E) is the union of the simultaneous graphs. We further show that both recognition problems are in general NP-complete if the number of simultaneous graphs is not fixed. The restriction to the sunflower case is in this sense necessary

Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings

We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the standard comparison-based computational model; hence, we make no assumptions about the distribution or bit complexities of edge weights, nor do we utilize unusual bit-level operations on memory words. Instead, our algorithms are based on a planarization method that "zeroes in" on edge crossings, together with methods for extending planar separator decompositions to geometric graphs with sublinearly many crossings. Incidentally, our planarization algorithm also solves an open computational geometry problem of Chazelle for triangulating a self-intersecting polygonal chain having n segments and k crossings in linear time, for the case when k is sublinear in n by an iterated logarithmic factor.Comment: Expanded version of a paper appearing at the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA09