The Formation of Planets

This paper reviews the dynamics of the growth of solid particles from micron-sized dust grains to planets in protostellar accretion disks. The formation and orbital evolution of giant protoplanets is also discussed.Comment: 37 pages, 12 figure

Using the DNA Testing of Arrestees to Reevaluate Fourth Amendment Doctrine

With the advent of DNA testing, numerous issues have arisen with regard to obtaining and using evidence developed from such testing. As courts have come to regard DNA testing as a reliable method for linking some people to crimes and for exonerating others, these issues are especially significant. The federal government and most states have enacted statutes that permit or direct the testing of those convicted of at least certain crimes. Courts have almost universally approved such testing, rejecting arguments that obtaining and using such evidence violates the Fourth Amendment. More recently governments have enacted laws permitting or directing the taking of DNA samples from those arrested, but not yet convicted, for certain serious crimes. Courts had been far more divided about the constitutionality of DNA testing for arrestees than they were for the comparable testing of those already convicted of crimes. Given the division in the holdings among both state and federal courts and the increasing importance of DNA evidence in criminal investigations, it was hardly surprising that the Supreme Court agreed to hear a case regarding the constitutionality of a Maryland statute allowing for such testing. Section II of this article will provide a brief description of the science of DNA testing as it is used in the criminal justice system. Section III will discuss the Supreme Court\u27s decision in Maryland v. King. Section IV will address the argument of the opponents of the DNA testing of arrestees - that it violates the presumption of innocence. The chief focus of the article will appear in Sections V and VI, which will respond to the arguments posed by those who claim such testing violates the Fourth Amendment. Section V will address the balancing test for such searches and seizures long employed by the Supreme Court. Section VI describes and critiques the use of the primary purpose test as an important factor in determining whether the Fourth Amendment has been violated. This test looks to whether the primary purpose of the government\u27s search or seizure was something other than to ferret out ordinary criminal wrongdoing, and only in such situations excuses the absence of individualized suspicion

Singularity of Data Analytic Operations

Statistical data by their very nature are indeterminate in the sense that if one repeated the process of collecting the data the new data set would be somewhat different from the original. Therefore, a statistical method, a map $\Phi$ taking a data set $x$ to a point in some space F, should be stable at $x$: Small perturbations in $x$ should result in a small change in $\Phi(x)$. Otherwise, $\Phi$ is useless at $x$ or -- and this is important -- near $x$. So one doesn't want $\Phi$ to have "singularities," data sets $x$ s.t.\ the the limit of $\Phi(y)$ as $y$ approaches $x$ doesn't exist. (Yes, the same issue arises elsewhere in applied math.) However, broad classes of statistical methods have topological obstructions of continuity: They must have singularities. We show why and give lower bounds on the Hausdorff dimension, even Hausdorff measure, of the set of singularities of such data maps. There seem to be numerous examples. We apply mainly topological methods to study the (topological) singularities of functions defined (on dense subsets of) "data spaces" and taking values in spaces with nontrivial homology. At least in this book, data spaces are usually compact manifolds. The purpose is to gain insight into the numerical conditioning of statistical description, data summarization, and inference and learning methods. We prove general results that can often be used to bound below the dimension of the singular set. We apply our topological results to develop lower bounds on Hausdorff measure of the singular set. We apply these methods to the study of plane fitting and measuring location of data on spheres. \emph{This is not a "final" version, merely another attempt.}Comment: 325 pages, 8 figure

Critical scaling of stochastic epidemic models

In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite populations of size $N$ are situated at the sites of a lattice and infectious contacts are limited to individuals at neighboring sites. Scaling laws for both the mean-field and spatial models are given when the infection parameter $p$ is such that the epidemics are critical. It is shown that in all cases there is a critical threshold for the numbers initially infected: below the threshold, the epidemic evolves in essentially the same manner as its branching envelope, but at the threshold evolves like a branching process with a size-dependent drift.Comment: Published at http://dx.doi.org/10.1214/074921707000000346 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Wolbachia and arbovirus inhibition in mosquitoes

Wolbachia is a maternally inherited intracellular bacteria that can manipulate the reproduction of their insect hosts, and cytoplasmic incompatibility allows them to spread through mosquito populations. When particular strains of Wolbachia are transferred into certain Aedes mosquito species, the transmission capacity of important arthropod-borne viruses can be suppressed or abolished in laboratory challenges. Viral inhibition is associated with higher densities of transinfecting Wolbachia compared with wild-type strains of the bacterium. The upregulation of innate immune effectors can contribute to virus inhibition in Aedes aegypti, but does not seem to be required. Modulation of autophagy and lipid metabolism, and intracellular competition between viruses and bacteria for lipids, provide promising hypotheses for the mechanism of inhibition. Transinfecting virus-inhibiting strains can produce higher fitness costs than wild-type mosquito Wolbachia; however, this is not always the case, and the wMel strain has already been introduced to high frequency in wild Ae. aegypti populations

Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces

Let $\Upsilon$ be a compact, negatively curved surface. From the (finite) set of all closed geodesics on $\Upsilon$ of length $\leq L$, choose one, say $\gamma_{L}$, at random and let $N (\gamma_{L})$ be the number of its self-intersections. It is known that there is a positive constant $\kappa$ depending on the metric such that $N (\gamma_{L})/L^{2} \rightarrow \kappa$ in probability as $L\rightarrow \infty$. The main results of this paper concern the size of typical fluctuations of $N (\gamma_{L})$ about $\kappa L^{2}$. It is proved that if the metric has constant curvature -1 then typical fluctuations are of order $L$, in particular, $(N (\gamma_{L})-\kappa L^{2})/L$ converges weakly to a nondegenerate probability distribution. In contrast, it is also proved that if the metric has variable negative curvature then fluctuations of $N (\gamma_{L})$ are of order $L^{3/2}$, in particular, $(N (\gamma_{L})-\kappa L^{2})/L^{3/2}$ converges weakly to a Gaussian distribution. Similar results are proved for generic geodesics, that is, geodesics whose initial tangent vectors are chosen randomly according to normalized Liouville measure