Many surgical procedures could benefit from guiding a bevel-tip needle along circular arcs to multiple treatment points in a patient. At each treatment point, the needle can inject a radioactive pellet into a cancerous region or extract a tissue sample. Our main result is an algorithm to steer a bevel-tip needle through a sequence of treatment points in the plane while minimizing the number of ...

We present a characterization of weakly compact cardinals in terms of generalized stationarity. We apply this characterization to construct a model with no partial square sequences. One of the striking features of weak compactness in the large cardinal hierarchy is the wide variety of characterizations of the concept. These characterizations meet many disparate areas of set theory, including me...

A hnite. indecomposabic partially ordered set is said to be critically indecomposahlc if. whenever an clement is removed. the resulting induced partially ordered set is not indccomposabic. The same terminology can be applied to graphs. tournaments, or any other relational structure whose relations are binary and irrcflexive. It will be shown in this paper that critically indecomposable partiall...

I propose the novel method of “gravitational-mass imaging” to detect and quantify luminous and dark-matter substructure in gravitational-lens galaxies. The method utilizes highly-magnified Einstein rings and arcs as sensitive probes of small perturbations in the lens potential (due to the presence of mass substructure), reconstructing the gravitational lens potential non-parametrically. Simulat...

Stars form with a complex and highly structured distribution. For a smooth star cluster to form from these initial conditions, the star cluster must erase this substructure. We study how substructure is removed using N-body simulations that realistically handle two-body relaxation. In contrast to previous studies, we find that hierarchical cluster formation occurs chiefly as a result of scatter...

The paper addresses aggregation issues for composite (modular) solutions. A systemic view point is suggested for various aggregation problems. Several solution structures are considered: sets, set morphologies, trees, etc. Mainly, the aggregation approach is targeted to set morphologies. The aggre-gation problems are based on basic structures as substructure, superstructure, median/consensus, a...

Numerical simulations have revealed the presence of long-lived substructure in Cold Dark Matter (CDM) halos. These surviving cores of past merger and accretion events vastly outnumber the known satellites of the Milky Way. This finding has prompted suggestions that substructure in cold dark matter (CDM) halos may be incompatible with observation and in conflict with the presence of thin, dynami...

Population substructure is a well-known confounder in population-based case-control genetic studies, but its impact in family-based studies is unclear. We performed population substructure analysis using extended families of admixed population to evaluate power and Type I error in an association study framework. Our analysis shows that power was improved by 1.5% after principal components adjus...

We use numerical simulations to examine the substructure within galactic and cluster mass halos that form within a hierarchical universe. Clusters are easily reproduced with a steep mass spectrum of thousands of substructure clumps that closely matches observations. However, the survival of dark matter substructure also occurs on galactic scales, leading to the remarkable result that galaxy hal...