Aspect ratio analysis for ground states of bosons in anisotropic traps

Characteristics of the initial condensate in the recent experiment on Bose-Einstein condensation (BEC) of ${}^{87}$Rb atoms in an anisotropic magnetic trap is discussed. Given the aspect ratio $R$, the quality of BEC is estimated. A simple analytical Ansatz for the initial condensate wave function is proposed as a function of the aspect ratio which, in contrast to the Baym-Pethick trial wave function, reproduces both the weak and the strong intaraction limits and which is in better agreement with numerical results than the latter.Comment: 12 pages, latex, 3 figures added, minor corrections; to appear in J. Res. Nat. Inst. of Standards and Technolog

A mathematical model of tumor self-seeding reveals secondary metastatic deposits as drivers of primary tumor growth

Two models of circulating tumor cell (CTC) dynamics have been proposed to explain the phenomenon of tumor 'self-seeding', whereby CTCs repopulate the primary tumor and accelerate growth: Primary Seeding, where cells from a primary tumor shed into the vasculature and return back to the primary themselves; and Secondary Seeding, where cells from the primary first metastasize in a secondary tissue and form microscopic secondary deposits, which then shed cells into the vasculature returning to the primary. These two models are difficult to distinguish experimentally, yet the differences between them is of great importance to both our understanding of the metastatic process and also for designing methods of intervention. Therefore we developed a mathematical model to test the relative likelihood of these two phenomena in the subset of tumours whose shed CTCs first encounter the lung capillary bed, and show that Secondary Seeding is several orders of magnitude more likely than Primary seeding. We suggest how this difference could affect tumour evolution, progression and therapy, and propose several possible methods of experimental validation.Comment: 20 pages, 4 figure

Tree-Independent Dual-Tree Algorithms

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.Comment: accepted in ICML 201

Investigating prostate cancer tumour-stroma interactions - clinical and biological insights from an evolutionary game

BACKGROUND: Tumours are made up of a mixed population of different types of cells that include normal structures as well as ones associated with the malignancy, and there are multiple interactions between the malignant cells and the local microenvironment. These intercellular interactions, modulated by the microenvironment, effect tumour progression and represent a largely under appreciated therapeutic target. We use observations of primary tumor biology from prostate cancer to extrapolate a mathematical model: specifically; it has been observed that in prostate cancer three disparate cellular outcomes predominate: (i) the tumour remains well differentiated and clinically indolent - in this case the local stromal cells may act to restrain the growth of the cancer; (ii) early in its genesis the tumour acquires a highly malignant phenotype, growing rapidly and displacing the original stromal population (often referred to as small cell prostate cancer) - these less common aggressive tumours are relatively independent of the local microenvironment; and, (iii) the tumour co-opts the local stroma - taking on a classic stromagenic phenotype where interactions with the local microenvironment are critical to the cancer growth. METHODS: We present an evolutionary game theoretical construct that models the influence of tumour-stroma interactions in driving these outcomes. We consider three characteristic and distinct cellular populations: stromal cells, tumour cells that are self-reliant in terms of microenvironmental factors and tumour cells that depend on the environment for resources but can also co-opt stroma. 
RESULTS: Using evolutionary game theory we explore a number of different scenarios that elucidate the impact of tumour-stromal interactions on the dynamics of prostate cancer growth and progression and how different treatments in the metastatic setting can affect different types of tumors.
CONCLUSIONS: The tumour microenvironment plays a crucial role selecting the traits of the tumour cells that will determine prostate cancer progression. Equally important, treatments like hormone therapy affect the selection of these cancer phenotypes making it very important to understand how they impact prostate cancer’s somatic evolution