Scales for co-compact embeddings of virtually free groups

Let $\Gamma$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(\Gamma)$ be the family of totally disconnected, locally compact groups containing $\Gamma$ as a co-compact lattice. We prove that the values of the scale function with respect to groups in $\mathcal{F}_{td}(\Gamma)$ evaluated on the subset $\Gamma$ have only finitely many prime divisors. This can be thought of as a uniform property of the family $\mathcal{F}_{td}(\Gamma)$.Comment: 12 pages; key words: uniform lattice, virtually free group, totally disconnected group, scale function (Error in references corrected in version 2

Computational modeling of cellular dynamics in tumor cell migration

Epithelial-mesenchymal plasticity (EMP) and tumor cell migration play an important role in cancer progression, and an improved understanding of the mechanisms underlying these concepts is essential for developing new targeted approaches. In this thesis, we studied these mechanisms using mathematical and computational approaches.First, we summarized and reviewed previous computational approaches that have been used to decipher EMP regulation. We then created mathematical models to explore (1) how different regulatory networks can explain epithelial-mesenchymal transition (EMT) in different cell contexts, and (2) how EMP and immune regulation can interact to cause tumor immunoevasion.Next, we studied the role of cell density in migration characteristics of triple-negative breast cancer cell lines by using a combined experimental and computational approach. We show how clustering and pseudopodial dynamics, potentially influenced by EMT-related factors, can alter the migratory behavior of these cell lines.Jointly, our work has shown that computational modeling can be used to test hypotheses based on experimental data, and generate testable hypotheses, making it a valuable addition to wet-lab experiments. Importantly, we identified mechanisms related to potential therapeutic targets, hopefully leading to improved targeted therapies and reduced cancer mortality.Toxicolog

Molecular diversity of arbuscular mycorrhizal fungi in onion roots from organic and conventional farming systems in the Netherlands

Diversity and colonization levels of naturally occurring arbuscular mycorrhizal fungi (AMF) in onion roots were studied to compare organic and conventional farming systems in the Netherlands. In 2004, 20 onion fields were sampled in a balanced survey between farming systems and between two regions, namely, Zeeland and Flevoland. In 2005, nine conventional and ten organic fields were additionally surveyed in Flevoland. AMF phylotypes were identified by rDNA sequencing. All plants were colonized, with 60% for arbuscular colonization and 84% for hyphal colonization as grand means. In Zeeland, onion roots from organic fields had higher fractional colonization levels than those from conventional fields. Onion yields in conventional farming were positively correlated with colonization level. Overall, 14 AMF phylotypes were identified. The number of phylotypes per field ranged from one to six. Two phylotypes associated with the Glomus mosseae-coronatum and the G. caledonium-geosporum species complexes were the most abundant, whereas other phylotypes were infrequently found. Organic and conventional farming systems had similar number of phylotypes per field and Shannon diversity indices. A few organic and conventional fields had larger number of phylotypes, including phylotypes associated with the genera Glomus-B, Archaeospora, and Paraglomus. This suggests that farming systems as such did not influence AMF diversity, but rather specific environmental conditions or agricultural practice

Revealed Competition for Greenfield Investments between European Regions

In the modern economy, cities are assumed to be in fierce competition over attracting foreign investments in leading sectors of the world economy. Despite the rich theoretical discourse on these 'wars', it remains unclear which territories are competing with each other over which types of investments Combining insights from international economics, international business, and urban systems literature, we develop an indicator to measure revealed competition between territories for investments based on the overlap of investment portfolios of regions. Taking competition for greenfield investments between European regions as a test subject, we identify competitive market segments, derive the competitive threat a region faces from other regions, the competitive threat regions pose to other regions, and the most important market segments in which regions compete. We show that European regions with similar locational endowments pose a fiercer competitive thre at to one another. In addition, regions that are sufficiently large and distinctive, face the smallest average competitive threat from all other regions

A Treatise on the Geographical Scale of Agglomeration Externalities and the Modifiable Areal Unit Problem

The modifiable areal unit problem (MAUP) refers to the sensitivity of statistical research results to the initial spatial nomenclature used. Despite a substantial literature in the related field of geography on the potential influence of the MAUP, the urban economic modeling tradition has not paid much attention to this issue. In this article, we test to what extent the MAUP moderates the effect of agglomeration externalities on areal sectoral employment growth by varying the initial geographical scale of analysis. Using spatial cross-regressive modeling in which we account for spatial spillover effects of agglomeration externalities, we find different effects of agglomeration forces across geographical scales. As the MAUP is a theoretical as well as a methodological problem, research should not only work with proper statistical specifications of spatial agglomeration models incorporating different geographical scales, but also relate this more explicitly to hypotheses concerning the geographical scale at which agglomeration externalities operate

Arithmeticity vs. non-linearity for irreducible lattices

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, such as for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page

Density-dependent migration characteristics of cancer cells driven by pseudopod interaction

The ability of cancer cells to invade neighboring tissue from primary tumors is an important determinant of metastatic behavior. Quantification of cell migration characteristics such as migration speed and persistence helps to understand the requirements for such invasiveness. One factor that may influence invasion is how local tumor cell density shapes cell migration characteristics, which we here investigate with a combined experimental and computational modeling approach. First, we generated and analyzed time-lapse imaging data on two aggressive Triple-Negative Breast Cancer (TNBC) cell lines, HCC38 and Hs578T, during 2D migration assays at various cell densities. HCC38 cells exhibited a counter-intuitive increase in speed and persistence with increasing density, whereas Hs578T did not exhibit such an increase. Moreover, HCC38 cells exhibited strong cluster formation with active pseudopod-driven migration, especially at low densities, whereas Hs578T cells maintained a dispersed positioning. In order to obtain a mechanistic understanding of the density-dependent cell migration characteristics and cluster formation, we developed realistic spatial simulations using a Cellular Potts Model (CPM) with an explicit description of pseudopod dynamics. Model analysis demonstrated that pseudopods exerting a pulling force on the cell and interacting via increased adhesion at pseudopod tips could explain the experimentally observed increase in speed and persistence with increasing density in HCC38 cells. Thus, the density-dependent migratory behavior could be an emergent property of single-cell characteristics without the need for additional mechanisms. This implies that pseudopod dynamics and interaction may play a role in the aggressive nature of cancers through mediating dispersal.NWO864.12.013Toxicolog

On the distortion of twin building lattices

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle

Higher-order mutual coherence of optical and matter waves

We use an operational approach to discuss ways to measure the higher-order cross-correlations between optical and matter-wave fields. We pay particular attention to the fact that atomic fields actually consist of composite particles that can easily be separated into their basic constituents by a detection process such as photoionization. In the case of bosonic fields, that we specifically consider here, this leads to the appearance in the detection signal of exchange contributions due to both the composite bosonic field and its individual fermionic constituents. We also show how time-gated counting schemes allow to isolate specific contributions to the signal, in particular involving different orderings of the Schr\"odinger and Maxwell fields.Comment: 11 pages, 2 figure