Bivariate causal mixture model quantifies polygenic overlap between complex traits beyond genetic correlation.

Accumulating evidence from genome wide association studies (GWAS) suggests an abundance of shared genetic influences among complex human traits and disorders, such as mental disorders. Here we introduce a statistical tool, MiXeR, which quantifies polygenic overlap irrespective of genetic correlation, using GWAS summary statistics. MiXeR results are presented as a Venn diagram of unique and shared polygenic components across traits. At 90% of SNP-heritability explained for each phenotype, MiXeR estimates that 8.3 K variants causally influence schizophrenia and 6.4 K influence bipolar disorder. Among these variants, 6.2 K are shared between the disorders, which have a high genetic correlation. Further, MiXeR uncovers polygenic overlap between schizophrenia and educational attainment. Despite a genetic correlation close to zero, the phenotypes share 8.3 K causal variants, while 2.5 K additional variants influence only educational attainment. By considering the polygenicity, discoverability and heritability of complex phenotypes, MiXeR analysis may improve our understanding of cross-trait genetic architectures

A mathematical model quantifies proliferation and motility effects of TGF--β\beta on cancer cells

Transforming growth factor (TGF) $\beta$ is known to have properties of both a tumor suppressor and a tumor promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell--cell adhesion. Coupling mathematical modeling and experiments, we investigate the growth and motility of oncogene--expressing human mammary epithelial cells under exposure to TGF--$\beta$. We use a version of the well--known Fisher--Kolmogorov equation, and prescribe a procedure for its parametrization. We quantify the simultaneous effects of TGF--$\beta$ to increase the tendency of individual cells and cell clusters to move randomly and to decrease overall population growth. We demonstrate that in experiments with TGF--$\beta$ treated cells \textit{in vitro}, TGF--$\beta$ increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.Comment: 15 pages, 4 figures; to appear in Computational and Mathematical Methods in Medicin

Phase transition in a mean-field model for sympatric speciation

We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field approximation may be decoupled. We find a phase transition leading to sympatric speciation as a parameter that quantifies competition strength is varied. This transition, previously found in a computational model, occurs to be of first order.Comment: accepted for Physica

Signatures of non-classicality in mixed-state quantum computation

We investigate signatures of non-classicality in quantum states, in particular, those involved in the DQC1 model of mixed-state quantum computation [Phys. Rev. Lett. 81, 5672 (1998)]. To do so, we consider two known non-classicality criteria. The first quantifies disturbance of a quantum state under locally noneffective unitary operations (LNU), which are local unitaries acting invariantly on a subsystem. The second quantifies measurement induced disturbance (MID) in the eigenbasis of the reduced density matrices. We study the role of both figures of non-classicality in the exponential speedup of the DQC1 model and compare them vis-a-vis the interpretation provided in terms of quantum discord. In particular, we prove that a non-zero quantum discord implies a non-zero shift under LNUs. We also use the MID measure to study the locking of classical correlations [Phys. Rev. Lett. 92, 067902 (2004)] using two mutually unbiased bases (MUB). We find the MID measure to exactly correspond to the number of locked bits of correlation. For three or more MUBs, it predicts the possibility of superior locking effects.Comment: Published version, containing additional discussion on the role of non-classicality in the locking of classical correlation

Quantifying long-range correlations in complex networks beyond nearest neighbors

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power-law behavior. The fractal network model comprises long-range anti-correlations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension

EFFECTS OF TRADE BARRIERS ON U.S. APPLE EXPORTS

We build a spatial equilibrium trade model for apples using demand and supply relations for each importing and exporting country. The model maximizes welfare subject to demand and production constraints. A trade barrier (free trade) scenario which incorporates (removes) import quotas and tariffs is run. Comparison of the solutions of the two scenarios quantifies the impacts of trade barriers on US apple exports.apples, spatial equilibrium model, trade barriers, International Relations/Trade, F10,