Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table

Approximation Techniques for Stochastic Analysis of Biological Systems

There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic probabilistic behaviors of complex genetic circuit designs. However, its inability to scale limits its applicability in practice. This chapter addresses the scalability problem by presenting a state-space approximation method to remove unlikely states resulting in a reduced, finite state representation of the infinite-state continuous-time Markov chain that is amenable to probabilistic model checking. The proposed method is evaluated on a design of a genetic toggle switch. Comparisons with another state-of-art tool demonstrates both accuracy and efficiency of the presented method

Association of the CHEK2 c.1100delC variant, radiotherapy, and systemic treatment with contralateral breast cancer risk and breast cancer-specific survival

Background Breast cancer (BC) patients with a germline CHEK2 c.1100delC variant have an increased risk of contralateral BC (CBC) and worse BC-specific survival (BCSS) compared to non-carriers. Aim To assessed the associations of CHEK2 c.1100delC, radiotherapy, and systemic treatment with CBC risk and BCSS. Methods Analyses were based on 82,701 women diagnosed with a first primary invasive BC including 963 CHEK2 c.1100delC carriers; median follow-up was 9.1 years. Differential associations with treatment by CHEK2 c.1100delC status were tested by including interaction terms in a multivariable Cox regression model. A multi-state model was used for further insight into the relation between CHEK2 c.1100delC status, treatment, CBC risk and death. Results There was no evidence for differential associations of therapy with CBC risk by CHEK2 c.1100delC status. The strongest association with reduced CBC risk was observed for the combination of chemotherapy and endocrine therapy [HR (95% CI): 0.66 (0.55–0.78)]. No association was observed with radiotherapy. Results from the multi-state model showed shorter BCSS for CHEK2 c.1100delC carriers versus non-carriers also after accounting for CBC occurrence [HR (95% CI): 1.30 (1.09–1.56)]. Conclusion Systemic therapy was associated with reduced CBC risk irrespective of CHEK2 c.1100delC status. Moreover, CHEK2 c.1100delC carriers had shorter BCSS, which appears not to be fully explained by their CBC risk