Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation

Building connectomes using diffusion MRI: why, how and but

Why has diffusion MRI become a principal modality for mapping connectomes in vivo? How do different image acquisition parameters, fiber tracking algorithms and other methodological choices affect connectome estimation? What are the main factors that dictate the success and failure of connectome reconstruction? These are some of the key questions that we aim to address in this review. We provide an overview of the key methods that can be used to estimate the nodes and edges of macroscale connectomes, and we discuss open problems and inherent limitations. We argue that diffusion MRI-based connectome mapping methods are still in their infancy and caution against blind application of deep white matter tractography due to the challenges inherent to connectome reconstruction. We review a number of studies that provide evidence of useful microstructural and network properties that can be extracted in various independent and biologically-relevant contexts. Finally, we highlight some of the key deficiencies of current macroscale connectome mapping methodologies and motivate future developments

Minimal Length Scale Scenarios for Quantum Gravity

We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.Comment: Published version available at http://www.livingreviews.org/lrr-2013-

Caspases mediate retinoic acid induced degradation of the acute promyelocytic leukemia PML-RARa fusion protein

All-trans-retinoic acid (RA) treatment induces morphological remission in acute promyelocytic leukemia (APL) patients carrying the t(15;17) and expressing the PML/RARalpha product by inducing terminal differentiation of the leukemic clone. RA treatment induces downregulation of PML/RARalpha and reorganization of the PML-nuclear bodies. These events have been proposed to be essential for the induction of APL cell differentiation by RA. Here, we show that in the APL-derived NB4 cell line as well as in myeloid precursor U937 cells expressing the PML/RARalpha (U937/PR9) and in blasts from APL patients, the PML/RARalpha fusion protein is cleaved by a caspase 3-like activity induced by RA treatment. In fact, a caspase 3-like activity is detectable in PML/RARalpha expressing cells after RA treatment, and selective caspase inhibitor peptides are able to prevent the RA-induced degradation of the fusion protein in vivo and in vitro. Using recombinant caspases and PML/RARalpha deletion mutants we mapped a caspase 3 cleavage site (Asp 522) within the alpha-helix region of the PML component of the fusion protein. The extent of PML/RARalpha cleavage directly correlates with the ability of RA to restore the normal PML nuclear bodies (NBs) pattern. However, RA-induced differentiation is not prevented by the persistence of the fusion product and occurs in the absence of normally structured PML NBs. These results indicate that PML/RARalpha is directly involved in conferring RA sensitivity of APL cells and that the RA-induced reassembly of PML NBs is the consequence of the disappearance of PML/RARalpha