Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in ${\bf Z}^2$, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate one, polls its 4 neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times $t< \infty$, but the cluster of a fixed site diverges (in diameter) as $t \to \infty$; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states.Comment: 16 pages, 1 figur

An oracle-based framework for robust combinatorial optimization

We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of uncertainty sets such as polytopes or ellipsoids. Concerning the underlying certain problem, the algorithm is entirely oracle-based, i.e., our approach only requires a (primal) algorithm for solving the certain problem. It is thus particularly useful in case the certain problem is well-studied but its combinatorial structure cannot be directly exploited in a tailored robust optimization approach, or in situations where the underlying problem is only defined implicitly by a given software. The idea of our algorithm is to solve the convex relaxation of the robust problem by a simplicial decomposition approach, the main challenge being the non-differentiability of the objective function in the case of discrete or polytopal uncertainty. The resulting dual bounds are then used within a tailored branch-and-bound framework for solving the robust problem to optimality. By a computational evaluation, we show that our method outperforms straightforward linearization approaches on the robust minimum spanning tree problem. Moreover, using the Concorde solver for the certain oracle, our approach computes much better dual bounds for the robust traveling salesman problem in the same amount of time

How PI3K-derived lipids control cell division

To succeed in cell division, intense cytoskeletal and membrane remodeling are required to allow accurate chromosome segregation and cytoplasm partitioning. Spatial restriction of the actin dynamics and vesicle trafficking define the cell symmetry and equivalent membrane scission events, respectively. Protein complexes coordinating mitosis are recruited to membrane microdomains characterized by the presence of the phosphatidylinositol lipid members (PtdIns), like PtdIns(3,4,5)P3, PtdIns(4,5)P2 and PtdIns(3)P. These PtdIns represent a minor component of cell membranes, defining membrane domain identity, ultimately controlling cytoskeleton and membrane dynamics during mitosis. The coordinated presence of PtdIns(3,4,5)P3 at the cell poles and PtdIns(4,5)P2 at the cleavage furrow controls the polarity of the actin cytoskeleton leading to symmetrical cell division. In the endosomal compartment, the trafficking of PtdIns(3)P positive vesicles allows the recruitment of the protein machinery required for the abscission

Scanning Nanocalorimetry at High Cooling Rate of Isotactic Polypropylene

A wide set of cooling scans and subsequent melting behavior of isotactic polypropylene (i-PP) were investigated using differential scanning calorimetry and nanocalorimetry at very high cooling rate. The latter technique offers, indeed, the distinctive possibility to perform heat capacity measurements at rates of more than 1000 K/s, both in cooling and in heating, to characterize the crystallization. When the i-PP sample was solidified with cooling rate larger than 160 K/s, a novel enthalpic process was observed that was related to the mesomorphic phase formation. Furthermore, at cooling rates higher than 1000 K/s, the i-PP sample did not crystallize neither in the α nor in the mesomorphic form. The subsequent heating scan starting from −15 °C showed an exothermic event, between 0 and 30 °C, ascribed to the mesophase cold crystallization