Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

QCD with dynamical Wilson fermions. II

We present results for the QCD spectrum and the matrix elements of scalar and axial-vector densities at β=6/g2=5.4, 5.5, 5.6. The lattice update was done using the hybrid Monte Carlo algorithm to include two flavors of dynamical Wilson fermions. We have explored quark masses in the range ms≤mq≤3ms. The results for the spectrum are similar to quenched simulations and mass ratios are consistent with phenomenological heavy-quark models. The results for matrix elements of the scalar density show that the contribution of sea quarks is comparable to that of the valence quarks. This has important implications for the pion-nucleon σ term.

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called `early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

ATM- and ATR-mediated phosphorylation of XRCC3 regulates DNA double-strand break-induced checkpoint activation and repair

The RAD51 paralogs XRCC3 and RAD51C have been implicated in homologous recombination (HR) and DNA damage responses. However, the molecular mechanism(s) by which these paralogs regulate HR and DNA damage signaling remains obscure. Here, we show that an SQ motif serine 225 in XRCC3 is phosphorylated by ATR kinase in an ATM signaling pathway. We find that RAD51C but not XRCC2 is essential for XRCC3 phosphorylation, and this modification follows end resection and is specific to S and G(2) phases. XRCC3 phosphorylation is required for chromatin loading of RAD51 and HR-mediated repair of double-strand breaks (DSBs). Notably, in response to DSBs, XRCC3 participates in the intra-S-phase checkpoint following its phosphorylation and in the G(2)/M checkpoint independently of its phosphorylation. Strikingly, we find that XRCC3 distinctly regulates recovery of stalled and collapsed replication forks such that phosphorylation is required for the HR-mediated recovery of collapsed replication forks but is dispensable for the restart of stalled replication forks. Together, these findings suggest that XRCC3 is a new player in the ATM/ATR-induced DNA damage responses to control checkpoint and HR-mediated repair.

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.