Phase transition in the countdown problem

We present a combinatorial decision problem, inspired by the celebrated quiz show called Countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.

Ab initio calculations of Ca III Stark broadening parameters,transition probabilities and radiative lifetimes

We have determined matrix elements for all experimental configurations of Ca III, including the 3s3p63d configuration. These values have been obtained using intermediate coupling (IC). For these IC calculations, we have used the standard method of least-squares fitting from the experimental energy levels, using the computer code developed by Robert Cowan. In this paper, using these matrix elements, we report the calculated values of the Ca III Stark widths and shifts for 148 spectral lines, of 56 Ca III spectral line transition probabilities and of eight radiative lifetimes of Ca III levels. The Stark widths and shifts, calculated using the Griem semi-empirical approach, correspond to the spectral lines of Ca III and are presented for an electron density of 1017 cm?3 and temperatures T = 1.0?10.0 (×104 K). The theoretical trends of the Stark broadening parameter versus the temperature are presented for transitions that are of astrophysical interest. There is good agreement between our calculations, for transition probabilities and radiative lifetimes, and the experimental values presented in the literature. We have not been able to find any values for the Stark parameters in the references.

Jasmonate-dependent modifications of the pectin matrix during potato development function as a defense mechanism targeted by Dickeya dadantii virulence factors

The plant cell wall constitutes an essential protection barrier against pathogen attack. In addition, cell-wall disruption leads to accumulation of jasmonates (JAs), which are key signaling molecules for activation of plant inducible defense responses. However, whether JAs in return modulate the cell-wall composition to reinforce this defensive barrier remains unknown. The enzyme 13-allene oxide synthase (13-AOS) catalyzes the first committed step towards biosynthesis of JAs. In potato (Solanum tuberosum), there are two putative St13-AOS genes, which we show here to be differentially induced upon wounding. We also determine that both genes complement an Arabidopsis aos null mutant, indicating that they encode functional 13-AOS enzymes. Indeed, transgenic potato plants lacking both St13-AOS genes (CoAOS1/2 lines) exhibited a significant reduction of JAs, a concomitant decrease in wound-responsive gene activation, and an increased severity of soft rot disease symptoms caused by Dickeya dadantii. Intriguingly, a hypovirulent D. dadantii pel strain lacking the five major pectate lyases, which causes limited tissue maceration on wild-type plants, regained infectivity in CoAOS1/2 plants. In line with this, we found differences in pectin methyl esterase activity and cell-wall pectin composition between wild-type and CoAOS1/2 plants. Importantly, wild-type plants had pectins with a lower degree of methyl esterification, which are the substrates of the pectate lyases mutated in the pel strain. These results suggest that, during development of potato plants, JAs mediate modification of the pectin matrix to form a defensive barrier that is counteracted by pectinolytic virulence factors from D. dadantii.