Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Secretome analysis of Trichoderma atroviride T17 biocontrol of Guignardia citricarpa

The fungal species Guignardia citricarpa is an important pathogen in citriculture. Members of the fungal genus Trichoderma are recognized as biocontrol agents but studies on the interactions between both fungi are scarce. This study aimed to identify extracellular proteins secreted by Trichoderma atroviride T17 that are related to the control of G. citricarpa. Two-dimensional gel electrophoresis (2D) was used to study the patterns of proteins secreted by T. atroviride T17 in medium containing glucose (control) and in medium containing G. citricarpa GC3 inactivated mycelium. We identified 59 of the 116 spots differentially expressed (50.86%) by LC–MS/MS. Of these, we highlight the presence of glycoside hydrolases (CAZy families 3, 43, 54, 76 and 93), chitinase, mutanase, a-1,3-glucanase, a-1,2-mannosidase, carboxylic hydrolase ester, carbohydrate-binding module family 13, glucan 1,3-b-glucosidase, a-galactosidase and Neutral protease 2. These proteins are related to mycoparasitism processes, stimuli and therefore to the biological control of pathogens. The results obtained are in agreement with reports describing an increase in the secretion of proteins related to mycoparasitism and biological control and a reduction in the secretion of proteins related to the metabolism of Trichoderma species grown in the presence of the pathogen. Moreover, these results are pioneer in understanding T. atroviride interaction with G. citricarpa. For the first time, we identified potential candidate proteins that may have a role in the antagonism mechanism of G. citricarpa by T. atroviride T17. Thus our results shed a light into the molecular mechanisms that T. atroviride use to control G. citricarpa.

Input-state-output representations of concatenated 2D convolutional codes

In this paper we investigate a novel model of concatenation of a pair of two-dimensional (2D) convolutional codes. We consider finite-support 2D convolutional codes and choose the so-called Fornasini-Marchesini input-state-output (ISO) model to represent these codes. More concretely, we interconnect in series two ISO representations of two 2D convolutional codes and derive the ISO representation of the ob- tained 2D convolutional code. We provide necessary condition for this representation to be minimal. Moreover, structural properties of modal reachability and modal observability of the resulting 2D convolutional codes are investigated.