Generic Morse–Smale property for the parabolic equation on the circle

In this paper, we show that, for scalar reaction–diffusion equations ut=u_xx+f(x,u,ux)$u_t=u_{xx}+f(x,u,u_x)$ on the circle S¹$S^1$, the Morse–Smale property is generic with respect to the non-linearity f. In Czaja and Rocha (2008) [13], Czaja and Rocha have proved that any connecting orbit, which connects two hyperbolic periodic orbits, is transverse and that there does not exist any homoclinic orbit, connecting a hyperbolic periodic orbit to itself. In Joly and Raugel (2010) [31], we have shown that, generically with respect to the non-linearity f, all the equilibria and periodic orbits are hyperbolic. Here we complete these results by showing that any connecting orbit between two hyperbolic equilibria with distinct Morse indices or between a hyperbolic equilibrium and a hyperbolic periodic orbit is automatically transverse. We also show that, generically with respect to f, there does not exist any connection between equilibria with the same Morse index. The above properties, together with the existence of a compact global attractor and the Poincaré–Bendixson property, allow us to deduce that, generically with respect to f, the non-wandering set consists in a finite number of hyperbolic equilibria and periodic orbits. The main tools in the proofs include the lap number property, exponential dichotomies and the Sard–Smale theorem. The proofs also require a careful analysis of the asymptotic behavior of solutions of the linearized equations along the connecting orbits.     

Branching random walk with trapping zones

We consider a branching random walk with values in a certain set $\mathbb{S}$, where the branching mechanism is different according to whether particles (individuals) are in a certain so called trapping set $A?\mathbb{S}$ or not. We are then interested, under different scenarios, in properties of either the transient random measure describing distribution of individuals on $\mathbb{S}$ over time or its asymptotic behaviour.     

Stabilization of nonlinear switched systems using control Lyapunov functions

In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution provides a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function; this is achieved with the converse Lyapunov theorem dedicated to switched systems. In the second part, an explicit construction of a common control Lyapunov function is addressed with respect to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.     

Robust competence assessment for job assignment

Allocating the right person to a task or job is a key issue for improving quality and performance of achievements, usually addressed using the concept of “competences”. Nevertheless, providing an accurate assessment of the competences of an individual may be in practice a difficult task. We suggest in this paper to model the uncertainty on the competences possessed by a person using a possibility distribution, and the imprecision on the competences required for a task using a fuzzy constraint, taking into account the possible interactions between competences using a Choquet integral. As a difference with comparable approaches, we then suggest to perform the allocation of persons to jobs using a robust optimisation approach, allowing to minimise the risk taken by the decision maker. We first apply this framework to the problem of selecting a candidate within n for a job, then extend the method to the problem of selecting c candidates for j jobs (c ? j) using the leximin criterion.     

Random walks,Kleinian groups,and bifurcation currents

Let (ρ _λ ) _λ∈Λ be a holomorphic family of representations of a finitely generated group G into PSL(2,ℂ), parameterized by a complex manifold Λ. We define a notion of bifurcation current in this context, that is, a positive closed current on Λ describing the bifurcations of this family of representations in a quantitative sense. It is the analogue of the bifurcation current introduced by DeMarco for holomorphic families of rational mappings on ℙ¹. Our definition relies on the theory of random products of matrices, so it depends on the choice of a probability measure μ on G.     

Undulator beamline optimization with integrated chicanes for X‐ray free‐electron‐laser facilities

An optimization of the undulator layout of X‐ray free‐electron‐laser (FEL) facilities based on placing small chicanes between the undulator modules is presented. The installation of magnetic chicanes offers the following benefits with respect to state‐of‐the‐art FEL facilities: reduction of the required undulator length to achieve FEL saturation, improvement of the longitudinal coherence of the FEL pulses, and the ability to produce shorter FEL pulses with higher power levels. Numerical simulations performed for the soft X‐ray beamline of the SwissFEL facility show that optimizing the advantages of the layout requires shorter undulator modules than the standard ones. This proposal allows a very compact undulator beamline that produces fully coherent FEL pulses and it makes possible new kinds of experiments that require very short and high‐power FEL pulses.     

Investigation on the reactivity of nucleophilic radiohalogens with arylboronic acids in water: access to an efficient single-step method for the radioiodination and astatination of antibodies

Easy access to radioiodinated and ²¹¹At-labelled bio(macro)molecules is essential to develop new strategies in nuclear imaging and targeted radionuclide therapy of cancers. Yet, the labelling of complex molecules with heavy radiohalogens is often poorly effective due to the multiple steps and intermediate purifications needed. Herein, we investigate the potential of arylboron chemistry as an alternative approach for the late stage labelling of antibodies. The reactivity of a model precursor, 4-chlorobenzeneboronic acid (1) with nucleophilic iodine-125 and astatine-211 was at first investigated in aqueous conditions. In the presence of a copper(ii) catalyst and 1,10-phenanthroline, quantitative radiochemical yields (RCYs) were achieved within 30 minutes at room temperature. The optimum conditions were then applied to a CD138 targeting monoclonal antibody (mAb) that has previously been validated for imaging and therapy in a preclinical model of multiple myeloma. RCYs remained high (>80% for ¹²⁵I-labelling and >95% for ²¹¹At-labelling), and the whole procedure led to increased specific activities within less time in comparison with previously reported methods. Biodistribution study in mice indicated that targeting properties of the radiolabelled mAb were well preserved, leading to a high tumour uptake in a CD138 expressing tumour model. The possibility of divergent synthesis from a common modified carrier protein demonstrated herein opens facilitated perspectives in radiotheranostic applications with the radioiodine/²¹¹At pairs. Overall, the possibility to develop radiolabelling kits offered by this procedure should facilitate its translation to clinical applications.

The high reactivity of astatine and iodine in water with arylboronic acids provides access to an efficient single-step antibody radiolabelling.     

Bisubstrate Inhibitors for the Enzyme Catechol O‐Methyltransferase (COMT): Dramatic Effects of Ribose Modifications on Binding Affinity and Binding Mode

Inhibition of the enzyme catechol O‐methyltransferase (COMT) is of significant interest in the therapy of Parkinson's disease. Described herein are structural analogs of the potent bisubstrate inhibitor (?)‐ 1 (IC₅₀=9 nM ; Table 1) for COMT, with target modifications of the central ribose moiety. Their synthesis involves, as key intermediates, adenosine derivatives, which are transformed to the potential bisubstrate inhibitors by a similar sequence of six steps (Schemes 1–4). The compounds were submitted to an enzymatic assay for determination of their in vitro inhibitory activity against COMT, and the inhibition mechanism with respect to the binding side of the cofactor S‐adenosylmethionine (SAM) was analyzed by kinetics measurements (Fig. 3). Both binding affinity and binding mode were exceedingly sensitive towards modifications of the ribose moiety (Table 1). Removal of the 2′‐OH group upon changing from (?)‐ 1 to (?)‐ 2 (IC₅₀=28 μM ) led to a reduction in binding affinity by more than three orders of magnitude. At the same time, competitive inhibition kinetics with respect to the SAM binding site was maintained, thereby supporting a bisubstrate binding mode. Unlike (?)‐ 2 , the dideoxyribose inhibitor (?)‐ 3 (IC₅₀=3 μM ) showed a mixed and the cyclopentane derivative (+)‐ 4 (IC₅₀=1 μM ) an uncompetitive inhibition mechanism with respect to the SAM binding site. In the complex of the latter, the adenine‐substituted cyclopentane ring orients most probably towards the surface of the enzyme into the surrounding solution. The enantiomeric compounds (?)‐ 5 (IC₅₀=43 μM ) and (+)‐ 5 (IC₅₀=141 μM ), wherein the ribose had been replaced by a pyrrolidine ring, showed only low binding affinity.     

Well-defined,air-stable (NHC)Pd(Allyl)Cl (NHC = N-heterocyclic carbene) catalysts for the arylation of ketones

A number of palladium-N-heterocyclic carbene (NHC) complexes were found to be active catalysts for the arylation of ketones. A large number of substrates, both aryl halides and ketones, are compatible with the reaction conditions. The ketone arylation reactions are achieved with low catalyst loading in short reaction times using aryl chlorides and triflates as reactive partners. [reaction: see text]