Supersymmetry and its spontaneous breaking in the random field Ising model

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the functional renormalization group flow. Breaking is shown to occur below a critical dimension d(DR) ? 5.1 and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.     

Efficient Access to Peptidyl‐RNA Conjugates for Picomolar Inhibition of Non‐ribosomal FemXWv Aminoacyl Transferase

Peptidyl–RNA conjugates have various applications in studying the ribosome and enzymes participating in tRNA‐dependent pathways such as Fem transferases in peptidoglycan synthesis. Herein a convergent synthesis of peptidyl–RNAs based on Huisgen–Sharpless cycloaddition for the final ligation step is developed. Azides and alkynes are introduced into tRNA and UDP‐MurNAc‐pentapeptide, respectively. Synthesis of 2′‐azido RNA helix starts from 2′‐azido‐2′‐deoxyadenosine that is coupled to deoxycytidine by phosphoramidite chemistry. The resulting dinucleotide is deprotected and ligated to a 22‐nt RNA helix mimicking the acceptor arm of Ala‐tRNA^Ala by T4 RNA ligase. For alkyne UDP‐MurNAc‐pentapeptide, meso‐cystine is enzymatically incorporated into the peptidoglycan precursor and reduced, and L ‐Cys is converted to dehydroalanine with O‐(mesitylenesulfonyl)hydroxylamine. Reaction of but‐3‐yne‐1‐thiol with dehydroalanine affords the alkyne‐containing UDP‐MurNAc‐pentapeptide. The Cu^I‐catalyzed azide alkyne cycloaddition reaction in the presence of tris[(1‐hydroxypropyl‐1H‐1,2,3‐triazol‐4‐yl)methyl]amine provided the peptidyl‐RNA conjugate, which was tested as an inhibitor of non‐ribosomal FemX_Wv aminoacyl transferase. The bi‐substrate analogue was found to inhibit FemX_Wv with an IC₅₀ of (89±9) pM , as both moieties of the peptidyl–RNA conjugate contribute to high‐affinity binding.     

Metric Subregularity in Generalized Equations

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.     

Constante de Bers en genre 2

We introduce a new tool, the contiguity graph, which enables us to determine the Bers’s constant in genus two.     

Rapid traveling waves in the nonlocal Fisher equation connect two unstable states

In this note, we give a positive answer to a question addressed in Nadin et al. (2011) [7]. To be precise, we prove that, for any kernel and any slope at the origin, there exist traveling wave solutions (actually those which are “rapid”) of the nonlocal Fisher equation that connect the two homogeneous steady states 0 (dynamically unstable) and 1. In particular, this allows situations where 1 is unstable in the sense of Turing. Our proof does not involve any maximum principle argument and applies to kernels with fat tails.     

Revealing Excited-State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

Photoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited-state trajectories of a diplatinum complex featuring photo-activated metal–metal σ-bond formation and associated Pt−Pt stretching motions were detected in real time using femtosecond wide-angle X-ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt−Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited-state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non-equilibrium processes along excited-state trajectories involving multiple excited-state PESs.     

PtCl2-catalyzed cycloisomerizations of 5-en-1-yn-3-ol systems

5-En-1-yn-3-ol substrates bearing a free hydroxyl group or an acyl group are highly versatile partners for PtCl2-catalyzed cycloisomerizations. Electrophilic activation of the alkyne moiety triggers at wish a hydride or an O-acyl migration yielding at the end to regioisomeric keto derivatives. The efficient preparation of Sabina ketone, an important monoterpene precursor, has been worked out.