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Stochastic processes on graphs can describe a great variety of phenomena ranging from neural activity to epidemic spreading. While many existing methods can accurately describe typical realizations of such processes, computing properties of extremely rare events is a hard task, particularly so in the case of recurrent models, in which variables may return to a previously visited state. Here, we build on the matrix product cavity method, extending it fundamentally in two directions: First, we show how it can be applied to Markov processes biased by arbitrary reweighting factors that concentrate most of the probability mass on rare events. Second, we introduce an efficient scheme to reduce the computational cost of a single node update from exponential to polynomial in the node degree. Two applications are considered: inference of infection probabilities from sparse observations within the SIRS epidemic model and the computation of both typical observables and large deviations of several kinetic Ising models. [ABSTRACT FROM AUTHOR]

The regioselective ring opening of 2-aryl-subsituted four-membered heterocyclic rings with phenols, including catechol, is achieved by using aryl borates in mild and neutral reaction conditions without the help of any transition metal catalysts. Intramolecular cyclization has allowed a new access to 2-aryl-1,5-benzodioxepins in an enantioenriched form when reactive functionalities are present in the [beta]-aryloxy alcohol.

In this article, the authors focus on a research published in the journal "Current Organic Synthesis" in 2013 related to synthesis of bio-medically relevant oligosaccharides by 1,2-cis-O-glycosylation and α-O-sialylation.

We consider a high-dimensional random constrained optimization problem in which a set of binary variables is subjected to a linear system of equations. The cost function is a simple linear cost, measuring the Hamming distance with respect to a reference configuration. Despite its apparent simplicity, this problem exhibits a rich phenomenology. We show that different situations arise depending on the random ensemble of linear systems. When each variable is involved in at most two linear constraints, we show that the problem can be partially solved analytically, in particular we show that upon convergence, the zero-temperature limit of the cavity equations returns the optimal solution. We then study the geometrical properties of more general random ensembles. In particular we observe a range in the density of constraints at which the system enters a glassy phase where the cost function has many minima. Interestingly, the algorithmic performances are only sensitive to another phase transition affecting the structure of configurations allowed by the linear constraints. We also extend our results to variables belonging to GF(q), the Galois field of order q. We show that increasing the value of q allows to achieve a better optimum, which is confirmed by the replica-symmetric cavity method predictions.

We have demonstrated that the insertion of alkyne-containing bifunctional linkers into the tyrosine residues of the carrier protein, followed by the copper mediated azide-alkyne [3 + 2] cycloaddition of carbohydrates, is a robust approach for the preparation of glycoconjugates with defined glycans, carrier, and connectivity. Conjugation of Group B Streptococcus (GBS) capsular polysaccharides to streptococcal pilus protein could extend the vaccine coverage to a variety of strains. Application of our protocol to these large charged polysaccharides occurred at low yields. Herein we developed a tyrosine-directed conjugation approach based on the copper-free click chemistry of sugars modified with cyclooctynes, which enables efficient condensation of synthetic carbohydrates. Most importantly, this strategy was demonstrated to be more effective than the corresponding copper catalyzed reaction for the insertion of GBS onto the tyrosine residues of GBS pilus proteins, previously selected as vaccine antigens through the so-called reverse vaccinology. Integrity of protein epitopes in the modified proteins was ascertained by competitive ELISA, and conjugation of polysaccharide to protein was confirmed by SDS page electrophoresis and immunoblot assays. The amount of conjugated polysaccharide was estimated by high-performance anion-exchange chromatography coupled with pulsed amperometric detection (HPAEC-PAD). The described technology is particularly suitable for proteins used with the dual role of vaccine antigen and carrier for the carbohydrate haptens.

Systematic characterisation of the reactivity of the lysine moieties in CRM197 towards N-hydroxysuccinimide linkers bearing alkynes or azides is described. This involves two-step conjugation of various glycans to CRM197 by click chemistry in a well-defined manner. By semiquantitative LC-MS/MS analysis of proteolytic digests of the conjugates formed, the reactivity of lysine residues in the protein was mapped and ranked. Computational analysis of the solvent accessibility of each lysine residue (based on the CRM197 crystal structure) established a correlation between reactivity and surface exposure. By this approach, conjugation involving lysine residues (normally a random process) can be controlled. It enables the preparation of lysine-mediated glycoconjugates with improved batch-to-batch reproducibility, thereby producing neo-glycoconjugates with more-consistent biological activity., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Upon treatment with the K- and Li-enolates of a methylene active compound, such as dimethyl malonate and dibenzoylmethane, D-allal- and D-galactal-derived vinyl N-mesyl aziridines are stereoselectively transformed, in a unique step, into diastereoisomeric, highly functionalized, enantiopure cis-2,5-disubstituted N-mesyl-2,5-dihydropyrroles.

A regioselective introduction of a methoxycarbonyl methyl group at the C(2) position of unsubstituted pyridine has been accomplished with catalytic amounts of copper(II) triflate in mild reaction conditions. The N-acetyl-1,2-dihydropyridyl acetic acid methyl ester obtained is a valuable building block for the synthesis of new polyfunctionalized piperidine derivatives bearing unconventional substitution patterns., (© 2011 American Chemical Society)

Ring opening with organometallic reagents of [2.2.2]-acylnitroso cycloadducts, including an enantioselective kinetic resolution of these compounds, has been accomplished for the first time. By the careful choice of reaction conditions, it was possible to obtain new cyclohexenyl hydroxamic acids with complete anti-stereoselectivity and a nice regioalternating control. A remarkable effect of the halogen of the Grignard reagent was observed during ring opening.

A mild ring opening of vinyl epoxides and aziridines with B(2)Pin(2) catalyzed by Ni(0)-Binap affords new functionalized allylic boron derivatives which undergo sequential transformations. The uncatalyzed allylation of aldehydes allows obtaining challenging bishomoallylic alicyclic 1,3-diols and 1,3-amino alcohols with remarkably high stereoselectivities. Valuable trans-bisallylic 1,4-amino alcohols can be obtained by a simple oxidation.

The first successful asymmetric transfer of rhodium-alkynyl species to symmetrical strained alkenes has been realized starting from bicyclic hydrazines and alkynylboronic esters.