Learning recursive probability trees from probabilistic potentials

A Recursive Probability Tree (RPT) is a data structure for representing the potentials involved in Probabilistic Graphical Models (PGMs). This structure is developed with the aim of capturing some types of independencies that cannot be represented with previous structures. This capability leads to improvements in memory space and computation time during inference. This paper describes a learning algorithm for building RPTs from probability distributions. The experimental analysis shows the proper behavior of the algorithm: it produces RPTs encoding good approximations of the original probability distributions.     

A Note on Convergence of the Equi-Energy Sampler

This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed.     

Direct C−H Borylation of Arenes Catalyzed by Saturated Hydride-Boryl-Iridium-POP Complexes: Kinetic Analysis of the Elemental Steps

The saturated trihydride IrH₃{κ³-P,O,P-[xant(PiPr₂)₂]} ( 1 ; xant(PiPr₂)₂=9,9-dimethyl-4,5-bis(diisopropylphosphino)xanthene) activates the B−H bond of two molecules of pinacolborane (HBpin) to give H₂, the hydride-boryl derivatives IrH₂(Bpin){κ³-P,O,P-[xant(PiPr₂)₂]} ( 2 ) and IrH(Bpin)₂{κ³-P,O,P-[xant(PiPr₂)₂]} ( 3 ) in a sequential manner. Complex 3 activates a C−H bond of two molecules of benzene to form PhBpin and regenerates 2 and 1 , also in a sequential manner. Thus, complexes 1 , 2 , and 3 define two cycles for the catalytic direct C−H borylation of arenes with HBpin, which have dihydride 2 as a common intermediate. C−H bond activation of the arenes is the rate-determining step of both cycles, as the C−H oxidative addition to 3 is faster than to 2 . The results from a kinetic study of the reactions of 1 and 2 with HBpin support a cooperative function of the hydride ligands in the B−H bond activation. The addition of the boron atom of the borane to a hydride facilitates the coordination of the B−H bond through the formation of κ¹- and κ²-dihydrideborate intermediates.     

A note on random walks with absorbing barriers and sequential Monte Carlo methods

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman–Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.     

Structural Diversity from the Transannular Cyclizations of Natural Germacrone and Epoxy Derivatives: A Theoretical–Experimental Study

Treatment of germacrone ( 1 ) with different electrophiles, and of its epoxy derivatives germacrone‐4,5‐epoxide ( 2 ), germacrone‐1,10‐epoxide ( 3 ) and isogermacrone‐4,5‐epoxide ( 4 ) with Brönsted/Lewis acids and Ti^III, gives rise to a great structural diversity. Thus, by using a maximum of two steps, the production of more than 40 compounds corresponding to 14 skeletons is described. Computational calculations rationalizing the structural divergence produced are also described. Finally, since some of the compounds generated are bioactive natural sesquiterpenes, the mechanisms of formation of these substances will provide new insights in their biosynthesis.     

Can A Denaturant Stabilize DNA? Pyridine Reverses DNA Denaturation in Acidic pH

The stability of DNA is highly dependent on the properties of the surrounding solvent, such as ionic strength, pH, and the presence of denaturants and osmolytes. Addition of pyridine is known to unfold DNA by replacing π–π stacking interactions between bases, stabilizing conformations in which the nucleotides are solvent exposed. We show here experimental and theoretical evidences that pyridine can change its role and in fact stabilize the DNA under acidic conditions. NMR spectroscopy and MD simulations demonstrate that the reversal in the denaturing role of pyridine is specific, and is related to its character as pseudo groove binder. The present study sheds light on the nature of DNA stability and on the relationship between DNA and solvent, with clear biotechnological implications.     

An axiomatic characterization of the potential decisiveness index

Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and that to achieve this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces for the probability of passing the issue at hand, is a good tool with which to acquire the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is shown.     

Probing the CH⋅⋅⋅π Weak Hydrogen Bond in Anesthetic Binding: The Sevoflurane–Benzene Cluster

Cooperativity between weak hydrogen bonds can be revealed in molecular clusters isolated in the gas phase. Here we examine the structure, internal dynamics, and origin of the weak intermolecular forces between sevoflurane and a benzene molecule, using multi‐isotopic broadband rotational spectra. This heterodimer is held together by a primary C? H???π hydrogen bond, assisted by multiple weak C? H???F interactions. The multiple nonbonding forces hinder the internal rotation of benzene around the isopropyl C? H bond in sevoflurane, producing detectable quantum tunneling effects in the rotational spectrum.