159 research outputs found
Recursive neural networks for density estimation over generalized random graphs
No full textStructured data in the form of labeled graphs (with variable order and topology) may be thought of as the outcomes of a random graph (RG) generating process characterized by an underlying probabilistic law. This paper formalizes the notions of generalized RG (GRG) and probability density function (pdf) for GRGs. Thence, a “universal” learning machine (combining the encoding module of a recursive neural network and a radial basis functions' network) is introduced for estimating the unknown pdf from an unsupervised sample of GRGs. A maximum likelihood training algorithm is presented and constrained so as to ensure that the resulting model satisfies the axioms of probability. Techniques for preventing the model from degenerate solutions are proposed, as well as variants of the algorithm suitable to the tasks of graphs classification and graphs clustering. The major properties of the machine are discussed. The approach is validated empirically through experimental investigations in the estimation of pdfs for synthetic and real-life GRGs, in the classification of images from the Caltech Benchmark data set and molecules from the Mutagenesis data set, and in clustering of images from the LabelMe data set
Portfolio optimization with short-selling and spin-glass
No full textIn this paper, we solve a general problem of optimizing a portfolio in a futures markets framework, extending the previous work of Galluccio et al. [Physica A 259, 449 (1998)]. We allow for long buying/short selling of a relatively large number of assets, assuming a fixed level of margin requirement. Because of non-linearity in the constraint, we derive a multiple equilibrium solution, in a size exponential respect to the number of assets. That means that we can not obtain the unique efficiency frontier, but many of them and each one is related to different levels of risk. Such a problem is analogous to that of finding the ground state in long-ranged Ising spin glass with external field. In order to get the best portfolio (i.e. that is along the best efficiency frontier), we have to implement a two-step procedure, performing the exhaustive enumeration of all local minima. We develop a concrete application, where the different part of the proposed solution are computed
Synthesis of Enantiomerically Pure Aziridine-2-imides by Cyclization of Chiral 3′-Benzyloxyamino Imide Enolates
No full textAziridine-2-imides are prepared both in high yield and high diastereoselectivity from chiral 3¢-benzyloxyamino imides 2, 3, and 8 by treatment with triethylamine in the presence of either TiCl4or AlMe2Cl. 2 and 3 are easily obtained by a diastereoselective conjugate addition of Obenzylhydroxylamine promoted by Lewis acids to R,â-unsaturated imides 1. The synthesis of 3¢-(benzyloxyamino)propanoyl 8 is performed by addition to the acryloyl compound 6 of N-BOC O-benzylhydroxylamine followed by deprotection. The cyclization of 2 and 3 affords complete trans selectivity and yields up to 97% of the corresponding 3¢-alkyl aziridines 4 and 5, while the cyclization of 8 affords a mixture of diasteroisomers 11, 12 in 86/14 ratio and a 95% yield. A mechanistic
study has been made to rationalize the trans selectivity observed in the cyclization of 2 and 3. AM1 computations allow us to deduce that the reaction proceeds through cyclic titanium or aluminum enolate formation, and they reveal that enolates leading to trans aziridines are more stable than those leading to cis
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