Search results for "combinatorial"
showing 10 items of 1208 documents
Descent distribution on Catalan words avoiding a pattern of length at most three
2018
Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern $p$ we provide a bivariate generating function where the coefficient of $x^ny^k$ in its series expansion is the number of length $n$ Catalan words with $k$ descents and avoiding $p$. As a byproduct, we enumerate the set of Catalan words avoiding $p$, and we provide the popularity of descents on this set. Some of the obtained enumerating sequences are not yet recorded in the On-line En…
Generating a Gray code for prefix normal words in amortized polylogarithmic time per word
2020
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal words of length $n$ as a combinatorial Gray code, where successive strings differ by at most two swaps or bit flips. This Gray code can be generated in $\Oh(\log^2 n)$ amortized time per word, while the best generation algorithm hitherto has $\Oh(n)$ running time per word. We also present a membership tester for prefix normal words, as well as a novel characterization of bubble languages.
Scalability of using Restricted Boltzmann Machines for Combinatorial Optimization
2014
Abstract Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Restricted Boltzmann Machines (RBMs) are generative neural networks with these desired properties. We integrate an RBM into an EDA and evaluate the performance of this system in solving combinatorial optimization problems with a single objective. We assess how the number of fitness evaluations and the CPU time scale with problem size and complexity. The results are compared to the Bayesian Optimization Algorithm (BOA), a state-of-the-art multivariate EDA, and the Dependency Tree Algorithm (DTA), which uses a simpler probability model requiring less computati…
Mahonian STAT on words
2016
In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…
The General Routing Problem polyhedron: Facets from the RPP and GTSP polyhedra
1998
[EN] In this paper we study the polyhedron associated with the General Routing Problem (GRP). This problem, first introduced by Orloff in 1974, is a generalization of both the Rural Postman Problem (RPP) and the Graphical Traveling Salesman Problem (GTSP) and, thus, is NP -hard. We describe a formulation of the problem such that from every non-trivial facet-inducing inequality for the RPP and GTSP polyhedra, we obtain facet-inducing inequalities for the GRP polyhedron, We describe a new family of facet-inducing inequalities for the GRP, the honeycomb constraints, which seem to be very useful for solving GRP and RPP instances. Finally, new classes of facets obtained by composition of facet-i…
Histamine, an effective initiator for the synthesis of polysulfides
2020
The synthesis of polysulfides from thioepoxides traditionally makes use of toxic organometallic initiators. We demonstrate the use of histamine as an efficient initiator. The polymerization can be carried out under solvent-free and metal-free conditions at mild temperature to obtain high-quality polysulfides. A synergistic acid and base catalysis mechanism is proposed. The results enable a safer and cleaner production of next-generation polymers.
Synthesis of Fluorinated Glycosyl Amino Acid Building Blocks for MUC1 Cancer Vaccine Candidates by Microreactor-Assisted Glycosylation
2012
Abstract MUC1-type glycopeptides have already shown their potential as possible cancer vaccine candidates. In addition, first examples of fluorinated antigen structures, especially containing the Thomsen–Friedenreich antigen, with similar antibody recognition have been reported. Using microreactor techniques for improvement of the crucial step, the complex glycosylation reactions, is an efficient way to find optimized reaction parameter as well as to circumvent well-known scale-up drawbacks. Besides, this is the first report of continuous flow glycosylations of glycosyl amino acids, in particular with fluorinated glycosyl building blocks.
Site-specific near-infrared fluorescent labelling of proteins on cysteine residues with meso -chloro-substituted heptamethine cyanine dyes
2018
International audience; Near-infrared (NIR) fluorescence imaging is a promising new medical imaging modality. Associated with a targeting molecule, NIR fluorophores can accumulate selectively in tissues of interest and become valuable tools for the diagnosis and therapy of various pathologies. To facilitate the design of targeted NIR imaging agents, it is important to identify simple and affordable fluorescent probes, allowing rapid labelling of biovectors such as proteins, ideally in a site-specific manner. Here, we demonstrate that heptamethine cyanine based fluorophores, such as IR-783, that contain a chloro-cyclohexyl moiety within their polymethine chain can react selectively, at neutr…
Zinc complexes as fluorescent chemosensors for nucleic acids: new perspectives for a “boring” element
2014
Zinc(ii) complexes are effective and selective nucleic acid-binders and strongly fluorescent molecules in the low energy range, from the visible to the near infrared. These two properties have often been exploited to quantitatively detect nucleic acids in biological samples, in both in vitro and in vivo models. In particular, the fluorescent emission of several zinc(ii) complexes is drastically enhanced or quenched by the binding to nucleic acids and/or upon visible light exposure, in a different fashion in bulk solution and when bound to DNA. The twofold objective of this perspective is (1) to review recent utilisations of zinc(ii) complexes as selective fluorescent probes for nucleic acid…
An ANRORC approach to the synthesis of perfluoroalkylated 1,2,4-triazole-carboxamides
2009
A series of perfluoroalkyl-1,2,4-triazole-carboxamides has been obtained through an ANRORClike rearrangement (Addition of Nucleophile, Ring-Opening and Ring-Closure) of 5- perfluoroalkyl-1,2,4-oxadiazole-3-carboxamides with methylhydrazine or hydrazine. The initial addition of the bidentate nucleophile to the electrophilic C(5) of the 1,2,4-oxadiazole ring, followed by ring opening and ring closure, leads to the formation of triazoles in good yield under mild experimental conditions. In some cases, a competitive ANRORC-enlargement reaction to form 1,2,4-triazin-6-ones was also observed. Obtained carboxamidotriazoles have also been explored as precursors for the synthesis of 3(5)-perfluoroal…