The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Xiaojun Chen - One of the best experts on this subject based on the ideXlab platform.
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Batalin–Vilkovisky coalgebra of string topology
Pacific Journal of Mathematics, 2010Co-Authors: Xiaojun ChenAbstract:We prove that the reduced Hochschild homology of a commutative DG Frobenius algebra has the Natural Structure of a Batalin-Vilkovisky coalgebra, and the reduced cyclic homology has the Natural Structure of a gravity coalgebra. As an application, this gives an algebraic model for a Batalin-Vilkovisky coalgebra Structure on the reduced homology of the free loop space of a simply connected closed oriented manifold, and a gravity coalgebra Structure on the reduced equivariant homology.
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Batalin-Vilkovisky coalgebra of string topology
arXiv: Quantum Algebra, 2008Co-Authors: Xiaojun ChenAbstract:We show that the reduced Hochschild homology of a DG open Frobenius algebra has the Natural Structure of a Batalin-Vilkovisky coalgebra, and the reduced cyclic homology has the Natural Structure of a gravity coalgebra. This gives an algebraic model for a Batalin-Vilkovisky coalgebra Structure on the reduced homology of the free loop space of a simply connected closed oriented manifold, and a gravity coalgebra Structure on the reduced equivariant homology.
Diego U. Ferreiro - One of the best experts on this subject based on the ideXlab platform.
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On the Natural Structure of Amino Acid Patterns in Families of Protein Sequences
Journal of Physical Chemistry B, 2018Co-Authors: Pablo Turjanski, Diego U. FerreiroAbstract:All known terrestrial proteins are coded as continuous strings of ≈20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the Natural architectures of protein families. We present a method to search for patterns and groupings of patterns in protein sequences using a mathematically precise definition for “repetition”, an efficient algorithmic implementation and a robust scoring system with no adjustable parameters. We show that the sequence patterns can be well-separated into disjoint classes according to their recurrence in nested Structures. The statistics of the occurrences of patterns indicate that short repetitions are sufficient to account for the differences between Natural families and randomized groups of sequences by more than 10 standard deviations, while contiguous sequence patterns shorter than 5 residues are effectively random in their occurrences. A small subset of patterns is sufficient to account for a robust ”familiarity” definition betw...
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On the Natural Structure of Amino Acid Patterns in Families of Protein Sequences.
arXiv: Biomolecules, 2018Co-Authors: Pablo Turjanski, Diego U. FerreiroAbstract:All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the Natural architectures of protein families. We present a method to search for patterns and groupings of patterns in protein sequences using a mathematically precise definition for 'repetition', an efficient algorithmic implementation and a robust scoring system with no adjustable parameters. We show that the sequence patterns can be well-separated into disjoint classes according to their recurrence in nested Structures. The statistics of pattern occurrences indicate that short repetitions are enough to account for the differences between Natural families and randomized groups by more than 10 standard deviations, while patterns shorter than 5 residues are effectively random. A small subset of patterns is sufficient to account for a robust ''familiarity'' definition of arbitrary sets of sequences.
C.m. Brown - One of the best experts on this subject based on the ideXlab platform.
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Sequences, Structure, and active vision
Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991Co-Authors: R.d. Rimey, C.m. BrownAbstract:Sequences of symbols generated by a visual and action sequence provide information about the Natural Structure of the world. HMMs (hidden Markov models) provide one way to learn (recover), store, produce, manipulate, and analyze both visual sequences and associated knowledge Structures for computer vision.
Maria Ronco - One of the best experts on this subject based on the ideXlab platform.
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Tridendriform Structure on combinatorial Hopf algebras
Journal of Algebra, 2010Co-Authors: Emily Burgunder, Maria RoncoAbstract:We extend the definition of tridendriform bialgebra by introducing a parameter q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative product and a Natural Structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber–Voronov algebras. We prove the equivalence between the categories of conilpotent q-tridendriform bialgebras and of q-Gerstenhaber–Voronov algebras. The space spanned by surjective maps between finite sets, as well as the space spanned by parking functions, have a Natural Structure of q-tridendriform bialgebra, denoted ST(q) and PQSym(q)∗, in such a way that ST(q) is a sub-tridendriform bialgebra of PQSym(q)∗. Finally we show that the bialgebra of M-permutations defined by T. Lam and P. Pylyavskyy comes from a q-tridendriform algebra which is a quotient of ST(q).
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Tridendriform Structure on combinatorial Hopf algebras
arXiv: Rings and Algebras, 2009Co-Authors: Emily Burgunder, Maria RoncoAbstract:We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative product and a Natural Structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber-Voronov algebras. We prove the equivalence between the categories of connected q-tridendriform bialgebras and of q-Gerstenhaber-Voronov algebras. The space spanned by surjective maps, as well as the space spanned by parking functions, have Natural Structures of q-tridendriform bialgebras, denoted ST(q) and PQSym(q)*, in such a way that ST(q) is a sub-tridendriform bialgebra of PQSym(q)*. Finally we show that the bialgebra of M-permutations defined by T. Lam and P. Pylyavskyy may be endowed with a Natural Structure of q-tridendriform algebra which is a quotient of ST(q).
D. Krob - One of the best experts on this subject based on the ideXlab platform.
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Acyclic Complexes Related to Noncommutative Symmetric Functions
Journal of Algebraic Combinatorics, 1997Co-Authors: F. Bergeron, D. KrobAbstract:In this paper, we show how to endow the algebra of noncommutative symmetric functions with a Natural Structure of cochain complex which strongly relies on the combinatorics of ribbons, and we prove that the corresponding complexes are acyclic.
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Acyclic Complexes Related to Noncommutative SymmetricFunctions
Journal of Algebraic Combinatorics, 1997Co-Authors: F. Bergeron, D. KrobAbstract:In this paper, we show how to endow the algebra of noncommutative symmetric functions with a Natural Structure of cochain complex which strongly relies on the combinatorics of ribbons, and we prove that the corresponding complexes are acyclic.
