Given a symplectic manifold (W,ω) with contact type boundary (M, ξ), one can define the symplectic homology of (W,ω) and the linearized contact homology of (M, ξ) with respect to its filling. We establish a Gysintype exact sequence relating these invariants and describe one of the maps therein in terms of rational holomorphic curves in the symplectization of (M, ξ).

We have exactly enumerated all sequences and conformations of hydrophobic-polar (HP) proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the HP model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a nondegenerate ground state. Furthermore we were interested in cha...

The Hochschild and (cotriple) cyclic homologies of crossed modules of (notnecessarily-unital) associative algebras are investigated. Wodzicki’s excision theorem is extended for inclusion crossed modules in the category of crossed modules of algebras. The cyclic and cotriple cyclic homologies of crossed modules are compared in terms of long exact homology sequence, generalising the relative cycl...

Likelihood-based Imprecise Regression (LIR) is a recently introduced approach to regression with imprecise data. Here we consider a robust regression method derived from the general LIR approach and we establish an exact algorithm to determine the set-valued result of the LIR analysis in the special case of simple linear regression with interval data.

This paper addresses the maintenance of discovered frequent patterns when a batch of transactions are removed from the original dataset. We conduct an in-depth investigation on how the frequent pattern space evolves under transaction removal updates using the concept of equivalence classes. Inspired by the evolution analysis, an effective and exact algorithm TRUM is proposed to maintain frequen...

Pairwise local alignment is one of the most important problems in sequence analysis in computational biology. Classical dynamic programming solution to this problem searches for two segments with maximum similarity score by discarding poorly conserved initial and terminal fragments. As a consequence, an alignment returned as optimal may contain a mosaic of well-conserved fragments arti cially c...

Frequent sequence mining is one of the main challenges in data mining and especially in large databases, which consist of millions of records. There is a number of different applications where frequent sequence mining is very important: medicine, finance, internet behavioural data, marketing data, etc. Exact frequent sequence mining methods make multiple passes over the database and if the data...

Let f : X → Y be a based map of simply connected spaces. The corresponding evaluation map ω : map(X, Y ; f)→ Y induces a homomorphism of homotopy groups whose image in πn(Y ) is called the nth evaluation subgroup of f . The nth Gottlieb group of X occurs as the special case in which Y = X and f = 1X . We identify the homomorphism induced on rational homotopy groups by this evaluation map, in te...

in this paper, he's highly prolic variational iteration method is applied ef-fectively for showing the existence, uniqueness and solving a class of singularsecond order two point boundary value problems. the process of nding solu-tion involves generation of a sequence of appropriate and approximate iterativesolution function equally likely to converge to the exact solution of the givenpr...