The backward {\lambda}-Lemma and Morse filtrations

Consider the infinite dimensional hyperbolic dynamical system provided by the (forward) heat semi-flow on the loop space of a closed Riemannian manifold M. We use the recently discovered backward {\lambda}-Lemma and elements of Conley theory to construct a Morse filtration of the loop space whose cellular filtration complex represents the Morse complex associated to the downward L2-gradient of the classical action functional. This paper is a survey. Details and proofs will be given in [6].Comment: Conference proceedings, 9 pages, 5 figures. v2: typos corrected, minor modification

Fall 2023 Human Resources Management Syllabus

Syllabus for Human Resources Management (ECO 31250 & PSY 31141

Fall 2023 Organizational Change Syllabus

Syllabus for Organizational Change (ECO 31651 & PSY 31651

Translated points and Rabinowitz Floer homology

We prove that if a contact manifold admits an exact filling then every local contactomorphism isotopic to the identity admits a translated point in the interior of its support, in the sense of Sandon [San11b]. In addition we prove that if the Rabinowitz Floer homology of the filling is non-zero then every contactomorphism isotopic to the identity admits a translated point, and if the Rabinowitz Floer homology of the filling is infinite dimensional then every contactmorphism isotopic to the identity has either infinitely many translated points, or a translated point on a closed leaf. Moreover if the contact manifold has dimension greater than or equal to 3, the latter option generically doesn't happen. Finally, we prove that a generic contactomorphism on $\mathbb{R}^{2n+1}$ has infinitely many geometrically distinct iterated translated points all of which lie in the interior of its support.Comment: 13 pages, v2: numerous corrections, results unchange

Topology and Homoclinic Trajectories of Discrete Dynamical Systems

We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of the linearization at the stationary branch are twisted in different ways.Comment: 19 pages, canceled the appendix (Properties of the index bundle) in order to avoid any text overlap with arXiv:1005.207

Influences of base excision repair defects on the lethality and mutagenicity induced by Me-lex, a sequence-selective N3-adenine methylating agent.

Due to its minor groove selectivity, Me-lex preferentially generates N3-methyladenine (3-MeA) adducts in double-stranded DNA. We undertook a genetic approach in yeast to establish the influence of base excision repair (BER) defects on the processing of Me-lex lesions on plasmid DNA that harbors the p53 cDNA as target. We constructed a panel of isogenic strains containing a reporter gene to test p53 function and the following gene deletions: deltamag1, deltaapn1apn2, and deltaapn1apn2mag1. When compared with the wild-type strain, a decrease in survival was observed in deltamag1, deltaapn1apn2, and deltaapn1apn2mag1. The Me-lex-induced mutation frequency increased in the following order: wild typedeltamag1deltaapn1apn2 = deltaapn1apn2mag1. A total of 77 mutants (23 in wild type, 31 in deltamag1, and 23 in deltaapn1apn2) were sequenced. Eighty-one independent mutations (24 in wild type, 34 in deltamag1, and 23 in deltaapn1apn2) were detected. The majority of base pair substitutions were AT-targeted in all strains (14/23, 61% in wild type; 20/34, 59%, in deltamag1; and 14/23, 61%, in deltaapn1apn2). The Mag1 deletion was associated with a significant decrease of GCAT transitions when compared with both the wild-type and the AP endonuclease mutants. This is the first time that the impact of Mag1 and/or AP endonuclease defects on the mutational spectra caused by 3-MeA has been determined. The results suggest that 3-MeA is critical for Me-lex cytotoxicity and that its mutagenicity is slightly elevated in the absence of Mag1 glycosylase activity but significantly higher in the absence of AP endonuclease activity