18 research outputs found
Bounding sequence extremal functions with formations
An -formation is a concatenation of permutations of letters.
If is a sequence with distinct letters, then let be
the maximum length of any -sparse sequence with distinct letters which
has no subsequence isomorphic to . For every sequence define
, the formation width of , to be the minimum for which
there exists such that there is a subsequence isomorphic to in every
-formation. We use to prove upper bounds on
for sequences such that contains an alternation
with the same formation width as .
We generalize Nivasch's bounds on by showing that
and for every and , such that denotes the inverse Ackermann function.
Upper bounds on have been used in other
papers to bound the maximum number of edges in -quasiplanar graphs on
vertices with no pair of edges intersecting in more than points.
If is any sequence of the form such that is a letter,
is a nonempty sequence excluding with no repeated letters and is
obtained from by only moving the first letter of to another place in
, then we show that and . Furthermore we prove that
and for every .Comment: 25 page
Periodic Floer homology and the smooth closing lemma for area-preserving surface diffeomorphisms
We prove a very general Weyl-type law for Periodic Floer Homology, estimating
the action of twisted Periodic Floer Homology classes over essentially any
coefficient ring in terms of the grading and the degree, and recovering the
Calabi invariant of Hamiltonians in the limit. We also prove a strong
non-vanishing result, showing that under a monotonicity assumption which holds
for a dense set of maps, the Periodic Floer Homology has infinite rank. An
application of these results yields that a -generic area-preserving
diffeomorphism of a closed surface has a dense set of periodic points. This
settles Smale's tenth problem in the special case of area-preserving
diffeomorphisms of closed surfaces.Comment: v4: A typo in the abstract is corrected and a few more expository
changes are made. 68 page
Periodic points of rational area-preserving homeomorphisms
An area-preserving homeomorphism isotopic to the identity is rational if its
rotation vector is a real multiple of a rational class. Rationality can always
be achieved by -small perturbations. We show that any area-preserving
homeomorphism of a compact surface of genus at least two, which is isotopic to
the identity and rational, is either the identity or has periodic points of
unbounded minimal period. We show a similar result, using a theorem of
Oxtoby-Ulam, when the map is only assumed to preserve a Borel probability
measure with full support. We also discuss maps which are not isotopic to the
identity and lower genus surfaces. The proofs of the main results rely on
periodic Floer homology.Comment: 13 pages + reference
Symplectic dynamics: Invariant measures, closing lemmas, and equidistribution
In this thesis, we develop and apply techniques in symplectic geometry and gauge theory to study symplectic dynamical systems. The first part devises a method to construct invariant measures of Hamiltonian flows from pseudoholomorphic curves, and applies it to show broad classes of these systems are not uniquely ergodic. The second part studies quantitative invariants from Periodic Floer homology, in particular using Seiberg–Witten theory to give a precise accounting of their high-degree asymptotics. The main dynamical application is a proof that a generic area-preserving diffeomorphism of a compact surface has an equidistributed sequence of periodic orbits
Contact homology and the strong closing lemma for ellipsoids
We prove a conjecture of Irie, stating that a strong version of the smooth
closing lemma holds for Reeb flows on ellipsoids in any dimension. The proof
involves analyzing a constrained cobordism map in contact homology, using
holomorphic intersection theory.Comment: 56 pages, 10 figures, comments welcome
Coincidences among skew Grothendieck polynomials
The question of when two skew Young diagrams produce the same skew Schur function has been well-studied. We investigate the same question in the case of stable Grothendieck polynomials, which are the K-theoretic analogues of the Schur functions. We prove a necessary condition for two skew shapes to give rise to the same dual stable Grothendieck polynomial. We also provide a necessary and sufficient condition in the case where the two skew shapes are ribbons
Kinetic analysis of a human chorionic gonadotropin- epitope-paratope interaction
Kinetics of protein-protein or ligand-ligate interaction has predominantly been studied by optical spectroscopy (particularly fluorescence) and surface plasmon resonance biosensors. Almost all such studies are based on association kinetics between ligand-ligate and suffer from certain methodological and interpretational limitations. Therefore, kinetic analyses of dissociation data of such interactions become indispensable. In the present investigation, the radiolabeled human chorionic gonadotropin- (125IhCG) was employed as a probe and nitrocellulose (NC) as a solid support to immobilize monoclonal antibody (MAb) G1G10.1. The NC-G1G10.1-125IhCG complex (NCcom) was prepared and the dissociation of radiolabeled hCG was carried out in the presence of excess unlabeled ligate. From the experimental dissociation data under varying ionic strength, dissociation constants (k-1), association constants (k+1) and affinity constants (ka) were calculated. The values obtained were utilized in exploring the amino acid residues constituting an epitopic region of hCG involved in interaction with the complementary paratope on MAb G1G10.1. Kinetic data of the present study supported our recently published findings [using single step-solid phase radioimmunoassay (SS-SPRIA)] that the core region of hCG epitope consists of Arg (94,95) and Asp (99) while a Lys (104) and a His (106) are in proximity to the core epitopic region. Based on the results of present investigation, we conclude that dissociation kinetics coupled with SS-SPRIA unequivocally provides considerable insight into the study of ligand-ligate interactions and epitope analysis
Evaluation of the free radical scavenging activities of ellagic acid and ellagic acid peracetate by EPR spectrometry
The purpose of this study was to examine the free radical scavenging and antioxidant activities of ellagic acid (EA) and ellagic acid peracetate (EAPA) by measuring their reactions with the radicals, 2,2-diphenyl-1-picrylhydrazyl and galvinoxyl using EPR spectroscopy. We have also evaluated the influence of EA and EAPA on the ROS production in L-6 myoblasts and rat liver microsomal lipid peroxidation catalyzed by NADPH. The results obtained clearly indicated that EA has tremendous ability to scavenge free radicals, even at concentration of 1 mu M. Interestingly even in the absence of esterase, EAPA, the acetylated product of EA, was also found to be a good scavenger but at a relatively slower rate. Kinetic studies revealed that both EA and EAPA have ability to scavenge free radicals at the concentrations of 1 mu M over extended periods of time. In cellular systems, EA and EAPA were found to have similar potentials for the inhibition of ROS production in L-6 myoblasts and NADPH-dependent catalyzed microsomal lipid peroxidation
Evaluation of the free radical scavenging activities of ellagic acid and ellagic acid peracetate by epr spectrometry
The purpose of this study was to examine the free radical scavenging and antioxidant activities of ellagic acid (EA) and ellagic acid peracetate (EAPA) by measuring their reactions with the radicals, 2,2-diphenyl-1-picrylhydrazyl and galvinoxyl using EPR spectroscopy. We have also evaluated the influence of EA and EAPA on the ROS production in L-6 myoblasts and rat liver microsomal lipid peroxidation catalyzed by NADPH. The results obtained clearly indicated that EA has tremendous ability to scavenge free radicals, even at concentration of 1 µM. Interestingly even in the absence of esterase, EAPA, the acetylated product of EA, was also found to be a good scavenger but at a relatively slower rate. Kinetic studies revealed that both EA and EAPA have ability to scavenge free radicals at the concentrations of 1 µM over extended periods of time. In cellular systems, EA and EAPA were found to have similar potentials for the inhibition of ROS production in L-6 myoblasts and NADPH-dependent catalyzed microsomal lipid peroxidation
Molecular dissection of an hCG-β epitope using single-step solid phase radioimmunoassa
Background: Peptides and proteins have both sequence-specific (contiguous) and conformation-specific (discontiguous) epitopes. Sequence-specific epitopes are delineated by peptide approach and other robust methods like competition assays, gene expression assays, synthetic peptide library based assays etc. Available methods for delineation of conformation-specific epitopes are cumbersome (X-ray crystallography etc.), time consuming and require costly sophisticated equipments. Hence, there is a need to develop a simple method for identification and mapping of conformation-specific epitopes.
Method: In the single-step solid phase radioimmunoassay (SS-SPRIA), an immunochemical bridge of ‘mouse IgG-anti-mouse IgG’ was prepared in the polypropylene wells followed by adsorption with hCG specific monoclonal antibody (MAb) . The extent of competitive inhibition in binding ability of with chemically or enzymatically modified hCG-β to immobilized MAb in comparison to hCG-β standards was utilized to identify the epitopic amino acid involved in epitope–paratope interaction.
Results: Data clearly suggest that the epitope under investigation consisted of Arg (94, 95) and Asp (99) at the core region with a Lys (104) and a His (106) in the proximity and absence of chymotrypsin susceptible Phe or Tyr in this region.
Conclusion: The data of SS-SPRIA revealed the 93–100 loop of amino acid sequence, as the core region of conformation-specific epitope of hCG-β at or near the receptor-binding region. Hence, SS-SPRIA seems to be a simple method for identification and mapping of conformation-specific epitopes