Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE in non-divergence form with bounded measurable coefficients. The method of proof is through a Bochner technique. The Heisenberg group is seen to be en extremal manifold for our inequality in the class of manifolds whose Ricci curvature is non-negative.Comment: 13 page

On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $\mu_4$ is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed

A Sulfhydryl-Reactive Ruthenium (II) Complex and Its Conjugation to Protein G as a Universal Reagent for Fluorescent Immunoassays

To develop a fluorescent ruthenium complex for biosensing, we synthesized a novel sulfhydryl-reactive compound, 4-bromophenanthroline bis-2,2′-dipyridine Ruthenium bis (hexafluorophosphate). The synthesized Ru(II) complex was crosslinked with thiol-modified protein G to form a universal reagent for fluorescent immunoassays. The resulting Ru(II)-protein G conjugates were identified by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). The emission peak wavelength of the Ru(II)-protein G conjugate was 602 nm at the excitation of 452 nm which is similar to the spectra of the Ru(II) complex, indicating that Ru(II)-protein G conjugates still remain the same fluorescence after conjugation. To test the usefulness of the conjugate for biosensing, immunoglobulin G (IgG) binding assay was conducted. The result showed that Ru(II)-protein G conjugates were capable of binding IgG and the more cross-linkers to modify protein G, the higher conjugation efficiency. To demonstrate the feasibility of Ru(II)-protein G conjugates for fluorescent immunoassays, the detection of recombinant histidine-tagged protein using the conjugates and anti-histidine antibody was developed. The results showed that the histidine-tagged protein was successfully detected with dose-response, indicating that Ru(II)-protein G conjugate is a useful universal fluorescent reagent for quantitative immunoassays

Influence of irrigant needle depth in removing bioluminescent bacteria inoculated into instrumented root canals using real-time imaging in vitro

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73506/1/j.1365-2591.2004.00906.x.pd

Performance Comparison of Ad-hoc Retrieval Models over Full-text vs. Titles of Documents

While there are many studies on information retrieval models using full-text, there are presently no comparison studies of full-text retrieval vs. retrieval only over the titles of documents. On the one hand, the full-text of documents like scientific papers is not always available due to, e. g., copyright policies of academic publishers. On the other hand, conducting a search based on titles alone has strong limitations. Titles are short and therefore may not contain enough information to yield satisfactory search results. In this paper, we compare different retrieval models regarding their search performance on the full-text vs. only titles of documents. We use different datasets, including the three digital library datasets: EconBiz, IREON, and PubMed. The results show that it is possible to build effective title-based retrieval models that provide competitive results comparable to full-text retrieval. The difference between the average evaluation results of the best title-based retrieval models is only % less than those of the best full-text-based retrieval models

DNA topoisomerases participate in fragility of the oncogene RET

Fragile site breakage was previously shown to result in rearrangement of the RET oncogene, resembling the rearrangements found in thyroid cancer. Common fragile sites are specific regions of the genome with a high susceptibility to DNA breakage under conditions that partially inhibit DNA replication, and often coincide with genes deleted, amplified, or rearranged in cancer. While a substantial amount of work has been performed investigating DNA repair and cell cycle checkpoint proteins vital for maintaining stability at fragile sites, little is known about the initial events leading to DNA breakage at these sites. The purpose of this study was to investigate these initial events through the detection of aphidicolin (APH)-induced DNA breakage within the RET oncogene, in which 144 APHinduced DNA breakpoints were mapped on the nucleotide level in human thyroid cells within intron 11 of RET, the breakpoint cluster region found in patients. These breakpoints were located at or near DNA topoisomerase I and/or II predicted cleavage sites, as well as at DNA secondary structural features recognized and preferentially cleaved by DNA topoisomerases I and II. Co-treatment of thyroid cells with APH and the topoisomerase catalytic inhibitors, betulinic acid and merbarone, significantly decreased APH-induced fragile site breakage within RET intron 11 and within the common fragile site FRA3B. These data demonstrate that DNA topoisomerases I and II are involved in initiating APH-induced common fragile site breakage at RET, and may engage the recognition of DNA secondary structures formed during perturbed DNA replication

Coarse-Grained Barrier Trees of Fitness Landscapes

Recent literature suggests that local optima in fitness landscapes are clustered, which offers an explanation of why perturbation-based metaheuristics often fail to find the global optimum: they become trapped in a sub-optimal cluster. We introduce a method to extract and visualize the global organization of these clusters in form of a barrier tree. Barrier trees have been used to visualize the barriers between local optima basins in fitness landscapes. Our method computes a more coarsely grained tree to reveal the barriers between clusters of local optima. The core element is a new variant of the flooding algorithm, applicable to local optima networks, a compressed representation of fitness landscapes. To identify the clusters, we apply a community detection algorithm. A sample of 200 NK fitness landscapes suggests that the depth of their coarse-grained barrier tree is related to their search difficulty

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page