The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these {\it extended-linear} symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forward fourth-order algorithms with arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.Comment: 12 pages, 2 figures, submitted to Phys. Rev. E, corrected typo

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Finite Generation of Canonical Ring by Analytic Method

In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a talk on the analytic approach to the finite generation of the canonical ring for a compact complex algebraic manifold of general type. This article is my contribution to the proceedings of that conference from my talk. In this article I give an overview of the analytic proof and focus on explaining how the analytic method handles the problem of infinite number of interminable blow-ups in the intuitive approach to prove the finite generation of the canonical ring. The proceedings of the LU Qikeng conference will appear as Issue No. 4 of Volume 51 of Science in China Series A: Mathematics (www.springer.com/math/applications/journal/11425)

Prospects for single-molecule electrostatic detection in molecular motor gliding motility assays

Molecular motor gliding motility assays based on myosin/actin or kinesin/microtubules are of interest for nanotechnology applications ranging from cargo-trafficking in lab-on-a-chip devices to novel biocomputation strategies. Prototype systems are typically monitored by expensive and bulky fluorescence microscopy systems and the development of integrated, direct electric detection of single filaments would strongly benefit applications and scale-up. We present estimates for the viability of such a detector by calculating the electrostatic potential change generated at a carbon nanotube transistor by a motile actin filament or microtubule under realistic gliding assay conditions. We combine this with detection limits based on previous state-of-the-art experiments using carbon nanotube transistors to detect catalysis by a bound lysozyme molecule and melting of a bound short-strand DNA molecule. Our results show that detection should be possible for both actin and microtubules using existing low ionic strength buffers given good device design, e.g., by raising the transistor slightly above the guiding channel floor. We perform studies as a function of buffer ionic strength, height of the transistor above the guiding channel floor, presence/absence of the casein surface passivation layer for microtubule assays and the linear charge density of the actin filaments/microtubules. We show that detection of microtubules is a more likely prospect given their smaller height of travel above the surface, higher negative charge density and the casein passivation, and may possibly be achieved with the nanoscale transistor sitting directly on the guiding channel floor.Comment: Submitted to New Journal of Physic

Low cost high efficiency GaAs monolithic RF module for SARSAT distress beacons

Low cost high performance (5 Watts output) 406 MHz beacons are urgently needed to realize the maximum utilization of the Search and Rescue Satellite-Aided Tracking (SARSAT) system spearheaded in the U.S. by NASA. Although current technology can produce beacons meeting the output power requirement, power consumption is high due to the low efficiency of available transmitters. Field performance is currently unsatisfactory due to the lack of safe and reliable high density batteries capable of operation at -40 C. Low cost production is also a crucial but elusive requirement for the ultimate wide scale utilization of this system. Microwave Monolithics Incorporated (MMInc.) has proposed to make both the technical and cost goals for the SARSAT beacon attainable by developing a monolithic GaAs chip set for the RF module. This chip set consists of a high efficiency power amplifier and a bi-phase modulator. In addition to implementing the RF module in Monolithic Microwave Integrated Circuit (MMIC) form to minimize ultimate production costs, the power amplifier has a power-added efficiency nearly twice that attained with current commercial technology. A distress beacon built using this RF module chip set will be significantly smaller in size and lighter in weight due to a smaller battery requirement, since the 406 MHz signal source and the digital controller have far lower power consumption compared to the 5 watt power amplifier. All the program tasks have been successfully completed. The GaAs MMIC RF module chip set has been designed to be compatible with the present 406 MHz signal source and digital controller. A complete high performance low cost SARSAT beacon can be realized with only additional minor iteration and systems integration

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Cohomology of bundles on homological Hopf manifold

We discuss the properties of complex manifolds having rational homology of $S^1 \times S^{2n-1}$ including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known vanishing properties of cohomology of bundles on such manifolds.As an application we consider degeneration of Hodge-deRham spectral sequence in this non Kahler setting.Comment: To appear in Proceedings of 2007 conference on Several complex variables and Complex Geometry. Xiamen. Chin

Elevation of methylated DNA in KILLIN/PTEN in the plasma of patients with thyroid and/or breast cancer

© 2014 Ng et al. Around 80% of mutations in the PTEN gene have been reported to be associated with diseases such as Cowden syndrome, which is an autosomal dominant disorder associated with an increased risk of developing breast, thyroid, and endometrial neoplasms. Recent studies have also demonstrated that KILLIN, which is located proximally to PTEN, shares the same transcription start site, and is assumed to be regulated by the same promoter, but is transcribed in the opposite direction. In this regard, we postulate that there may be a connection between KILLIN/PTEN genes and breast and thyroid cancers. Using real-time quantitative polymerase chain reaction (qPCR), we found that expression of KILLIN, but not PTEN, was significantly decreased in 23 Chinese women with a personal history of breast and thyroid cancer or a personal history of breast cancer and a family history of thyroid cancer, or vice versa, and at least two persons in the family with thyroid cancer or at a young age ,40 years, when compared with healthy controls (P<0.0001). No PTEN mutations were found in these 23 patients. We then developed a simple methylation-sensitive restriction enzyme digestion followed by real-time quantitative assay to quantify plasma methylated KILLIN/PTEN DNA in these patients. Plasma levels of methylated KILLIN/PTEN DNA were significantly increased in these patients when compared with healthy controls (P<0.05). This study shows that plasma methylated KILLIN/PTEN DNA was significantly elevated, suggesting hypermethylation of the KILLIN/PTEN promoter in breast and thyroid cancer patients.published_or_final_versio

Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and we show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we proved some properties of semistable Higgs sheaves.Comment: 18 pages; some typos correcte