HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Hilbert scheme topological invariants of plane curve singularities are identified to framed threefold stable pair invariants. As a result, the conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve singularities is given a Calabi-Yau threefold interpretation. The motivic Donaldson-Thomas theory developed by M. Kontsevich and the third author then yields natural motivic invariants for algebraic knots. This construction is motivated by previous work of V. Shende, C. Vafa and the first author on the large $N$ duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition improved, proofs expanded, results unchanged, to appear in Comm. Num. Th. Phy

Sedimentation of the Lower Cretaceous Xiagou formation and Its Response to Regional Tectonics in the Qingxi Sag, Jiuquan Basin, NW China

Under the constraint of an isochronous sequence stratigraphic framework, sediment infill of the Xiagou Formation reflects the overall control of dynamic tectonic movements and episodic sedimentations in the Qingxi Sag. Structure reactivity during post-depositional processes could cause stratigraphic variations in longitudinal time and lateral space. This study documents sediment infill features and their response to the tectonic evolutions of the Qingxi Sag. The data sets include comparison of cores, well drilling, 3D seismic, inter-well correlation, wave impedance inversion profiles, original strata recovery data, sedimentary fades spatial evolution and their superimposition with paleogeomorphology. The Jiuquan Basin is a Mesozoic-Cenozoic superposition basin comprising an early rifting graben phase and a later compression phase. Since the Early Cretaceous, the basin has undergone four major tectonic episodes: 1) extension during the Early Cretaceous, 2) tectonic inversion caused by northwest-southeast contraction from the Late Cretaceous to the Paleocene, 3) weak extension from the Eocene to the Miocene and 4) contraction from the Miocene to the present. Therefore, the Jiuquan Basin is the product of taphrogenic, collisional and shearing movements. Seismic interpretations of sequence and maximum flooding surface divide the Xiagou Formation into three third order sequences: SQK1g(0), SQK1g(1) and SQK1g(2+3). Five sedimentary facies associations are identified: the shoreland plain, fan delta dominated sedimentary systems, turbidite deposits, shallow lakes and half-deep lake systems. From K1g(0) to K1g(2+3), decreased sandstone percentages in three fan delta areas indicate a continuously transgressive process, which shows the transition from proximal to distal sites in most statistic wells and an obvious decrease of fan delta scales. The northeast-southwest faults control the lakeward distributions of delta fronts and turbidite fans. The correspondence of sedimentary infill and its response to tectonic movements have been demonstrated in the Qingxi Sag. The more active eastern part of the northeastern boundary fault has an important influence on the northeastward migration of depocenters in the Xiagou Formation. The topography developed continuously from K1g(0) to K1g(2+3), but the diminished subsidence indicates the dominant geological process varying from intense fault rifting in an early period to relatively gentle and overall subsidence in a later period during the Early Cretaceous. (C) 2013 Elsevier Ltd. All rights reserved.Key Laboratory of Tectonics and Petroleum Resources, Ministry of Education TPR-2011-09Project of "Double strong effect, driving mechanism and hydrocarbon significance of tectonic activity during depositional period of Dongying Formation in Qikou and Nanpu Sag, Eastern China" 41272122Geological Science

Set multi-covering via inclusion-exclusion

Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusion-exclusion principle. The presented ESMC (Exact Set Multi-Covering) algorithm takes O* ((2 t)n) time and O* ((t + 1)n) space where t is the maximum value in the coverage requirement set (The O* (f (n)) notation omits a p o l y log (f (n)) factor). We also propose the other three exact algorithms through different tradeoffs of the time and space complexities. To the best of our knowledge, this present paper is the first one to give exact algorithms for the set multi-covering problem with nontrivial time and space complexities. This paper can also be regarded as a generalization of the exact algorithm for the set covering problem given in [A. Björklund, T. Husfeldt, M. Koivisto, Set partitioning via inclusion-exclusion, SIAM Journal on Computing, in: FOCS 2006 (in press, special issue)]. © 2009 Elsevier B.V. All rights reserved.postprin

Distributed local broadcasting algorithms in the physical interference model

Given a set of sensor nodes V where each node wants to broadcast a message to all its neighbors that are within a certain broadcasting range, the local broadcasting problem is to schedule all these requests in as few timeslots as possible. In this paper, assuming the more realistic physical interference model and no knowledge of the topology, we present three distributed local broadcasting algorithms where the first one is for the asynchronized model and the other two are for the synchronized model. Under the asynchronized model, nodes may join the execution of the protocol at any time and do not have access to a global clock, for which we give a distributed randomized algorithm with approximation ratio O(log n).published_or_final_versionThe 2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS), Barcelona, Spain, 27-29 June 2011. In Proceedings of DCOSS, 2011, p. 1-

Dynamic programming based algorithms for set multicover and multiset multicover problems

Given a universe N containing n elements and a collection of multisets or sets over N, the multiset multicover (MSMC) problem or the set multicover (SMC) problem is to cover all elements at least a number of times as specified in their coverage requirements with the minimum number of multisets or sets. In this paper, we give various exact algorithms for these two problems with or without constraints on the number of times a multiset or set may be chosen. First, we show that the MSMC without multiplicity constraints problem can be solved in O* ((b + 1)n | F |) time and polynomial space, where b is the maximum coverage requirement and | F | denotes the total number of given multisets over N. (The O* notation suppresses a factor polynomial in n.) To our knowledge, this is the first known exact algorithm for the MSMC without multiplicity constraints problem. Second, by combining dynamic programming and the inclusion-exclusion principle, we can exactly solve the SMC without multiplicity constraints problem in O ((b + 2)n) time. Compared with two recent results, in [Q.-S. Hua, Y. Wang, D. Yu, F.C.M. Lau, Set multi-covering via inclusion-exclusion, Theoretical Computer Science, 410 (38-40) (2009) 3882-3892] and [J. Nederlof, Inclusion exclusion for hard problems, Master Thesis, Utrecht University, The Netherlands, 2008], respectively, ours is the fastest exact algorithm for the SMC without multiplicity constraints problem. Finally, by directly using dynamic programming, we give the first known exact algorithm for the MSMC or the SMC with multiplicity constraints problem in O ((b + 1)n | F |) time and O* ((b + 1)n) space. This algorithm can also be easily adapted as a constructive algorithm for the MSMC without multiplicity constraints problem. © 2010 Elsevier B.V. All rights reserved.postprin

Effects of RNAi-mediated cathepsin L gene silencing on bionomics of hepatoma carcinoma cells

This study aimed to explore the effects of RNAi-mediated cathepsin L gene silencing on bionomics of hepatoma carcinoma cells. In this study, cathepsin L siRNA silencing group (silencing group), blank hepatoma carcinoma cells group (blank group) and the siRNA fluorescin group (fluorescence control group) were set. The observing time include 1, 3 and 6 days after RNA interference for cathepsin L. The transfection efficiency of each group was observed. The expression of cathepsin L in hepatoma carcinoma cells was detected by immunofluorescence, reverse transcription polymerase chain reaction (RT-PCR) and western blot. Cell viability was detected by methyl thiazolyl tetrazolium (MTT) assay. The changes of cell cycle and apoptosis were observed by flow cytometry. The changes of invasiveness of hepatoma carcinoma cells were detected by Boyden chamber. Compared with the blank group and fluorescence control group, mRNA and protein level of cathepsin L decreased significantly, and cell growth was inhibited. Meanwhile, the proliferation index decreased significantly, while the apoptosis index increased significantly in the experimental group. The invasiveness of hepatoma carcinoma cells was also found to decrease. The study indicated that RNA interference could inhibit cathepsin L expression, and decrease cell proliferation and cell invasiveness of hepatoma carcinoma cells efficiently.Key words: RNA interference, liver cancer; Cathepsin L

Non-Thermal X-ray Properties of Rotation Powered Pulsars and Their Wind Nebulae

We present a statistical study of the non-thermal X-ray emission of 27 young rotation powered pulsars (RPPs) and 24 pulsar wind nebulae (PWNe) by using the Chandra and the XMM-Newton observations, which with the high spatial resolutions enable us to spatially resolve pulsars from their surrounding PWNe. We obtain the X-ray luminosities and spectra separately for RPPs and PWNe, and then investigate their distribution and relation to each other as well as the relation with the pulsar rotational parameters. In the pair-correlation analysis we find that: (1) the X-ray (2-10 keV) luminosities of both pulsar and PWN (L_{psr} and L_{pwn}) display a strong correlation with pulsar spin down power Edot and characteristic age, and the scalings resulting from a simple linear fit to the data are L_{psr} \propto Edot^{0.92 \pm 0.04} and L_{pwn} \propto Edot^{1.45 \pm 0.08} (68% confidence level), respectively, however, both the fits are not statistically acceptable; (2) L_{psr} also shows a possible weak correlation with pulsar period P and period derivative Pdot, whereas L_{pwn} manifests a similar weak correlation with Pdot only; (3) The PWN photon index Gamma_{pwn} is positively correlated with L_{pwn} and L_{pwn}/Edot. We also found that the PWN X-ray luminosity is typically 1 to 10 times larger than that from the underlying pulsar, and the PWN photon indices span a range of ~1.5 to ~2. The statistic study of PWN spectral properties supports the particle wind model in which the X-ray emitting electrons are accelerated by the termination shock of the wind.Comment: 15 pages, 9 figures, 3 Tables, ApJ accepted version. Substantial revision, especially luminosity uncertainty taken into accounted and one fig added. Main conclusions unchange

Super-soft symmetry energy encountering non-Newtonian gravity in neutron stars

Considering the non-Newtonian gravity proposed in the grand unification theories, we show that the stability and observed global properties of neutron stars can not rule out the super-soft nuclear symmetry energies at supra-saturation densities. The degree of possible violation of the Inverse-Square-Law of gravity in neutron stars is estimated using an Equation of State (EOS) of neutron-rich nuclear matter consistent with the available terrestrial laboratory data.Comment: Version accepted by Physical Review Letter

A Critical Examination of Hypernova Remnant Candidates in M101. II. NGC 5471B

NGC 5471B has been suggested to contain a hypernova remnant because of its extraordinarily bright X-ray emission. To assess its true nature, we have obtained high-resolution images in continuum bands and nebular lines with the Hubble Space Telescope, and high-dispersion long-slit spectra with the Kitt Peak National Observatory 4-m echelle spectrograph. The images reveal three supernova remnant (SNR) candidates in the giant HII region NGC 5471, with the brightest one being the 77x60 pc shell in NGC 5471B. The Ha velocity profile of NGC 5471B can be decomposed into a narrow component (FWHM = 41 km/s) from the background HII region and a broad component (FWHM = 148 km/s) from the SNR shell. Using the brightness ratio of the broad to narrow components and the Ha flux measured from the WFPC2 Ha image, we derive an Ha luminosity of (1.4+-0.1)x10^39 ergs/s for the SNR shell. The [SII]6716,6731 doublet ratio of the broad velocity component is used to derive an electron density of ~700 cm^-3 in the SNR shell. The mass of the SNR shell is thus 4600+-500 Mo. With a \~330 km/s expansion velocity implied by the extreme velocity extent of the broad component, the kinetic energy of the SNR shell is determined to be 5x10^51 ergs. This requires an explosion energy greater than 10^52 ergs, which can be provided by one hypernova or multiple supernovae. Comparing to SNRs in nearby active star formation regions, the SNR shell in NGC 5471B appears truly unique and energetic. We conclude that the optical observations support the existence of a hypernova remnant in NGC 5471B.Comment: 27 pages, 9 figures, to appear in May 2002 issue of The Astronomical Journa