540 research outputs found
Independent individual addressing of multiple neutral atom qubits with a MEMS beam steering system
We demonstrate a scalable approach to addressing multiple atomic qubits for
use in quantum information processing. Individually trapped 87Rb atoms in a
linear array are selectively manipulated with a single laser guided by a MEMS
beam steering system. Single qubit oscillations are shown on multiple sites at
frequencies of ~3.5 MHz with negligible crosstalk to neighboring sites.
Switching times between the central atom and its closest neighbor were measured
to be 6-7 us while moving between the central atom and an atom two trap sites
away took 10-14 us.Comment: 9 pages, 3 figure
A construction of Frobenius manifolds with logarithmic poles and applications
A construction theorem for Frobenius manifolds with logarithmic poles is
established. This is a generalization of a theorem of Hertling and Manin. As an
application we prove a generalization of the reconstruction theorem of
Kontsevich and Manin for projective smooth varieties with convergent
Gromov-Witten potential. A second application is a construction of Frobenius
manifolds out of a variation of polarized Hodge structures which degenerates
along a normal crossing divisor when certain generation conditions are
fulfilled.Comment: 46 page
Critical points and resonance of hyperplane arrangements
If F is a master function corresponding to a hyperplane arrangement A and a
collection of weights y, we investigate the relationship between the critical
set of F, the variety defined by the vanishing of the one-form w = d log F, and
the resonance of y. For arrangements satisfying certain conditions, we show
that if y is resonant in dimension p, then the critical set of F has
codimension at most p. These include all free arrangements and all rank 3
arrangements.Comment: revised version, Canadian Journal of Mathematics, to appea
Chamber basis of the Orlik-Solomon algebra and Aomoto complex
We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so
called chamber basis. We consider structure constants of the Orlik-Solomon
algebra with respect to the chamber basis and prove that these structure
constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page
Differential Forms on Log Canonical Spaces
The present paper is concerned with differential forms on log canonical
varieties. It is shown that any p-form defined on the smooth locus of a variety
with canonical or klt singularities extends regularly to any resolution of
singularities. In fact, a much more general theorem for log canonical pairs is
established. The proof relies on vanishing theorems for log canonical varieties
and on methods of the minimal model program. In addition, a theory of
differential forms on dlt pairs is developed. It is shown that many of the
fundamental theorems and techniques known for sheaves of logarithmic
differentials on smooth varieties also hold in the dlt setting.
Immediate applications include the existence of a pull-back map for reflexive
differentials, generalisations of Bogomolov-Sommese type vanishing results, and
a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared
in Publications math\'ematiques de l'IH\'ES. The final publication is
available at http://www.springerlink.co
The Waldschmidt constant for squarefree monomial ideals
Given a squarefree monomial ideal , we show
that , the Waldschmidt constant of , can be expressed as
the optimal solution to a linear program constructed from the primary
decomposition of . By applying results from fractional graph theory, we can
then express in terms of the fractional chromatic number of
a hypergraph also constructed from the primary decomposition of . Moreover,
expressing as the solution to a linear program enables us
to prove a Chudnovsky-like lower bound on , thus verifying a
conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree
case. As an application, we compute the Waldschmidt constant and the resurgence
for some families of squarefree monomial ideals. For example, we determine both
constants for unions of general linear subspaces of with few
components compared to , and we find the Waldschmidt constant for the
Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches
Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of
Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February
2015. Comments are welcome. Revised version corrects some typos, updates the
references, and clarifies some hypotheses. To appear in the Journal of
Algebraic Combinatoric
The class of the locus of intermediate Jacobians of cubic threefolds
We study the locus of intermediate Jacobians of cubic threefolds within the
moduli space of complex principally polarized abelian fivefolds, and its
generalization to arbitrary genus - the locus of abelian varieties with a
singular odd two-torsion point on the theta divisor. Assuming that this locus
has expected codimension (which we show to be true for genus up to 5), we
compute the class of this locus, and of is closure in the perfect cone toroidal
compactification, in the Chow, homology, and the tautological ring.
We work out the cases of genus up to 5 in detail, obtaining explicit
expressions for the classes of the closures of the locus of products of an
elliptic curve and a hyperelliptic genus 3 curve, in moduli of principally
polarized abelian fourfolds, and of the locus of intermediate Jacobians in
genus 5. In the course of our computation we also deal with various
intersections of boundary divisors of a level toroidal compactification, which
is of independent interest in understanding the cohomology and Chow rings of
the moduli spaces.Comment: v2: new section 9 on the geometry of the boundary of the locus of
intermediate Jacobians of cubic threefolds. Final version to appear in
Invent. Mat
A Class of Topological Actions
We review definitions of generalized parallel transports in terms of
Cheeger-Simons differential characters. Integration formulae are given in terms
of Deligne-Beilinson cohomology classes. These representations of parallel
transport can be extended to situations involving distributions as is
appropriate in the context of quantized fields.Comment: 41 pages, no figure
Enrichment analysis of Alu elements with different spatial chromatin proximity in the human genome
Transposable elements (TEs) have no longer been totally considered as “junk DNA” for quite a time since the continual discoveries of their multifunctional roles in eukaryote genomes. As one of the most important and abundant TEs that still active in human genome, Alu, a SINE family, has demonstrated its indispensable regulatory functions at sequence level, but its spatial roles are still unclear. Technologies based on 3C(chromosomeconformation capture) have revealed the mysterious three-dimensional structure of chromatin, and make it possible to study the distal chromatin interaction in the genome. To find the role TE
playing in distal regulation in human genome, we compiled the new released Hi-C data, TE annotation, histone marker annotations, and the genome-wide methylation data to operate correlation analysis, and found that the density of Alu elements showed a strong positive correlation with the level of chromatin interactions (hESC: r=0.9, P<2.2×1016; IMR90 fibroblasts: r = 0.94, P < 2.2 × 1016) and also have a significant positive correlation withsomeremote functional DNA elements like enhancers and promoters (Enhancer: hESC: r=0.997, P=2.3×10−4; IMR90: r=0.934, P=2×10−2; Promoter: hESC: r = 0.995, P = 3.8 × 10−4; IMR90: r = 0.996, P = 3.2 × 10−4). Further investigation involving GC content and methylation status showed the GC content of Alu covered sequences shared a similar pattern with that of the overall sequence, suggesting that Alu elements also function as the GC nucleotide and CpG site provider. In all, our results suggest that the Alu elements may act as an alternative parameter to evaluate the Hi-C data, which is confirmed by the correlation analysis of Alu elements and histone markers. Moreover, the GC-rich Alu sequence can bring high GC content and methylation flexibility to the regions with more distal chromatin contact, regulating the transcription of tissue-specific genes
Surface-functionalization with NFL peptide of Lipid NanoCapsules LNC: preferential entry into human glioblastoma cells
Glioblastoma (GBM) is one of the most fatal brain cancers with median survival of only 14.6 months. Hence, more efficacious therapies are necessary. Ferrocifen (FcTriOH) is an organometallic antitumor compound, selectively active on cancer cells [1]. However, this metallocomplexe is highly insoluble in water, requiring a formulation stage before being in vivo administered. Lipid nanocapsules (LNC), prepared via a solvent free process of emulsion phase inversion, could be a suitable vehicle for FcTriOH [2]. Moreover, NFL peptide is able to enter massively into glioblastoma cells, and poorly in healthy neurons and astrocytes (NHA) [3]. Indeed, the aim of the study was to evaluate the effect of the surface-functionalizing NFL concentrations on LNC uptake in U87MG human GBM cells. Moreover, FcTriOH was encapsulated in LNC and their in vitro efficacy on U87MG cells was evaluated. Finally, in vivo antitumor effect was evaluated in ectopic and orthotopic murine U87MG tumor models.
Fluorescent LNC (F1), LNC with 0.86% w/w and LNC with 2.58% w/w surface-adsorbed NFL (F2 and F3 respectively) were prepared and characterized. FACS analysis revealed that cellular uptake of F3 into U87MG cells was 31.5 and 1.6-folds higher after 6 h compared to F1 and F2 respectively. Moreover, uptake of F3 was significantly higher in the GBM cells compared to NHA, whereas F1 was internalized preferentially in NHA. Uptake of F3 in U87MG cells was energy dependent. Macropinocytosis was possibly the major uptake pathway, followed by clathrin-dependent endocytosis.
Then, FcTriOH loaded LNCs have been successfully prepared with a drug loading of 2.4 % and an encapsulation efficacy of 99 %. MTS assay on U87MG cells revealed an IC50 of 0.46 µM for F3-FcTriOH (free FcTriOH: IC50 = 1.31 µM).
Preliminary in vivo experiments on subcutaneous U87MG tumor bearing nude mice showed significantly reduced relative tumor volume after two intravenous injections of F1-FcTriOH and F3-FcTriOH compared to saline. Moreover, intracranial administration of F3/F3-FcTriOH in orthotopic U87MG tumor bearing mice revealed 2 to 3-folds higher apparent diffusion coefficients (ADC) near the injection site in diffusion tensor imaging, compared to F1/F1-FcTriOH. Although dose adjustment will be necessary to avoid toxic effects, the results are promising as therapy induced increased ADC values could indicate possible cell necrosis/lysis.
References
[1] Laine A.L. et al. (2014), Nanomedicine, 10, pp.1667-1677.
[2] Heurtault B. et al. (2003), EJPS, 8, pp. 55-61.
[3] Balzeau J. et al. (2013), Biomaterials, 34, pp.3381-3389
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