657 research outputs found
Fourier Magnetic Imaging with Nanoscale Resolution and Compressed Sensing Speed-up using Electronic Spins in Diamond
Optically-detected magnetic resonance using Nitrogen Vacancy (NV) color
centres in diamond is a leading modality for nanoscale magnetic field imaging,
as it provides single electron spin sensitivity, three-dimensional resolution
better than 1 nm, and applicability to a wide range of physical and biological
samples under ambient conditions. To date, however, NV-diamond magnetic imaging
has been performed using real space techniques, which are either limited by
optical diffraction to 250 nm resolution or require slow, point-by-point
scanning for nanoscale resolution, e.g., using an atomic force microscope,
magnetic tip, or super-resolution optical imaging. Here we introduce an
alternative technique of Fourier magnetic imaging using NV-diamond. In analogy
with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic
field gradients to phase-encode spatial information on NV electronic spins in
wavenumber or k-space followed by a fast Fourier transform to yield real-space
images with nanoscale resolution, wide field-of-view (FOV), and compressed
sensing speed-up.Comment: 31 pages, 10 figure
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
We show that the zeroth cohomology of M. Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber
operad. They are parameterized by grt_1, up to one class (or two, depending on
the definitions). More generally, the homotopy derivations of the (non-unital)
E_n operads may be expressed through the cohomology of a suitable graph
complex. Our methods also give a second proof of a result of H. Furusho,
stating that the pentagon equation for grt_1-elements implies the hexagon
equation
On 3d extensions of AGT relation
An extension of the AGT relation from two to three dimensions begins from
connecting the theory on domain wall between some two S-dual SYM models with
the 3d Chern-Simons theory. The simplest kind of such a relation would
presumably connect traces of the modular kernels in 2d conformal theory with
knot invariants. Indeed, the both quantities are very similar, especially if
represented as integrals of the products of quantum dilogarithm functions.
However, there are also various differences, especially in the "conservation
laws" for integration variables, which hold for the monodromy traces, but not
for the knot invariants. We also discuss another possibility: interpretation of
knot invariants as solutions to the Baxter equations for the relativistic Toda
system. This implies another AGT like relation: between 3d Chern-Simons theory
and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence of partial sums, but also explicit estimates
for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of
Mathematical Physic
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
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
Single Molecule Statistics and the Polynucleotide Unzipping Transition
We present an extensive theoretical investigation of the mechanical unzipping
of double-stranded DNA under the influence of an applied force. In the limit of
long polymers, there is a thermodynamic unzipping transition at a critical
force value of order 10 pN, with different critical behavior for homopolymers
and for random heteropolymers. We extend results on the disorder-averaged
behavior of DNA's with random sequences to the more experimentally accessible
problem of unzipping a single DNA molecule. As the applied force approaches the
critical value, the double-stranded DNA unravels in a series of discrete,
sequence-dependent steps that allow it to reach successively deeper energy
minima. Plots of extension versus force thus take the striking form of a series
of plateaus separated by sharp jumps. Similar qualitative features should
reappear in micromanipulation experiments on proteins and on folded RNA
molecules. Despite their unusual form, the extension versus force curves for
single molecules still reveal remnants of the disorder-averaged critical
behavior. Above the transition, the dynamics of the unzipping fork is related
to that of a particle diffusing in a random force field; anomalous,
disorder-dominated behavior is expected until the applied force exceeds the
critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure
Differential Regulation of Adhesion Complex Turnover by ROCK1 and ROCK2
ROCK1 and ROCK2 are serine/threonine kinases that function downstream of the small GTP-binding protein RhoA. Rho signalling via ROCK regulates a number of cellular functions including organisation of the actin cytoskeleton, cell adhesion and cell migration.In this study we use RNAi to specifically knockdown ROCK1 and ROCK2 and analyse their role in assembly of adhesion complexes in human epidermal keratinocytes. We observe that loss of ROCK1 inhibits signalling via focal adhesion kinase resulting in a failure of immature adhesion complexes to form mature stable focal adhesions. In contrast, loss of ROCK2 expression results in a significant reduction in adhesion complex turnover leading to formation of large, stable focal adhesions. Interestingly, loss of either ROCK1 or ROCK2 expression significantly impairs cell migration indicating both ROCK isoforms are required for normal keratinocyte migration.ROCK1 and ROCK2 have distinct and separate roles in adhesion complex assembly and turnover in human epidermal keratinocytes
Lithic technological responses to Late Pleistocene glacial cycling at Pinnacle Point Site 5-6, South Africa
There are multiple hypotheses for human responses to glacial cycling in the Late Pleistocene, including changes in population size, interconnectedness, and mobility. Lithic technological analysis informs us of human responses to environmental change because lithic assemblage characteristics are a reflection of raw material transport, reduction, and discard behaviors that depend on hunter-gatherer social and economic decisions. Pinnacle Point Site 5-6 (PP5-6), Western Cape, South Africa is an ideal locality for examining the influence of glacial cycling on early modern human behaviors because it preserves a long sequence spanning marine isotope stages (MIS) 5, 4, and 3 and is associated with robust records of paleoenvironmental change. The analysis presented here addresses the question, what, if any, lithic assemblage traits at PP5-6 represent changing behavioral responses to the MIS 5-4-3 interglacial-glacial cycle? It statistically evaluates changes in 93 traits with no a priori assumptions about which traits may significantly associate with MIS. In contrast to other studies that claim that there is little relationship between broad-scale patterns of climate change and lithic technology, we identified the following characteristics that are associated with MIS 4: increased use of quartz, increased evidence for outcrop sources of quartzite and silcrete, increased evidence for earlier stages of reduction in silcrete, evidence for increased flaking efficiency in all raw material types, and changes in tool types and function for silcrete. Based on these results, we suggest that foragers responded to MIS 4 glacial environmental conditions at PP5-6 with increased population or group sizes, 'place provisioning', longer and/or more intense site occupations, and decreased residential mobility. Several other traits, including silcrete frequency, do not exhibit an association with MIS. Backed pieces, once they appear in the PP5-6 record during MIS 4, persist through MIS 3. Changing paleoenvironments explain some, but not all temporal technological variability at PP5-6.Social Science and Humanities Research Council of Canada; NORAM; American-Scandinavian Foundation; Fundacao para a Ciencia e Tecnologia [SFRH/BPD/73598/2010]; IGERT [DGE 0801634]; Hyde Family Foundations; Institute of Human Origins; National Science Foundation [BCS-9912465, BCS-0130713, BCS-0524087, BCS-1138073]; John Templeton Foundation to the Institute of Human Origins at Arizona State Universit
- …