5,263 research outputs found
Euler characteristic and quadrilaterals of normal surfaces
Let be a compact 3-manifold with a triangulation . We give an
inequality relating the Euler characteristic of a surface normally embedded
in with the number of normal quadrilaterals in . This gives a relation
between a topological invariant of the surface and a quantity derived from its
combinatorial description. Secondly, we obtain an inequality relating the
number of normal triangles and normal quadrilaterals of , that depends on
the maximum number of tetrahedrons that share a vertex in .Comment: 7 pages, 1 figur
Theoretical description of a DNA-linked nanoparticle self-assembly
Nanoparticles tethered with DNA strands are promising building blocks for
bottom-up nanotechnology, and a theoretical understanding is important for
future development. Here we build on approaches developed in polymer physics to
provide theoretical descriptions for the equilibrium clustering and dynamics,
as well as the self-assembly kinetics of DNA-linked nanoparticles. Striking
agreement is observed between the theory and molecular modeling of DNA tethered
nanoparticles.Comment: Accepted for publication in Physical Review Letter
Mining Frequent Graph Patterns with Differential Privacy
Discovering frequent graph patterns in a graph database offers valuable
information in a variety of applications. However, if the graph dataset
contains sensitive data of individuals such as mobile phone-call graphs and
web-click graphs, releasing discovered frequent patterns may present a threat
to the privacy of individuals. {\em Differential privacy} has recently emerged
as the {\em de facto} standard for private data analysis due to its provable
privacy guarantee. In this paper we propose the first differentially private
algorithm for mining frequent graph patterns.
We first show that previous techniques on differentially private discovery of
frequent {\em itemsets} cannot apply in mining frequent graph patterns due to
the inherent complexity of handling structural information in graphs. We then
address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling
based algorithm. Unlike previous work on frequent itemset mining, our
techniques do not rely on the output of a non-private mining algorithm.
Instead, we observe that both frequent graph pattern mining and the guarantee
of differential privacy can be unified into an MCMC sampling framework. In
addition, we establish the privacy and utility guarantee of our algorithm and
propose an efficient neighboring pattern counting technique as well.
Experimental results show that the proposed algorithm is able to output
frequent patterns with good precision
On the unsteady behavior of turbulence models
Periodically forced turbulence is used as a test case to evaluate the
predictions of two-equation and multiple-scale turbulence models in unsteady
flows. The limitations of the two-equation model are shown to originate in the
basic assumption of spectral equilibrium. A multiple-scale model based on a
picture of stepwise energy cascade overcomes some of these limitations, but the
absence of nonlocal interactions proves to lead to poor predictions of the time
variation of the dissipation rate. A new multiple-scale model that includes
nonlocal interactions is proposed and shown to reproduce the main features of
the frequency response correctly
Autocorrelation of Random Matrix Polynomials
We calculate the autocorrelation functions (or shifted moments) of the
characteristic polynomials of matrices drawn uniformly with respect to Haar
measure from the groups U(N), O(2N) and USp(2N). In each case the result can be
expressed in three equivalent forms: as a determinant sum (and hence in terms
of symmetric polynomials), as a combinatorial sum, and as a multiple contour
integral. These formulae are analogous to those previously obtained for the
Gaussian ensembles of Random Matrix Theory, but in this case are identities for
any size of matrix, rather than large-matrix asymptotic approximations. They
also mirror exactly autocorrelation formulae conjectured to hold for
L-functions in a companion paper. This then provides further evidence in
support of the connection between Random Matrix Theory and the theory of
L-functions
Lower order terms in the full moment conjecture for the Riemann zeta function
We describe an algorithm for obtaining explicit expressions for lower terms
for the conjectured full asymptotics of the moments of the Riemann zeta
function, and give two distinct methods for obtaining numerical values of these
coefficients. We also provide some numerical evidence in favour of the
conjecture.Comment: 37 pages, 4 figure
Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects
We study the friction between a flat solid surface where polymer chains have
been end-grafted and a cross-linked elastomer at low sliding velocity. The
contribution of isolated grafted chains' penetration in the sliding elastomer
has been early identified as a weakly velocity dependent pull-out force. Recent
experiments have shown that the interactions between the grafted chains at high
grafting density modify the friction force by grafted chain. We develop here a
simple model that takes into account those interactions and gives a limit
grafting density beyond which the friction no longer increases with the
grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter
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