111,717 research outputs found
On the efficiency of estimating penetrating rank on large graphs
P-Rank (Penetrating Rank) has been suggested as a useful measure of structural similarity that takes account of both incoming and outgoing edges in ubiquitous networks. Existing work often utilizes memoization to compute P-Rank similarity in an iterative fashion, which requires cubic time in the worst case. Besides, previous methods mainly focus on the deterministic computation of P-Rank, but lack the probabilistic framework that scales well for large graphs. In this paper, we propose two efficient algorithms for computing P-Rank on large graphs. The first observation is that a large body of objects in a real graph usually share similar neighborhood structures. By merging such objects with an explicit low-rank factorization, we devise a deterministic algorithm to compute P-Rank in quadratic time. The second observation is that by converting the iterative form of P-Rank into a matrix power series form, we can leverage the random sampling approach to probabilistically compute P-Rank in linear time with provable accuracy guarantees. The empirical results on both real and synthetic datasets show that our approaches achieve high time efficiency with controlled error and outperform the baseline algorithms by at least one order of magnitude
Optimal transfer of an unknown state via a bipartite operation
A fundamental task in quantum information science is to transfer an unknown
state from particle to particle (often in remote space locations) by
using a bipartite quantum operation . We suggest the power of
for quantum state transfer (QST) to be the maximal average
probability of QST over the initial states of particle and the
identifications of the state vectors between and . We find the QST power
of a bipartite quantum operations satisfies four desired properties between two
-dimensional Hilbert spaces. When and are qubits, the analytical
expressions of the QST power is given. In particular, we obtain the exact
results of the QST power for a general two-qubit unitary transformation.Comment: 6 pages, 1 figur
Monte-Carlo approach to calculate the proton stopping in warm dense matter within particle-in-cell simulations
A Monte-Carlo approach to proton stopping in warm dense matter is implemented
into an existing particle-in-cell code. The model is based on multiple
binary-collisions among electron-electron, electron-ion and ion-ion, taking
into account contributions from both free and bound electrons, and allows to
calculate particle stopping in much more natural manner. At low temperature
limit, when ``all'' electron are bounded at the nucleus, the stopping power
converges to the predictions of Bethe-Bloch theory, which shows good
consistency with data provided by the NIST. With the rising of temperatures,
more and more bound electron are ionized, thus giving rise to an increased
stopping power to cold matter, which is consistent with the report of a
recently experimental measurement [Phys. Rev. Lett. 114, 215002 (2015)]. When
temperature is further increased, with ionizations reaching the maximum,
lowered stopping power is observed, which is due to the suppression of
collision frequency between projected proton beam and hot plasmas in the
target.Comment: 6 pages, 4 figure
Evidence for contact delocalization in atomic scale friction
We analyze an advanced two-spring model with an ultra-low effective tip mass
to predict nontrivial and physically rich 'fine structure' in the atomic
stick-slip motion in Friction Force Microscopy (FFM) experiments. We
demonstrate that this fine structure is present in recent, puzzling
experiments. This shows that the tip apex can be completely or partially
delocalized, thus shedding new light on what is measured in FFM and, possibly,
what can happen with the asperities that establish the contact between
macroscopic sliding bodies.Comment: 4 pages text and 3 figure
Magneto-controlled nonlinear optical materials
We exploit theoretically a magneto-controlled nonlinear optical material
which contains ferromagnetic nanoparticles with a non-magnetic metallic
nonlinear shell in a host fluid. Such an optical material can have anisotropic
linear and nonlinear optical properties and a giant enhancement of
nonlinearity, as well as an attractive figure of merit.Comment: 11 pages, 2 figures. To be published in Appl. Phys. Let
Monte-Carlo approach to calculate the ionization of warm dense matter within particle-in-cell simulations
A physical model based on a Monte-Carlo approach is proposed to calculate the
ionization dynam- ics of warm dense matters (WDM) within particle-in-cell
simulations, and where the impact (col- lision) ionization (CI), electron-ion
recombination (RE) and ionization potential depression (IPD) by surrounding
plasmas are taken into consideration self-consistently. When compared with
other models, which are applied in the literature for plasmas near thermal
equilibrium, the temporal re- laxation of ionization dynamics can also be
simulated by the proposed model. Besides, this model is general and can be
applied for both single elements and alloys with quite different composi-
tions. The proposed model is implemented into a particle-in-cell (PIC) code,
with (final) ionization equilibriums sustained by competitions between CI and
its inverse process (i.e., RE). Comparisons between the full model and model
without IPD or RE are performed. Our results indicate that for bulk aluminium
in the WDM regime, i) the averaged ionization degree increases by including
IPD; while ii) the averaged ionization degree is significantly over estimated
when the RE is neglected. A direct comparison from the PIC code is made with
the existing models for the dependence of averaged ionization degree on thermal
equilibrium temperatures, and shows good agreements with that generated from
Saha-Boltzmann model or/and FLYCHK code.Comment: 7 pages, 4 figure
J_AW,WA functions in Passarino-Veltman reduction
In this paper we continue to study a special class of Passarino-Veltman
functions J arising at the reduction of infrared divergent box diagrams. We
describe a procedure of separation of two types of singularities, infrared and
mass singularities, which are absorbed in simple C0 functions. The infrared
divergences of C0's can be regularized then by any method: photon mass,
dimensionally or by the width of an unstable particle. Functions J, in turn,
are represented as certain linear combinations of the standard D0 and C0
Passarino-Veltman functions. The former are free of both types of singularities
and are expressed as explicit and compact linear combinations of logarithms and
dilogarithm functions. We present extensive comparisons of numerical results
with those obtained with the aid of the LoopTools package
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