49,442 research outputs found
Dynamic Graph Stream Algorithms in Space
In this paper we study graph problems in dynamic streaming model, where the
input is defined by a sequence of edge insertions and deletions. As many
natural problems require space, where is the number of
vertices, existing works mainly focused on designing space
algorithms. Although sublinear in the number of edges for dense graphs, it
could still be too large for many applications (e.g. is huge or the graph
is sparse). In this work, we give single-pass algorithms beating this space
barrier for two classes of problems.
We present space algorithms for estimating the number of connected
components with additive error and
-approximating the weight of minimum spanning tree, for any
small constant . The latter improves previous
space algorithm given by Ahn et al. (SODA 2012) for connected graphs with
bounded edge weights.
We initiate the study of approximate graph property testing in the dynamic
streaming model, where we want to distinguish graphs satisfying the property
from graphs that are -far from having the property. We consider
the problem of testing -edge connectivity, -vertex connectivity,
cycle-freeness and bipartiteness (of planar graphs), for which, we provide
algorithms using roughly space, which is
for any constant .
To complement our algorithms, we present space
lower bounds for these problems, which show that such a dependence on
is necessary.Comment: ICALP 201
Analytic properties of force-free jets in the Kerr spacetime -- III: uniform field solution
The structure of steady axisymmetric force-free magnetosphere of a Kerr black
hole (BH) is governed by a second-order partial differential equation of
depending on two "free" functions and ,
where is the component of the vector potential of the
electromagnetic field, is the angular velocity of the magnetic field
lines and is the poloidal electric current. In this paper, we investigate
the solution uniqueness. Taking asymptotically uniform field as an example,
analytic studies imply that there are infinitely many solutions approaching
uniform field at infinity, while only a unique one is found in general
relativistic magnetohydrodynamic simulations. To settle down the disagreement,
we reinvestigate the structure of the governing equation and numerically solve
it with given constraint condition and boundary condition. We find that the
constraint condition (field lines smoothly crossing the light surface (LS)) and
boundary conditions at horizon and at infinity are connected via radiation
conditions at horizon and at infinity, rather than being independent. With
appropriate constraint condition and boundary condition, we numerically solve
the governing equation and find a unique solution. Contrary to naive
expectation, our numerical solution yields a discontinuity in the angular
velocity of the field lines and a current sheet along the last field line
crossing the event horizon. We also briefly discuss the applicability of the
perturbation approach to solving the governing equation
A New Technique for the Design of Multi-Phase Voltage Controlled Oscillators
© 2017 World Scientific Publishing Company.In this work, a novel circuit structure for second-harmonic multi-phase voltage controlled oscillator (MVCO) is presented. The proposed MVCO is composed of (Formula presented.) ((Formula presented.) being an integer number and (Formula presented.)2) identical inductor–capacitor ((Formula presented.)) tank VCOs. In theory, this MVCO can provide 2(Formula presented.) different phase sinusoidal signals. A six-phase VCO based on the proposed structure is designed in a TSMC 0.18(Formula presented.)um CMOS process. Simulation results show that at the supply voltage of 0.8(Formula presented.)V, the total power consumption of the six-phase VCO circuit is about 1(Formula presented.)mW, the oscillation frequency is tunable from 2.3(Formula presented.)GHz to 2.5(Formula presented.)GHz when the control voltage varies from 0(Formula presented.)V to 0.8(Formula presented.)V, and the phase noise is lower than (Formula presented.)128(Formula presented.)dBc/Hz at 1(Formula presented.)MHz offset frequency. The proposed MVCO has lower phase noise, lower power consumption and more outputs than other related works in the literature.Peer reviewedFinal Accepted Versio
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