269 research outputs found
Field theoretic approach to the counting problem of Hamiltonian cycles of graphs
A Hamiltonian cycle of a graph is a closed path that visits each site once
and only once. I study a field theoretic representation for the number of
Hamiltonian cycles for arbitrary graphs. By integrating out quadratic
fluctuations around the saddle point, one obtains an estimate for the number
which reflects characteristics of graphs well. The accuracy of the estimate is
verified by applying it to 2d square lattices with various boundary conditions.
This is the first example of extracting meaningful information from the
quadratic approximation to the field theory representation.Comment: 5 pages, 3 figures, uses epsf.sty. Estimates for the site entropy and
the gamma exponent indicated explicitl
Some Controversial Opinions on Software-Defined Data Plane Services
Several recent proposals, namely Software Defined Networks (SDN), Network Functions Virtualization (NFV) and Network Service Chaining (NSC), aim to transform the network into a programmable platform, focusing respectively on the control plane (SDN) and on the data plane (NFV/NSC). This paper sits on the same line of the NFV/NSC proposals but with a more long-term horizon, and it presents its considerations on some controversial aspects that arise when considering the programmability of the data plane. Particularly, this paper discusses the relevance of data plane vs control plane services, the importance of the hardware platform, and the necessity to standardize northbound and southbound interfaces in future software-defined data plane service
The effects of the pre-pulse on capillary discharge extreme ultraviolet laser
In the past few years collisionally pumped extreme ultraviolet (XUV) lasers
utilizing a capillary discharge were demonstrated. An intense current pulse is
applied to a gas filled capillary, inducing magnetic collapse (Z-pinch) and
formation of a highly ionized plasma column. Usually, a small current pulse
(pre-pulse) is applied to the gas in order to pre-ionize it prior to the onset
of the main current pulse. In this paper we investigate the effects of the
pre-pulse on a capillary discharge Ne-like Ar XUV laser (46.9nm). The
importance of the pre-pulse in achieving suitable initial conditions of the gas
column and preventing instabilities during the collapse is demonstrated.
Furthermore, measurements of the amplified spontaneous emission (ASE)
properties (intensity, duration) in different pre-pulse currents revealed
unexpected sensitivity. Increasing the pre-pulse current by a factor of two
caused the ASE intensity to decrease by an order of magnitude - and to nearly
disappear. This effect is accompanied by a slight increase in the lasing
duration. We attribute this effect to axial flow in the gas during the
pre-pulse.Comment: 4 pages, 4 figure
The Effect of Neutral Atoms on Capillary Discharge Z-pinch
We study the effect of neutral atoms on the dynamics of a capillary discharge
Z-pinch, in a regime for which a large soft-x-ray amplification has been
demonstrated. We extended the commonly used one-fluid magneto-hydrodynamics
(MHD) model by separating out the neutral atoms as a second fluid. Numerical
calculations using this extended model yield new predictions for the dynamics
of the pinch collapse, and better agreement with known measured data.Comment: 4 pages, 4 postscript figures, to be published in Phys. Rev. Let
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the
connective constant for self-avoiding walks on the hypercubic lattice .
The method is based on loop erasure and restoration, and does not require exact
enumeration data. Our bounds are best for high , and in fact agree with the
first four terms of the expansion for the connective constant. The bounds
are the best to date for dimensions , but do not produce good results
in two dimensions. For , respectively, our lower bound is within
2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0
Scaling of Self-Avoiding Walks in High Dimensions
We examine self-avoiding walks in dimensions 4 to 8 using high-precision
Monte-Carlo simulations up to length N=16384, providing the first such results
in dimensions on which we concentrate our analysis. We analyse the
scaling behaviour of the partition function and the statistics of
nearest-neighbour contacts, as well as the average geometric size of the walks,
and compare our results to -expansions and to excellent rigorous bounds
that exist. In particular, we obtain precise values for the connective
constants, , , ,
and give a revised estimate of . All of
these are by at least one order of magnitude more accurate than those
previously given (from other approaches in and all approaches in ).
Our results are consistent with most theoretical predictions, though in
we find clear evidence of anomalous -corrections for the scaling of
the geometric size of the walks, which we understand as a non-analytic
correction to scaling of the general form (not present in pure
Gaussian random walks).Comment: 14 pages, 2 figure
A new picture of the Lifshitz critical behavior
New field theoretic renormalization group methods are developed to describe
in a unified fashion the critical exponents of an m-fold Lifshitz point at the
two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close
to 8) situations. The general theory is illustrated for the N-vector phi^4
model describing a d-dimensional system. A new regularization and
renormalization procedure is presented for both types of Lifshitz behavior. The
anisotropic cases are formulated with two independent renormalization group
transformations. The description of the isotropic behavior requires only one
type of renormalization group transformation. We point out the conceptual
advantages implicit in this picture and show how this framework is related to
other previous renormalization group treatments for the Lifshitz problem. The
Feynman diagrams of arbitrary loop-order can be performed analytically provided
these integrals are considered to be homogeneous functions of the external
momenta scales. The anisotropic universality class (N,d,m) reduces easily to
the Ising-like (N,d) when m=0. We show that the isotropic universality class
(N,m) when m is close to 8 cannot be obtained from the anisotropic one in the
limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in
good agreement with recent Monte Carlo simulations for the ANNNI model.Comment: 48 pages, no figures, two typos fixe
Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization
We present a practical implementation of an optimal first-order method, due
to Nesterov, for large-scale total variation regularization in tomographic
reconstruction, image deblurring, etc. The algorithm applies to -strongly
convex objective functions with -Lipschitz continuous gradient. In the
framework of Nesterov both and are assumed known -- an assumption
that is seldom satisfied in practice. We propose to incorporate mechanisms to
estimate locally sufficient and during the iterations. The mechanisms
also allow for the application to non-strongly convex functions. We discuss the
iteration complexity of several first-order methods, including the proposed
algorithm, and we use a 3D tomography problem to compare the performance of
these methods. The results show that for ill-conditioned problems solved to
high accuracy, the proposed method significantly outperforms state-of-the-art
first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure
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