8,859 research outputs found
Optimal Rates for Random Fourier Features
Kernel methods represent one of the most powerful tools in machine learning
to tackle problems expressed in terms of function values and derivatives due to
their capability to represent and model complex relations. While these methods
show good versatility, they are computationally intensive and have poor
scalability to large data as they require operations on Gram matrices. In order
to mitigate this serious computational limitation, recently randomized
constructions have been proposed in the literature, which allow the application
of fast linear algorithms. Random Fourier features (RFF) are among the most
popular and widely applied constructions: they provide an easily computable,
low-dimensional feature representation for shift-invariant kernels. Despite the
popularity of RFFs, very little is understood theoretically about their
approximation quality. In this paper, we provide a detailed finite-sample
theoretical analysis about the approximation quality of RFFs by (i)
establishing optimal (in terms of the RFF dimension, and growing set size)
performance guarantees in uniform norm, and (ii) presenting guarantees in
() norms. We also propose an RFF approximation to derivatives of
a kernel with a theoretical study on its approximation quality.Comment: To appear at NIPS-201
The equation of state at high temperatures from lattice QCD
We present results for the equation of state upto previously unreachable,
high temperatures. Since the temperature range is quite large, a comparison
with perturbation theory can be done directly.Comment: 7 pages, 5 figures, Lattice 200
The nature of the finite temperature QCD transition as a function of the quark masses
The finite temperature QCD transition for physical quark masses is a
crossover. For smaller quark masses a first-order phase transition is expected.
Using Symanzik improved gauge and stout improved fermion action for 2+1 flavour
staggered QCD we give estimates/bounds for the phase line separating the
first-order region from the crossover one. The calculations are carried out on
two different lattice spacings. Our conclusion for the critical mass is for and for lattices.Comment: Talk presented at the XXV International Symposium on Lattice Field
Theory, July 30 - August 4 2007, Regensburg, Germany. 7 pages, 6 figure
CCD photometry and new models of 5 minor planets
We present new R filtered CCD observations of 5 faint and moderately faint
asteroids carried out between October, 1998 and January, 1999. The achieved
accuracy is between 0.01-0.03 mag, depending mainly on the target brightness.
The obtained sinodic periods and amplitudes:
683 Lanzia - 4.6+/-0.2 h, 0.13 mag; 725 Amanda - >3.0 h, >=0.40 mag; 852
Wladilena - 4.62+/-0.01 h, 0.32 mag (December, 1998) and 0.27 mag (January,
1999); 1627 Ivar - 4.80+/-0.01, 0.77 mag (December, 1998) and 0.92 mag
(January, 1999). The Near Earth Object 1998 PG unambiguously showed
doubly-periodic lightcurve, suggesting the possibility of a relatively fast
precession (P_1=1.3 h, P_2=5.3 h).
Collecting all data from the literature, we determined new models for 3 minor
planets. The resulting spin vectors and triaxial ellipsoids have been
calculated by an amplitude-method. Sidereal periods and senses of rotation were
calculated for two asteroids (683 and 1627) by a modified epoch-method. The
results are:
683 - lambda_p=15/195+/-25 deg, beta_p=52+/-15 deg, a/b=1.15+/-0.05,
b/c=1.05+/-0.05, P_sid=0.1964156+/-0.0000001 d, retrograde; 852 -
lambda_p=30/210+/-20 deg, beta_p=30+/-10 deg, a/b=2.3+/-0.3, b/c=1.2+/-0.2;
1627 - lambda_p=145/325+/-8 deg, beta_p=34+/-6 deg, a/b=2.0+/-0.1,
b/c=1.09+/-0.05, P_sid=0.1999154+/-0.0000003 d, retrograde. The obtained shape
of 1627 is in good agreement with radar images by Ostro et al. (1990).Comment: 8 pages, accepted for publication in Astronomy and Astrophysics
Suppl. Serie
Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
We obtain the exact non-perturbative solution of a scalar field theory
defined on a space with noncommuting position and momentum coordinates. The
model describes non-locally interacting charged particles in a background
magnetic field. It is an exactly solvable quantum field theory which has
non-trivial interactions only when it is defined with a finite ultraviolet
cutoff. We propose that small perturbations of this theory can produce solvable
models with renormalizable interactions.Comment: 9 Pages AMSTeX; Typos correcte
Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations
on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical
symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show
that the solutions imply an equivalence between instantons on R^{2n}_\theta x
S^2 and nonabelian vortices on R^{2n}_\theta, which can be interpreted as a
blowing-up of a chain of D0-branes on R^{2n}_\theta into a chain of spherical
D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is
described by a quiver gauge theory which can be formulated in terms of new
geometrical objects generalizing superconnections. This formalism enables the
explicit assignment of D0-brane charges in equivariant K-theory to the
instanton solutions.Comment: 45 pages, 4 figures; v2: minor correction
Lattice SU(3) thermodynamics and the onset of perturbative behaviour
We present the equation of state (pressure, trace anomaly, energy density and
entropy density) of the SU(3) gauge theory from lattice field theory in an
unprecedented precision and temperature range. We control both finite size and
cut-off effects. The studied temperature window () stretches
from the glueball dominated system into the perturbative regime, which allows
us to discuss the range of validity of these approaches. From the critical
couplings on fine lattices we get T_c/\Lambdamsbar=1.26(7) and use this ratio
to express the perturbative free energy in units. We also determine the
preferred renormalization scale of the Hard Thermal Loop scheme and we fit the
unknown order perturbative coefficient at extreme high temperatures
. We furthermore quantify the nonperturbative contribution to the
trace anomaly using two simple functional forms.Comment: 7 pages, Contribution to the The XXVIII International Symposium on
Lattice Field Theory; June 14 - 19, 2010, Villasimius, Sardinia, Ital
- …