28,991 research outputs found
An interior point algorithm for minimum sum-of-squares clustering
Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds
National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec
Suppression of hole-hole scattering in GaAs/AlGaAs heterostructures under uniaxial compression
Resistance, magnetoresistance and their temperature dependencies have been
investigated in the 2D hole gas at a [001] p-GaAs/AlGaAs
heterointerface under [110] uniaxial compression. Analysis performed in the
frame of hole-hole scattering between carriers in the two spin splitted
subbands of the ground heavy hole state indicates, that h-h scattering is
strongly suppressed by uniaxial compression. The decay time of the
relative momentum reveals 4.5 times increase at a uniaxial compression of 1.3
kbar.Comment: 5 pages, 3 figures. submitted to Phys.Rev.
Structure, phase behavior and inhomogeneous fluid properties of binary dendrimer mixtures
The effective pair potentials between different kinds of dendrimers in
solution can be well approximated by appropriate Gaussian functions. We find
that in binary dendrimer mixtures the range and strength of the effective
interactions depend strongly upon the specific dendrimer architecture. We
consider two different types of dendrimer mixtures, employing the Gaussian
effective pair potentials, to determine the bulk fluid structure and phase
behavior. Using a simple mean field density functional theory (DFT) we find
good agreement between theory and simulation results for the bulk fluid
structure. Depending on the mixture, we find bulk fluid-fluid phase separation
(macro-phase separation) or micro-phase separation, i.e., a transition to a
state characterized by undamped periodic concentration fluctuations. We also
determine the inhomogeneous fluid structure for confinement in spherical
cavities. Again, we find good agreement between the DFT and simulation results.
For the dendrimer mixture exhibiting micro-phase separation, we observe rather
striking pattern formation under confinement.Comment: 8 pages, 10 figure
Some properties of two Nambu--Jona-Lasinio -type models with inputs from lattice QCD
We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero
chemical potential. The calculations are performed in the light and strange
quark sectors (, , ), which includes the 't Hooft instanton induced
interaction term that breaks the axial symmetry, and the quarks are coupled to
the (spatially constant) temporal background gauge field. On one hand, a
special attention is payed to the critical end point (CEP). The strength of the
flavor-mixing interaction alters the CEP location, since when it becomes weaker
the CEP moves to low temperatures and can even disappear. On the other hand, we
also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type
model and the Landau gauge gluon propagator. Possible links between the
quenched gluon propagator and low energy hadronic phenomenology are
investigated.Comment: Contribution to the International Meeting "Excited QCD", Peniche,
Portugal, 06 - 12 May 201
Continuous loading of S calcium atoms into an optical dipole trap
We demonstrate an efficient scheme for continuous trap loading based upon
spatially selective optical pumping. We discuss the case of S
calcium atoms in an optical dipole trap (ODT), however, similar strategies
should be applicable to a wide range of atomic species. Our starting point is a
reservoir of moderately cold (K) metastable
P-atoms prepared by means of a magneto-optic trap (triplet-MOT). A
focused 532 nm laser beam produces a strongly elongated optical potential for
S-atoms with up to 350 K well depth. A weak focused laser beam
at 430 nm, carefully superimposed upon the ODT beam, selectively pumps the
P-atoms inside the capture volume to the singlet state, where they
are confined by the ODT. The triplet-MOT perpetually refills the capture volume
with P-atoms thus providing a continuous stream of cold atoms into
the ODT at a rate of s. Limited by evaporation loss, in 200 ms we
typically load atoms with an initial radial temperature of 85
K. After terminating the loading we observe evaporation during 50 ms
leaving us with atoms at radial temperatures close to 40 K and a
peak phase space density of . We point out that a
comparable scheme could be employed to load a dipole trap with
P-atoms.Comment: 4 pages, 4 figure
Gas-liquid critical parameters of asymmetric models of ionic fluids
The effects of size and charge asymmetry on the gas-liquid critical
parameters of a primitive model (PM) of ionic fluids are studied within the
framework of the statistical field theory based on the collective variables
method. Recently, this approach has enabled us to obtain the correct trends of
the both critical parameters of the equisize charge-asymmetric PM without
assuming ionic association. In this paper we focus on the general case of an
asymmetric PM characterized by the two parameters: hard-sphere diameter-,
and charge, , ratios of the
two ionic species. We derive an explicit expression for the chemical potential
conjugate to the order parameter which includes the effects of correlations up
to the third order. Based on this expression we consider the three versions of
PM: a monovalent size-asymmetric PM (, ), an equisize
charge-asymmetric PM (, ) and a size- and charge-asymmetric
PM (, ). Similar to simulations, our theory predicts that
the critical temperature and the critical density decrease with the increase of
size asymmetry. Regarding the effects of charge asymmetry, we obtain the
correct trend of the critical temperature with , while the trend of the
critical density obtained in this approximation is inconsistent with
simulations, as well as with our previous results found in the higher-order
approximation. We expect that the consideration of the higher-order
correlations will lead to the correct trend of the critical density with charge
asymmetry.Comment: 23 pages, 6 figure
A reduced coupled-mode description for the electron-ion energy relaxation in dense matter
We present a simplified model for the electron-ion energy relaxation in dense two-temperature systems that includes the effects of coupled collective modes. It also extends the standard Spitzer result to both degenerate and strongly coupled systems. Starting from the general coupled-mode description, we are able to solve analytically for the temperature relaxation time in warm dense matter and strongly coupled plasmas. This was achieved by decoupling the electron-ion dynamics and by representing the ion response in terms of the mode frequencies. The presented reduced model allows for a fast description of temperature equilibration within hydrodynamic simulations and an easy comparison for experimental investigations. For warm dense matter, both fluid and solid, the model gives a slower electron-ion equilibration than predicted by the classical Spitzer result
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