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

On the frequency and remnants of Hypernovae

Under the hypothesis that some fraction of massive stellar core collapses give rise to unusually energetic events, termed hypernovae, I examine the required rates assuming some fraction of such events yield gamma ray bursts. I then discuss evidence from studies of pulsars and r-process nucleosynthesis that independently suggests the existence of a class of unusually energetic events. Finally I describe a scenario which links these different lines of evidence as supporting the hypernova hypothesis.Comment: TeX, To appear in ApJ Letter

Resonant absorption at the vortex-core states in d-wave superconductors

We predict a resonant microwave absorption on collective vortex modes in a superclean d-wave superconductor. Energies of the collective modes are multiples of the distance between the exact quantum levels of bound states in the vortex core at lower temperatures and involve delocalized states for higher temperatures. We calculate the vortex mass in a d-wave superconductor as a response to a slow acceleration of the vortex. The universal flux-flow regime predicted by N. Kopnin and G. Volovik [Phys. Rev. Lett. 79, 1377 (1997)] is discussed in more detail.Comment: RevTex file, 10 page

Estimate solar contribution to the global surface warming using the ACRIM TSI satellite composite

We study, by using a wavelet decomposition methodology, the solar signature on global surface temperature data using the ACRIM total solar irradiance satellite composite by Willson and Mordvinov. These data present a +0.047%/decade trend between minima during solar cycles 21-23 (1980-2002). We estimate that the ACRIM upward trend might have minimally contributed $\sim$10-30% of the global surface temperature warming over the period 1980-2002

Real-Time Data Processing in the Muon System of the D0 Detector

This paper presents a real-time application of the 16-bit fixed point Digital Signal Processors (DSPs), in the Muon System of the D0 detector located at the Fermilab Tevatron, presently the world's highest-energy hadron collider. As part of the Upgrade for a run beginning in the year 2000, the system is required to process data at an input event rate of 10 KHz without incurring significant deadtime in readout. The ADSP21csp01 processor has high I/O bandwidth, single cycle instruction execution and fast task switching support to provide efficient multisignal processing. The processor's internal memory consists of 4K words of Program Memory and 4K words of Data Memory. In addition there is an external memory of 32K words for general event buffering and 16K words of Dual Port Memory for input data queuing. This DSP fulfills the requirement of the Muon subdetector systems for data readout. All error handling, buffering, formatting and transferring of the data to the various trigger levels of the data acquisition system is done in software. The algorithms developed for the system complete these tasks in about 20 microseconds per event.Comment: 4 pages, Presented and published at the 11th IEEE NPSS Real Time Conference, held at Santa Fe, New Mexico, USA, from June 14-18, 199

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods

The short--time self diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction. For low rod concentrations the correction to the Einstein diffusion constant of the sphere is a linear function of the rod volume fraction with the slope proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two--body hydrodynamic interactions are calculated using the so--called bead model in which the rod is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated numerically using the multipole method. Also an analytical expression for the diffusion coefficient as a function of the rod aspect ratio is derived in the limit of very long rods. We show that in this limit the correction to the Einstein diffusion constant does not depend on the size of the tracer sphere. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.Comment: 11 pages, 6 figure

Parity Violation in Neutrino Transport and the Origin of Pulsar Kicks

In proto-neutron stars with strong magnetic fields, the neutrino-nucleon scattering/absorption cross sections depend on the direction of neutrino momentum with respect to the magnetic field axis, a manifestation of parity violation in weak interactions. We study the deleptonization and thermal cooling (via neutrino emission) of proto-neutron stars in the presence of such asymmetric neutrino opacities. Significant asymmetry in neutrino emission is obtained due to multiple neutrino-nucleon scatterings. For an ordered magnetic field threading the neutron star interior, the fractional asymmetry in neutrino emission is about $0.006 (B/10^{14}G)$, corresponding to a pulsar kick velocity of about $200 (B/10^{14}G)$ km/s for a total radiated neutrino energy of $3\times 10^{53}$ erg.Comment: AASTeX, 10 pages including 2 ps figures; ApJ Letter in press (March 10, 1998). Shortened to agree with the published versio