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

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

The Thorium Molten Salt Reactor : Moving on from the MSBR

A re-evaluation of the Molten Salt Breeder Reactor concept has revealed problems related to its safety and to the complexity of the reprocessing considered. A reflection is carried out anew in view of finding innovative solutions leading to the Thorium Molten Salt Reactor concept. Several main constraints are established and serve as guides to parametric evaluations. These then give an understanding of the influence of important core parameters on the reactor's operation. The aim of this paper is to discuss this vast research domain and to single out the Molten Salt Reactor configurations that deserve further evaluation.Comment: 11 pages, 8 figures, 6 table

Correlations of the elements of the neutrino mass matrix

Assuming Majorana nature of neutrinos, we re-investigate, in the light of the recent measurement of the reactor mixing angle, the allowed ranges for the absolute values of the elements of the neutrino mass matrix in the basis where the charged-lepton mass matrix is diagonal. Apart from the derivation of upper and lower bounds on the values of the matrix elements, we also study their correlations. Moreover, we analyse the sensitivity of bounds and correlations to the global fit results of the neutrino oscillation parameters which are available in the literature.Comment: 37 pages, 146 figures, minor corrections, 17 additional figures, version for publication in JHE

Pedestal properties of H-modes with negative triangularity using the EPED-CH model

The EPED model has been designed to predict the pedestal height and width from a minimal set of parameters and using the stability of the pedestal region for global MHD peeling-ballooning (P-B) modes as well as local kinetic ballooning modes (KBMs). This approach has been validated for type-I ELMy H-modes and quiescent H-modes (QH) but can also be used for other types of H-modes where it usually sets an upper limit on the achievable pedestal height. Using the recently developed EPED-like model called EPED-CH and based on the equilibrium codes CHEASE and CAXE and the MHD stability code KINX, we investigate in this work the effect of negative triangularity on the pedestal structure. Our simulation results confirm the experimental results from TCV where a reduction of the pedestal height was observed when going from positive to negative top triangularity. This was interpreted as a degradation of the peeling-ballooning stability due to the closed access to the second stability region for ballooning modes in the case of negative triangularity. This effect is further enhanced by the coupling to the KBM stability criterion in EPED simulations. The novel concept of the negative triangularity tokamak (a DEMO-sized machine) is also investigated. Again a strong reduction of the pedestal height and width is observed going from positive to negative triangularity for upâdown symmetric equilibria. The pedestal height is also reduced going to more upâdown asymmetric cases. The beneficial effect of the global β value on the pedestal height, which is linked to the second stability access, is strongly reduced for negative triangularity

Intermittent or Continuous Therapy of Experimental Meningitis Due to Streptococcus pneumoniae in Rabbits: Preliminary Observations on the Postantibiotic Effect in Vivo

The relative effectiveness of bolus vs. constant intravenous administration of equivalent doses of penicillin G in killing bacteria in vivo was studied in a rabbit model of meningitis due to Streptococcus pneumoniae. Samples of cerebrospinal fluid (CSF) and serum were obtained from 30 rabbits at intervals of ⩽8 hr after treatment for determination of antibiotic concentrations and titers of viable bacteria in the CSF. When penicillin G was given by continuous infusion (105 units/hr after an initial l05-unit loading dose), concentrations of drug in serum and CSF reached a steady state in 1 hr. With intermittent bolus administration of 4 × 105 units every 4 hr, higher peak and lower trough concentrations were achieved, and these concentrations paralleled those in the CSF. Although an initial acceleration in bactericidal rate was observed with the bolus infusion between the first and second hour of therapy, after the second hour the rate of bacterial killing was identical for the two methods of administration. The duration of therapy required for sterilization of the CSF was dependent only on the bacterial count before treatment and not on the mode of drug administration. The effect of single bolus intravenous administration of ampicillin was examined in experimental pneumococcal meningitis. Ampicillin was given at various dosages (3.25-62.5 mg/kg), and frequent samples of CSF were obtained for determination of concentrations of pneumococci and ampicillin. A long postantibiotic effect was observed in the CSF of all animals, and this effect consistently was longer than that observed in vitr

Fast Thorium Molten Salt Reactors started with Plutonium

One of the pending questions concerning Molten Salt Reactors based on the 232Th/233U fuel cycle is the supply of the fissile matter, and as a consequence the deployment possibilities of a fleet of Molten Salt Reactors, since 233U does not exist on earth and is not yet produced in the current operating reactors. A solution may consist in producing 233U in special devices containing Thorium, in Pressurized Water or Fast Neutrons Reactors. Two alternatives to produce 233U are examined here: directly in standard Molten Salt Reactors started with Plutonium as fissile matter and then operated in the Th/233U cycle; or in dedicated Molten Salt Reactors started and fed with Plutonium as fissile matter and Thorium as fertile matter. The idea is to design a critical reactor able to burn the Plutonium and the minor actinides presently produced in PWRs, and consequently to convert this Plutonium into 233U. A particular reactor configuration is used, called unique channel configuration in which there is no moderator in the core, leading to a quasi fast neutron spectrum, allowing Plutonium to be used as fissile matter. The conversion capacities of such Molten Salt Reactors are excellent. For Molten Salt Reactors only started with Plutonium, the assets of the Thorium fuel cycle turn out to be quickly recovered and the reactors characteristics turn out to be equivalent to Molten Salt Reactors operated with 233U only. Using a combination of Molten Salt Reactors started or operated with Plutonium and of Molten Salt Reactors started with 233U, the deployment capabilities of these reactors fully satisfy the condition of sustainability