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

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

MTSS1 is a critical epigenetically regulated tumor suppressor in CML

Chronic myeloid leukemia (CML) is driven by malignant stem cells that can persist despite therapy. We have identified Metastasis suppressor 1 (Mtss1/MIM) to be downregulated in hematopoietic stem and progenitor cells from leukemic transgenic SCLtTA/Bcr-Abl mice and in patients with CML at diagnosis, and Mtss1 was restored when patients achieved complete remission. Forced expression of Mtss1 decreased clonogenic capacity and motility of murine myeloid progenitor cells and reduced tumor growth. Viral transduction of Mtss1 into lineage depleted SCLtTA/Bcr-Abl bone marrow cells decreased leukemic cell burden in recipients, and leukemogenesis was reduced upon injection of Mtss1 overexpressing murine myeloid 32D cells. Tyrosine kinase inhibitor (TKI) therapy and reversion of Bcr-Abl expression increased Mtss1 expression but failed to restore it to control levels. CML patient samples revealed higher DNA methylation of specific Mtss1 promoter CpG sites that contain binding sites for Kaiso and Rest transcription factors. In summary, we identified a novel tumor suppressor in CML stem cells that is downregulated by both Bcr-Abl kinase-dependent and -independent mechanisms. Restored Mtss1 expression markedly inhibits primitive leukemic cell biology in vivo, providing a therapeutic rationale for the Bcr-Abl-Mtss1 axis to target TKI resistant CML stem cells in patients

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

Prompt reactivity determination in a subcritical assembly through the response to a Dirac pulse

The full understanding of the kinetics of a subcritical assembly is a key issue for its online reactivity control. Point kinetics is not sufficient to determine the prompt reactivity of a subcritical assembly through the response to a dirac pulse, in particular in the cases of a large reflector, a small reactor, or a large subcriticality.Taking into account the distribution of intergeneration times, which appears as a robust characteristic of each type of reactor, helps to understand this behaviour.Eventually, a method is proposed for the determination of the prompt reactivity. It provides a decrease rate function depending on the prompt multiplication coefficient Keffp. Fitting a measured decrease rate with this function, calculated once for the reactor, gives the true value of keffp. The robustness of the method is tested. (Elsevier

Constraining New Physics with a Positive or Negative Signal of Neutrino-less Double Beta Decay

We investigate numerically how accurately one could constrain the strengths of different short-range contributions to neutrino-less double beta decay in effective field theory. Depending on the outcome of near-future experiments yielding information on the neutrino masses, the corresponding bounds or estimates can be stronger or weaker. A particularly interesting case, resulting in strong bounds, would be a positive signal of neutrino-less double beta decay that is consistent with complementary information from neutrino oscillation experiments, kinematical determinations of the neutrino mass, and measurements of the sum of light neutrino masses from cosmological observations. The keys to more robust bounds are improvements of the knowledge of the nuclear physics involved and a better experimental accuracy.Comment: 23 pages, 3 figures. Minor changes. Matches version published in JHE