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

The availability of base elements (Ca, Mg, Na, K) in some important soil types in Serbia

In this paper results are presented of agrochemical and mineralogical analyses of 14 types of important soils in Serbia (Vojvodina and Central Serbia) and total content and availability of base alkali elements (Ca, Mg Na, K) are determined. Total element content was as follows: Ca 2.22%; K 1.77%; Na 0.85% and Mg 0.61%. Total content of alkali metals in the soils investigated and their variations within and between the soil types, is in very good/close correlation with contents of primary and secondary minerals as well as their rates of weathering. Taking in account the average availabilities the most abundant is calcium with 947 mg/100 g, whilst the averages of the other elements (Mg, K and Na) are quite similar and are about of 40 mg/100 g of soil. The results obtained have shown that the soils investigated are well to moderate provided with K, Ca and Mg and that their deficit could not be expected in plant nutrition, apart for some plants/cultures in the case of magnesium due to occasionally higher Ca/Mg and K/Mg ratios

Detekcija mehanizama rezistencije na karbapeneme kod enterobakterija i vrste Pseudomonas aeruginosa

The aims of the research: to examine the presence of genes which encode carbapenemases among enterobacteria and Pseudomonas aeruginosa isolates with reduced sensitivity to carbapenems by using the polymerase chain reaction (PCR); to determine the most common mechanisms of resistance to carbapenems using phenotypic methods. To evaluate the phenotypic methods in relation to PCR as a reference method, and determine the most common phenotypes. Methods: 107 isolates from the Enterobacteriaceae family and 75 isolates of the species Pseudomonas aeruginosa were examined. Antimicrobial susceptibility was determined by the Kirby-Bauer disc-diffusion method and the automated Vitek2 system according to the recommendations of the Institute for Clinical and Laboratory Standards (CLSI). Using PCR and phenotypic methods, 56 enterobacterial isolates and 14 isolates of P. aeruginosa were tested. The results of the phenotypic tests were validated by a comparison with genotypic data and expressed through sensitivity, specificity, and positive and negative predictive value (PPV and NPV). Results: Carbapenemase genes were detected by the PCR method in 52 Enterobacteriaceae isolates: 24 blaNDM, 16 blaOXA-48, 10 blaNDM/ blaOXA-48, one isolate blaNDM/ blaOXA-48/ blaKPC , one isolate blaKPC/ blaNDM and six blaNDM genes in Pseudomonas aeruginosa. All of the tested isolates were negative for the blaVIM genes. Among the applied phenotypic tests, high specificity (in excess of 95%) was found for the modified Hodge test, the CARBA NP test, combined disc test and synergistic test, while high sensitivity (greater than 95%) was determined for thechromID CARBA agar. The most common phenotypes of resistance in enterobacteria were isolates resistant to all the tested antibiotics except for colistin and tigecycline, and in the case of Pseudomonas aeruginosa to colistin and piperacillin-tazobactam. Conclusions: Based on the results of sensitivity, specificity, PPV and NPV, the phenotypic methods for the detection of carbapenemase production represent reliable tests for the detection of this resistance mechanism both in enterobacteria and in Pseudomonas aeruginosa

Procurement model for copper and polymer electrical products

Procurement model for copper and polymer electrical products. Electrical cable structure (wire, insulation, filling and mantle) is in accordance with the technical specifications of individual cable components in terms of the incorporated materials. Materials used in cable manufacture are copper, aluminum, rubber and polyvinyl chloride. One of the key issues in managing the flow of goods pertains to the timing of procurement. The combination of the two concepts can take advantage of individual strengths of fuzzy logic and neural networks in hybrid systems of homogeneous structure. The model has high practical significance, as, with minor modifications, it can be applied in any enterprise responsible for managing the goods flows

Procurement model for copper and polymer electrical products

Procurement model for copper and polymer electrical products. Electrical cable structure (wire, insulation, filling and mantle) is in accordance with the technical specifications of individual cable components in terms of the incorporated materials. Materials used in cable manufacture are copper, aluminum, rubber and polyvinyl chloride. One of the key issues in managing the flow of goods pertains to the timing of procurement. The combination of the two concepts can take advantage of individual strengths of fuzzy logic and neural networks in hybrid systems of homogeneous structure. The model has high practical significance, as, with minor modifications, it can be applied in any enterprise responsible for managing the goods flows

Korelacija morfoloških i proizvodnih osobina društava medonosne pčele sa područja Srbije

State of mutual or reciprocal relationship between traits is determined by the correlation coefficients. Correlation of morphological and production traits was determined in two generations of honey bee colonies. In the first generation, mother queen bees were studied, and in the second generation, their offspring. The study of one generation lasted two years. Morphological traits were determined in the beginning of the study and production traits were determined in the spring and autumn inspections of every year. In the first generation, the positive and mostly high correlation between morphological traits, and honey yield and hygienic behavior was determined. Correlation of morphological traits, colony strength and food supplies per colony ranged from highly positive to slightly negative values. It was found that there was a high correlation between some production traits (colony strength in the spring and autumn inspections and honey yield per colony). In the analysis of offspring (second generation), most traits that were positively correlated in mother generation now, also, showed a similar relationship. The only difference, in contrast to mother generation, was that, for most traits, the intensity of interaction increased.Stanje uzajamne ili recipročne povezanosti jedne osobine od druge utvrđuje se na osnovu koeficijenta korelacije. Korelacija morfoloških i proizvodnih osobina utvrđivana je kroz dve generacije društava medonosne pčele. U prvoj generaciji praćene su majke matice, a u drugoj njihovo potomstvo. Ispitivanje po jednoj generaciji trajalo je dve godine. Morfološke osobine su utvrđene na početku praćenja generacija, a proizvodne na prolećnom i jesenjem pregledu svake godine. U prvoj generaciji utvrđena je pozitivna i mahom visoka korelacija između morfoloških osobina, prinosa meda i higijenskog ponašanja. Stepen korelacije morfoloških osobina, snage društva i zaliha hrane po društvu bio je od visoko pozitivne do slabo negativne vrednosti. Ustanovljeno je da postoji i visok stepen korelacije između pojedinih proizvodnih osobina (snaga društava na prolećnom i jesenjem pregledu i prinosa meda po društvu). Prilikom testiranja potomstva (II generacija) većina osobina koje su bile u pozitivnoj korelaciji kod roditelja i sada su pokazivala uzajamni odnos. Jedina razlika u odnosu na roditelje je u tome da se, za većinu osobina, intezitet međusobnog uticaja povećao

Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

Application of the HDM-4 model on local road network: case study of the Herzegovina-Neretva Canton in Bosnia and Herzegovina

The World Bank Highway Development and Management (HDM-4) tool has been used extensively for the management of road networks, particularly in developing countries. The paper describes the application of HDM-4 model for local roads in Bosnia and Herzegovina (BiH), in the Herzegovina-Neretva Canton (HNC). The HDM-4 study was performed with the aim to define road works program and investment priorities by analyzing impacts of different budgets on future network condition. The 396 km-long HNC road network consists of 13 roads that are either graveled or paved. A large part of these roads do not have sufficient pavement width. This road network is in relatively poor condition due to its age (the average age is over 30 years) and limited spending on maintenance in the past. Only a small percentage of the network has been reconstructed in recent years. The Average Annual Daily Traffic (AADT) has a wide range, and varies from 27 to 12735 vpd. The major challenge in the study was to obtain HDM-4 input data with limited resources, since usually this task requires extensive investigations. In addition to inventory data, it is necessary to define the condition of the road network, traffic volume, traffic data, etc. Road geometry data were obtained from previous studies and project documentations. The IRI data were taken from the earlier surveys or estimated where no data were available. Other parameters were obtained by field tests. Traffic data were available from regular network traffic counts. After analyzing the parameters, the network was divided into 65 homogeneous sections, based on the AADT and road condition (IRI and other parameters) classes. HDM-4 program analysis was performed for a period of 30 years. Due to very low traffic loading and relatively large investment needed for improvement, for majority of sections a negative NPV and IRR were obtained for maintenance alternatives other than routine maintenance, and for significant number of sections they were on the verge. Out of 65 homogeneous sections, only 29 sections proved cost-effective (NPV/CAP ratio is positive). The implementation of developed road work programs would result in a substantial improvement of the overall network condition. The IRI of paved road network would change from current value of 4.5 m/km to 4.0 m/km and 3.7 m/km for budget levels of 2.0 and 3.0 mill. BAM after five years. The better road network condition would also result in improved traffic safety, social and economic impacts, since many of these roads are crucial links in the HNC

Fitting censored quantile regression by variable neighborhood search

Quantile regression is an increasingly important topic in statistical analysis. However, fitting censored quantile regression is hard to solve numerically because the objective function to be minimized is not convex nor concave in regressors. Performance of standard methods is not satisfactory, particularly if a high degree of censoring is present. The usual approach is to simplify (linearize) estimator function, and to show theoretically that such approximation converges to optimal values. In this paper, we suggest a new approach, to solve optimization problem (nonlinear, nonconvex, and nondifferentiable) directly. Our method is based on variable neighborhood search approach, a recent successful technique for solving global optimization problems. The presented results indicate that our method can improve quality of censored quantizing regressors estimator considerably

Physico-chemical and mechanical properties of geopolymer/zircon composites

The effect of zircon (ZrSiO4) on the physico-chemical and mechanical properties of geopolymer/zircon composites was examined in this study. Four geopolymer/zircon composites containing 10, 20, 30 and 40 wt.% zircon were prepared from metakaolin with alkali activators. Characterization of the obtained geopolymers was performed by X-ray diffraction (XRD), Scanning electron microscope (SEM-EDS), Fourier transform infrared spectroscopy (FTIR) and Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF). XRD results did not confirmed the formation of interconnected phases between added zircon, starting aluminum silicates and alkali activators. Compressive strength of prepared geopolymer was examined. The maximum obtained compressive strength of 70.15 MPa was measured in sample containing the smallest fraction of zircon, i.e., 10 wt.%. Addition of larger amount of zircon (20 wt.%) hinders the progress of geopolymerization reaction and consequently decreases compressive strength