87 research outputs found
A special nonlinear least-squares problem
AbstractIn this paper we consider the existence of the solution of a special nonlinear least-squares problem. We find the necessary conditions on the data, which insure the existence of the optimal parameters for the asymmetric S-function in the sense of the least squares
Surface generating on the basis of experimental data
The problem of surface generating on the basis of experimental data is presented in this lecture.
Special attention is given to the implementation of moving ordinary least squares and moving total least squares. Some results done in the
Institute for Applied Mathematics in Osijek are mentioned which were
published in the last several years
Reconstruction of the Earth\u27s Meridian Ellipse on the Basis of Experimental Measurements
Na bazi novih metoda matematiÄke optimizacije analizira se stari problem rekonstrukcije Zemljina rotacijskog elipsoida na bazi podataka mjerenja, koji je veÄ poÄetkom 18. stoljeÄa promatrao francuski matematiÄar i astronom markiz Pierre-Simon de Laplace. Posebno je analizirana, ilustrirana i modificirana efikasna metoda iz rada (Sabo i Scitovski 2009) za traženje optimalnih parametara najbolje l1 linearne aproksimacije. U znanstvenoj literaturi problem procjene najbolje l1 aproksimacije obiÄno se povezuje s imenom hrvatskog znanstvenika J. R. BoÅ”koviÄa. Metode za traženje najbolje l1 aproksimacije u posljednje vrijeme dobivaju novi zamah u razliÄitim tehniÄkim primjenama zbog svojstva robusnosti i moguÄnosti implementacije u realnom vremenu na suvremenim raÄunalima.On the basis of new mathematical optimization methods this paper analyzes an old problem of reconstructing the Earth\u27s ellipsoid of rotation on the basis of measurement data, which was considered by the French mathematician and astronomer marquis Pierre-Simon de Laplace as early as the beginning of the 18th century. An efficient method from the paper (Sabo and Scitovski 2009) for searching optimal parameters of the best least absolute deviations linear approximation is especially analyzed, illustrated and modified. In the scientific literature the best l1 approximation is usually associated with the name of Croatian scientist J. R. BoÅ”koviÄ. The least absolute deviations methods have recently started to be extensively applied in different technical applications due to their property of robustness and the possibility of implementation in real time on modern computers
Analysis of solution of the least squares problem
For the given data , we consider the
existence problem of the best parameter approximation of the exponential model function in the sense of ordinary least squares and total least squares.
Results related to that problem which have been obtained and published by the authors so far are given in the paper, as well as some new results on nonuniqueness of the best parameter approximation
Parameter identification in the mathematical model of glucose and insulin tolerance test - the mathematical markers of diabetes
Glucose tolerance test (GTT) is standard diagnostic procedure that tests the efficiency of blood glucose-lowering hormones (insulin, incretins, leptin). Contrary, insulin tolerance test (ITT) is probing efficiency of blood glucose-rising hormones (glucagon, thyroxine, growth hormone, glucocorticoids, adrenalin, noradrenalin). These two hormone systems together maintain blood glucose levels in a narrow range. Various pathophysiological mechanisms give rise to a reversible condition - prediabetes which then progresses to an irreversible chronic disease - diabetes, both marked with deviation of blood glucose levels outside the set range. In diagnostic purpose, the patient is given glucose load, and blood glucose is measured right before and 2 hours after load. Measurements are more frequent after insulin injection (ITT) or if both tests are performed on experimental animals. In this paper we analyse the mathematical model for GTT and ITT. The obtained model function is an useful tool in describing the dynamics of blood glucose changes
SHORT-TERM AND LONG-TERM WATER LEVEL PREDICTION AT ONE RIVER MEASUREMENT LOCATION
Global hydrological cycles mainly depend on climate changes whose occurrence is predominantly triggered by solar and terrestrial influence, and the knowledge of the high water regime is widely
applied in hydrology. Regular monitoring and studying of river water level behavior is important from several perspectives. On the basis of the given data, by using modifications of general approaches
known from literature, especially from investigation in hydrology, the problem of long- and short-term water level forecast at one river measurement location is considered in the paper. Long-term
forecasting is considered as the problem of investigating the periodicity of water level behavior by using linear-trigonometric regression and short-term forecasting is based on the modification of the nearest neighbor method. The proposed methods are tested on data referring to the Drava River level by Donji Miholjac, Croatia, in the period between the beginning of 1900 and the end of 2012
Least-squares fitting Gompertz curve
AbstractIn this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,ā¦,m, mā©¾3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples
A fast and efficient method for solving the multiple line detection problem
In this paper, we consider the multiple line detection problem on the basis of a data points set coming from a number of lines not known in advance. A new and efficient method is proposed, which is based upon center-based clustering, and it solves this problem quickly and precisely. The method has been tested on 100 randomly generated data sets. In comparison to the incremental algorithm, the method gives significantly better results. Also, in order to identify a partition with the most appropriate number of clusters, a new index has been proposed for the case of a cluster whose lines are cluster-centers. The index can also be generalized for other geometrical objects
A model to determine growth rate of heavy hybrid turkeys
U radu je istražena primjena generalizirane logistiÄke funkcije u modeliranju rasta teÅ”kog hibrida pura. Istraživanje je trajalo 19 tjedana, tijekom kojih je kontroliran rast 20 muÅ”kih i 20 ženskih pura provenijencije Nicholas 700. Tijekom Äitavog razdoblja tova razlike u živim težinama izmeÄu purana i pura bile su statistiÄki vrlo visoko znaÄajne (P<0,001). Na kraju istraživanja purani su u prosjeku bili teÅ”ki 15,17 kg, a pure 10,88 kg. Purani su od pura bili teži za otprilike 4,3 kg ili 39,53%. ProsjeÄni tjedni prirasti kod purana bili su 795 g, a kod pura 577 g, dok su prosjeÄne stope rasta u tovu teÅ”kog hibrida bile 12,45% (mužjaci) i 12,11% (ženke). Procjene toÄke infleksije i pojedinih faza rasta po spolu pura obavljene su primjenom generalizirane logistiÄke funkcije:
Koeficijenti asimetrije bili su Ī³=0,2 (purani) i Ī³=0,3 (pure). BioloÅ”ki maksimum za purane bio je 18,57 kg a za pure 12,63 kg. Prema izraÄunatim parametrima toÄka infleksije kod pura je poÄetkom, a kod purana sredinom 10.tjedna tova kada su teÅ”ki 5,27 kg (pure) i 7,46 kg (purani). Na temelju rezultata primijenjenog modela (generalizirana logistiÄka funkcija) u opisivanju rasta pura teÅ”kog hibrida može se istaknuti skako ženke zavrÅ”avaju intenzivnu fazu rasta skoro tjedan dana ranije nego mužjaci, a toÄka infleksije kod pura nastupa ranije nego kod purana.The objective of this study was to investigate the application of generalized logistic function to the heavy hybrid turkey growth modeling. The growth of 20 turkey toms and 20 turkey hens of Nicholas 700 provenience was monitored over 19 weeks. During the whole fattening period, differences in live weights between males and females were statistically highly significant (P<0.001). At the end of the experiment, turkey toms weighed on average 15.17 kg, compared to 10.88 kg of average turkey hens live weight. Males weighed approximately 4.3 kg or 39.53% more than females. Average weekly gain of turkey toms was 795 g, and of turkey hens 577 g. Average growth rate of turkey toms was 12.45% and of turkey hens 12.11%. Evaluation of inflection point and each growth phase for both turkey sexes was carried out by using generalized logistic function:
Coefficients of asymmetry were Ī³=0.2 (males) and Ī³=0.3 (females). Biological maximum was 18.57 kg for males, and 12.63 kg for females. According to calculated parameters, inflection point in turkey hens occurred at the beginning of the 10th week of fattening, when they reached 5.27 kg; in turkey toms it occurred in the middle of the 10th week, at the weight of 7.46 kg. On the basis of the results obtained by using the model of generalized logistic function for turkey growth rate description, it was concluded that turkey hens ended their intensive growth phase about a week earlier than turkey toms, with the inflection point also starting earlier than in turkey toms
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