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

Reconstruction of the Earth\u27s Meridian Ellipse on the Basis of Experimental Measurements

Na bazi novih metoda matematičke optimizacije analizira se stari problem rekonstrukcije Zemljina rotacijskog elipsoida na bazi podataka mjerenja, koji je već početkom 18. stoljeća promatrao francuski matematičar 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 obično se povezuje s imenom hrvatskog znanstvenika J. R. Boškovića. Metode za traženje najbolje l1 aproksimacije u posljednje vrijeme dobivaju novi zamah u različitim tehničkim primjenama zbog svojstva robusnosti i mogućnosti implementacije u realnom vremenu na suvremenim računalima.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. Bošković. 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

Reconstruction of the Earth\u27s Meridian Ellipse on the Basis of Experimental Measurements

Na bazi novih metoda matematičke optimizacije analizira se stari problem rekonstrukcije Zemljina rotacijskog elipsoida na bazi podataka mjerenja, koji je već početkom 18. stoljeća promatrao francuski matematičar 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 obično se povezuje s imenom hrvatskog znanstvenika J. R. Boškovića. Metode za traženje najbolje l1 aproksimacije u posljednje vrijeme dobivaju novi zamah u različitim tehničkim primjenama zbog svojstva robusnosti i mogućnosti implementacije u realnom vremenu na suvremenim računalima.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. Bošković. 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

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,…,m, m⩾3. 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 logističke funkcije u modeliranju rasta teškog hibrida pura. Istraživanje je trajalo 19 tjedana, tijekom kojih je kontroliran rast 20 muških i 20 ženskih pura provenijencije Nicholas 700. Tijekom čitavog razdoblja tova razlike u živim težinama između purana i pura bile su statistički vrlo visoko značajne (P<0,001). Na kraju istraživanja purani su u prosjeku bili teški 15,17 kg, a pure 10,88 kg. Purani su od pura bili teži za otprilike 4,3 kg ili 39,53%. Prosječni tjedni prirasti kod purana bili su 795 g, a kod pura 577 g, dok su prosječne stope rasta u tovu teškog hibrida bile 12,45% (mužjaci) i 12,11% (ženke). Procjene točke infleksije i pojedinih faza rasta po spolu pura obavljene su primjenom generalizirane logističke funkcije: Koeficijenti asimetrije bili su γ=0,2 (purani) i γ=0,3 (pure). Biološki maksimum za purane bio je 18,57 kg a za pure 12,63 kg. Prema izračunatim parametrima točka infleksije kod pura je početkom, a kod purana sredinom 10.tjedna tova kada su teški 5,27 kg (pure) i 7,46 kg (purani). Na temelju rezultata primijenjenog modela (generalizirana logistička funkcija) u opisivanju rasta pura teškog hibrida može se istaknuti skako ženke završavaju intenzivnu fazu rasta skoro tjedan dana ranije nego mužjaci, a točka 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 γ=0.2 (males) and γ=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

Matematičko modeliranje ekonomskih pojava koje teže zasićenju

U ekonomskim istraživanjima često je potrebno neku pojavu opisati funkcijom čija se vrijednost asimptotski približava razini zasićenja. U radu se promatra klasa tzv. S-funkcija, koje služe za kratkoročne i dugoročne prognoze. Poseban naglasak dat je na analizu klasa funkcija, koje ovisno o parametru, mogu imati pozitivnu ili negativnu asimetriju ili se mogu preobraziti u poznatu logističku funkciju. Procjenjivanje parametara ovakvih funkcija je složen nelinearni problem najmanjih kvadrata, koji ne mora uvijek imati rješenje. Ekonomska interpretacija svojstava tih funkcija je izuzetno značajna za strategijsko upravljanje ekonomskim sistemima

Cluster analysis and artificial neural networks in predicting energy efficiency of public buildings as a cost-saving approach

Although energy efficiency is a hot topic in the context of global climate change, in the European Union directives and in national energy policies, methodology for estimating energy efficiency still relies on standard techniques defined by experts in the field. Recent research shows a potential of machine learning methods that can produce models to assess energy efficiency based on available previous data. In this paper, we analyse a real dataset of public buildings in Croatia, extract their most important features based on the correlation analysis and chi-square tests, cluster the buildings based on three selected features, and create a prediction model of energy efficiency for each cluster of buildings using the artificial neural network (ANN) methodology. The main objective of this research was to investigate whether a clustering procedure improves the accuracy of a neural network prediction model or not. For that purpose, the symmetric mean average percentage error (SMAPE) was used to compare the accuracy of the initial prediction model obtained on the whole dataset and the separate models obtained on each cluster. The results show that the clustering procedure has not increased the prediction accuracy of the models. Those preliminary findings can be used to set goals for future research, which can be focused on estimating clusters using more features, conducted more extensive variable reduction, and testing more machine learning algorithms to obtain more accurate models which will enable reducing costs in the public sector