Least squares regression with errors in both variables: case studies

Analytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is discussed as an alternative approach in order to take into account the error in the x variable. Four examples are presented to illustrate deviation between the results from both regression methods. The examples studied show that, in some situations, ODR coefficients must substitute for those of OLS, and, in other situations, the difference is not significant.

Cinética e caracterização de ramnolipídeos produzidos por Pseudomonas aeruginosa MSIC02 utilizando glicerol como fonte de carbono

Glycerol, a co-product of biodiesel production, was used as a carbon source for the kinetics studies and production of biosurfactants by P. aeruginosa MSIC02. The highest fermentative parameters (Y PX = 3.04 g g-1; Y PS = 0.189 g g-1, P B = 31.94 mg L-1 h-1 and P X = 10.5 mg L-1 h-1) were obtained at concentrations of 0.4% (w/v) NaNO3 and 2% (w/v) glycerol. The rhamnolipid exhibited 80% of emulsification on kerosene, surface tension of 32.5 mN m-1, CMC = 28.2 mg L-1, C20 (concentration of surfactant in the bulk phase that produces a reduction of 20 dyn/cm in the surface tension of the solvent) = 0.99 mg L-1, Γm (surface concentration excess) = 2.4 x 10-26 mol Å-2 and S (surface area) = 70.4 Ų molecule-1 with solutions containing 10% NaCl. A mathematical model based on logistic equation was considered to representing the process. Model parameters were estimated by non-linear regression method. This approach was able to give a good description of the process.

Mathematical equation correction to spectral and transport interferences in high-resolution continuum source flame atomic absorption spectrometry: determination of lead in phosphoric acid

In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.

Automated, adaptive methods for forest inventory

Forest inventories are used to estimate forest characteristics and the condition of forest for many different applications: operational tree logging for forest industry, forest health state estimation, carbon balance estimation, land-cover and land use analysis in order to avoid forest degradation etc. Recent inventory methods are strongly based on remote sensing data combined with field sample measurements, which are used to define estimates covering the whole area of interest. Remote sensing data from satellites, aerial photographs or aerial laser scannings are used, depending on the scale of inventory. To be applicable in operational use, forest inventory methods need to be easily adjusted to local conditions of the study area at hand. All the data handling and parameter tuning should be objective and automated as much as possible. The methods also need to be robust when applied to different forest types. Since there generally are no extensive direct physical models connecting the remote sensing data from different sources to the forest parameters that are estimated, mathematical estimation models are of "black-box" type, connecting the independent auxiliary data to dependent response data with linear or nonlinear arbitrary models. To avoid redundant complexity and over-fitting of the model, which is based on up to hundreds of possibly collinear variables extracted from the auxiliary data, variable selection is needed. To connect the auxiliary data to the inventory parameters that are estimated, field work must be performed. In larger study areas with dense forests, field work is expensive, and should therefore be minimized. To get cost-efficient inventories, field work could partly be replaced with information from formerly measured sites, databases. The work in this thesis is devoted to the development of automated, adaptive computation methods for aerial forest inventory. The mathematical model parameter definition steps are automated, and the cost-efficiency is improved by setting up a procedure that utilizes databases in the estimation of new area characteristics.

Keille yliopiston portit avautuvat? Tutkimus suomalaisiin yliopistoihin ja eri tieteenaloille valikoitumisesta 2000-luvun alussa

Tutkimuksessa tarkastellaan suomalaisiin yliopistoihin valikoitumista 2000-luvun alussa. Tarkastelu pohjautuu yliopistoon hakeneiden, opiskelemaan hyväksyttyjen ja opiskelupaikkaa ilman jääneiden taustojen vertailuun. Tutkimuksen tarkoituksena on selvittää, miten koulutuksellinen tasa-arvo toteutuu opiskelemaan pääsyssä. Erityistä huomiota kiinnitetään sukupuolten, eri-ikäisten, sosiaalisten ryhmien sekä eri alueella asuvien opiskelijavalinnoissa pärjäämiseen. Lisäksi pohditaan, millaiset taustatekijät ovat yhteydessä opiskelemaan pääsyyn ja miten suomalainen yliopistokenttä on lohkoutunut yliopistoittain ja aloittain hakijoiden ja sisään päässeiden taustojen perusteella. Tutkimuksen pääaineistona on henkilöpohjainen rekisteriaineisto, joka on laadittu valtakunnallisen hakijarekisterin (HAREK) ja Tilastokeskuksen yhteistyönä. Aineisto käsittää 40 %:n satunnaisotoksen vuonna 2003 suomalaisiin yliopistoihin hakeneista (N = 55 790). Aineiston muuttujat kuvaavat hakijoiden taustoja, elämäntilannetta, aiempaa koulutusta ja lapsuudenperheen asemaa. Tutkimuksessa hyödynnetään lisäksi kokonaisjoukosta muodostettua taulukkoaineistoa (N = 139 668). Yliopistoihin hakevat eivät ole yhtenäinen ryhmä. Vaikka suurin osa hakijoista oli nuoria, oli joukossa myös varttuneempia hakijoita, jotka olivat ehtineet hankkia koulutusta ja muuta elämänkokemusta. Päävalinnat toimivat siten myös aikuishakijoiden hakuväylänä; erillisvalintoja eivät hyödynnä läheskään kaikki, joilla siihen olisi mahdollisuus. Klusterianalyysin avulla hakijoista voitiin erottaa neljä ryhmää: 1) nuoret ylioppilaat, 2) toisen tutkinnon suorittajat, 3) koulutuspääoman kartuttajat sekä 4) aikuiset lisäkouluttautujat. Opiskelemaan pääsyyn vaikuttavia tekijöitä analysoitiin logistisen regressioanalyysin avulla. Analyysin mukaan hakijan iällä oli muista taustatekijöistä riippumaton vaikutus opiskelemaan pääsyyn niin, että todennäköisyys päästä yliopistoon vähenee hakijan iän kohotessa. Parhaiten opiskelemaan pääsivät kaikkein nuorimmat, alle 20-vuotiaat hakijat, jotka siis useimmiten ovat saman kevään ylioppilaita. Vanhemmille hakijoille oli usein kertynyt jo koulutusta, mutta aiemmat tutkinnot paransivat sisäänpääsyn mahdollisuuksia vain, mikäli ne olivat korkea-asteelta. Alemmilla ammatillisilla tutkinnoilla oli pikemminkin opiskelemaan pääsyä heikentävä vaikutus. Myös se, mitä hakija oli tehnyt ennen valintakokeita, vaikutti sisäänpääsyn mahdollisuuksiin. Parhaiten valinnoissa pärjäsivät päätoimiset opiskelijat, heikoiten työttömät hakijat. Vaikka miesten hyväksymisprosentit olivat keskimäärin korkeammat kuin naisten, sukupuoli ei osoittautunut itsenäiseksi opiskelemaan pääsyä selittäväksi tekijäksi. Naisten huonompi pärjääminen valinnoissa selittyykin pitkälti sukupuolten eriytyneillä alavalinnoilla. Naisten suosimat alat kun ovat pääsääntöisesti vaikeapääsyisempiä kuin miesten. Tutkimuksessa selvisi myös, että kaupunkilaisuus lisäsi todennäköisyyttä tulla hyväksytyksi. Toisaalta opiskelemaan pääsy erosi myös asuinmaakunnittain, mikä kertoo lähinnä siitä, että eri yliopistojen sisäänpääsyasteissa on varsin suuria eroja. Yliopistojen lohkoutuminen hakijoiden sosiaalisen taustan mukaan oli paljon selvempää kuin alojen. Kaikki pääkaupunkiseudun yliopistot – lukuun ottamatta Teatterikorkeakoulua – luokittuivat isän asemalla mitaten elitistisiksi. Matalimmista taustoista haettiin Lapin, Joensuun ja Vaasan yliopistoihin. Alojen paikka elitistisyyskansanomaisuus -ulottuvuudella vaihteli suuresti yliopistoittain. Teknillistieteellinen, matemaattis-luonnontieteellinen ja kauppatieteellinen ala sijoittuivat kuitenkin keskimääräistä ylemmäs, kun taas kasvatustiede ja farmasia olivat kansanomaisimpia hakukohteita. Opiskelijaksi valikoitumisen peruselementit toistuivat myös tässä tutkimuksessa: koulutetuimpien ja hyvässä asemassa olevien vanhempien jälkeläiset saivat opiskelupaikan useammin kuin muut. Yliopistolaitoksessa vuosikymmenten saatossa toteutetut rakenteelliset muutokset eivät siis ole muuttaneet valikoitumisen peruslinjaa, joskin uutena huomiona nousi maanviljelijöiden jälkeläisten hyvä valinnoissa pärjääminen. Maanviljelijäperheestä tulevien opiskelemaan pääsyn todennäköisyys oli kaikkein suurin.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Logistic regression to estimate the welfare of broiler breeders in relation to environmental and behavioral variables

The increasing demand of consumer markets for the welfare of birds in poultry house has motivated many scientific researches to monitor and classify the welfare according to the production environment. Given the complexity between the birds and the environment of the aviary, the correct interpretation of the conduct becomes an important way to estimate the welfare of these birds. This study obtained multiple logistic regression models with capacity of estimating the welfare of broiler breeders in relation to the environment of the aviaries and behaviors expressed by the birds. In the experiment, were observed several behaviors expressed by breeders housed in a climatic chamber under controlled temperatures and three different ammonia concentrations from the air monitored daily. From the analysis of the data it was obtained two logistic regression models, of which the first model uses a value of ammonia concentration measured by unit and the second model uses a binary value to classify the ammonia concentration that is assigned by a person through his olfactory perception. The analysis showed that both models classified the broiler breeder's welfare successfully.

Spatio-temporal modelling of the duration of the cotton cycle in the State Of Goiás, Brazil

The objective of this work was to develop and validate a mathematical model to estimate the duration of cotton (Gossypium hirsutum L. r. latifolium hutch) cycle in the State of Goiás, Brazil, by applying the method of growing degree-days (GD), and considering, simultaneously, its time-space variation. The model was developed as a linear combination of elevation, latitude, longitude, and Fourier series of time variation. The model parameters were adjusted by using multiple-linear regression to the observed GD accumulated with air temperature in the range of 15°C to 40°C. The minimum and maximum temperature records used to calculate the GD were obtained from 21 meteorological stations, considering data varying from 8 to 20 years of observation. The coefficient of determination, resulting from the comparison between the estimated and calculated GD along the year was 0.84. Model validation was done by comparing estimated and measured crop cycle in the period from cotton germination to the stage when 90 percent of bolls were opened in commercial crop fields. Comparative results showed that the model performed very well, as indicated by the Pearson correlation coefficient of 0.90 and Willmott agreement index of 0.94, resulting in a performance index of 0.85.

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I-100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.