A comparative analysis of preprocessing techniques of cardiac event series for the study of heart rhythm variability using simulated signals

In the present study, using noise-free simulated signals, we performed a comparative examination of several preprocessing techniques that are used to transform the cardiac event series in a regularly sampled time series, appropriate for spectral analysis of heart rhythm variability (HRV). First, a group of noise-free simulated point event series, which represents a time series of heartbeats, was generated by an integral pulse frequency modulation model. In order to evaluate the performance of the preprocessing methods, the differences between the spectra of the preprocessed simulated signals and the true spectrum (spectrum of the model input modulating signals) were surveyed by visual analysis and by contrasting merit indices. It is desired that estimated spectra match the true spectrum as close as possible, showing a minimum of harmonic components and other artifacts. The merit indices proposed to quantify these mismatches were the leakage rate, defined as a measure of leakage components (located outside some narrow windows centered at frequencies of model input modulating signals) with respect to the whole spectral components, and the numbers of leakage components with amplitudes greater than 1%, 5% and 10% of the total spectral components. Our data, obtained from a noise-free simulation, indicate that the utilization of heart rate values instead of heart period values in the derivation of signals representative of heart rhythm results in more accurate spectra. Furthermore, our data support the efficiency of the widely used preprocessing technique based on the convolution of inverse interval function values with a rectangular window, and suggest the preprocessing technique based on a cubic polynomial interpolation of inverse interval function values and succeeding spectral analysis as another efficient and fast method for the analysis of HRV signals

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Antioxidant activity of rosemary and oregano ethanol extracts in soybean oil under thermal oxidation

Four experiments were conducted to measure the antioxidant activity of ethanol extracts of rosemary and oregano compared with synthetic antioxidants such as TBHQ and BHA/BHT. The antioxidant activity was determined and results differed from those of the Oven test at 63º C. Peroxide values and absorptivities at 232 nm of soybean oil under Oven test were lower in treatments with 25, 50, 75, 100 and 200 mg.Kg-1 TBHQ than in treatments with 1000 mg.Kg-1 oregano extract (O), 500 mg.Kg-1 rosemary extract (R) and their mixture R+O. All the treatments were effective in controlling the thermal oxidation of oils; the natural extracts were as effective as BHA+BHT and less effective than TBHQ. The natural extracts were mixed with 25, 50, 75 and 100 mg.Kg-1 TBHQ and then added to the oil. No improvement in antioxidative properties was observed. The best antioxidant concentration could be determined from polynomial regression and quadratic equation from the experimental data.

Shirshovin lause PI-algebroissa

Tässä työssä esitetään venäläisen matemaatikon A.I. Shirshovin teorioita ja tuloksia sanojen kombinatoriikasta. Lisäksi näytetään miten ne soveltuvat PI-algebrojen maailmaan. Shirshovin tuloksia tarkasteltaessa käsitellään sanoja erillisinä kombinatorisina objekteina ja todistetaan Shirshovin Lemma, joka on tämän työn perusta. Lemmanmukaan tarpeeksi pitkille sanoille saadaan tiettyä säännönmukaisuutta ja se todistetaan kolme kertaa. Ensimmäisestä saadaan tarpeeksi pitkän sanan olemassaolo.Toinen todistus mukailee Shirshovin alkuperäistä todistusta. Kolmannessa todistuksessa annetaan tarpeeksi pitkälle sanalle paremmin käytäntöön soveltuva raja. Tämän jälkeen käsitellään sanoja algebrallisina objekteina. Työn päätuloksena todistetaan Shirshovin Korkeuslause, jonka mukaan jokainen äärellisesti generoidunPI-algebran alkio on sanojen ω1k1 ···ωdkd lineaarikombinaatio, missä sanojen ωi pi-tuudet sekä indeksi i ovat rajatut. Shirshovin Korkeuslauseesta seuraa suoraan positiivinen ratkaisu Kurochin ongelmaan PI-algebroilla sekä saadaan raja alkioiden lukumäärälle, jolla algebra generoituu moduliksi. Lisäksi esitetään toisena sovelluksena ilman todistuksia Shirshovin soveltuvuus Jacobsonin radikaalin nilpotenttisuuteen. Pääsääntöisenä lähteenä käytetään A. Kanel-Belowin ja L. H. Rowenin kirjaa: Computational aspects of polynomial identities.

Rheological and thermophysical properties of blackberry juice

Rheological and thermophysical properties were determined for blackberry juice, which was produced from blackberry fruit at 9.1 ± 0.5 °Brix and density of 1.0334 ± 0.0043 g cm-3. The concentration process was performed using a roto evaporator, under vacuum, to obtain concentrated juice at about 60 °Brix. In order to obtain different concentrations, concentrated juice was diluted with distilled water. Rheological measurements were carried out using a Rheotest 2.1 Searle type rheometer. In the tested ranges, the samples behaved as pseudoplastic fluids, and the Power-Law model was satisfactorily fitted to the experimental data. The friction factor was measured for blackberry juice in laminar flow conditions of pseudoplastic behavior. Thermal conductivity, thermal diffusivity and density of blackberry juice at 9.4 to 58.4 °Brix were determined, in triplicate, at 0.5 to 80.8 °C. Polynomial regression was performed to fit experimental data obtaining a good fit. Both temperature and concentration showed a strong influence on thermophysical properties of blackberry juice. Calculated apparent specific heat values varied from 2.416 to 4.300 kJ.kg-1 °C in the studied interval.

Defining Contexts in Context-Free Grammars

This thesis introduces an extension of Chomsky’s context-free grammars equipped with operators for referring to left and right contexts of strings.The new model is called grammar with contexts. The semantics of these grammars are given in two equivalent ways — by language equations and by logical deduction, where a grammar is understood as a logic for the recursive definition of syntax. The motivation for grammars with contexts comes from an extensive example that completely defines the syntax and static semantics of a simple typed programming language. Grammars with contexts maintain most important practical properties of context-free grammars, including a variant of the Chomsky normal form. For grammars with one-sided contexts (that is, either left or right), there is a cubic-time tabular parsing algorithm, applicable to an arbitrary grammar. The time complexity of this algorithm can be improved to quadratic,provided that the grammar is unambiguous, that is, it only allows one parsefor every string it defines. A tabular parsing algorithm for grammars withtwo-sided contexts has fourth power time complexity. For these grammarsthere is a recognition algorithm that uses a linear amount of space. For certain subclasses of grammars with contexts there are low-degree polynomial parsing algorithms. One of them is an extension of the classical recursive descent for context-free grammars; the version for grammars with contexts still works in linear time like its prototype. Another algorithm, with time complexity varying from linear to cubic depending on the particular grammar, adapts deterministic LR parsing to the new model. If all context operators in a grammar define regular languages, then such a grammar can be transformed to an equivalent grammar without context operators at all. This allows one to represent the syntax of languages in a more succinct way by utilizing context specifications. Linear grammars with contexts turned out to be non-trivial already over a one-letter alphabet. This fact leads to some undecidability results for this family of grammars

A statistical approach to define some tofu processing conditions

The aim of this work was to make tofu from soybean cultivar BRS 267 under different processing conditions in order to evaluate the influence of each treatment on the product quality. A fractional factorial 2(5-1) design was used, in which independent variables (thermal treatment, coagulant concentration, coagulation time, curd cutting, and draining time) were tested at two different levels. The response variables studied were hardness, yield, total solids, and protein content of tofu. Polynomial models were generated for each response. To obtain tofu with desirable characteristics (hardness ~4 N, yield 306 g tofu.100 g-1 soybeans, 12 g proteins.100 g-1 tofu and 22 g solids.100 g-1 tofu), the following processing conditions were selected: heating until boiling plus 10 minutes in water bath, 2% dihydrated CaSO4 w/w, 10 minutes coagulation, curd cutting, and 30 minutes draining time.

Optimization of the extraction of carrageenan from Kappaphycus alvarezii using response surface methodology

This study aims to optimize an alternative method of extraction of carrageenan without previous alkaline treatment and ethanol precipitation using Response Surface Methodology (RSM). In order to introduce an innovation in the isolation step, atomization drying was used reducing the time for obtaining dry carrageenan powder. The effects of extraction time and temperature on yield, gel strength, and viscosity were evaluated. Furthermore, the extracted material was submitted to structural analysis, by infrared spectroscopy and nuclear magnetic resonance spectroscopy (¹H-NMR), and chemical composition analysis. Results showed that the generated regression models adequately explained the data variation. Carrageenan yield and gel viscosity were influenced only by the extraction temperature. However, gel strength was influenced by both, extraction time and extraction temperature. Optimal extraction conditions were 74 ºC and 4 hours. In these conditions, the carrageenan extract properties determined by the polynomial model were 31.17%, 158.27 g.cm-2, and 29.5 cP for yield, gel strength, and viscosity, respectively, while under the experimental conditions they were 35.8 ± 4.68%, 112.50 ± 4.96 g.cm-2, and 16.01 ± 1.03 cP, respectively. The chemical composition, nuclear magnetic resonance spectroscopy, and infrared spectroscopy analyses showed that the crude carrageenan extracted is composed mainly of κ-carrageenan.

Optimization and functionality of millet supplemented pasta

Abstract Millets are having superior nutritional qualities and health benefits; hence they can be used for supplementation of pasta. Pasta was prepared using composite flour (CF) of durum wheat semolina (96%) and carrot pomace (4%) supplemented with finger millet flour (FMF, 0-20g), pearl millet flour (PMF, 0-30g) and carboxy methyl cellulose (CMC, 2-4g). Second order polynomial described the effect of FMF, PMF and CMC on lightness, firmness, gruel loss and overall acceptability of extruded pasta products. Results indicate that an increasing proportion of finger and pearl millet flour had signed (p≤0.05) negative effect on lightness, firmness, gruel loss and overall acceptability. However, CMC addition showed significant (p≤0. 05) positive effect on firmness, overall acceptability and negative effect on gruel loss of cooked pasta samples. Numeric optimization results showed that optimum values for extruded pasta were 20g FMF, 12g PMF and 4g CMC per 100g of CF and 34ml water with 0.981 desirability. The pasta developed is nutritionally rich as it contains protein (10.16g), fat (6g), dietary fiber (16.71g), calcium (4.23mg), iron (3.99mg) and zinc (1.682mg) per 100g.

Modeling and kinetic study of bio-ethanol production from soy protein concentrate by-product

Abstract The aim of this work was to evaluate a non-agitated process of bioethanol production from soybean molasses and the kinetic parameters of fermentation using a strain of Saccharomyces cerevisiae (ATCC® 2345). Kinetic experiment was conducted in medium with 30% (w v-1) of soluble solids without supplementation or pH adjustment. The maximum ethanol concentration was in 44 hours, the ethanol productivity was 0.946 g L-1 h-1, the yield over total initial sugars (Y1) was 47.87%, over consumed sugars (Y2) was 88.08% and specific cells production rate was 0.006 h-1. The mathematical polynomial was adjusted to the experimental data and provided very similar parameters of yield and productivity. Based in this study, for one ton of soybean molasses can be produced 103 kg of anhydrous bioethanol.

Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

Socio-demographic factors, smoking, symptoms, morbidities and pulmonary function and quality of life in individuals with a heavy smoking history

Objective: To determine which socio-demographic, exposure, morbidity and symptom variables are associated with health-related quality of life among former and current heavy smokers. Methods: Cross sectional data from 2537 participants were studied. All participants were at ≥2% risk of developing lung cancer within 6 years. Linear and logistic regression models utilizing a multivariable fractional polynomial selection process identified variables associated with health-related quality of life, measured by the EQ-5D. Results: Upstream and downstream associations between smoking cessation and higher health-related quality of life were evident. Significant upstream associations, such as education level and current working status and were explained by the addition of morbidities and symptoms to regression models. Having arthritis, decreased forced expiratory volume in one second, fatigue, poor appetite or dyspnea were most highly and commonly associated with decreased HRQoL. Discussion: Upstream factors such as educational attainment, employment status and smoking cessation should be targeted to prevent decreased health-related quality of life. Practitioners should focus treatment on downstream factors, especially symptoms, to improve health-related quality of life.

Reduced power output in skeletal muscles devoid of skMLCK: RLC phosphorylation contributes to peak performance

Regulatory light chain (RLC) phosphorylation in fast twitch muscle is catalyzed by skeletal myosin light chain kinase (skMLCK), a reaction known to increase muscle force, work, and power. The purpose of this study was to explore the contribution of RLC phosphorylation on the power of mouse fast muscle during high frequency (100 Hz) concentric contractions. To determine peak power shortening ramps (1.05 to 0.90 Lo) were applied to Wildtype (WT) and skMLCK knockout (skMLCK-/-) EDL muscles at a range of shortening velocities between 0.05-0.65 of maximal shortening velocity (Vmax), before and after a conditioning stimulus (CS). As a result, mean power was increased to 1.28 ± 0.05 and 1.11 ± .05 of pre-CS values, when collapsed for shortening velocity in WT and skMLCK-/-, respectively (n = 10). In addition, fitting each data set to a second order polynomial revealed that WT mice had significantly higher peak power output (27.67 ± 1.12 W/ kg-1) than skMLCK-/- (25.97 ± 1.02 W/ kg-1), (p < .05). No significant differences in optimal velocity for peak power were found between conditions and genotypes (p > .05). Analysis with Urea Glycerol PAGE determined that RLC phosphate content had been elevated in WT muscles from 8 to 63 % while minimal changes were observed in skMLCK-/- muscles: 3 and 8 %, respectively. Therefore, the lack of stimulation induced increase in RLC phosphate content resulted in a ~40 % smaller enhancement of mean power in skMLCK-/-. The increase in power output in WT mice suggests that RLC phosphorylation is a major potentiating component required for achieving peak muscle performance during brief high frequency concentric contractions.