Limit Cycle Prediction of Systems with Fractional Controllers and Backlash

This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

Aortic stenosis. Gender influence on left ventricular geometry and function in patients under 70 years of age

OBJECTIVE: To verify if adaptive left ventricle (LV) characteristics are also present in individuals under 70 years of age with severe aortic stenosis (AS). METHODS: The study comprised 40 consecutive patients under 70 years of age with AS and no associated coronary artery disease, referred for valve surgery. Out of the 40 patients, 22 were men and 18 women, and the mean age was 49.8±14.3 years. Cardiac symptoms, presence of systemic hypertension (SH), functional class according to the New York Heart Association (NYHA), and valve lesion etiology were considered. LV cavity dimensions, ejection fraction (EF), fractional shortening (FS), mass (MS), and relative diastolic thickness (RDT) were examined by Doppler echocardiography. RESULTS: Fourteen (63.6%) men and 11 (61.6%) women were classified as NYHA class III/IV (p=0.70). There was no difference in the frequency of angina, syncope or dyspnea between genders. The incidence of SH was greater in women than in men (10 versus 2, p=0.0044). Women had a smaller LV end-diastolic diameter index (32.1±6.5 x 36.5±5.3mm/m², p=0.027), LV end-systolic diameter index (19.9±5.9 x 26.5±6.4mm/m², p=0.0022) and LV mass index (MS) (211.4±71.1 x 270.9±74.9g/m², p=0.017) when compared with men. EF (66.2±13.4 x 52.0±14.6%, p=0.0032), FS (37.6±10.7 x 27.9±9.6%, p=0.0046) and RDT (0.58±0.22 x 0.44±0.09, p=0.0095) were significantly greater in women than in men. CONCLUSION: It is the patient gender rather than age that influences left ventricular adaptive response to AS.

Follow-up study of morphology and cardiac function in rats undergoing induction of supravalvular aortic stenosis

OBJECTIVE: To characterize the follow-up of an experimental model of left ventricular hypertrophy (LVH) induced by supravalvular ascending aortic stenosis in young rats. METHODS: Wistar rats were submitted to thoracotomy and aortic stenosis was created by placing a clip on the ascending aorta (AoS group, n=12). Age-matched control animals underwent a sham operation (C group, n=12). Cardiac function was analysed by echocardiograms performed 6, 12, and 21 weeks after aortic banding. Myocardial morphological features and myocardial hydroxyproline concentration (HOP) were evaluated 2, 6, 12, and 21 weeks after surgery in additional animals. RESULTS: Aortic banding promoted early concentric LVH and a progressive increase in HOP. Under light microscopy, we observed myocyte hypertrophy and wall thickening of the intramural branches of the coronary arteries due to medial hypertrophy. Cardiac function was supranormal after 6 weeks (percentage of fractional shortening - EAo6: 70.3±10.8; C6: 61.3±5.4; p<0.05), and depressed in the last period. Diastolic dysfunction was detected after 12 weeks (ratio of early-to-late filling velocity - EAo12: 4.20±3.25; C12: 1.61±0.16; p<0.05). CONCLUSION: Ascending aortic stenosis promotes concentric LVH with myocardial fibrosis and minimal histological changes. According to the period of evaluation, cardiac function may be improved, normal, or depressed. The model is suitable and useful for studies on pathophysiology and treatment of the different phases of cardiac hypertrophy.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Impaired renal function in owl monkeys (Aotus nancymai) infected with Plasmodium falciparum

Impaired renal function was observed in sixteen Aotus nancymai 25 and 3 months following infection with the Uganda Palo Alto strain of Plasmodium falciparum. Decrease were noted in the clearance of endogenous creatinine, creatinine excretion, and urine volume while increases were observed in serum urea nitrogen, urine protein, urine potassium, fractional excretion of phosphorus and potassium, and activities of urinary enzymes. The results were suggestive of glomerulonephropathy and chronic renal disease.

Association of CYP3A5 genotypes with blood pressure and renal function in African families.

OBJECTIVE: Renal cytochrome P450 3A5 (CYP3A5) activity has been associated with blood pressure and salt sensitivity in humans. We determined whether CYP3A5 polymorphisms are associated with ambulatory blood pressure (ABP) and with glomerular filtration rate (GFR) in African families. METHODS: Using a cross-sectional design, 375 individuals from 72 families, each with at least two hypertensive siblings, were recruited through a hypertension register in the Seychelles (Indian Ocean). We analyzed the association between the CYP3A5 alleles (*1, *3, *6 and *7) and ABP, GFR and renal sodium handling (fractional excretion of lithium), from pedigree data, allowing for other covariates and familial correlations. RESULTS: CYP3A5*1 carriers increased their daytime systolic and diastolic ABP with age (0.55 and 0.23 mmHg/year) more than non-carriers (0.21 and 0.04 mmHg/year). CYP3A5*1 had a significant main effect on daytime systolic/diastolic ABP [regression coefficient (SE): -29.6 (10.0)/-8.2 (4.1) mmHg, P = 0.003/0.045, respectively] and this effect was modified by age (CYP3A5*1 x age interactions, P = 0.017/0.018). For night-time ABP, the effect of CYP3A5*1 was modified by urinary sodium excretion, not by age. For renal function, CYP3A5*1 carriers had a 7.6(3.8) ml/min lower GFR (P = 0.045) than non-carriers. Proximal sodium reabsorption decreased with age in non-carriers, but not in CYP3A5*1 carriers (P for interaction = 0.02). CONCLUSIONS: These data demonstrate that CYP3A5 polymorphisms are associated with ambulatory BP, CYP3A5*1 carriers showing a higher age- and sodium- related increase in ABP than non-carriers. The age effect may be due, in part, to the action of CYP3A5 on renal sodium handling.

In Bacillus subtilis W23, the duet sigmaXsigmaM, two sigma factors of the extracytoplasmic function subfamily, are required for septum and wall synthesis under batch culture conditions.

The synthesis of poly(RboP), the main Bacillus subtilis W23 teichoic acid, is encoded by tarDF-tarABIJKL operons, the latter being controlled by two promoters designated PtarA-int and PtarA-ext. Analysis by lacZ fusions reveals that PtarA-int activity exhibits sharp increases at the beginning and end of the transition between exponential and stationary growth phase. As confirmed by mRNA quantification, these increases are mediated by ECF sigma factors sigmaX and sigmaM respectively. In liquid media, strain W23 sigX sigM double mutants experience serious difficulties in the transition and stationary growth phases. Inactivation of sigmaX- and sigmaM-controlled regulons, which precludes transcription from PtarA-int, leads to (i) delays in chromosome segregation and septation and (ii) a transient loss of up to 30% of the culture OD or lysis. However, specific inactivation of PtarA-int, leading mainly to a shortage of poly(RboP), does not affect growth while, nevertheless, interfering with normal septation, as revealed by electron microscopy. The different sigM transcription in strains W23 and 168 is discussed. In W23, expression of tarA and sigM, which is shown to control divIC, is inversely correlated with growth rate, suggesting that the sigM regulon is involved in the control of cell division.

A direct approach to the discounted penalty function

This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods.

Cannabidiol Protects against Doxorubicin-Induced Cardiomyopathy by Modulating Mitochondrial Function and Biogenesis.

Doxorubicin (DOX) is a widely used, potent chemotherapeutic agent; however, its clinical application is limited because of its dose-dependent cardiotoxicity. DOX's cardiotoxicity involves increased oxidative/nitrative stress, impaired mitochondrial function in cardiomyocytes/endothelial cells and cell death. Cannabidiol (CBD) is a nonpsychotropic constituent of marijuana, which is well tolerated in humans, with antioxidant, antiinflammatory and recently discovered antitumor properties. We aimed to explore the effects of CBD in a well-established mouse model of DOX-induced cardiomyopathy. DOX-induced cardiomyopathy was characterized by increased myocardial injury (elevated serum creatine kinase and lactate dehydrogenase levels), myocardial oxidative and nitrative stress (decreased total glutathione content and glutathione peroxidase 1 activity, increased lipid peroxidation, 3-nitrotyrosine formation and expression of inducible nitric oxide synthase mRNA), myocardial cell death (apoptotic and poly[ADP]-ribose polymerase 1 [PARP]-dependent) and cardiac dysfunction (decline in ejection fraction and left ventricular fractional shortening). DOX also impaired myocardial mitochondrial biogenesis (decreased mitochondrial copy number, mRNA expression of peroxisome proliferator-activated receptor γ coactivator 1-alpha, peroxisome proliferator-activated receptor alpha, estrogen-related receptor alpha), reduced mitochondrial function (attenuated complex I and II activities) and decreased myocardial expression of uncoupling protein 2 and 3 and medium-chain acyl-CoA dehydrogenase mRNA. Treatment with CBD markedly improved DOX-induced cardiac dysfunction, oxidative/nitrative stress and cell death. CBD also enhanced the DOX-induced impaired cardiac mitochondrial function and biogenesis. These data suggest that CBD may represent a novel cardioprotective strategy against DOX-induced cardiotoxicity, and the above-described effects on mitochondrial function and biogenesis may contribute to its beneficial properties described in numerous other models of tissue injury.

5C.09: Heritability of renal function parameters and electrolyte levels in the Swiss population

OBJECTIVE: Electrolytes handling by the kidney is essential for volume and blood pressure (BP) homeostasis but their distribution and heritability are not well described. We estimated the heritability of kidney function as well as of serum and urine concentrations, renal clearances and fractional excretions for sodium, chloride, potassium, calcium, phosphate and magnesium in a Swiss population-based study. DESIGN AND METHOD: Nuclear families were randomly selected from the general population in Switzerland. We estimated glomerular filtration rate (eGFR) using the CKD-EPI and MDRD equations. Urine was collected separately during day and night over 24-hour. We used the ASSOC program (S.A.G.E.) to estimate narrow sense heritability, including as covariates in the model: age, sex, body mass index and study center. RESULTS: The 1128 participants (537 men and 591 women from 273 families), had mean (sd) age of 47.4(17.5) years, body mass index of 25.0 (4.5) kg/m2 and CKD-EPI of 98.0(18.5) mL/min/1.73 m2. Heritability estimates (SE) were 46.0% (0.06), 48.0% (0.06) and 18.0% (0.06) for CKD-EPI, MDRD and 24-hour creatinine clearance (P < 0.05), respectively. Heritability [SE] of serum concentration was highest for calcium (37%[0.06]) and lowest for sodium (13%[0.05]). Heritabilities [SE] of 24-h urine concentrations and excretions, and of fractional excretions were highest for calcium (51%[0.06], 44%[0.06] and 51%[0.06], respectively) and lowest for potassium (11%[0.05], 10%[0.05] and 16%[0.06], respectively). All results were statistically different from zero.(Figure is included in full-text article.) CONCLUSIONS: : Serum and urine levels, urinary excretions and renal handling of electrolytes, particularly calcium, are heritable in the general adult population. Identifying genetic variants involved in electrolytes homeostasis may provide useful insight into the pathophysiological mechanisms involved in common chronic diseases such as kidney diseases, hypertension and diabetes.

On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

Temporal variability of soil CO2 emission after conventional and reduced tillage described by an exponential decay in time model

To study Assessing the impact of tillage practices on soil carbon losses dependents it is necessary to describe the temporal variability of soil CO2 emission after tillage. It has been argued that large amounts of CO2 emitted after tillage may serve as an indicator for longer-term changes in soil carbon stocks. Here we present a two-step function model based on soil temperature and soil moisture including an exponential decay in time component that is efficient in fitting intermediate-term emission after disk plow followed by a leveling harrow (conventional), and chisel plow coupled with a roller for clod breaking (reduced) tillage. Emission after reduced tillage was described using a non-linear estimator with determination coefficient (R²) as high as 0.98. Results indicate that when emission after tillage is addressed it is important to consider an exponential decay in time in order to predict the impact of tillage in short-term emissions.

Effect of chronic fish oil supplementation on renal function of normal and cachectic rats

In the present study we determined the effect of chronic diet supplementation with n-3 PUFA on renal function of healthy and cachectic subjects by providing fish oil (1 g/kg body weight) to female rats throughout pregnancy and lactation and then to their offspring post-weaning and examined its effect on renal function parameters during their adulthood. The animals were divided into four groups of 5-10 rats in each group: control, control supplemented with fish oil (P), cachectic Walker 256 tumor-bearing (W), and W supplemented with fish oil (WP). Food intake was significantly lower in the W group compared to control (12.66 ± 4.24 vs 25.30 ± 1.07 g/day). Treatment with fish oil significantly reversed this reduction (22.70 ± 2.94 g/day). Tumor growth rate was markedly reduced in the P group (16.41 ± 2.09 for WP vs 24.06 ± 2.64 g for W). WP group showed a significant increase in mean glomerular filtration rate compared to P and control (1.520 ± 0.214 ml min-1 kg body weight-1; P < 0.05). Tumor-bearing groups had low urine osmolality compared to control rats. The fractional sodium excretion decreased in the W group compared to control (0.43 ± 0.16 vs 2.99 ± 0.87%; P < 0.05), and partially recovered in the WP group (0.90 ± 0.20%). In summary, the chronic supplementation with fish oil used in this study increased the amount of fat in the diet by only 0.1%, but caused remarkable changes in tumor growth rate and cachexia, also showing a renoprotective function.