Polynomial Optimization with Applications to Stability Analysis and Control - Alternatives to Sum of Squares

In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation Linear Techniques, Blossoming and Groebner basis methods, our main focus is on algorithms defined by Polya's theorem, Bernstein's theorem and Handelman's theorem. We first formulate polynomial optimization problems as verifying the feasibility of semi-algebraic sets. Then, we discuss how Polya's algorithm, Bernstein's algorithm and Handelman's algorithm reduce the intractable problem of feasibility of semi-algebraic sets to linear and/or semi-definite programming. We apply these algorithms to different problems in robust stability analysis and stability of nonlinear dynamical systems. As one contribution of this paper, we apply Polya's algorithm to the problem of H_infinity control of systems with parametric uncertainty. Numerical examples are provided to compare the accuracy of these algorithms with other polynomial optimization algorithms in the literature.Comment: AIMS Journal of Discrete and Continuous Dynamical Systems - Series

A Multi-objective Approach to Optimal Battery Storage in The Presence of Demand Charges

In this paper, we propose an optimization framework for optimal energy storage, in the form of batteries, by residential customers. Our goal is to determine the value of battery storage to those customers whose electricity bills consist of both Time-of-Use charges ($/kWh, with different rates for on-peak and off-peak hours) and demand charges ($/kW, proportional to the peak rate of consumption in a month). The customers may have access to a local power generating source in the form of solar PhotoVoltaic (PV). In order to quantify the benefits from the battery storage, we pose a battery optimization problem which minimizes the monthly electricity bill 30 poff ∑k∈off q(k)Δt + 30 pon ∑k∈on q(k)Δt + pd supk∈on q(k), where poff, pon, pd are the off-peak, on-peak and demand prices, and q(k) is the power delivered by the utility company to the customer. We consider this power to be used according to q(k) = qb(k) + qa(k) - qsolar(k), where qa is the power consumed by the appliances, qsolar is the power provided by the solar PV, and qb is the power given to or taken from the battery. We assume that the rate of the energy stored in the battery is proportional to qb and the stored energy is bounded by the battery’s capacity (kWh). Furthermore, we account for the battery degradation by modeling the battery’s capacity as a function of the number of charging/discharging cycles and the depth of discharge. Because of the presence of demand charges (supk q(k)), the objective function of our battery optimization problem is not separable in time - a property (time separability) which is a sufficient for the dynamic programming algorithm to converge to an optimal solution. We establish a provably convergent algorithm for the non-separable optimization problem in the following two steps. First, we replace supk q(k) in the objective function using the following approximation                                                           supk∈on q(k) = q(k) l∞ = (∑k∈on q(k)p)1/p for some large p. Then, we construct a multi-objective problem (a class of optimization problems involving at least two objective functions to be minimized simultaneously) defined by a parameterized set of dynamic programs expressed in terms of the time-separable functions J1(q) = ∑k q(k) J2(q) = ∑k∈on q(k)p Each of these parameterized dynamic programs can be solved using the standard dynamic programming algorithms. The set of solutions to these parameterized problems form a Pareto front - a set which is guaranteed to contain the solution to the original battery optimization problem as p → ∞. We apply our algorithm to multiple scenarios described by a range battery sizes, solar generation levels and appliances loads to quantify the savings from the batteries for a wide range of residential customers. The proposed approach can be potentially used to: 1) Model customers response to changes in electricity prices; 2) Quantify the benefits of energy storage to utility companies

Sex-specific-differences in cardiovascular risk in type-1-diabetes : a cross sectional study

Background: Little is known about the impact of sex-specific differences in the management of type 1 diabetes (T1DM). Thus, we evaluated the influence of gender on risk factors, complications, clinical care and adherence in patients with T1DM. Methods: In a cross-sectional study, sex-specific disparities in glycaemic control, cardiovascular risk factors, diabetic complications, concomitant medication use and adherence to treatment recommendations were evaluated in 225 consecutive patients (45.3% women) who were comparable with respect to age, diabetes duration, and body mass index. Results: Although women with T1DM had a higher total cholesterol than men, triglycerides were higher in obese men and males with HbA1c>7% than in their female counterparts. No sex differences were observed in glycaemic control and in micro- or macrovascular complications. However, the subgroup analysis showed that nephropathy was more common in obese men, hyperlipidaemic women and all hypertensive patients, whereas peripheral neuropathy was more common in hyperlipidaemic women. Retinopathy was found more frequently in women with HbA1c>7%, obese men and in both sexes with a long duration of diabetes. The multivariate analysis revealed that microvascular complications were associated with the duration of disease and BMI in both sexes and with hyperlipidaemia in males. The overall adherence to interventions according to the guidelines was higher in men than in women. This adherence was concerned particularly with co-medication in patients diagnosed with hypertension, aspirin prescription in elderly patients and the achievement of target lipid levels following the prescription of statins. Conclusions: Our data showed sex differences in lipids and overweight in patients with T1DM. Although glycaemic control and the frequency of diabetic complications were comparable between the sexes, the overall adherence to guidelines, particularly with respect to the prescription of statins and aspirin, was lower in women than in men

Chlamydia pneumoniae and Helicobacter pylori IgG seropositivities are not predictors of osteoporosis‑associated bone loss: a prospective cohort study

The potential link between infection with Chlamydia pneumoniae or Helicobacter pylori and osteoporosis has not been investigated in population-based longitudinal studies. A total of 250 healthy postmenopausal women who participated in a prospective cohort study were evaluated for IgG antibodies directed against C. pneumoniae and H. pylori, osteoprotegerin (OPG), the receptor activator of nuclear factor kappa B ligand (RANKL), CrossLaps, and osteocalcin. Bone mineral density (BMD) was measured at the femoral neck and lumbar spine at baseline and at follow- up 5.8 years later. There were no significant differences in age-adjusted bone turnover markers, OPG, RANKL, the RANKL/OPG ratio, and BMD between the C. pneumoniae and H. pylori IgG seropositive and seronegative subjects (P > 0.05). Neither C. pneumoniae nor H. pylori IgG seropositivity was associated with age-and body massindex-adjusted BMD at the femoral neck and lumbar spine or bone loss at the 5.8-year follow-up. In logistic regression analysis, neither C. pneumoniae nor H. pylori IgG seropositivities predicted incident lumbar or spine osteoporosis 5.8 years later. In conclusion, neither C. pneumoniae nor H. pylori IgG seropositivity was associated with bone turnover markers, the RANKL/OPG ratio, BMD, or bone loss in postmenopausal women. In addition, chronic infection with C. pneumoniae or H. pylori did not predict incident osteoporosis among this group of wome

Testosterone Level and Coronary Artery Disease in Iranian Men; a Systematic Review

Coronary artery disease (CAD) is among the most common cardiovascular diseases (CVDs), caused by the formation of plaques of lipids, calcium, and inflammatory cells. In Iran, CAD is responsible for about 50% of all deaths per year. There is also a probability of the role of androgens deficiency in CAD in men. We aimed to systematically review all the related original studies to achieve an overall insight into the associations of testosterone and CAD in Iranian men.  MedLine, Web of Science, Scopus, and Google scholar databases were searched from inception to January 2021. All types of studies on Iranian men older than 40 years of age, reporting results of comparing testosterone in normal individuals and those with CAD were included. The main findings of the articles were compared to achieve an overall statement. Ultimately, six studies were included. Most (66.7%) had directly stated that lower levels of testosterone are associated with CAD or the level of testosterone is lower in patients with proven CAD. Among them, in 3 (50%) studies, the mean age of the participants had no significant difference between patients with CAD and the normal group. It is clear that low testosterone level is associated with increased risk of cardiovascular events but it is not definitely determined whether it is independent of age in Iranian men.  Further well-designed studies are needed to clearly exclude all confounding variables including age and show the net effect of testosterone on CAD

Enhancement of heavy metals sorption via nanocomposites of rice straw and Fe3O4 nanoparticles using artificial neural network (ANN)

The artificial neural network (ANN) modeling of adsorption of Pb(II) and Cu(II) was carried out for determination of the optimum values of the variables to get the maximum removal efficiency. The input variables were initial ion concentration, adsorbent dosage, and removal time, while the removal efficiency was considered as output. The performed experiments were designed into two data sets including training, and testing sets. To acquire the optimum topologies, ANN was trained by quick propagation (QP), Batch Back Propagation (BBP), Incremental Back Propagation (IBP), genetic algorithm (GA) and Levenberg-Marquardt (LM) algorithms for testing data set. The topologies were defined by the indicator of minimized root mean squared error (RMSE) for each algorithm. According to the indicator, the IBP-3-9-2 was selected as the optimized topologies for heavy metal removal, due to the minimum RMSE and maximum R-squared