Stable denominators for the simplification of z-Transfer Functions

A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m₁ and m₂ = m−m₁ zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m₁=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method.     

Induction of Multiple Sclerosis and Response to Tyrosine Kinase Inhibitors

The goal of this work is to determine the role of the autoimmune cells in multiple sclerosis (MS) induction and the immunomodulatory mechanism of therapy with tyrosine kinase inhibitors (TKIs) in MS attenuation. Samples (5 × 10⁵ cells per well) of C6 and primary rat astrocytes were stimulated with 10 ng/mL of platelet-derived growth factor (PDGFbb) as a positive control forming a mouse model of MS. PDGFbb was added to the astrocytes in the absence or presence of 0.1 and 1 μM of imatinib. Proliferation of C6 and primary rat astrocytes samples were assessed for samples staging by the addition of 1 μCi of ³H-thymidine per well. Samples of RAW 264.7 cells were stimulated for 48 h with 10 ng/mL of PDGFbb in the absence or presence of 0.1 and 1 μM of sorafenib. Tumour necrotic factor (TNF) levels in culture supernatants from RAW 264.7 cells were measured by ELISA. The histologic grade (H_G) and the level of TNF of the mouse model of MS was 1/5 and 5 times respectively of those in the control one to clarify that MS induction is due to a major decrease in H_G inversely proportional to the accompanied increase in TNF level perpetuating local inflammation and demyelination in MS lesion. The addition of 0.1 and 1 μM doses of imatinib increased H_G of the mouse model of MS by 6 and 11 times respectively while 0.1 and 1 μM doses of sorafenib decreased TNF level to be 1/2 and 1/5 of that in the mouse model of MS respectively restoring normal rate of TNF level of normal lesion to show that H_Gand TNF level would be strongly inversely correlated (r = −0.99) in attenuating MS effectively by TKIs therapy but not in an inverse proportion as in MS induction.     

Theory of nonlinear systems

This paper gives a general review of the Theory of Nonlinear Systems. In 1960, the author presented a paper “Theory of Nonlinear Control” at the First IFAC Congress at Moscow. Professor Norbert Wiener, who attended this Congress, drew attention to his work on the synthesis and analysis of nonlinear systems in terms of Hermitian polynomials in the Laguerre coefficients of the past of the input.Wiener's original idea was to use white noise as a probe on any nonlinear system. Applying this input to a Laguerre network gives u₁, u₂,…, u_s, and then to a Hermite polynomial generator gives V(α)'s. Applying the same input to the actual nonlinear system gives output c(t). Putting c(t) and V(α)'s through a product averaging device, we get $\text{c(t)V(α)}\text{=}\text{A}{}_{\mathrm{\alpha }}\text{2л}{}^{\mathrm{<mtext>s</mtext><mtext>2</mtext>}}$, where the upper bar denotes time average and A_α's can be considered as characteristic coefficients of the nonlinear system. A desired output z(itt) may replace c(itt) to get a new set of A_α's.The Volterra functional method suggested by Wiener in 1942 has been greatlydeveloped from 1955 to the present. The method involves a multi-dimensional convolution integral with multi- dimensional kernels. The associated multi-dimensional transforms are given by Y.H. Ku and A.A. Wolf (J. Franklin Inst., Vol. 281, pp. 9–26, 1966). Wiener extended the Volterra functionals by forming an orthogonal set of functionals known as G-functionals, using Gaussian white noise as input. Volterra kernels and Wiener kernels can be correlated and form the characteristic functions of nonlinear systems.From an extension of the linear system to the nonlinear system, the input-output crosscorrelation φ_xy can be shown to be equal to the convolution of system impulse response h₁ with the autocorrelation φ_xx. Using the white noise as input, where its power density spectrum is a constant, say, A, the crosscorrelation is given by φ_xy(σ) = Ah₁(σ), while the autocorrelation is φ_xx(τ) = Au(τ). This extension forms the basis of an optimum method for nonlinear system identification. Measurement of kernels can be made through proper circuitry.Parallel to the Volterra series and the Wiener series, another series based on Taylor-Cauchy transforms developed since 1959 are given for comparison. The Taylor-Cauchy transform method can be applied in the analysis of simultaneous nonlinear systems. It is noted that the Volterra functional method and the Taylor-Cauchy transform method give identical final results.A selected Bibliography is appended not only to include other aspects of nonlinear system theory but also to show the wide application of nonlinear system characterization and identification to problems in biology, ecology, physiology, cybernetics, control theory, socio- economic systems, etc.     

Symmetric and innerwise matrices for the root-clustering and root-distribution of a polynomial

The general problem of root-clustering and root-distribution of a polynomial in a certain region Γ in the complex plane has been investigated in this paper. The region Γ is general and includes all the previously investigated regions. For the root-clustering problem, it is shown that by using a certain transformation, the necessary and sufficient condition can be represented either in terms of positive definite (p.d.) or positive innerwise (p.i.) matrices. The entries in these matrices are rational functions of the coefficients of the polynomial. The connection between p.d. and p.i. matrices is established in terms of matrix multiplication.     

Possible Role of microRNA-122 in Modulating Multidrug Resistance of Hepatocellular Carcinoma

Hepatocellular carcinoma (HCC) is a hypervascular primary liver cancer characterized by rapid progression, besides, resistance to traditional chemotherapeutic agents. It has been shown that microRNAs play critical roles in regulation of tumor cell sensitivity to drugs through modulating the expression of genes involved in drug transport. The present study investigated whether restoration of miR-122 in HCC cells could alter the cell cycle distribution and the expression of multidrug resistance (MDR)-related genes (ABCB1, ABCC1, ABCG2 and ABCF2). After overexpression of miR-122 in HepG2 cells treated or untreated with doxorubicin doses, total RNAs and protein extracts were isolated for application of QRT-PCR and western blotting techniques. Moreover, cell cycle distribution was monitored by flow cytometry. Our results revealed that, the over expression of miR-122 in HepG2 cells treated or untreated with doxorubicin could modulate the sensitivity of cells to chemotherapeutic drug through downregulation of MDR-related genes, ABCB1 and ABCF2. Interpretation of cell cycle distribution revealed that, the anti-proliferative effect of miR-122 is associated with the accumulation of cells in G₀/G1 phase. Moreover, treatment with miR-122 and doxorubicin resulted in high percentage of HCC cells in G₀/G1 phase. Taken together, our findings revealed that, overexpression of miR-122 inhibited HCC cell growth by inducing cell cycle arrest and this arrest is associated with down-regulation of MDR-related genes.     

Lack of precision in HbA1c values on variant II in cases of hemoglobin Q India

This study was carried out to check the precision of HbA_1c values on Bio-Rad Variant II in cases of a rare hemoglobin variant Q India. The study was carried out over a three month period on samples collected for HbA_1c estimation. Seven out of eleven patients showed variable results of HbA_1c with a very high and unacceptable intraday mean coefficient of variation (CV) of 9.93%. We conclude, that the results of HbA_1c on Variant II can not be reported without adversely affecting HbA_1c as a marker of long-term glycemic control in patients who have hemoglobin Q India. The HbA_1c value of these patients needs to be assessed by a different instrument/method or the glycemic control be monitored by an alternate test like serum Fructosamine.     

Relationship between free iron and glycated hemoglobin in uncontrolled type 2 diabetes patients associated with complications

Free iron in serum has been found in several disease conditions including diabetes. In the present work, we studied the relationship between free iron, fasting blood glucose (FBG) and glycated haemoglobin (HbA_1c). Study was carried out on 50 type 2 diabetes cases under poor glycemic control associated with complications, 53 type 2 diabetes cases under good glycemic control and 40 healthy controls. We estimated free iron, both ferrous (Fe⁺²) and ferric (Fe⁺³) form, protein thiols, lipid hydroperoxides, FBG, HbA1c and serum ferritin levels in serum. There was a significant increase in free iron in Fe⁺³ state (p <0.01), HbA_1c (p<0.01), serum ferritin (p<0.01), lipid hydroperoxides (p<0.01) and significant decrease in protein thiols (<0.01) in diabetes cases under poor glycemic control compared to diabetes cases under good glycemic control and healthy controls. Free iron correlated positively with HbA_1c (p<0.01). Poor glycemic control and increase in glycation of haemoglobin is contributing to the increase in free iron pool which is known to increase oxidant generation.     

Periodic solutions to systems of reaction-diffusion equations

In this paper, necessary and sufficient conditions are derived for the existence of temporally periodic “dissipative structure” solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion equations ?c_i/?t = D_i?²c_i+Q_i(c), where the enumerator index i runs 1 to n, c_i = c_i(x, t) denotes the concentration or density of the ith participating molecular or biological species, D_i is the diffusivity constant for the ith species and Q_i(c), an algebraic function of the n-tuple c = (c₁,\3., c_n), expresses the local rate of production of the ith species due to chemical reactions or biological interactions.     

Central suboptimal H∞ filtering for nonlinear polynomial systems with multiplicative noise

This paper presents the central finite-dimensional H_∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in [1]. The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H₂ filter given in [31]. The central suboptimal H_∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.     

The inverse lure problem of optimal control

Given the linear system $\text{x}\text{}$ = Ax - bu, y = c^Tx, it is shown that, for a certain non-quadratic cost functional, the optimal control is given by u_opt(x) = h(c^Tx), where the function h(y) must satisfy the conditions ky²?h(y)y>0 for y≠0, h(0) = 0 and existence of h^-1 everywhere. The linear system considered must satisfy the Popov condition 1/k + (1 +?ωβ) G(?ω)>0 for all ω, G(s) being the y(s)/u(s) transfer function.     

A test for robust Hurwitz stability of convex combinations of complex polynomials

In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p₀(s)+λp₁(s), where λ∈[0,1] and p₀(s) and p₁(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure.     

A new approach to numerical integration by means of steady-state flux in a slab

The definite integral is generally interpreted geometrically as an “area”. An alternate interpretation as a steady-state “flux” through a unit slab is derived, which leads to a new method of numerical integration. The usual sum of a large number of approximate areas is replaced by the flux through a “single” increment.The method involves the solution of a system of linear finite difference equations. The coefficient matrix is tri-diagonal and is solved efficiently by the Thomas algorithm. During the iterative process the coefficients are determined by simple quadrature schemes applied to each increment.Error analysis revealed that an expression could be derived for the roundoff error associated with the final Thomas iteration. It is shown that the roundoff error is smallest when the matrix coefficients a_k\S>1. The method is shown to be superior to the classical methods due to its simplicity and tolerance for variable increment size. In addition, a new function is determined which is useful in diffusion studies. Numerical data are presented confirming these results.     

Interpreting HbA1c in Presence of Deficiency Anemias

HbA1c is used extensively for the diagnosis and management of diabetes mellitus. It constitutes 80% of glycated HbA1(Glycated haemoglobin(GHb)A), and depends upon blood glucose and RBC life span. RBC life span varies with anemia, leading to a consequent alteration in the HbA1c value irrespective of the circulating blood glucose concentration. But to the best of our knowledge no Hb cut offs have been derived for appropriate interpretation of HbA1c. The prevalence of anemia in Indian population is nearly 40% as per its definition by WHO—Hb < 12 g/dL in females and < 13 g/dL in males—with most cases attributable to nutritional deficiencies. Hence, we aimed to identify Hb cut-off for accurate interpretation of HbA_1c in presence of deficiency anemias. Partial correlation between random blood glucose (RBG) and HbA_1c was studied in 1312 subjects, 470 of whom had deficiency-related anemia]. The data was adjusted for age, sex and Hb. Partial correlation between RBG and HbA1c was highly significant (p < 0.0001) till Hb of 8.1 gm/dL. Significance reduced to p = 0.003 and p = 0.006 as the cut off of Hb reduced to 7.1 gm/dL and 5.0 gm/dL, respectively, but was not lost. Hence, caution in interpretation of HbA_1c is not required till an Hb of 5 g/dL.     

A new approach to the design of coupling networks

Mathematical results are derived, which enable one to find a vector of parameters k⁰ such that (P₁(s,k⁰)?H)∩(P₂(k⁰)=0), where P₁(s,k) is a polynomial in s and in the components of k,P₂(k) is a polynomial in the components of k, and H is the set of Hurwitz polynomials. The algorithm is based on an extension of the root locus technique to the multiparameter case. The design problem of coupling networks between a resistive generator and a passive load, under prescribed power gain characteristics, is translated into the above formulation. A numerical example is provided.     

Charmonium and charmoniumlike states at the BESIII experiment

Charmonium is a bound state of a charmed quark and a charmed antiquark, and a charmoniumlike state is a resonant structure that contains a charmed quark and antiquark pair but has properties that are incompatible with a conventional charmonium state. While operating at center-of-mass energies from 2 to 5 GeV, the BESIII experiment can access a wide mass range of charmonium and charmoniumlike states, and has contributed significantly in this field. We review BESIII results involving conventional charmonium states, including the first observation of the M1 transition ψ(2S) → γη_c(2S) and the discovery of the ψ₂(3823) state; and report on studies of charmoniumlike states, including the discoveries of the Z_c(3900) and Z_c(4020) tetraquark candidates, the resolution of the fine structure of the Y(4260) state, the discovery of the new production process e⁺e⁻ → γX(3872) and the uncovering of strong evidence for the commonality among the X(3872), Y(4260) and Z_c(3900) states. The prospects for further research at BESIII and proposed future facilities are also presented.     

Nonlinear H∞ feedback control with integrator for polynomial discrete-time systems

This paper investigates the problem of designing a nonlinear _H∞$H_{\infty }$ feedback controller for polynomial discrete-time systems with and without polytopic uncertainties. The objective is to design a controller such that the ratio between the energy of the regulated outputs and the energy of the exogenous disturbance/inputs is minimized or guaranteed to be less or equal to a prescribed value. It is well known that the state dependant or parameter dependant Lyapunov function is always chosen for synthesizing polynomial discrete-time systems. This leads the solution to be nonconvex because the Lyapunov function and the controller matrix are coupled and therefore cannot be solved by semidefinite programming (SDP). Hence, in this paper, an integrator is proposed to be incorporated into the controller structure. In doing so, the coupling of Lyapunov function and controller matrix can be eliminated effectively. This somehow simplifies the numerical solution of the problem. Then, by using SOS decomposition approach, sufficient conditions for the existence of the proposed controller are provided in terms of solvability of the state-dependent linear matrix inequalities (SDLMIs) which can be solved by SDP. A tunnel diode circuit is used to demonstrate the effectiveness of this integrator approach.     

A multivariable bounded-reality criterion

The multivariable approach to the synthesis of networks composed of a finite number of uniform lossless transmission lines, commensurable or incommensurable, and lumped passive elements is verified by showing that the multivariable rational matrix, W(λ₀,λ₁, .. ,λn) is bounded real in (n + 1) complex variables if and only if W is bounded real in p after substituting, λ₀ = α₀p + β₀ and λ_i = tanh (α_ip + β_i) for λ_i (1?i?n) where all the α's and β's are nonnegative and arbitrary, except for being not simultaneously zero in like indexed pairs. Consequences of this result are discussed.     

Ethanolic leaves extract of <Emphasis Type="Italic">Trianthema portulacastrum</Emphasis> L. ameliorates aflatoxin B<Subscript>1</Subscript> induced hepatic damage in rats

Aflatoxins are potent hepatotoxic and hepatocarcinogenic agents. Reactive oxygen species and consequent peroxidative damage caused by aflatoxin are considered to be the main mechanisms leading to hepatotoxicity. The present investigation aims at assessing the hepatoprotective effect of ethanolic leaves extract of Trianthema portulacastrum on aflatoxin B₁ (AFB₁)-induced hepatotoxicity in a rat model. The hepatoprotection of T. portulacastrum is compared with silymarin, a well known standard hepatoprotectant. Lactate dehydrogenase, alkaline phosphatase, alanine and aspartate aminotransferases were found to be significantly increased in the serum and decreased in the liver of AFB₁ administered (1 mg/kg bw, orally) rats, suggesting hepatic damage. Marked increase in the lipid peroxide levels and a concomitant decrease in the enzymic (superoxide dismutase, catalase, glutathione peroxidase, glutathione reductase, glucose-6-phosphate dehydrogenase and glutathione-S-transferase) and nonenzymic (reduced glutathione, vitamin C and vitamin E) antioxidants in the hepatic tissue were observed in AFB1 administered rats. Pretreatment with T. portulacastrum (100 mg/kg/p.o) and silymarin (100 mg/kg /p.o) for 7 days reverted the condition to near normal. The results of this study indicate that the ethanolic leaves extract of T. portulacastrum is a potent hepatoprotectant as silymarin.     

Haemoglobin A1c-based screening for prediabetes and diabetes mellitus: a multi-center study in Croatian adult population

IntroductionBased on the hypothesis that there is a substantial rate of adults with prediabetes and undiagnosed diabetes mellitus (DM), our aim was to perform haemoglobin A1c (HbA_1c)-based screening in a cohort of Croatian adults and estimate the prevalence of prediabetes and undiagnosed DM according to American Diabetes Association criteria.Materials and methodsThis multi-center, cross-sectional study performed in six Croatian hospitals included 5527 patients aged 40 to 70 years admitted to the Emergency Department or undergoing a primary care check-up. Haemoglobin A1c was measured from leftover whole blood samples using the enzymatic method on either Alinity c or Architect c-series analyser (Abbott Laboratories, Chicago, USA). Haemoglobin A1c between 39-47 mmol/mol was classified as prediabetes, while ≥ 48 mmol/mol as undiagnosed DM.ResultsAfter exclusion of 435 patients with known DM, the final cohort included 5092 patients (median age 57; 56% males). A total of 882 (17.3%) patients had HbA_1c values between 39 and 47 mmol/mol. There were 214 (4.2%) patients with HbA_1c ≥ 48 mmol/mol. Prediabetes prevalence ranged from 14.2% to 20.5%, while undiagnosed DM from 3.3% to 7.3%, with statistically significant differences among settings (P < 0.001). Age-stratified analysis showed that prediabetes and undiagnosed DM prevalence increase with age (P < 0.001), being 25.4% and 5.8%, respectively, in patients aged 60 to 70 years.ConclusionUnderlying impairment of glucose metabolism was identified in about one in five adults, with significant number of patients with already overt DM. These results should serve as a starting point for further steps directed towards promotion of preventive measures for DM in Croatia.