Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Nature, stability and bonding of the peroxy group in peroxy titanium compounds

Some physicochemical properties of peroxy titanium compounds are explained by assigning a strained triangular ring structure to the peroxy titanyl group, with a bent and reduced overlap of the O---O bonding orbitals. The stability of the peroxy group is found to depend on the stability of the other ligands. The decreasing order of stability of the peroxy group in the compounds is as: oxalato > meleato > malonato > sulphato > peroxide of titanium.

On self-interacting oligoribonucleotides. I. Absorption and optical rotatory dispersion of 2′-5′- and 3′-5′-oligoguanylic acids

A series of 2′-5′-oligoguanylic acids are prepared by reacting G(cyclic)p with takadiastase T1 ribonuclease and separating the products chromatographically. The 3′-5′-oligoguanylic acids are obtained by separating the products of alkaline degradation of 3′-5′-poly(G). The optical rotatory dispersion and hypochromism of both 2′-5′- and 3′-5′-oligoguanylic acids are studied at two different pH. The optical rotatory dispersion spectrum of 2′-5′-GpG is significantly different from that of 3′-5′-GpG. The magnitude of rotation of the long-wavelength peak of 2′-5′-GpG is larger than that of 3′-5′-GpG. This finding contradicts the explanation that the extra stability and more intense circular dichroism band of other 3′-5′-dinucleoside monophosphates is due to H-bond formation between 2′-OH and either the base or the phosphate oxygen. The end phosphate group has a marked effect on the spectrum of GpG between 230 and 250 mμ. In addition the optical rotatory dispersion spectra of 2′-5′ exhibit strong pH, temperature, and solvent dependence between 230 and 250 mμ. ΔH and AS for order ⇌ disorder transition is estimated to be 9.7 kcal/mole and 35.2 eu, respectively. The optical rotatory dispersion spectra of guanine-rich oligoribonucleotides, GpGpC, GpGpU, GpGpGpC, and GpGpGpU are compared to the calculated optical rotatory dispersion from the semiempirical expression of Cantor and Tinoco, using measured optical rotatory dispersion of dimers. Contrary to previous studies, agreement is found not at all satisfactory. However, optical rotatory dispersion of 3′-5′-GpGpGpC and GpGpGpU can be estimated from the semiempirical expression, if a next-nearest interaction parameter is introduced empirically. Such interaction parameter can be calculated from the measured properties of trinucleotide sequences like GpGpG, GpGpC, and GpGpU, assuming that only the nearest-neighbor interaction is important. The optical rotatory dispersion of single-stranded poly(G) is also predicted. The importance of syn-anti equilibrium and next-nearest-neighbor interaction in oligoguanylic acids is suggested as a probable explanation.

Expression of lactate transporters MCT1, MCT2, MCT4 and the ancillary protein CD147 in horse muscle and red blood cells

Monocarboxylate transporters (MCTs) transport lactate and protons across cell membranes. During intense exercise, lactate and protons accumulate in the exercising muscle and are transported to the plasma. In the horse, MCTs are responsible for the majority of lactate and proton removal from exercising muscle, and are therefore also the main mechanism to hinder the decline in pH in muscle cells. Two isoforms, MCT1 and MCT4, which need an ancillary protein CD147, are expressed in equine muscle. In the horse, as in other species, MCT1 is predominantly expressed in oxidative fibres, where its likely role is to transport lactate into the fibre to be used as a fuel at rest and during light work, and to remove lactate during intensive exercise when anaerobic energy production is needed. The expression of CD147 follows the fibre type distribution of MCT1. These proteins were detected in both the cytoplasm and sarcolemma of muscle cells in the horse breeds studied: Standardbred and Coldblood trotters. In humans, training increases the expression of both MCT1 and MCT4. In this study, the proportion of oxidative fibres in the muscle of Norwegian-Swedish Coldblood trotters increased with training. Simultaneously, the expression of MCT1 and CD147, measured immunohistochemically, seemed to increase more in the cytoplasm of oxidative fibres than in the fast fibre type IIB. Horse MCT4 antibody failed to work in immunohistochemistry. In the future, a quantitative method should be introduced to examine the effect of training on muscle MCT expression in the horse. Lactate can be taken up from plasma by red blood cells (RBCs). In horses, two isoforms, MCT1 and MCT2, and the ancillary protein CD147 are expressed in RBC membranes. The horse is the only species studied in which RBCs have been found to express MCT2, and the physiological role of this protein in RBCs is unknown. The majority of horses express all three proteins, but 10-20% of horses express little or no MCT1 or CD147. This leads to large interindividual variation in the capacity to transport lactate into RBCs. Here, the expression level of MCT1 and CD147 was bimodally distributed in three studied horse breeds: Finnhorse, Standardbred and Thoroughbred. The level of MCT2 expression was distributed unimodally. The expression level of lactate transporters could not be linked to performance markers in Thoroughbred racehorses. In the future, better performance indexes should be developed to better enable the assessment of whether the level of MCT expression affects athletic performance. In human subjects, several mutations in MCT1 have been shown to cause decreased lactate transport activity in muscle and signs of myopathy. In the horse, two amino acid sequence variations, one of which was novel, were detected in MCT1 (V432I and K457Q). The mutations found in horses were in different areas compared to mutations found in humans. One mutation (M125V) was detected in CD147. The mutations found could not be linked with exercise-induced myopathy. MCT4 cDNA was sequenced for the first time in the horse, but no mutations could be detected in this protein.

Generalizations and Models in Ecology : Lawlikeness, Invariance, Stability, and Robustness

The question at issue in this dissertation is the epistemic role played by ecological generalizations and models. I investigate and analyze such properties of generalizations as lawlikeness, invariance, and stability, and I ask which of these properties are relevant in the context of scientific explanations. I will claim that there are generalizable and reliable causal explanations in ecology by generalizations, which are invariant and stable. An invariant generalization continues to hold or be valid under a special change called an intervention that changes the value of its variables. Whether a generalization remains invariant during its interventions is the criterion that determines whether it is explanatory. A generalization can be invariant and explanatory regardless of its lawlike status. Stability deals with a generality that has to do with holding of a generalization in possible background conditions. The more stable a generalization, the less dependent it is on background conditions to remain true. Although it is invariance rather than stability of generalizations that furnishes us with explanatory generalizations, there is an important function that stability has in this context of explanations, namely, stability furnishes us with extrapolability and reliability of scientific explanations. I also discuss non-empirical investigations of models that I call robustness and sensitivity analyses. I call sensitivity analyses investigations in which one model is studied with regard to its stability conditions by making changes and variations to the values of the model s parameters. As a general definition of robustness analyses I propose investigations of variations in modeling assumptions of different models of the same phenomenon in which the focus is on whether they produce similar or convergent results or not. Robustness and sensitivity analyses are powerful tools for studying the conditions and assumptions where models break down and they are especially powerful in pointing out reasons as to why they do this. They show which conditions or assumptions the results of models depend on. Key words: ecology, generalizations, invariance, lawlikeness, philosophy of science, robustness, explanation, models, stability

Role of entropy in the stability of cobalt titanates

The standard molar Gibbs free energy of formation of Co2TiO4, CoTiO3,and CoTi2O5 as a function of temperature over an extended range (900 to 1675) K was measured using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte, with CoO as reference electrode and appropriate working electrodes. For the formation of the three compounds from their component oxides CoO with rock-salt and TiO2 with rutile structure, the Gibbs free energy changes are given by:Delta(f)G degrees((ox))(Co2TiO4) +/- 104/(J . mol(-1)) = -18865 - 4.108 (T/K)Delta(f)G degrees((ox))(CoTiO3) +/- 56/(J . mol(-1)) = -19627 + 2.542 (T/K) Delta(f)G degrees((ox))(CoTi2O5) +/- 52/(J . mol(-1)) = -6223 - 6.933 (T/K) Accurate values for enthalpy and entropy of formation were derived. The compounds Co2TiO4 with spinel structure and CoTi2O5 with pseudo-brookite structure were found to be entropy stabilized. The relatively high entropy of these compounds arises from the mixing of cations on specific crystallographic sites. The stoichiometry of CoTiO3 was confirmed by inert gas fusion analysis for oxygen. Because of partial oxidation of cobalt in air, the composition corresponding to the compound Co2TiO4 falls inside a two-phase field containing the spinet solid solution Co2TiO4-Co3O4 and CoTiO3. The spinel solid solution becomes progressively enriched in Co3O4 with decreasing temperature. (c) 2010 Elsevier Ltd. All rights reserved.

Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Japanese Encephalitis Virus Utilizes the Canonical Pathway To Activate NF-kappa B but It Utilizes the Type I Interferon Pathway To Induce Major Histocompatibility Complex Class I Expression in Mouse Embryonic Fibroblasts

Flaviviruses have been shown to induce cell surface expression of major histocompatibility complex class I (MHC-I) through the activation of NF-kappa B. Using IKK1(-/-), IKK2(-/-), NEMO-/-, and IKK1-/- IKK2-/- double mutant as well as p50(-/-) RelA(-/-) cRel(-/-) triple mutant mouse embryonic fibroblasts infected with Japanese encephalitis virus (JEV), we show that this flavivirus utilizes the canonical pathway to activate NF-kappa B in an IKK2- and NEMO-, but not IKK1-, dependent manner. NF-kappa B DNA binding activity induced upon virus infection was shown to be composed of RelA: p50 dimers in these fibroblasts. Type I interferon (IFN) production was significantly decreased but not completely abolished upon virus infection in cells defective in NF-kappa B activation. In contrast, induction of classical MHC-I (class 1a) genes and their cell surface expression remained unaffected in these NF-kappa B-defective cells. However, MHC-I induction was impaired in IFNAR(-/-) cells that lack the alpha/beta IFN receptor, indicating a dominant role of type I IFNs but not NF-kappa B for the induction of MHC-I molecules by Japanese encephalitis virus. Our further analysis revealed that the residual type I IFN signaling in NF-kappa B-deficient cells is sufficient to drive MHC-I gene expression upon virus infection in mouse embryonic fibroblasts. However, NF-kappa B could indirectly regulate MHC-I expression, since JEV-induced type I IFN expression was found to be critically dependent on it.