Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

An Exact Analysis of Unsteady Convective Diffusion in an Annular Pipe

An exact solution to the unsteady convective diffusion equation for the dispersion of a solute in a fully developed laminar flow in an annular pipe is obtained. Generalized dispersion model which is valid for all time after the injection of solute in the flow is used to evaluate the dispersion coefficients as functions of time. It is observed that the axial dispersion decreases with an increase in the radius of the inner cylinder.

Generalized pencils of rays in statistical wave optics

The recently introduced generalized pencil of Sudarshan which gives an exact ray picture of wave optics is analysed in some situations of interest to wave optics. A relationship between ray dispersion and statistical inhomogeneity of the field is obtained. A paraxial approximation which preserves the rectilinear propagation character of the generalized pencils is presented. Under this approximation the pencils can be computed directly from the field conditions on a plane, without the necessity to compute the cross-spectral density function in the entire space as an intermediate quantity. The paraxial results are illustrated with examples. The pencils are shown to exhibit an interesting scaling behaviour in the far-zone. This scaling leads to a natural generalization of the Fraunhofer range criterion and of the classical van Cittert-Zernike theorem to planar sources of arbitrary state of coherence. The recently derived results of radiometry with partially coherent sources are shown to be simple consequences of this scaling.

Comment on “path integration of a quadratic action with a generalized memory

Using the promeasure technique, we give an alternative evaluation of a path integral corresponding to a quadratic action with a generalized memory.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Application of Haar functions for transmission line and transformer differential protection

The development of algorithms, based on Haar functions, for extracting the desired frequency components from transient power-system relaying signals is presented. The applications of these algorithms to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. For transmission line protection, three modes of application of the Haar algorithms are described: a full-cycle window algorithm, an approximate full-cycle window algorithm, and a half-cycle window algorithm. For power transformer differential protection, the combined second and fifth harmonic magnitude of the differential current is compared with that of fundamental to arrive at a trip decision. The proposed line protection algorithms are evaluated, under different fault conditions, using realistic relaying signals obtained from transient analysis conducted on a model 400 kV, 3-phase system. The transformer differential protection algorithms are also evaluated using a variety of simulated inrush and internal fault signals.

Microprocessor-based polynomial generator

A new method of generating polynomials using microprocessors is proposed. The polynomial is generated as a 16-bit digital word. The algorithm for generating a variety of basic 'building block' functions and its implementation is discussed. A technique for generating a generalized polynomial based on the proposed algorithm is indicated. The performance of the proposed generator is evaluated using a commercially available microprocessor kit.

Androgen receptor-dependent and independent functions of ARIP4

Androgen receptor (AR) is necessary for normal male phenotype development and essential for spermatogenesis. AR is a classical steroid receptor mediating actions of male sex steroids testosterone and 5-alpha-dihydrotestosterone. Numerous coregulators interact with the receptor and regulate AR activity on target genes. This study deals with the characterization of androgen receptor-interacting protein 4 (ARIP4). ARIP4 binds DNA, interacts with AR in vitro and in cultured yeast and mammalian cells, and modulates AR-dependent transactivation. ARIP4 is an active DNA-dependent ATPase, and this enzymatic activity is essential for the ability of ARIP4 to modulate AR function. On the basis of sequence homology in its ATPase domain, ARIP4 belongs to the SNF2 family of proteins involved in chromatin remodeling, DNA repair, and homologous recombination. Similar to its closest homologs ATRX and Rad54, ARIP4 does not seem to be a classical chromatin remodeling protein in that it does not appear to form large protein complexes in vivo or remodel mononucleosomes in vitro. However, ARIP4 is able to generate superhelical torsion on linear DNA fragments. ARIP4 is covalently modified by SUMO-1, and mutation of six potential SUMO attachment sites abolishes the ability of ARIP4 to bind DNA, hydrolyze ATP, and activate AR function. ARIP4 expression starts in early embryonic development. In mouse embryo ARIP4 is present mainly in the neural tube and limb buds. In adult mouse tissues ARIP4 expression is virtually ubiquitous. In mouse testis ARIP4 is expressed in the nuclei of Sertoli cells in a stage-dependent manner. ARIP4 is also present in the nuclei of Leydig cells, spermatogonia, pachytene and diplotene spermatocytes. Testicular expression pattern of ARIP4 does not differ significantly in wild-type, FSHRKO, and LuRKO mice. In the testis of hpg mice, ARIP4 is found mainly in interstitial cells and has very low, if any, expression in Sertoli and germ cells. Heterozygous Arip4+/ mice are fertile and appear normal; however, they are haploinsufficient with regard to androgen action in Sertoli cells. In contrast, Arip4 / embryos are not viable. They have significantly reduced body size at E9.5 and die by E11.5. Compared to wild-type littermates, Arip4 / embryos possess a higher percentage of apoptotic cells at E9.5 and E10.5. Fibroblasts derived from Arip4 / embryos cease growing after 2-3 passages and exhibit a significantly increased apoptosis and decreased proliferation rate than cells from wild-type embryos. Our findings demonstrate that ARIP4 plays an essential role in mouse embryonic development. In addition, testicular expression and AR coregulatory activity of ARIP4 suggest a role of ARIP4-AR interaction in the somatic cells of the testis.

Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Orphan nuclear receptor subfamily NR4A their interplay with other nuclear receptors and functions in osteoblasts

Nurr1, NGFI-B and Nor1 (NR4A2, NR4A1 and NR4A3, respectively) belong to the NR4A subfamily of nuclear receptors. The NR4A receptors are orphan nuclear receptors which means that activating or repressing ligands for these receptors have not been found. NR4A expression is rapidly induced in response to various stimuli including growth factors and the parathyroid hormone (PTH). The studies concerning the NR4A receptors in the central nervous system have demonstrated that they have a major role in the development and function of the dopaminergic neurons of the midbrain and in regulating hypothalamus-pituitary-adrenal-axis. However, the peripheral functions of the NR4A family are largely unknown. Cultured mouse primary osteoblasts, a preosteoblastic cell line and several osteoblastic cell lines were used to investigate the role of NR4A receptors in osteoblasts. NR4A receptors were shown to directly bind to and activate the promoter of the osteopontin gene (OPN) in osteoblastic cells, thus regulating its expression. OPN is a major bone matrix protein expressed throughout the differentiation of preosteoblastic cells into osteoblasts. The activation of the OPN promoter was shown to be dependent on the activation function-1 located in the N-terminal part of Nurr1 and to occur in both monomeric and RXR heterodimeric forms of NR4A receptors. Furthermore, PTH was shown to upregulate OPN expression through the NR4A family. It was also demonstrated that the fibroblast growth factor-8b (FGF-8b) induces the expression of NR4A receptors in osteoblasts as immediate early genes. This induction involved phosphatidylinositol-3 kinase, protein kinase C, and mitogen activated protein kinase, which are all major pathways of FGF signalling. Nurr1 and NGFI-B were shown to induce the proliferation of preosteoblastic cells and to reduce their apoptosis. FGF-8b was shown to stimulate the proliferation of osteoblastic cells through the NR4A receptors. These results suggest that NR4A receptors have a role both in the differentiation of osteoblasts and in the proliferation and apoptosis of preosteoblast. The NR4A receptors were found to bind to the same response element on OPN as the members of the NR3B family of orphan receptors do. Mutual repression was observed between the NR4A receptors and the NR3B receptors. This repression was shown to be dependent on the DNA-binding domains of both receptor families, but to result neither from the competition of DNA binding nor from the competition for coactivators. As the repression was dependent on the relative expression levels of the NR4As and NR3Bs, it seems likely that the ratio of the receptors mediates their activity on their response elements. Rapid induction of the NR4As in response to various stimuli and differential expression of the NR3Bs can effectively control the gene activation by the NR4A receptors. NR4A receptors can bind DNA as monomers, and Nurr1 and NGFI-B can form permissive heterodimers with the retinoid X receptor (RXR). Permissive heterodimers can be activated with RXR agonists, unlike non-permissive heterodimers, which are formed by RXR and retinoic acid receptor or thyroid hormone receptor (RAR and TR, respectively). Non-permissive heterodimers can only be activated by the agonists of the heterodimerizing partner. The mechanisms behind differential response to RXR agonists have remained unresolved. As there are no activating or repressing ligands for the NR4A receptors, it would be important to find out, how they are regulated. Permissiviness of Nurr1/RXR heterodimers was linked to the N-terminal part of Nurr1 ligand-binding domain. This region has previously been shown to mediate the interaction between NRs and corepressors. Non-permissive RAR and TR, permissive Nurr1 and NGFI-B, and RXR were overexpressed with corepressors silencing mediator for retinoic acid and thyroid hormone receptors (SMRT), and with nuclear receptor corepressor in several cell lines. Nurr1 and NGFI-B were found to be repressed by SMRT. The interaction of RXR heterodimers with corepressors was weak in permissive heterodimers and much stronger in non-permissive heterodimers. Non-permissive heterodimers also released corepressors only in response to the agonist of the heterodimeric partner of RXR. In the permissive Nurr1/RXR heterodimer, however, SMRT was released following the treatment with RXR agonists. Corepressor release in response to ligands was found to differentiate permissive heterodimers from non-permissive ones. Corepressors were thus connected to the regulation of NR4A functions. In summary, the studies presented here linked the NR4A family of orphan nuclear receptors to the regulation of osteoblasts. Nurr1 and NGFI-B were found to control the proliferation and apoptosis of preosteoblasts. The studies also demonstrated that cross-talk with the NR3B receptors controls the activity of these orphan receptors. The results clarified the mechanism of permissiviness of RXR-heterodimers. New information was obtained on the regulation and functions of NR4A receptors, for which the ligands are unknown.

The Functions and Regulation of Ornithine Decarboxylase

Ornithine decarboxylase (ODC) regulates the synthesis of polyamines which are involved in many cellular functions e.g. proliferation and differentiation. Due to its critical role, ODC is a tightly regulated enzyme by antizymes and antizyme inhibitors. If the regulation fails, the activity of ODC increases and may lead to malignant transformation of a cell. Increased ODC activity is found in many common cancers, including colon, prostate, and breast cancer. In a transformed cell, dynamics of the actin cytoskeleton is disturbed. A small G-protein, RhoA regulates organization of the cytoskeleton, and its overactivity increases malignant potential of the cell. The present results indicate that covalent attachment of polyamines by transglutaminase is a physiological means of regulating the activity of RhoA. The translocation of RhoA to the plasma membrane, where it exerts its activity is dependent on the presence of catalytically active ODC. As the overactivity of ODC and RhoA are implicated in cell transformation, the results provide a mechanistic explanation of the interrelationship between the polyamine metabolism and the reorganization of the actin cytoskeleton occurring in cancer cells. ODC and polyamines have also an important role in the function of central nervous system. They participate in the regulation of brain morphogenesis in embryos. In adult nervous tissue, polyamines regulate K+ and glutamate channels. K+ inward rectifying channels control membrane potentials and NMDA-type glutamate receptors (NMDAR) regulate synaptic plasticity. High ODC activity and polyamine levels are considered important in the development of ischemic brain damage and they are implicated in the pathogenesis of Alzheimer s disease (AD). A homolog of ODC was cloned from a human brain cDNA library, and several alternatively spliced variants were detected in human brain and testis. The novel protein was nevertheless devoid of ODC catalytic activity. It was subsequently found to be a novel inductor of ODC activity and polyamine synthesis, called antizyme inhibitor 2 (AZIN2). The accumulation of AZIN2 in vesicle-like formations along the axons and beneath the plasma membrane of neurons as well as in steroid hormone producing Leydig cells and luteal cells of the gonads implies that AZIN2 plays a role in secretion and vesicle trafficking. An accumulation of AZIN2 was detected also in specimens of AD brains. This increased expression of AZIN2 was specific for AD and was not found in brains with other neurodegenerative diseases including CADASIL or dementia with Lewy bodies.