Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.

The presence of a vocal ligament in fetuses: a histochemical and ultrastructural study

Although it is currently believed that the vocal ligament of humans undergoes considerable development postnatally, there is no consensus as to the age at which it first emerges. In the newborn infant, the lamina propria has been described as containing a sparse collection of relatively unorganized fibres. In this study we obtained larynges from autopsy of human fetuses aged 7-9 months and used light and electron microscopy to study the collagenous and elastic system fibres in the lamina propria of the vocal fold. Collagen fibres were viewed using the Picrosirius polarization method and elastic system fibres were stained using Weigert`s resorcin-fuchsin after oxidation with oxone. The histochemical and electron microscopic observations were consistent, showing collagen populations with an asymmetric distribution across different compartments of the lamina propria. In the central region, the collagen appeared as thin, weakly birefringent, greenish fibres when viewed using the Picrosirius polarization method, whereas the superficial and deep regions contained thick collagen fibres that displayed a strong red or yellow birefringence. These findings suggest that the thin fibres in the central region consist mainly of type III collagen, whereas type I collagen predominates in the superficial and deep regions, as has been reported in studies of adult vocal folds. Similarly, elastic system fibres showed a differential distribution throughout the lamina propria. Their distribution pattern was complementary to that of collagen fibres, with a much greater density of elastic fibres apparent in the central region than in the superficial and deep regions. This distribution of collagen and elastic fibres in the fetal vocal fold mirrors that classically described for the adult vocal ligament, suggesting that a vocal ligament has already begun to develop by the time of birth. The apparently high level of organization of connective tissue components in the newborn is in contrast to current hypotheses that argue that the mechanical stimuli of phonation are essential to the determination of the layered structure of the lamina propria and suggests that genetic factors may play a more significant role in the development of the vocal ligament than previously believed.

Posterior reversible encephalopathy syndrome after liver transplantation in children: A rare complication related to calcineurin inhibitor effects

PRES is a neuroclinical and radiological syndrome that results from treatment with calcineurin inhibitor immunosuppressives. Severe hypertension is commonly present, but some patients may be normotensive. We report herein two children who received liver transplants, as treatment for biliary atresia in the first case and for Alagille`s syndrome in the second one. In the early postoperative, both patients presented hypertension and seizures. In both cases, the image findings suggested the diagnosis of PRES. The CT scan showed alterations in the posterior area of the brain, and brain MRI demonstrated parietal and occipital areas of high signal intensity. Both children were treated by switching the immunosuppressive regimen and controlling arterial blood pressure. They displayed full recuperation without any neurologic sequelae. Probably, the pathophysiology of PRES results from sparse sympathetic innervation of the vertebrobasilar circulation, which is responsible for supplying blood to the posterior areas of the brain. In conclusion, all liver-transplanted children who present with neurological symptoms PRES should be considered in the differential diagnosis, although this is a rare complication. As treatment, we recommend rigorous control of arterial blood pressure and switching the immunosuppressive regimen.

NONINVASIVE MONITORING OF ANDROGENS IN MALE AMAZONIAN MANATEE (TRICHECHUS INUNGUIS): BIOLOGIC VALIDATION

The Amazonian manatee (Trichechus inunguis) is endemic in the Amazonian basin and is the only exclusively fresh water sirenian. Historically hunted on a large scale, this species is now considered endangered, and Studies on the reproductive physiology are critical for the improvement of reproductive management of captive and wild Populations of manatees. The aim of this Study was to verify the viability of androgen measurement in saliva, lacrimal, urine, and fecal samples of the Amazonian manatee by conducting a hormone challenge. Two adult male manatees (A-1 and A-2) were Submitted to an experimentation protocol of 12 day (D1 to D10). On D0, the animals received an intramuscular injection of gonadotropin-releasing hormone (GnRH)-analogue. Salivary, lacrimal, urinary, and fecal samples were collected daily (between 0800 hours and 0900 hours) and frozen at -20 degrees C until assayed. Fecal samples were lyophilized, extracted with 80% methanol, and diluted in buffer before the radioimmunoassay (RIA). Urine samples underwent acid hydrolysis and were diluted in depleted bovine serum. Salivary and lacrimal samples were assayed without the extraction step. Hormonal assays were conducted with a commercial testosterone RIA kit. An androgen peak (>median + 2 interquartile range [IQR]) was observed in all matrices of both animals, although it was less prominent in the lacrimal samples of A-2. However, the fecal androgen peak (A-1 peak = 293.78 ng/g dry feces, median [IQR] = 143.58 [32.38] ng/g dry feces; A-2 peak = 686.72 ng/g dry feces, median [IQR] = 243.82 [193.16] ng/g dry feces) occurred later than urinary (A-1 peak = 648.16 ng/mg creatinine [Cr], median [IQR] = 23.88 [30.44] ng/mg Cr; A-2 peak = 370.44 ng/mg Cr, median [IQR] = 113.87 [117.73] ng/mg Cr) and salivary (A-1 peak = 678.89 pg/ml, median [IQR] = 103.69 [119.86] pg/ml; A-2 peak = 733.71 pg/ml, median [IQR] = 262.92 [211.44] pg/ml) androgen peaks. These intervals appear to be correlated with the long digesta passage time in this species. The salivary and urinary peaks were closely associated. These results demonstrate that androgen concentrations in saliva, urine, or feces samples reflect reliably physiologic events and are a powerful tool for noninvasive reproductive monitoring of Amazonian manatees.

Long-term stability of dentin matrix following treatment with various natural collagen cross-linkers

Objectives: Collagen disorganization is one of the main degradation patterns found in unsuccessful adhesive restorations. The hypothesis of this study was that pretreatment using natural collagen cross-linking agents rich in proanthocyanidin (PA) would improve mechanical properties and stability over time of the dentin collagen and, thus, confer a more resistant and lasting substrate for adhesive restorations. Methods: PA-based extracts, from grape seed (GSE), cocoa seed (CSE), cranberry (CRE), cinnamon (CNE) and acai berry (ACE) were applied over the demineralized dentin. The apparent elastic modulus (E) of the treated dentin collagen was analyzed over a 12 month period. Specimens were immersed in the respective solution and E values were obtained by a micro-flexural test at baseline, 10, 30, 60, 120 and 240 min. Samples were stored in artificial saliva and re-tested after 3, 6 and 12 months. Data was analyzed using ANOVA and Tukey test. Results: GSE and CSE extracts showed a time-dependent effect and were able to improve [240 min (MPa): GSE = 108.96 +/- 56.08: CSE = 59.21 +/- 24.87] and stabilize the E of the organic matrix [12 months (MPa): GSE = 40.91 +/- 19.69; CSE = 42.11 +/- 13.46]. CRE and CNE extracts were able to maintain the E of collagen matrices constant over 12 months [CRE = 11.17 +/- 7.22; CNE = 9.96 +/- 6.11; MPa]. ACE (2.64 +/- 1.22 MPa) and control groups immersed in neat distilled water (1.37 +/- 0.69 MPa) and ethanol-water (0.95 +/- 0.33 MPa) showed no effect over dentin organic matrix and enable their degradation and reduction of mechanical properties. Significance: Some PA-based extracts were capable of improving and stabilizing collagen matrices through exogenous cross-links induction. (C) 2011 Elsevier Ltd. All rights reserved.

Growth hormone induces bone morphogenetic proteins and bone-related proteins in the developing rat periodontium

The hypothesis that growth hormone (GH) up-regulates the expression of enzymes, matrix proteins, and differentiation markers involved in mineralization of tooth and bone matrices was tested by the treatment of Lewis dwarf rats with GH over 5 days, The molar teeth and associated alveolar bone were processed for immunohistochemical demonstration of bone morphogenetic proteins 2 and 4 (BMP-2 and -4), bone morphogenetic protein type IA receptor (BMPR-IA), bone alkaline phosphatase (ALP), osteocalcin (OC), osteopontin (OPN), bone sialoprotein (BSP), and E11 protein (E11), The cementoblasts, osteoblasts, and periodontal ligament (PDL) cells responded to GH by expressing BMP-2 and -4, BMPR-IA, ALP, OC, and OPN and increasing the numbers of these cells. No changes were found in patterns of expression of the late differentiation markers BSP and E11 in response to GH, Thus, GH evokes expression of bone markers of early differentiation in cementoblasts, PDL cells, and osteoblasts of the periodontium. We propose that the induction of BMP-2 and -4 and their receptor by GH compliments the role of GH-induced insulin-like growth factor 1 (IGF-1) in promoting bone and tooth root formation.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Exact solution for the Bariev model with boundary fields

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four sets or Bethe ansatz equations as well as their corresponding energy expressions are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

A new integrable model of strongly correlated electrons with Hubbard-like interaction

A new completely integrable model of strongly correlated electrons is proposed which describes two competitive interactions: one is the correlated one-particle hopping, the other is the Hubbard-like interaction. The integrability follows from the fact that the Hamiltonian is derivable from a one-parameter family of commuting transfer matrices. The Bethe ansatz equations are derived by algebraic Bethe ansatz method.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.