Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras

We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a general algebraic framework to find the solutions and to compute the structure of the quotient ring R/I from the null space of a Macaulay-type matrix. The affine dense, affine sparse, homogeneous and multi-homogeneous cases are treated. In the presented framework, the concept of a border basis is generalized by relaxing the conditions on the set of basis elements. This allows for algorithms to adapt the choice of basis in order to enhance the numerical stability. We present such an algorithm and show numerical results

Beitrag zur Physiologie des N. Vagus. I. Mitteilung : Uber die Funktion des N. vagus auf die Atmung

1) Der Gaswechsel und der Respirationsquotient des Einrecurrenskaninchens (Lungenvagusfreienkaninchens, vgl. II. Mitteilung) scheint fast keinen Unterschied im Vergleich mit den normalen und Kontrolltieren zu zeigen. Beim Versuch wurde der von Saeki (1931) am hiesigen Institut verbesserte Haldensche Apparat angewendet. Aus diesem Resultat gelangt der Verfasser zu dem Schluss, dass die Ausschaltung des Lungenvagus auf den Gaswechsel und den Respirationsquotienten fast keinen Einfluss ausubt. 2) Bei der Durchschneidungsmethode, die sicher den Lungenvagus auschaltet, tritt immer die typische Vagusatmung auf. 3) Was die Vagusatmung des Einrecurrenskaninchens nach der Operation betrifft, so kehrt wieder allmahlich im Verlauf der Zeit ersichtlich der normale Atmungszustand zuruck, aber durch eine leichte Storung, z. B. durch die Anlegung der Gasmaske, kann die typische Vagusatmung hervorgerufen werden. Um an wiedererholte Erhaltung des normalen Atmungszustandes nach der Ausschaltung des Lungenvagus zu denken, muss man voraussetzen, dass es anstatt des Lungenvagus noch einen anderen Regulations-mechanismus fur den normalen Atmungszustand geben; falls der Regulationsmechanismus durch eine leichte Storung gestort wird, tritt die Vagusatmung auf. Es ist sehr schwer zu denken, an welchem Ort und auf welche Weise die Regulation ausgeubt wird, aber der Verfasser vermutet, dass das Atemzentrum durch die centripetalen Impulse von uberangestrengtem Atemmuskel und Zwerchfell nach der Lungenvagusaus-schaltung wieder die regulatorische centrifugale Wirkung zum Atemmuskel und Zwerchfell sendet, wodurch der Regulationsmechanismus entsteht. 4) Die Abnahme der Atmungszahl nach der doppelseitigen Vagotomie am Halse kann nicht durch die Schafersche Glottislahmungstheorie oder Hymansche Aorten-Sinusnervenlahmungstheorie erklart werden, sondern durch die Ausschaltung des Lungen-vagus selbst. 5) Beim Einrecurrenskaninchen sieht man keine Apnoe beim Einblasen der Lunge. Es gilt als eine Bestatigung dafur, dass alle Vagusaste nach der Lunge

Chemical Composition and Physical Properties of “Pale Yellow” Naphtalan

The Pale Yellow (PY) Naphthalan is potentially a new treatment modality for some oral mucosal and dermatological diseases. Its chemical composition and physical properties were studied by standard and sophisticated methods. Special attention was paid to steranes and hopanes as favorable components and to aromatics as unfavorable compounds. PY Naphthalan is predominantly composed of saturated aliphatic hydrocarbons of different structures, and of hydrocarbons comprising aromatic ring(s) (< 15%). Among aromatics, 98% were monoaromatics and 2% diaromatics, while 16 polycyclic aromatic hydrocarbons designated by US Environmental Protection Agency as priority pollutants were found at minimum detectability levels. Steranes and hopanes appeared in native geogenic clusters of homologs and each of identified compounds was in native geogenic configuration. Steranes were in the range from norcholestanes up to propyl cholestanes and hopanes up to pentakishomohopanes. The content of steranes and hopanes was relatively high. Compared to the other naphthalan products, the composition of PY Naphthalan is remarkably improved. Physical properties make PY Naphthalan convenient for application. (doi: 10.5562/cca1886

Polynomial Equations: Theory and Practice

Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts. The theory is illustrated by many examples using different software packages.Comment: This article will appear as a chapter of a forthcoming book presenting research acitivies conducted in the European Network POEMA. It discusses polynomial equations, with optimization as point of entry. 24 pages, 7 figure

Phase 1 Study of the E-Selectin Inhibitor GMI 1070 in Patients with Sickle Cell Anemia

Background\ud \ud Sickle cell anemia is an inherited disorder of hemoglobin that leads to a variety of acute and chronic complications. Abnormal cellular adhesion, mediated in part by selectins, has been implicated in the pathophysiology of the vaso-occlusion seen in sickle cell anemia, and selectin inhibition was able to restore blood flow in a mouse model of sickle cell disease.\ud \ud Methods\ud \ud We performed a Phase 1 study of the selectin inhibitor GMI 1070 in patients with sickle cell anemia. Fifteen patients who were clinically stable received GMI 1070 in two infusions.\ud \ud Results\ud \ud The drug was well tolerated without significant adverse events. There was a modest increase in total peripheral white blood cell count without clinical symptoms. Plasma concentrations were well-described by a two-compartment model with an elimination T1/2 of 7.7 hours and CLr of 19.6 mL/hour/kg. Computer-assisted intravital microscopy showed transient increases in red blood cell velocity in 3 of the 4 patients studied.\ud \ud Conclusions\ud \ud GMI 1070 was safe in stable patients with sickle cell anemia, and there was suggestion of increased blood flow in a subset of patients. At some time points between 4 and 48 hours after treatment with GMI 1070, there were significant decreases in biomarkers of endothelial activation (sE-selectin, sP-selectin, sICAM), leukocyte activation (MAC-1, LFA-1, PM aggregates) and the coagulation cascade (tissue factor, thrombin-antithrombin complexes). Development of GMI 1070 for the treatment of acute vaso-occlusive crisis is ongoing

GASDS: A kinetic-based package for biomass and coal gasification

In this paper, a simulation package called GASDS is introduced. It is particularly suited to evaluate the pyrolysis, gasification and combustion of biomass and coal feedstocks. The aim of this work is to describe the package from a numerical point of view and its interface. Additionally, experimental results for a countercurrent fixed-bed biomass gasification reactor are reproduced. The influence of reactor and particle discretizations are investigated with respect to accuracy and computational time. Some differences are present between experimental and simulation results. In order to improve the agreement between simulation and experimental results it is suggested to improve the kinetic scheme of the solid phase and gas-solid reactions. The negligible differences in terms of predictions, instead, do not justify the adoption of finer discretizations for the particle and reactor, which imply longer computational times

Proudfoot-Speyer degenerations of scattering equations

We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equationsWe study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations