Canonical Forms for Matrices over Polynomial Rings

One of the important concepts in matrix algebra is rank of matrices. If the entries of such matrices are from fields or principal ideal domains, then this concept of rank is well-defined. However, when such matrices are defined over the ring of polynomials F[x_1, . . . , x_k ], k ≥ 2 (polynomial matrices in more than one indeterminate), the concept of rank has different but inequivalent definitions. Despite this flaw, some theories, in relation to ranks, can still be applied to polynomial matrices in more than one indeterminate. One of the outcomes of these theories is that lower and upper bounds for ranks of such polynomial matrices in more than one indeterminate can be obtained. Just like matrices over fields or principal ideal domains can be reduced to some simpler or canonical forms, there are algorithms that can be used to reduce matrices over polynomial rings in more than one indeterminate to some simpler forms, though these reduced forms do not always tell the ranks of such polynomial matrices in more than one indeterminate. In this thesis, these algorithms will be presented with examples

The FK506 binding protein 13 kDa (FKBP13) interacts with the C-chain of complement C1q

BACKGROUND: The pharmacological action of specific immunosuppressants is mediated by immunophilins. While cyclosporin A binds to cyclophilins, FK506/tacrolimus, rapamycin, and others bind to FK506 binding proteins (FKBPs). Different physiological actions of immunophilins were described but their genuine function, however, remains elusive and is still under investigation. A yeast two-hybrid screen was performed using the FK506 binding protein 13 kDa (FKBP13) as a bait and a fetal liver expression library as a prey. RESULTS: The C-chain of complement C1q (C1q-C) was detected to interact with FKBP13 in the yeast two-hybrid system and in a protein complementation assay. Neither FKBP12, FKBP25, FKBP52 nor the unrelated immunophilin CypA did react with C1q-C in the yeast system stressing the specificity of the interaction. Binding of C1q-C to FKBP13 could not be prevented in the presence of FK506, demonstrating that possibly other regions than the binding pocket of the drug are responsible for the interaction of the two proteins. CONCLUSION: It is concluded that exclusively FKBP13 but no other FKBPs tested so far interact with the C-chain of complement C1q in the two different assays and further work will be initiated to investigate the physiological relevance of the interaction

Grobner bases via linkage for classes of generalized determinantal ideals

Grobner bases are an important tool for working with ideals in polynomial rings. They have both computational and theoretical importance. In this dissertation, we produce Grobner bases for some families of generalized determinantal ideals. Our main contribution is a Grobner basis for Schubert patch ideals. Schubert patch ideals are prime defining ideals of open patches of Schubert varieties in the type A flag variety. We adapt E. Gorla, J. Migliore, and U. Nagel's "Grobner basis via linkage" technique to prove a conjecture of A. Yong, namely, the essential minors of every Schubert patch ideal form a Grobner basis. Using the same approach, we recover the result of A. Woo and A. Yong that the essential minors of a Kazhdan-Lusztig ideal (and hence, essential minors of a Schubert determinantal ideal) form a Grobner basis with respect to an appropriate term order. In addition, with respect to the standard grading, we show that homogeneous Schubert patch ideals, homogeneous Kazhdan-Lusztig ideals and Schubert determinantal ideals are glicci. In the last chapter of this dissertation, we briefly discuss some future directions

Models of asthma: density-equalizing mapping and output benchmarking

Despite the large amount of experimental studies already conducted on bronchial asthma, further insights into the molecular basics of the disease are required to establish new therapeutic approaches. As a basis for this research different animal models of asthma have been developed in the past years. However, precise bibliometric data on the use of different models do not exist so far. Therefore the present study was conducted to establish a data base of the existing experimental approaches. Density-equalizing algorithms were used and data was retrieved from a Thomson Institute for Scientific Information database. During the period from 1900 to 2006 a number of 3489 filed items were connected to animal models of asthma, the first being published in the year 1968. The studies were published by 52 countries with the US, Japan and the UK being the most productive suppliers, participating in 55.8% of all published items. Analyzing the average citation per item as an indicator for research quality Switzerland ranked first (30.54/item) and New Zealand ranked second for countries with more than 10 published studies. The 10 most productive journals included 4 with a main focus allergy and immunology and 4 with a main focus on the respiratory system. Two journals focussed on pharmacology or pharmacy. In all assigned subject categories examined for a relation to animal models of asthma, immunology ranked first. Assessing numbers of published items in relation to animal species it was found that mice were the preferred species followed by guinea pigs. In summary it can be concluded from density-equalizing calculations that the use of animal models of asthma is restricted to a relatively small number of countries. There are also differences in the use of species. These differences are based on variations in the research focus as assessed by subject category analysis

Mobile Air Quality Studies (MAQS) - an international project

Due to an increasing awareness of the potential hazardousness of air pollutants, new laws, rules and guidelines have recently been implemented globally. In this respect, numerous studies have addressed traffic-related exposure to particulate matter using stationary technology so far. By contrast, only few studies used the advanced technology of mobile exposure analysis. The Mobile Air Quality Study (MAQS) addresses the issue of air pollutant exposure by combining advanced high-granularity spatial-temporal analysis with vehicle-mounted, person-mounted and roadside sensors. The MAQS-platform will be used by international collaborators in order 1) to assess air pollutant exposure in relation to road structure, 2) to assess air pollutant exposure in relation to traffic density, 3) to assess air pollutant exposure in relation to weather conditions, 4) to compare exposure within vehicles between front and back seat (children) positions, and 5) to evaluate "traffic zone"- exposure in relation to non-"traffic zone"-exposure. Primarily, the MAQS-platform will focus on particulate matter. With the establishment of advanced mobile analysis tools, it is planed to extend the analysis to other pollutants including including NO2, SO2, nanoparticles, and ozone

The role of gasotransmitters NO, H S, CO in myocardial ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning

Ischemic heart disease is one of the leading causes of morbidity and mortality worldwide. The development of cardioprotective therapeutic agents remains a partially unmet need and a challenge for both medicine and industry, with significant financial and social implications. Protection of the myocardium can be achieved by mechanical vascular occlusions such as preconditioning (PC) when brief episodes of ischemia/reperfusion are subjected prior to ischemia; postconditioning (PostC) when the brief episodes are subjected at the immediate onset of reperfusion, as well as remote conditioning (RC) when the brief episodes are subjected in another vascular territory. The elucidation of the signaling pathways which underlie the protective effects of PC, PostC and RC would be expected to reveal novel molecular targets for cardioprotection that could be manipulated by pharmacological agents to prevent reperfusion injury. Gasotransmitters including nitric oxide (NO), hydrogen sulphide (H2 S) and carbon monoxide (CO) are a growing family of regulatory molecules which impact on physiological and pathological functions. NO, H2 S and CO share several common properties; they are beneficial at low concentrations but hazardous in higher amounts, they relax smooth muscle cells, inhibit apoptosis, and exert anti-inflammatory effects. In the cardiovascular system, both NO, H2 S and CO induce vasorelaxation, and promote cardioprotection. In this review article, we summarize current knowledge on the role of the gasotransmitters NO, H2 S, and CO in myocardial ischemia/reperfusion injury and cardioprotection provided by conditioning strategies and highlight future perspectives in cardioprotection by NO, H2 S, CO, as well as their donor molecules