On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.

Fast matrix transposition computer implementation

Eklundh's (1972) algorithm to transpose a large matrix stored on an external device such as a disc has been programmed and tested. A simple description of computer implementation is given in this note.

Don't-cares in the concurrency matrix for bit steering

The concurrency matrix aids the detection of bit steerability of microcommand sets in a microprogram. In the present work, the concept of don't-cares is introduced into the concurrency matrix to identify the bit steerable microcommand sets.

Fast Public Key Cryptosystem Based On Matrix Rings

A public key cryptosystem is proposed, which is based on the assumption that finding the square root of an element in a large finite ring is computationally infeasible in the absence of a knowledge of the ring structure. The encryption and decryption operations are very fast, and the data expansion is 1:2.

Estimation in a multiplicative mixed model involving a genetic relationship matrix.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

The climate change risk management matrix for the grazing industry of northern Australia

The complexity, variability and vastness of the northern Australian rangelands make it difficult to assess the risks associated with climate change. In this paper we present a methodology to help industry and primary producers assess risks associated with climate change and to assess the effectiveness of adaptation options in managing those risks. Our assessment involved three steps. Initially, the impacts and adaptation responses were documented in matrices by ‘experts’ (rangeland and climate scientists). Then, a modified risk management framework was used to develop risk management matrices that identified important impacts, areas of greatest vulnerability (combination of potential impact and adaptive capacity) and priority areas for action at the industry level. The process was easy to implement and useful for arranging and analysing large amounts of information (both complex and interacting). Lastly, regional extension officers (after minimal ‘climate literacy’ training) could build on existing knowledge provided here and implement the risk management process in workshops with rangeland land managers. Their participation is likely to identify relevant and robust adaptive responses that are most likely to be included in regional and property management decisions. The process developed here for the grazing industry could be modified and used in other industries and sectors. By 2030, some areas of northern Australia will experience more droughts and lower summer rainfall. This poses a serious threat to the rangelands. Although the impacts and adaptive responses will vary between ecological and geographic systems, climate change is expected to have noticeable detrimental effects: reduced pasture growth and surface water availability; increased competition from woody vegetation; decreased production per head (beef and wool) and gross margin; and adverse impacts on biodiversity. Further research and development is needed to identify the most vulnerable regions, and to inform policy in time to facilitate transitional change and enable land managers to implement those changes.

Direct estimation of an element of order matrix from H-1 NMR spectra of strongly dipolar coupled spins

NMR spectra of molecules oriented in thermotropic liquid crystalline media provide information on the molecular structure and order. The spins are generally strongly dipolar coupled and the spectral analyse require the tedious and time consuming numerical iterative calculations. The present study demonstrates the application of multiple quantum spin state selective detection of single quantum transitions for mimicking the homonuclear decoupling and the direct estimation of an element of ordering matrix. This information is utilized to estimate the nearly accurate starting dipolar couplings for iterative calculations. The studies on the spectra of strongly dipolar coupled five and six interacting spin systems are reported.

Low temperature electrical transport properties of carbon matrix containing iron nanoparticles

We present a comparative study of the low temperature electrical transport properties of the carbon matrix containing iron nanoparticles and the films. The conductivity of the nanoparticles located just below the metal-insulator transition exhibits metallic behavior with a logarithmic temperature dependence over a large temperature interval. The zero-field conductivity and the negative magnetoresistance, showing a characteristic upturn at liquid helium temperature, are consistently explained by incorporating the Kondo relation and the two dimensional electron-electron interaction. The films, in contrast, exhibit a crossover of the conductivity from power-law dependence at high temperatures to an activated hopping law dependence in the low temperature region. The transition is attributed to changes in the energy dependence of the density of states near the Fermi level. The observed magnetoresistance is discussed in terms of quantum interference effect on a three-dimensional variable range hopping mechanism.

Foldable compatibility matrix for the folding of programmable logic arrays

This paper describes a switching theoretic algorithm for the folding of programmable logic arrays (PLA). The algorithm is valid for both column and row folding, although it has been presented considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), a new concept introduced by the author, is then derived from the compatibility matrix. A new theorem called the folding theorem is then proved. The theorem states that the existence of an m by 2m FCM is both necessary and sufficient to fold 2m columns of the n column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the re-ordering of the rows are readily determined.

Role of Basement Membrane and Extracellular Matrix Proteins in the Adhesion and Spreading of Immortalized Human Corneal Epithelial Cells

The repair of corneal wounds requires both epithelial cell adhesion and migration. Basement membrane (BM) and extracellular matrix (ECM) proteins function in these processes via integrin and non-integrin receptors. We have studied the adhesion, spreading and migration of immortalized human corneal epithelial (HCE) cells and their interactions with the laminins (Lms), fibronectins and tenascins produced. Human corneal BM expresses Lms-332 and -511, while Lm-111 was not found in these experiments. HCE cells produced both processed and unprocessed Lm-332, whereas neither Lm-111 nor Lm-511 was produced. Because HCE cells did not produce Lm-511, although it was present in corneal BM, we suggest that Lm-511 is produced by stromal keratocytes. The adhesion of HCE cells to Lms-111, -332 and -511 was studied first by determining the receptor composition of HCE cells and then by using quantitative cell adhesion assays. Immunofluorescence studies revealed the presence of integrin α2, α3, α6, β1 and β4 subunits. Among the non-integrin receptors, Lutheran (Lu) was found on adhering HCE cells. The cells adhered via integrin α3β1 to both purified human Lms-332 and -511 as well as to endogenous Lm-332. However, only integrin β1 subunit functioned in HCE cell adhesion to mouse Lm-111. The adhesion of HCE cells to Lm-511 was also mediated by Lu. Since Lm-511 did not induce Lu into focal adhesions in HCE cells, we suggest that Lm-511 serves as an ECM ligand enabling cell motility. HCE cells produced extradomain-A fibronectin, oncofetal fibronectin and tenascin-C (Tn-C), which are also found during corneal wound healing. Monoclonal antibodies (MAbs) against integrins α5β1 and αvβ6 as well as the arginine-glycine-aspartic acid (RGD) peptide inhibited the adhesion of HCE cells to fibronectin. Although the cells did not adhere to Tn-C, they adhered to the fibronectin/Tn-C coat and were then more efficiently inhibited by the function-blocking MAbs and RGD peptide. During the early adhesion, HCE cells codeposited Lm-332 and the large subunit of tenascin-C (Tn-CL) beneath the cells via the Golgi apparatus and microtubules. Integrin β4 subunit, which is a hemidesmosomal component, did not mediate the early adhesion of HCE cells to Lm-332 or Lm-332/Tn-C. Based on these results, we suggest that the adhesion of HCE cells is initiated by Lm-332 and modulated by Tn-CL, as it has been reported to prevent the assembly of hemidesmosomes. Thereby, Tn-CL functions in the motility of HCE cells during wound healing. The different distribution of processed and unprocessed Lm-332 in adhering, spreading and migrating HCE cells suggests a distinct role for these isoforms. We conclude that the processed Lm-332 functions in cell adhesion, whereas the unprocessed Lm-332 participates in cell spreading and migration.

Characterization of cytokines, matrix metalloproteinases and toll-like receptors in human periodontal tissue destruction

Periodontal Disease affects the supporting structures of the teeth and is initiated by a microbial biofilm called dental plaque. Severity ranges from superficial inflammation of the gingiva (gingivitis) to extensive destruction of connective tissue and bone leading to tooth loss (periodontitis). In periodontitis the destruction of tissue is caused by a cascade of microbial and host factors together with proteolytic enzymes. Matrix metalloproteinases (MMPs) are known to be central mediators of the pathologic destruction in periodontitis. Initially plaque bacteria provide pathogen-associated molecular patterns (PAMPs) which are sensed by Toll-like receptors (TLRs), and initiate intracellular signaling cascades leading to host inflammation. Our aim was to characterize TNF-α (tumor necrosis factor-alpha) and its type I and II receptors in periodontal tissues, as well as, the effects of TNF-α, IL-1β (interleukin-1beta) and IL-17 on the production and/or activation of MMP-3, MMP-8 and MMP-9. Furthermore we mapped the TLRs in periodontal tissues and assessed how some of the PAMPs binding to the key TLRs found in periodontal tissues affect production of TNF-α and IL-1β by gingival epithelial cells with or without combination of IL-17. TNF-α and its receptors were detected in pericoronitis. Furthermore, increased expression of interleukin-1β and vascular cell adhesion molecule-1 was found as a biological indicator of TNF-α ligand-receptor interaction. MMP-3, -8, and 9 were investigated in periodontitis affected human gingival crevicular fluid and gingival fibroblasts produced pro-MMP-3. Following that, the effect of IL-17 was studied on MMP and pro-inflammatory cytokine production. IL-17 was increased in periodontitis and up-regulated IL-1β, TNF-α, MMP-1 and MMP-3. We continued by demonstrating TLRs in gingival tissues, in which significant differences between patients with periodontitis and healthy controls were found. Finally, enzyme-linked immunosorbent assays were performed to show that the gingival cells response to inflammatory responses in a TLR-dependent manner. Briefly, this thesis demonstrates that TLRs are present in periodontal tissues and present differences in periodontitis compared to healthy controls. The cells of gingival tissues respond to inflammatory process in a TLR-dependent manner by producing pro-inflammatory cytokines. During the destruction of periodontal tissues, the release (IL-1β and TNF-α) and co-operation with other pro-inflammatory cytokines (IL-17), which in turn increase the inflammation and thus be more harmful to the host with the increased presence of MMPs (MMP-1, MMP-3, MMP-8, MMP-9) in diseased over healthy sites.

Studies on Matrix Metalloproteinase (MMP-2, -9 and -14) and β2 Integrin Targeting as Potential Anticancer Therapeutics

Proteolytic enzymes, such as matrix metalloproteinases (MMP), are associated to the progression of several cancers. They degrade extracellular components, which helps tumors to expand and cancer cells to escape from the primary site. Of all MMPs, gelatinases (MMP-2 and -9) and membrane type-1 matrix metalloproteinase (MT1-MMP, MMP-14), in particular, are often associated to more aggressive types of head and neck carcinomas as well as to a poorer outcome in patient survival. Although therapies during the last decades have advanced, the mortality of the disease is still rather high and adjuvant therapies are searched for continuously. MMP-9 and MT1-MMP are also involved in neo-angiogenesis, which is necessary for tumor expansion. For this reason, we have identified synthetic peptides-targeting gelatinases and MT1-MMP, and have also evaluated their anticancer effects in vitro and in vivo. Antigelatinolytic peptides effectively inhibited tongue-carcinoma cell invasion and reduced the growth of xenografted tumors. In tumor samples of mice that were treated with antigelatinolytic peptides, the micro-vessel density was significantly reduced. We also identified a novel MT1-MMP targeting peptide and demonstrated that it exerted anticancer effects against several malignant cell lines in vitro. The effects of MT1-MMP inhibition on tongue-squamous cell carcinomas were evaluated by using xenograft tumors, which it effectively inhibited. Tranexamic acid was also demonstrated to inhibit tongue-squamous cell carcinoma invasion, most probably due to its ability to prevent the plasmin-mediated activation of proMMP-9. Leukocyte β2 integrins are another interesting option when evaluating targets for the therapeutic intervention of inflammatory conditions or malignancies of hematopoietic origin, since β2 integrins are expressed mainly by leukocytes. We identified a novel technique for screening small-molecule libraries against β2 integrins, and by using this technique we identified a novel αMβ2 integrin-binding chemical (IMB-10). IMB-10 significantly enhances leukocyte adhesion and inhibits their motility. We also demonstrated that IMB-10 can be used to inhibit inflammation and lymphoma growth in vivo. Interestingly, IMB-10 also reduced leukocyte tumor infiltration and inhibited tumor invasion.