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.

Changes in the Activities of two membrane-bound enzymes during solar eclipse on February 16, 1980

ON Saturday February 16, 1980 total solar eclipse Occurred for a period of 2-3 min in a belt of 135 km during the eclipse from 14'17 to 17'00 hrs across peninsular India. The city of Bangalore, being just outside this belt, had witnessed 92% eclipse for about 2. 1/2 min at the peak period of 15.44 hr at which time a temperature drop of 2' C and a considerable dimness of the light were experienced. In view of the interest in our laboratory on biochemical adaptation under conditions of environmental stress, we designed an experiment to study the possible changes in enzyme activities during the solar eclipse on February 16, 1980.

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.

Cholesterol-Esterifying Enzymes in Developing Rat Brain

A cholesterol-esterifying enzyme which incorporates exogenous fatty acids into cholesterol esters in the presence of ATP and coenzyme A was demonstrated in 15-day-old rat brain. This enzyme was maximally active at pH 7.4 and distinct from the cholesterol-esterifying enzyme reported earlier (Eto and Suzuki, 1971), which has a pH optimum at 5.2 and does not require cofactors. Properties of the two enzymes have been compared. Both the enzymes showed negligible esterification with acetate and were maximally active with oleic acid. The pH 5.2 enzyme esterified desmosterol, lanosterol and cholesterol at about the same rate, while the pH 7.4 enzyme was only 50% as active ith lanosterol as it was with cholesterol and desmosterol. Phosphatidyl serine stimulated the pH 5.2 enzyme but not the pH 7.4 enzyme. Phosphatidyl choline and sodium taurocholate showed no effect on either of the enzymes. Both the enzymes were associated with particulate fractions, but the pH 7.4 enzyme was localized more in the microsomes. Purified myelin showed 2.6-fold and 1.5-fold higher specific activities of pH 5.2 and 7.4 enzymes respectively, when compared with homogenate. About 7-10% of total activity of both the enzymes was associated with purified myelin. Brain stem and spinal cord showed higher specific activity of pH 5.2 enzyme than cerebral cortex and cerebellum, while pH 7.4 enzyme specific activity was higher in cerebellum and brain stem than in cerebral cortex and spinal cord. Microsomal pH 7.4 activity showed progressive increase prior to the active period of myelination, reaching a maximum on the 15th day after birth and declined to 20% of the peak activity by 30 days. In contrast, pH 5.2 enzyme reached maximum activity about the 6th day after birth and remained at this level well into adulthood. In 15-day-old rat brain, pH 7.4 enzyme had five to six times higher specific activity than pH 5.2 enzyme, while in adults the activities were equal. The pH 7.4 enzyme showed a threefold higher specific activity than pH 5.2 enzyme in myelin from 15-day-old rats, but in adults the reverse was true. Key Words: Cholesterol esterifying enzymes-Developing rat brain-Myelination. Jagannatha H. M. and Sastry P. S. Cholesterol-esterifying enzymes in developing rat brain. J. Neurochem. 36, 1352- 1360 (1981).

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.

Expression of cytochrome P450 enzymes and metabolism of timolol in human ocular tissue

Glaucoma is a group of progressive optic neuropathies causing irreversible blindness if not diagnosed and treated in the early state of progression. Disease is often, but not always, associated with increased intraocular pressure (IOP), which is also the most important risk factor for glaucoma. Ophthlamic timolol preparations have been used for decades to lower increased intraocular pressure (IOP). Timolol is locally well tolerated but may cause e.g. cardiovascular and pulmonary adverse effects due to systemic absorption. It has been reported that approximately 80% of a topically administered eye drop is systemically absorbed. However, only limited information is available on timolol metabolism in the liver or especially in the human eye. The aim of this work was to investigate metabolism of timolol in human liver and human ocular tissues. The expression of drug metabolizing cytochrome P450 (CYP) enzymes in the human ciliary epithelial cells was studied. The metabolism of timolol and the interaction potential of timolol with other commercially available medicines were investigated in vitro using different liver preparations. The absorption of timolol to the aqueous humor from two commercially available products: 0.1% eye gel and 0.5% eye drops and the presence of timolol metabolites in the aqueous humor were investigated in a clinical trial. Timolol was confirmed to be metabolized mainly by CYP2D6 as previously suggested. Potent CYP2D6 inhibitors especially fluoxetine, paroxetine and quinidine inhibited the metabolism of timolol. The inhibition may be of clinical significance in patients using ophthalmic timolol products. CYP1A1 and CYP1B1 mRNAs were expressed in the human ciliary epithelial cells. CYP1B1 was also expressed at protein level and the expression was strongly induced by a known potent CYP1B1 inducer 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). The CYP1B1 induction is suggested to be mediated by aryl hydrocarbon receptor (AHR). Low levels of CYP2D6 mRNA splice variants were expressed in the human ciliary epithelial cells and very low levels of timolol metabolites were detected in the human aqueous humor. It seems that negligible amount of CYP2D6 protein is expressed in the human ocular tissues. Timolol 0.1% eye gel leads to aqueous humor concentration high enough to achieve therapeutic effect. Inter-individual variation in concentrations is low and intraocular as well as systemic safety can be increased when using this product with lower timolol concentration instead of timolol 0.5% eye drops.

ADAMs, Osteoclastogenesis and Bone Destruction in the Loosening of the Totally Replaced Hip

Total hip replacement is the golden standard treatment for severe osteoarthritis refractory for conservative treatment. Aseptic loosening and osteolysis are the major long-term complications after total hip replacement. Foreign body giant cells and osteoclasts are locally formed around aseptically loosening implants from precursor cells by cell fusion. When the foreign body response is fully developed, it mediates inflammatory and destructive host responses, such as collagen degradation. In the present study, it was hypothesized that the wear debris and foreign body inflammation are the forces driving local osteoclast formation, peri-implant bone resorption and enhanced tissue remodeling. Therefore the object was to characterize the eventual expression and the role of fusion molecules, ADAMs (an abbreviation for A Disintegrin And Metalloproteinase, ADAM9 and ADAM12) in the fusion of progenitor cells into multinuclear giant cells. For generation of such cells, activated macrophages trying to respond to foreign debris play an important role. Matured osteoclasts together with activated macrophages mediate bone destruction by secreting protons and proteinases, including matrix metalloproteinases (MMPs) and cathepsin K. Thus this study also assessed collagen degradation and its relationship to some of the key collagenolytic proteinases in the aggressive synovial membrane-like interface tissue around aseptically loosened hip replacement implants. ADAMs were found in the interface tissues of revision total hip replacement patients. Increased expression of ADAMs at both transcriptional and translational levels was found in synovial membrane-like interface tissue of revision total hip replacement (THR) samples compared with that in primary THR samples. These studies also demonstrate that multinucleate cell formation from monocytes by stimulation with macrophage-colony stimiulating factor (M-CSF) and receptor activator of nuclear factor kappa B ligand (RANKL) is characterized by time dependent changes of the proportion of ADAMs positive cells. This was observed both in the interface membrane in patients and in two different in vitro models. In addition to an already established MCS-F and RANKL driven model, a new virally (parainfluenza 2) driven model (of human salivary adenocarcinoma (HSY) cells or green monkey kidney (GMK) cells) was developed to study various fusion molecules and their role in cell fusion in general. In interface membranes, collagen was highly degraded and collagen degradation significantly correlated with the number of local cells containing collagenolytic enzymes, particularly cathepsin K. As a conclusion, fusion molecules ADAM9 and ADAM12 seem to be dynamically involved in cell-cell fusion processes and multinucleate cell formation. The highly significant correlation between collagen degradation and collagenolytic enzymes, particularly cathepsin K, indicates that the local acidity of the interface membrane in the pathologic bone and soft tissue destruction. This study provides profound knowledge about cell fusion and mechanism responsible for aseptic loosening as well as increases knowledge helpful for prevention and treatment.

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.

The influence of HIV infection to the periodontium; a clinical, microbiological, and enzymological study

The main targets of human immunodeficiency virus (HIV) are CD4 receptors of CD4+ lymphocytes and many other cells such as monocytes/macrophages, megakaryocytes, peripheral blood dendritic cells, follicular dendritic cells (DC), epidermal Langerhans cells, and astrocytes. Infection and killing of CD4+ lymphocytes or false reaction of the body to HIV infection and the spontaneous apoptosis of CD4+ lymphocytes decrease CD4+ lymphocyte counts leading to immunosuppression, further disease progression, and appearance of opportunistic infections and malignancies. Oral manifestations are considered to be among the first signs of HIV infection. Enhanced degradation of extracellular matrix and basement membrane components in oral diseases including periodontitis is caused by Zn-dependent enzymes called matrix metalloproteinases (MMPs). The levels and degrees of activation of MMP-1, -2, -3, -7, -8, -9, -25, -26, tissue inhibitors of MMPs (TIMP)-1 and -2, and myeloperoxidase (MPO) and collagenolytic/gelatinolytic activities, and also Ig A, -G, and -M, total protein, and albumin levels in a two-year follow-up were studied from salivary samples. The expression of MMP-7, -8, -9, -25, and -26 immunoreactivities in gingival tissue specimens were studied. Healthy HIV-negative subjects served as controls. All studied clinical periodontal parameters and microbiological evaluation of the periodontopathogens showed that periodontal health of the HIV-positive patients was moderately decreased in comparison to the healthy controls. The levels of Candida in the periodontal pockets and salivary MPO increased with the severity of HIV infection. Immunoreactivities and levels of MMPs and TIMPs, and MMP activities (collagenase, gelatinase) were enhanced in the HIV-positive patient salivary samples relative to the healthy controls regardless of the phase of HIV infection. However, these parameters did not reflect periodontal status in a similar way as in the generally healthy periodontitis patients. Salivary total protein, albumin, IgA, -G, and -M levels were significantly higher in all phases of HIV infection compared to the controls, and salivary total protein, IgG and IgM levels remained higher after two years follow-up, partly correlating with the disease progression and which may reflect the leakage of serum components into the mouth and thus a decreased mucosal barrier. Salivary analyses of MMPs and TIMPs with immunohistochemical analyses showed that HIV infection could predispose to periodontal destruction when compared with healthy controls or the body s defence reactions associated with HIV infection may have been reflected or mediated by MMPs.