Matrix-Norm Approach of Computing Levenberg-Marquardt Reg- ularization Parameter for Nonlinear Equations

In this paper, we present Levenberg-Marquardt method for solving nonlinear systems of  equations. Here, both the objective function and the symmetric Jacobian matrix are assumed to be Lipchitz continuous. The regularization parameter is derived using Matrix-Norm approach. Numerical performance on some benchmark problems that demonstrates the effectiveness and efficiency of our approach are reported and have shown that the proposed algorithm is very promising.Mathematics Subject Classification: 65H10, 65K05, 65F22, 65F35.keywords: Nonlinear system of equations. Levenberg-Marquardt method. Regularization. Matrix-norm. Global convergence

Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising

A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations

We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance

NeuroGrid: recording action potentials from the surface of the brain.

Recording from neural networks at the resolution of action potentials is critical for understanding how information is processed in the brain. Here, we address this challenge by developing an organic material-based, ultraconformable, biocompatible and scalable neural interface array (the 'NeuroGrid') that can record both local field potentials(LFPs) and action potentials from superficial cortical neurons without penetrating the brain surface. Spikes with features of interneurons and pyramidal cells were simultaneously acquired by multiple neighboring electrodes of the NeuroGrid, allowing for the isolation of putative single neurons in rats. Spiking activity demonstrated consistent phase modulation by ongoing brain oscillations and was stable in recordings exceeding 1 week's duration. We also recorded LFP-modulated spiking activity intraoperatively in patients undergoing epilepsy surgery. The NeuroGrid constitutes an effective method for large-scale, stable recording of neuronal spikes in concert with local population synaptic activity, enhancing comprehension of neural processes across spatiotemporal scales and potentially facilitating diagnosis and therapy for brain disorders

HTLV-1 Tax Mediated Downregulation of miRNAs Associated with Chromatin Remodeling Factors in T Cells with Stably Integrated Viral Promoter

RNA interference (RNAi) is a natural cellular mechanism to silence gene expression and is predominantly mediated by microRNAs (miRNAs) that target messenger RNA. Viruses can manipulate the cellular processes necessary for their replication by targeting the host RNAi machinery. This study explores the effect of human T-cell leukemia virus type 1 (HTLV-1) transactivating protein Tax on the RNAi pathway in the context of a chromosomally integrated viral long terminal repeat (LTR) using a CD4+ T-cell line, Jurkat. Transcription factor profiling of the HTLV-1 LTR stably integrated T-cell clone transfected with Tax demonstrates increased activation of substrates and factors associated with chromatin remodeling complexes. Using a miRNA microarray and bioinformatics experimental approach, Tax was also shown to downregulate the expression of miRNAs associated with the translational regulation of factors required for chromatin remodeling. These observations were validated with selected miRNAs and an HTLV-1 infected T cells line, MT-2. miR-149 and miR-873 were found to be capable of directly targeting p300 and p/CAF, chromatin remodeling factors known to play critical role in HTLV-1 pathogenesis. Overall, these results are first in line establishing HTLV-1/Tax-miRNA-chromatin concept and open new avenues toward understanding retroviral latency and/or replication in a given cell type

Carbapenem resistance expressed by Gram-negative bacilli isolated from a cohort of Libyan patients

Background and objectives: Carbapenem-resistant Enterobacteriaceae (CRE) and other Gram-negative bacteria are among the most common pathogens responsible for both community and hospital acquired infection. The global spread of cephalosporinases in Enterobacteriaceae has led to the increased use of carbapenems resulting in the emergence and rapid spread of CRE. This has become an alarming public health concern, yet the condition in Libya remains unclear. The aim of this study was to obtain a better understanding of CRE strains prevalent in Libyan patients by investigating their phenotypic characteristics and antibiograms. Methods: Gram-negative bacterial species were collected from Misrata Central Hospital, Misrata Cancer Centre and Privet Pathology Laboratories. Clinical samples and swabs were obtained from hospitalised and non-hospitalised patients and from mechanical ventilation and suction machines. Patients who had received antibiotic therapy for at least three days prior to the study were excluded. The identification and characterization of the isolated species were achieved using the growth characteristics on MacConkey and blood agar, spot tests and API 20E or API 20NE biochemical testing systems. Screening for carbapenem resistance was performed using the disk diffusion method with carbapenem 10 μg and cephalosporin 30 μg disks and minimum inhibitory concentrations (MIC) determined using the Sensititre Gram-negative Xtra plate format (GNX2F). All strains demonstrating resistance or reduced susceptibility to one of the four carbapenems were subjected to carbapenememase activity detection using the RAPIDEC CARBA NP test, Modified Hodge test and carbapenem inactivation methods. Results: A total of one hundred and forty isolates representing fourteen bacterial species were isolated from 140 non-duplicated specimens. Clinical specimens included urine samples (96/140, 68.57%), sputum (15/140, 10.71%), surgical wound swabs (18/140, 12.85%), foot swabs from diabetes mellitus (DM) patients (6/140, 4.29%), ear swabs (3/140, 2.14%) and wound swabs (2/140, 1.43%). Thirty-four (24.29%) isolates demonstrated resistance to at least one of the four carbapenems with Klebsiella pneumoniae representing 73.53% (25 isolates) of all carbapenem resistant species, followed by 8.82% for Pseudomonas aeruginosa (3 isolates), 5.88% for both Proteus mirabilis (2 isolates) and Escherichia coli (2 isolates) and 2.94% for both Citrobacter koseri (1 isolate) and Rahnella aquatilis (1 isolate). The other isolates were either susceptible or cephalosporinase producers. Conclusion: This study has revealed the high rate of carbapenem resistance amongst Libyan patients and emphasizes the crucial need for accurate screening, identification and susceptibility testing to prevent further spread of nosocomial and community acquired resistance. This may be achieved through the establishment of antibiotic stewardship programmes along with firm infection control practices.National Research Foundation of South Africa; Libyan GovernmentWeb of Scienc