Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Environmental monitoring of bacterial contamination and antibiotic resistance patterns of the fecal coliforms isolated from Cauvery River, a major drinking water source in Karnataka, India

The present study focuses prudent elucidation of microbial pollution and antibiotic sensitivity profiling of the fecal coliforms isolated from River Cauvery, a major drinking water source in Karnataka, India. Water samples were collected from ten hotspots during the year 2011-2012. The physiochemical characteristics and microbial count of water samples collected from most of the hotspots exhibited greater biological oxygen demand and bacterial count especially coliforms in comparison with control samples (p <= 0.01). The antibiotic sensitivity testing was performed using 48 antibiotics against the bacterial isolates by disk-diffusion assay. The current study showed that out of 848 bacterial isolates, 93.51 % (n=793) of the isolates were found to be multidrug-resistant to most of the current generation antibiotics. Among the major isolates, 96.46 % (n=273) of the isolates were found to be multidrug-resistant to 30 antibiotics and they were identified to be Escherichia coli by 16S rDNA gene sequencing. Similarly, 93.85 % (n=107), 94.49 % (n=103), and 90.22 % (n=157) of the isolates exhibited multiple drug resistance to 32, 40, and 37 antibiotics, and they were identified to be Enterobacter cloacae, Pseudomonas trivialis, and Shigella sonnei, respectively. The molecular studies suggested the prevalence of blaTEM genes in all the four isolates and dhfr gene in Escherichia coli and Sh. sonnei. Analogously, most of the other Gram-negative bacteria were found to be multidrug-resistant and the Gram-positive bacteria, Staphylococcus spp. isolated from the water samples were found to be methicillin and vancomycin-resistant Staphylococcus aureus. This is probably the first study elucidating the bacterial pollution and antibiotic sensitivity profiling of fecal coliforms isolated from River Cauvery, Karnataka, India.

Enhanced sunlight photocatalytic activity of Ag3PO4 decorated novel combustion synthesis derived TiO2 nanobelts for dye and bacterial degradation

This study demonstrates the synthesis of TiO2 nanobelts using solution combustion derived TiO2 with enhanced photocatalytic activity for dye degradation and bacterial inactivation. Hydrothermal treatment of combustion synthesized TiO2 resulted in unique partially etched TiO2 nanobelts and Ag3PO4 was decorated using the co-precipitation method. The catalyst particles were characterized using X-ray diffraction analysis, BET surface area analysis, diffuse reflectance and electron microscopy. The photocatalytic properties of the composites of Ag3PO4 with pristine combustion synthesized TiO2 and commercial TiO2 under sunlight were compared. Therefore the studies conducted proved that the novel Ag3PO4/unique combustion synthesis derived TiO2 nanobelt composites exhibited extended light absorption, better charge transfer mechanism and higher generation of hydroxyl and hole radicals. These properties resulted in enhanced photodegradation of dyes and bacteria when compared to the commercial TiO2 nanocomposite. These findings have important implications in designing new photocatalysts for water purification.

Evolution of bacterial transcription factors: how proteins take on new tasks, but do not always stop doing the old ones

Many bacterial transcription factors do not behave as per the textbook operon model. We draw on whole genome work, as well as reported diversity across different bacteria, to argue that transcription factors may have evolved from nucleoid-associated proteins. This view would explain a large amount of recent data gleaned from high-throughput sequencing and bioinformatic analyses.

BT-benzo-29 inhibits bacterial cell proliferation by perturbing FtsZ assembly

We have identified a potent antibacterial agent N-(4-sec-butylphenyl)-2-(thiophen-2-yl)-1H-benzod]imidazole-4-carboxa mide (BT-benzo-29) from a library of benzimidazole derivatives that stalled bacterial division by inhibiting FtsZ assembly. A short (5 min) exposure of BT-benzo-29 disassembled the cytokinetic Z-ring in Bacillus subtilis cells without affecting the cell length and nucleoids. BT-benzo-29 also perturbed the localization of early and late division proteins such as FtsA, ZapA and SepF at the mid-cell. Further, BT-benzo-29 bound to FtsZ with a dissociation constant of 24 +/- 3 m and inhibited the assembly and GTPase activity of purified FtsZ. A docking analysis suggested that BT-benzo-29 may bind to FtsZ at the C-terminal domain near the T7 loop. BT-benzo-29 displayed significantly weaker inhibitory effects on the assembly and GTPase activity of two mutants (L272A and V275A) of FtsZ supporting the prediction of the docking analysis. Further, BT-benzo-29 did not appear to inhibit DNA duplication and nucleoid segregation and it did not perturb the membrane potential of B. subtilis cells. The results suggested that BT-benzo-29 exerts its potent antibacterial activity by inhibiting FtsZ assembly. Interestingly, BT-benzo-29 did not affect the membrane integrity of mammalian red blood cells. BT-benzo-29 bound to tubulin with a much weaker affinity than FtsZ and exerted significantly weaker effects on mammalian cells than on the bacterial cells indicating that the compound may have a strong antibacterial potential.

Systematic Analysis of Mycobacterial Acylation Reveals First Example of Acylation-mediated Regulation of Enzyme Activity of a Bacterial Phosphatase

Protein lysine acetylation is known to regulate multiple aspects of bacterial metabolism. However, its presence in mycobacterial signal transduction and virulence-associated proteins has not been studied. In this study, analysis of mycobacterial proteins from different cellular fractions indicated dynamic and widespread occurrence of lysine acetylation. Mycobacterium tuberculosis proteins regulating diverse physiological processes were then selected and expressed in the surrogate host Mycobacterium smegmatis. The purified proteins were analyzed for the presence of lysine acetylation, leading to the identification of 24 acetylated proteins. In addition, novel lysine succinylation and propionylation events were found to co-occur with acetylation on several proteins. Protein-tyrosine phosphatase B (PtpB), a secretory phosphatase that regulates phosphorylation of host proteins and plays a critical role in Mycobacterium infection, is modified by acetylation and succinylation at Lys-224. This residue is situated in a lid region that covers the enzyme's active site. Consequently, acetylation and succinylation negatively regulate the activity of PtpB.

A Bacterial Foraging Optimization and Learning Automata Based Feature Selection for Motor Imagery EEG Classification

Selection of relevant features is an open problem in Brain-computer interfacing (BCI) research. Sometimes, features extracted from brain signals are high dimensional which in turn affects the accuracy of the classifier. Selection of the most relevant features improves the performance of the classifier and reduces the computational cost of the system. In this study, we have used a combination of Bacterial Foraging Optimization and Learning Automata to determine the best subset of features from a given motor imagery electroencephalography (EEG) based BCI dataset. Here, we have employed Discrete Wavelet Transform to obtain a high dimensional feature set and classified it by Distance Likelihood Ratio Test. Our proposed feature selector produced an accuracy of 80.291% in 216 seconds.

Optimal Guidance for Accurate Lunar Soft Landing with Minimum Fuel Consumption using Model Predictive Static Programming

In this paper the soft lunar landing with minimum fuel expenditure is formulated as a nonlinear optimal guidance problem. The realization of pinpoint soft landing with terminal velocity and position constraints is achieved using Model Predictive Static Programming (MPSP). The high accuracy of the terminal conditions is ensured as the formulation of the MPSP inherently poses final conditions as a set of hard constraints. The computational efficiency and fast convergence make the MPSP preferable for fixed final time onboard optimal guidance algorithm. It has also been observed that the minimum fuel requirement strongly depends on the choice of the final time (a critical point that is not given due importance in many literature). Hence, to optimally select the final time, a neural network is used to learn the mapping between various initial conditions in the domain of interest and the corresponding optimal flight time. To generate the training data set, the optimal final time is computed offline using a gradient based optimization technique. The effectiveness of the proposed method is demonstrated with rigorous simulation results.

Multiple oligomeric structures of a bacterial small heat shock protein

Small heat shock proteins are ubiquitous molecular chaperones that form the first line of defence against the detrimental effects of cellular stress. Under conditions of stress they undergo drastic conformational rearrangements in order to bind to misfolded substrate proteins and prevent cellular protein aggregation. Owing to the dynamic nature of small heat shock protein oligomers, elucidating the structural basis of chaperone action and oligomerization still remains a challenge. In order to understand the organization of sHSP oligomers, we have determined crystal structures of a small heat shock protein from Salmonella typhimurium in a dimeric form and two higher oligomeric forms: an 18-mer and a 24-mer. Though the core dimer structure is conserved in all the forms, structural heterogeneity arises due to variation in the terminal regions.

Modelling within-host spatiotemporal dynamics of invasive bacterial disease

Mechanistic determinants of bacterial growth, death, and spread within mammalian hosts cannot be fully resolved studying a single bacterial population. They are also currently poorly understood. Here, we report on the application of sophisticated experimental approaches to map spatiotemporal population dynamics of bacteria during an infection. We analyzed heterogeneous traits of simultaneous infections with tagged Salmonella enterica populations (wild-type isogenic tagged strains [WITS]) in wild-type and gene-targeted mice. WITS are phenotypically identical but can be distinguished and enumerated by quantitative PCR, making it possible, using probabilistic models, to estimate bacterial death rate based on the disappearance of strains through time. This multidisciplinary approach allowed us to establish the timing, relative occurrence, and immune control of key infection parameters in a true host-pathogen combination. Our analyses support a model in which shortly after infection, concomitant death and rapid bacterial replication lead to the establishment of independent bacterial subpopulations in different organs, a process controlled by host antimicrobial mechanisms. Later, decreased microbial mortality leads to an exponential increase in the number of bacteria that spread locally, with subsequent mixing of bacteria between organs via bacteraemia and further stochastic selection. This approach provides us with an unprecedented outlook on the pathogenesis of S. enterica infections, illustrating the complex spatial and stochastic effects that drive an infectious disease. The application of the novel method that we present in appropriate and diverse host-pathogen combinations, together with modelling of the data that result, will facilitate a comprehensive view of the spatial and stochastic nature of within-host dynamics. © 2008 Grant et al.

Bacterial growth rate and host factors as determinants of intracellular bacterial distributions in systemic Salmonella enterica infections.

Bacteria of the species Salmonella enterica cause a range of life-threatening diseases in humans and animals worldwide. The within-host quantitative, spatial, and temporal dynamics of S. enterica interactions are key to understanding how immunity acts on these infections and how bacteria evade immune surveillance. In this study, we test hypotheses generated from mathematical models of in vivo dynamics of Salmonella infections with experimental observation of bacteria at the single-cell level in infected mouse organs to improve our understanding of the dynamic interactions between host and bacterial mechanisms that determine net growth rates of S. enterica within the host. We show that both bacterial and host factors determine the numerical distributions of bacteria within host cells and thus the level of dispersiveness of the infection.

Probing biomolecular interaction forces using an anharmonic acoustic technique for selective detection of bacterial spores.

Receptor-based detection of pathogens often suffers from non-specific interactions, and as most detection techniques cannot distinguish between affinities of interactions, false positive responses remain a plaguing reality. Here, we report an anharmonic acoustic based method of detection that addresses the inherent weakness of current ligand dependant assays. Spores of Bacillus subtilis (Bacillus anthracis simulant) were immobilized on a thickness-shear mode AT-cut quartz crystal functionalized with anti-spore antibody and the sensor was driven by a pure sinusoidal oscillation at increasing amplitude. Biomolecular interaction forces between the coupled spores and the accelerating surface caused a nonlinear modulation of the acoustic response of the crystal. In particular, the deviation in the third harmonic of the transduced electrical response versus oscillation amplitude of the sensor (signal) was found to be significant. Signals from the specifically-bound spores were clearly distinguishable in shape from those of the physisorbed streptavidin-coated polystyrene microbeads. The analytical model presented here enables estimation of the biomolecular interaction forces from the measured response. Thus, probing biomolecular interaction forces using the described technique can quantitatively detect pathogens and distinguish specific from non-specific interactions, with potential applicability to rapid point-of-care detection. This also serves as a potential tool for rapid force-spectroscopy, affinity-based biomolecular screening and mapping of molecular interaction networks.