Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Observers for linear systems with unknown inputs

This paper presents a constructive solution to the problem of designing a reduced-order Luenberger observer for linear systems subject to arbitrary unknown inputs.

Fatigue Laws Via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner's rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson's Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading', Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner's rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.

Functional programming systems revisited

Functional Programming (FP) systems are modified and extended to form Nondeterministic Functional Programming (NFP) systems in which nondeterministic programs can be specified and both deterministic and nondeterministic programs can be verified essentially within the system. It is shown that the algebra of NFP programs has simpler laws in comparison with the algebra of FP programs. "Regular" forms are introduced to put forward a disciplined way of reasoning about programs. Finally, an alternative definition of "linear" forms is proposed for reasoning about recursively defined programs. This definition, when used to test the linearity of forms, results in simpler verification conditions than those generated by the original definition of linear forms.

Characterization of DNA Strand Transfer Promoted by Mycobacterium smegmatis RecA Reveals Functional Diversity with Mycobacterium tuberculosis RecA†

The RecA-like proteins constitute a group of DNA strand transfer proteins ubiquitous in eubacteria, eukarya, and archaea. However, the functional relationship among RecA proteins is poorly understood. For instance, Mycobacterium tuberculosis RecA is synthesized as a large precursor, which undergoes an unusual protein-splicing reaction to generate an active form. Whereas the precursor was inactive, the active form promoted DNA strand transfer less efficiently compared to EcRecA. Furthermore, gene disruption studies have indicated that the frequencies of allele exchange are relatively lower in Mycobacterium tuberculosis compared to Mycobacterium smegmatis. The mechanistic basis and the factors that contribute to differences in allele exchange remain to be understood. Here, we show that the extent of DNA strand transfer promoted by the M. smegmatis RecA in vitro differs significantly from that of M. tuberculosis RecA. Importantly, M. smegmatis RecA by itself was unable to promote strand transfer, but cognate or noncognate SSBs rendered it efficient even when added prior to RecA. In the presence of SSB, MsRecA or MtRecA catalyzed strand transfer between ssDNA and varying lengths of linear duplex DNA with distinctly different pH profiles. The factors that were able to suppress the formation of DNA networks greatly stimulated strand transfer reactions promoted by MsRecA or MtRecA. Although the rate and pH profiles of dATP hydrolysis catalyzed by MtRecA and MsRecA were similar, only MsRecA was able to couple dATP hydrolysis to DNA strand transfer. Together, these results provide insights into the functional diversity in DNA strand transfer promoted by RecA proteins of pathogenic and nonpathogenic species of mycobacteria.

Direct Synthesis of Terminally ``Clickable'' Linear and Hyperbranched Polyesters

1,3-Dipolar cycloaddition of an organic azide and an acetylenic unit,often referred to as the ``click reaction'', has become an important ligation tool both in the context of materials chemistry and biology. Thus, development of simple approaches to directly generate polymers that bear either an azide or an alkyne unit has gained considerable importance. We describe here a straightforward approach to directly prepare linear and hyperbranched polyesters that carry terminal propargyl groups. To achieve the former, we designed an AB-type monomer that carries a hydroxyl group and a propargyl ester, which upon self-condensation under standard transesterification conditions yielded a polyester that carries a single propargyl group at one of its chain-ends. Similarly, an AB(2) type monomer that carries one hydroxyl group and two propargyl ester groups, when polymerized under the same conditions yielded a hyperbranched polymer with numerous clickable'' propargyl groups at its molecular periphery. These propargyl groups can be readily clicked with different organic azides, such as benzyl azide, omega-azido heptaethyleneglycol monomethylether or 9-azidomethyl anthracene. When an anthracene chromophore is clicked, the molecular weight of the linear polyester could be readily estimated using both UV-visible and fluorescence spectroscopic measurements. Furthermore, the reactive propargyl end group could also provide an opportunity to prepare block copolymers in the case of linear polyesters and to generate nanodimensional scaffolds to anchor variety of functional units, in the case of the hyperbranched polymer. (C) 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3200-3208, 2010.

Actuator fault detection and isolation in linear systems

A scheme for the detection and isolation of actuator faults in linear systems is proposed. A bank of unknown input observers is constructed to generate residual signals which will deviate in characteristic ways in the presence of actuator faults. Residual signals are unaffected by the unknown inputs acting on the system and this decreases the false alarm and miss probabilities. The results are illustrated through a simulation study of actuator fault detection and isolation in a pilot plant doubleeffect evaporator.

Linear gramicidin activates neutrophil functions and the activation is blocked by chemotactic peptide receptor antagonist

The activation of functional responses in rabbit peritoneal neutrophils by gramicidin and the chemotactic peptide, N-formyl-methionyl-leucyl-phenylalanine methyl ester, was studied. Gramicidin activated superoxide generation, lysosomal enzyme release and a decrease in fluorescence of chlortetracycline-loaded cells, as for the chemotactic peptide. The maximum intensities of the responses by gramicidin were lower than that by chemotactic peptide. Responses by both these peptides could be inhibited by t-butyloxycarbonyl-methionyl-leucyl-phenylalanine, a chemotactic peptide receptor antagonist. Gramicidin gave responses at low doses comparable to that of the chemotactic peptide.

Synthesis, biological studies of linear and branched arabinofuranoside-containing glycolipids and their interaction with surfactant protein A

Oligoarabinofuranoside-containing glycolipids relevant to mycobacterial cell wall components were synthesized in order to understand the functional roles of such glycolipids. A series of linear tetra-, hexa-, octa-and a branched heptasaccharide oligoarabinofuranosides, with 1 -> 2 and 1 -> 5 a-linkages between the furanoside residues, were synthesized by chemical methods from readily available monomer building blocks. Upon the synthesis of glycolipids, constituted with a double alkyl chain-substituted sn-glycerol core and oligosaccharide fragments, biological studies were performed to identify the effect of synthetic glycolipids on the biofilm formation and sliding motilities of Mycobacterium smegmatis. Synthetic glycolipids and arabinofuranosides displayed an inhibitory effect on the growth profile, but mostly on the biofilm formation and maturation. Similarly, synthetic compounds also influenced the sliding motility of the bacteria. Further, biophysical studies were undertaken, so as to identify the interactions of the glycolipids with a pulmonary surfactant protein, namely surfactant protein A (SP-A), with the aid of the surface plasmon resonance technique. Specificities of each glycolipid interacting with SP-A were thus evaluated. From this study, glycolipids were found to exhibit higher apparent association constants than the corresponding oligosaccharide portion alone, without the double alkyl group-substituted glycerol core.

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric ``correlation between probabilities of recurrence'' (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of ``how much'' information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on ``what'' is coded by primary afferents. Amongst the kinematic variables tested-position, velocity, and acceleration-primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.

Cu-II-Azide Polynuclear Complexes of Three Different Building Clusters with the Same Schiff-Base Ligand: Synthesis, Structures, Magnetic Behavior, and Density Functional Theory Studies

Three copper-azido complexes Cu-4(N-3)(8)(L-1)(2)(MeOH)(2)](n) (1), Cu-4(N-3)(8)(L-1)(2)] (2), and Cu-5(N-3)(10)(L-1)(2)](n) (3) L-1 is the imine resulting from the condensation of pyridine-2-carboxaldehyde with 2-(2-pyridyl)ethylamine] have been synthesized using lower molar equivalents of the Schiff base ligand with Cu(NO3)(2)center dot 3H(2)O and an excess of NaN3. Single crystal X-ray structures show that the basic unit of the complexes 1 and 2 contains Cu-4(II) building blocks; however, they have distinct basic and overall structures due to a small change in the bridging mode of the peripheral pair of copper atoms in the linear tetranudear structures. Interestingly, these changes are the result of changing the solvent system (MeOH/H2O to EtOH/H2O) used for the synthesis, without changing the proportions of the components (metal to ligand ratio 2:1). Using even lower proportions of the ligand, another unique complex was isolated with Cu-5(II) building units, forming a two-dimensional complex (3). Magnetic susceptibility measurements over a wide range of temperature exhibit the presence of both antiferromagnetic (very weak) and ferromagnetic exchanges within the tetranuclear unit structures. Density functional theory calculations (using B3LYP functional, and two different basis sets) have been performed on the complexes 1 and 2 to provide a qualitative theoretical interpretation of their overall magnetic behavior.

Molecular and Functional Characterization of RecD, a Novel Member of the SF1 Family of Helicases, from Mycobacterium tuberculosis

Background: The heterotrimeric M. tuberculosis RecBCD complex, or each of its individual subunits, remains uncharacterized. Results: MtRecD exists as a homodimer in solution, catalyzes ssDNA-dependent ATP hydrolysis, unwinding of DNA replication/recombination intermediates, and interacts with RecA. Conclusion: MtRecD possesses strong 5 3- and weak 3 5-helicase activities. Significance: These findings provide insights into the mechanism underlying DSB repair and homologous recombination in mycobacteria. The annotated whole-genome sequence of Mycobacterium tuberculosis revealed the presence of a putative recD gene; however, the biochemical characteristics of its encoded protein product (MtRecD) remain largely unknown. Here, we show that MtRecD exists in solution as a stable homodimer. Protein-DNA binding assays revealed that MtRecD binds efficiently to single-stranded DNA and linear duplexes containing 5 overhangs relative to the 3 overhangs but not to blunt-ended duplex. Furthermore, MtRecD bound more robustly to a variety of Y-shaped DNA structures having 18-nucleotide overhangs but not to a similar substrate containing 5-nucleotide overhangs. MtRecD formed more salt-tolerant complexes with Y-shaped structures compared with linear duplex having 3 overhangs. The intrinsic ATPase activity of MtRecD was stimulated by single-stranded DNA. Site-specific mutagenesis of Lys-179 in motif I abolished the ATPase activity of MtRecD. Interestingly, although MtRecD-catalyzed unwinding showed a markedly higher preference for duplex substrates with 5 overhangs, it could also catalyze significant unwinding of substrates containing 3 overhangs. These results support the notion that MtRecD is a bipolar helicase with strong 5 3 and weak 3 5 unwinding activities. The extent of unwinding of Y-shaped DNA structures was approximate to 3-fold lower compared with duplexes with 5 overhangs. Notably, direct interaction between MtRecD and its cognate RecA led to inhibition of DNA strand exchange promoted by RecA. Altogether, these studies provide the first detailed characterization of MtRecD and present important insights into the type of DNA structure the enzyme is likely to act upon during the processes of DNA repair or homologous recombination.