Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Opportunities and challenges : combining distance and on-campus students in concurrent courses

Through its Electronic Delivery of Gator Engineering (EDGE) program, University of Florida (UF) offers online master’s degrees from participating departments within the UF College of Engineering. Each master’s degree requires 10 courses (3 credit hours each). One interesting and unique aspect of the EDGE pro-gram is that distance learners are registered concurrently in the same courses with traditional on-campus students. This paper examines the specific challenges involved in integrating distance students into on-campus courses, including communication, interaction, access to resources, and equal grading practices.

Copyright Protection of object-oriented software

language (such as C++ and Java). The model used allows to insert watermarks on three “orthogonal” levels. For the first level, watermarks are injected into objects. The second level watermarking is used to select proper variants of the source code. The third level uses transition function that can be used to generate copies with different functionalities. Generic watermarking schemes were presented and their security discussed.

Pulsed dc- and sine-wave-excited cold atmospheric plasma plumes: A comparative analysis

Cold atmospheric-pressure plasma plumes are generated in the ambient air by a single-electrode plasma jet device powered by pulsed dc and ac sine-wave excitation sources. Comprehensive comparisons of the plasma characteristics, including electrical properties, optical emission spectra, gas temperatures, plasma dynamics, and bacterial inactivation ability of the two plasmas are carried out. It is shown that the dc pulse excited plasma features a much larger discharge current and stronger optical emission than the sine-wave excited plasma. The gas temperature in the former discharge remains very close to the room temperature across the entire plume length; the sine-wave driven discharge also shows a uniform temperature profile, which is 20-30 degrees higher than the room temperature. The dc pulse excited plasma also shows a better performance in the inactivation of gram-positive staphylococcus aureus bacteria. These results suggest that the pulsed dc electric field is more effective for the generation of nonequilibrium atmospheric pressure plasma plumes for advanced plasma health care applications.

Integrated plasma-aided nanofabrication facility: Operation, parameters, and assembly of quantum structures and functional nanomaterials

The development, operation, and applications of two configurations of an integrated plasma-aided nanofabrication facility (IPANF) comprising low-frequency inductively coupled plasma-assisted, low-pressure, multiple-target RF magnetron sputtering plasma source, are reported. The two configurations of the plasma source have different arrangements of the RF inductive coil: a conventional external flat spiral "pancake" coil and an in-house developed internal antenna comprising two orthogonal RF current sheets. The internal antenna configuration generates a "unidirectional" RF current that deeply penetrates into the plasma bulk and results in an excellent uniformity of the plasma over large areas and volumes. The IPANF has been employed for various applications, including low-temperature plasma-enhanced chemical vapor deposition of vertically aligned single-crystalline carbon nanotips, growth of ultra-high aspect ratio semiconductor nanowires, assembly of optoelectronically important Si, SiC, and Al1-xInxN quantum dots, and plasma-based synthesis of bioactive hydroxyapatite for orthopedic implants.

Discharge mode transitions in low-frequency inductively coupled plasmas with internal oscillating current sheets

Transitions between the two discharge modes in a low-frequency (∼460 kHz) inductively coupled plasma sustained by an internal oscillating radio frequency (rf) current sheet are studied. The unidirectional rf current sheet is generated by an internal antenna comprising two orthogonal sets of synphased rf currents driven in alternately reconnected copper litz wires. It is shown that in the low-to-intermediate pressure range the plasma source can be operated in the electrostatic (E) and electromagnetic (H) discharge modes. The brightness of the E -mode argon plasma glow is found remarkably higher than in inductively coupled plasmas with external flat spiral "pancake" coils. The cyclic variations of the input rf power result in pronounced hysteretic variations of the optical emission intensity and main circuit parameters of the plasma source. Under certain conditions, it appears possible to achieve a spontaneous E→H transition ("self-transition"). The observed phenomenon can be attributed to the thermal drift of the plasma parameters due to the overheating of the working gas. The discharge destabilizing factors due to the gas heating and step-wise ionization are also discussed. © 2005 American Vacuum Society.

Magnetic fields and uniformity of radio frequency power deposition in low-frequency inductively coupled plasmas with crossed internal oscillating currents

Radial and axial distributions of magnetic fields in a low-frequency (∼460 kHz)inductively coupled plasmasource with two internal crossed planar rf current sheets are reported. The internal antenna configuration comprises two orthogonal sets of eight alternately reconnected parallel and equidistant copper litz wires in quartz enclosures and generates three magnetic (H z, H r, and H φ) and two electric (E φ and E r) field components at the fundamental frequency. The measurements have been performed in rarefied and dense plasmas generated in the electrostatic(E) and electromagnetic (H)discharge modes using two miniature magnetic probes. It is shown that the radial uniformity and depth of the rf power deposition can be improved as compared with conventional sources of inductively coupled plasmas with external flat spiral (“pancake”) antennas. Relatively deeper rf power deposition in the plasma source results in more uniform profiles of the optical emission intensity, which indicates on the improvement of the plasma uniformity over large chamber volumes. The results of the numerical modeling of the radial magnetic field profiles are found in a reasonable agreement with the experimental data.

Finite-SNR diversity-multiplexing trade-off of inter-vehicular cooperative diversity protocols

The finite-signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of cooperative diversity protocols are investigated in vehicular networks based on cascaded Rayleigh fading. Lower bounds of DMT at finite SNR for orthogonal and non-orthogonal protocols are derived. The results showcase the first look into the achievable DMT trade-off of cooperative diversity in volatile vehicular environments. It is shown that the diversity gains are significantly suboptimal at realistic SNRs.

The antigen 43 structure reveals a molecular velcro-like mechanism of autotransporter-mediated bacterial clumping

Aggregation and biofilm formation are critical mechanisms for bacterial resistance to host immune factors and antibiotics. Autotransporter (AT) proteins, which represent the largest group of outer-membrane and secreted proteins in Gram-negative bacteria, contribute significantly to these phenotypes. Despite their abundance and role in bacterial pathogenesis, most AT proteins have not been structurally characterized, and there is a paucity of detailed information with regard to their mode of action. Here we report the structure–function relationships of Antigen 43 (Ag43a), a prototypic self-associating AT protein from uropathogenic Escherichia coli. The functional domain of Ag43a displays a twisted L-shaped β-helical structure firmly stabilized by a 3D hydrogen-bonded scaffold. Notably, the distinctive Ag43a L shape facilitates self-association and cell aggregation. Combining all our data, we define a molecular “Velcro-like” mechanism of AT-mediated bacterial clumping, which can be tailored to fit different bacterial lifestyles such as the formation of biofilms.

The serum resistome of a globally disseminated multidrug resistant uropathogenic Escherichia coli Clone

Escherichia coli ST131 is a globally disseminated, multidrug resistant clone responsible for a high proportion of urinary tract and bloodstream infections. The rapid emergence and successful spread of E. coli ST131 is strongly associated with antibiotic resistance; however, this phenotype alone is unlikely to explain its dominance amongst multidrug resistant uropathogens circulating worldwide in hospitals and the community. Thus, a greater understanding of the molecular mechanisms that underpin the fitness of E. coli ST131 is required. In this study, we employed hyper-saturated transposon mutagenesis in combination with multiplexed transposon directed insertion-site sequencing to define the essential genes required for in vitro growth and the serum resistome (i.e. genes required for resistance to human serum) of E. coli EC958, a representative of the predominant E. coli ST131 clonal lineage. We identified 315 essential genes in E. coli EC958, 231 (73%) of which were also essential in E. coli K-12. The serum resistome comprised 56 genes, the majority of which encode membrane proteins or factors involved in lipopolysaccharide (LPS) biosynthesis. Targeted mutagenesis confirmed a role in serum resistance for 46 (82%) of these genes. The murein lipoprotein Lpp, along with two lipid A-core biosynthesis enzymes WaaP and WaaG, were most strongly associated with serum resistance. While LPS was the main resistance mechanism defined for E. coli EC958 in serum, the enterobacterial common antigen and colanic acid also impacted on this phenotype. Our analysis also identified a novel function for two genes, hyxA and hyxR, as minor regulators of O-antigen chain length. This study offers novel insight into the genetic make-up of E. coli ST131, and provides a framework for future research on E. coli and other Gram-negative pathogens to define their essential gene repertoire and to dissect the molecular mechanisms that enable them to survive in the bloodstream and cause disease.

Chaperone-usher fimbriae of Escherichia coli

Chaperone-usher (CU) fimbriae are adhesive surface organelles common to many Gram-negative bacteria. Escherichia coli genomes contain a large variety of characterised and putative CU fimbrial operons, however, the classification and annotation of individual loci remains problematic. Here we describe a classification model based on usher phylogeny and genomic locus position to categorise the CU fimbrial types of E. coli. Using the BLASTp algorithm, an iterative usher protein search was performed to identify CU fimbrial operons from 35 E. coli (and one Escherichia fergusonnii) genomes representing different pathogenic and phylogenic lineages, as well as 132 Escherichia spp. plasmids. A total of 458 CU fimbrial operons were identified, which represent 38 distinct fimbrial types based on genomic locus position and usher phylogeny. The majority of fimbrial operon types occupied a specific locus position on the E. coli chromosome; exceptions were associated with mobile genetic elements. A group of core-associated E. coli CU fimbriae were defined and include the Type 1, Yad, Yeh, Yfc, Mat, F9 and Ybg fimbriae. These genes were present as intact or disrupted operons at the same genetic locus in almost all genomes examined. Evaluation of the distribution and prevalence of CU fimbrial types among different pathogenic and phylogenic groups provides an overview of group specific fimbrial profiles and insight into the ancestry and evolution of CU fimbriae in E. coli.

Molecular characterization of the EhaG and UpaG trimeric autotransporter proteins from pathogenic Escherichia coli

Trimeric autotransporter proteins (TAAs) are important virulence factors of many Gram-negative bacterial pathogens. A common feature of most TAAs is the ability to mediate adherence to eukaryotic cells or extracellular matrix (ECM) proteins via a cell surface-exposed passenger domain. Here we describe the characterization of EhaG, a TAA identified from enterohemorrhagic Escherichia coli (EHEC) O157:H7. EhaG is a positional orthologue of the recently characterized UpaG TAA from uropathogenic E. coli (UPEC). Similarly to UpaG, EhaG localized at the bacterial cell surface and promoted cell aggregation, biofilm formation, and adherence to a range of ECM proteins. However, the two orthologues display differential cellular binding: EhaG mediates specific adhesion to colorectal epithelial cells while UpaG promotes specific binding to bladder epithelial cells. The EhaG and UpaG TAAs contain extensive sequence divergence in their respective passenger domains that could account for these differences. Indeed, sequence analyses of UpaG and EhaG homologues from several E. coli genomes revealed grouping of the proteins in clades almost exclusively represented by distinct E. coli pathotypes. The expression of EhaG (in EHEC) and UpaG (in UPEC) was also investigated and shown to be significantly enhanced in an hns isogenic mutant, suggesting that H-NS acts as a negative regulator of both TAAs. Thus, while the EhaG and UpaG TAAs contain some conserved binding and regulatory features, they also possess important differences that correlate with the distinct pathogenic lifestyles of EHEC and UPEC.

Characterisation of a cell wall-anchored protein of Staphylococcus saprophyticus associated with linoleic acid resistance

The Gram-positive bacterium Staphylococcus saprophyticus is the second most frequent causative agent of community-acquired urinary tract infections (UTI), accounting for up to 20% of cases. A common feature of staphylococci is colonisation of the human skin. This involves survival against innate immune defenses including antibacterial unsaturated free fatty acids such as linoleic acid which act by disrupting bacterial cell membranes. Indeed, S. saprophyticus UTI is usually preceded by perineal skin colonisation.

Molecular analysis of type 3 fimbrial genes from Escherichia coli, Klebsiella and Citrobacter species

Background Catheter-associated urinary tract infection (CAUTI) is the most common nosocomial infection in the United States and is caused by a range of uropathogens. Biofilm formation by uropathogens that cause CAUTI is often mediated by cell surface structures such as fimbriae. In this study, we characterised the genes encoding type 3 fimbriae from CAUTI strains of Escherichia coli, Klebsiella pneumoniae, Klebsiella oxytoca, Citrobacter koseri and Citrobacter freundii. Results Phylogenetic analysis of the type 3 fimbrial genes (mrkABCD) from 39 strains revealed they clustered into five distinct clades (A-E) ranging from one to twenty-three members. The majority of sequences grouped in clade A, which was represented by the mrk gene cluster from the genome sequenced K. pneumoniae MGH78578. The E. coli and K. pneumoniae mrkABCD gene sequences clustered together in two distinct clades, supporting previous evidence for the occurrence of inter-genera lateral gene transfer. All of the strains examined caused type 3 fimbriae mediated agglutination of tannic acid treated human erythrocytes despite sequence variation in the mrkD-encoding adhesin gene. Type 3 fimbriae deletion mutants were constructed in 13 representative strains and were used to demonstrate a direct role for type 3 fimbriae in biofilm formation. Conclusions The expression of functional type 3 fimbriae is common to many Gram-negative pathogens that cause CAUTI and is strongly associated with biofilm growth. Our data provides additional evidence for the spread of type 3 fimbrial genes by lateral gene transfer. Further work is now required to substantiate the clade structure reported here by examining more strains as well as other bacterial genera that make type 3 fimbriae and cause CAUTI.