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.

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.

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.

Identifying product families using data mining techniques in manufacturing paradigm

Identifying product families has been considered as an effective way to accommodate the increasing product varieties across the diverse market niches. In this paper, we propose a novel framework to identifying product families by using a similarity measure for a common product design data BOM (Bill of Materials) based on data mining techniques such as frequent mining and clus-tering. For calculating the similarity between BOMs, a novel Extended Augmented Adjacency Matrix (EAAM) representation is introduced that consists of information not only of the content and topology but also of the fre-quent structural dependency among the various parts of a product design. These EAAM representations of BOMs are compared to calculate the similarity between products and used as a clustering input to group the product fami-lies. When applied on a real-life manufacturing data, the proposed framework outperforms a current baseline that uses orthogonal Procrustes for grouping product families.

Age-related changes in perception of movement in driving scenes

Purpose Age-related changes in motion sensitivity have been found to relate to reductions in various indices of driving performance and safety. The aim of this study was to investigate the basis of this relationship in terms of determining which aspects of motion perception are most relevant to driving. Methods Participants included 61 regular drivers (age range 22–87 years). Visual performance was measured binocularly. Measures included visual acuity, contrast sensitivity and motion sensitivity assessed using four different approaches: (1) threshold minimum drift rate for a drifting Gabor patch, (2) Dmin from a random dot display, (3) threshold coherence from a random dot display, and (4) threshold drift rate for a second-order (contrast modulated) sinusoidal grating. Participants then completed the Hazard Perception Test (HPT) in which they were required to identify moving hazards in videos of real driving scenes, and also a Direction of Heading task (DOH) in which they identified deviations from normal lane keeping in brief videos of driving filmed from the interior of a vehicle. Results In bivariate correlation analyses, all motion sensitivity measures significantly declined with age. Motion coherence thresholds, and minimum drift rate threshold for the first-order stimulus (Gabor patch) both significantly predicted HPT performance even after controlling for age, visual acuity and contrast sensitivity. Bootstrap mediation analysis showed that individual differences in DOH accuracy partly explained these relationships, where those individuals with poorer motion sensitivity on the coherence and Gabor tests showed decreased ability to perceive deviations in motion in the driving videos, which related in turn to their ability to detect the moving hazards. Conclusions The ability to detect subtle movements in the driving environment (as determined by the DOH task) may be an important contributor to effective hazard perception, and is associated with age, and an individuals' performance on tests of motion sensitivity. The locus of the processing deficits appears to lie in first-order, rather than second-order motion pathways.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Modular design of profluorescent polymer sensors

A simple modular strategy for the synthesis of profluorescent nitroxide containing polymers is described. The incorporation of an epoxide as a pendant functionality on a polymer backbone synthesized using ATRP and subsequent nucleophilic ring-opening with sodium azide gave hydroxyl and azide functionality within a 3-bond radius. Orthogonal coupling chemistry then allowed the independent attachment of fluorophore and nitroxide groups in close proximity, giving rise to a profluorescent polymer. Validation of the viability of these materials as fluorescent sensors is demonstrated through efficient fluorescence switch-on observed when the materials are exposed to a model reductant or carbon-centred radical source.

Deriving word association networks from text corpora

This article presents and evaluates a model to automatically derive word association networks from text corpora. Two aspects were evaluated: To what degree can corpus-based word association networks (CANs) approximate human word association networks with respect to (1) their ability to quantitatively predict word associations and (2) their structural network characteristics. Word association networks are the basis of the human mental lexicon. However, extracting such networks from human subjects is laborious, time consuming and thus necessarily limited in relation to the breadth of human vocabulary. Automatic derivation of word associations from text corpora would address these limitations. In both evaluations corpus-based processing provided vector representations for words. These representations were then employed to derive CANs using two measures: (1) the well known cosine metric, which is a symmetric measure, and (2) a new asymmetric measure computed from orthogonal vector projections. For both evaluations, the full set of 4068 free association networks (FANs) from the University of South Florida word association norms were used as baseline human data. Two corpus based models were benchmarked for comparison: a latent topic model and latent semantic analysis (LSA). We observed that CANs constructed using the asymmetric measure were slightly less effective than the topic model in quantitatively predicting free associates, and slightly better than LSA. The structural networks analysis revealed that CANs do approximate the FANs to an encouraging degree.

Analytical study of implementation issues of NTRU

Nth-Dimensional Truncated Polynomial Ring (NTRU) is a lattice-based public-key cryptosystem that offers encryption and digital signature solutions. It was designed by Silverman, Hoffstein and Pipher. The NTRU cryptosystem was patented by NTRU Cryptosystems Inc. (which was later acquired by Security Innovations) and available as IEEE 1363.1 and X9.98 standards. NTRU is resistant to attacks based on Quantum computing, to which the standard RSA and ECC public-key cryptosystems are vulnerable to. In addition, NTRU has higher performance advantages over these cryptosystems. Considering this importance of NTRU, it is highly recommended to adopt NTRU as part of a cipher suite along with widely used cryptosystems for internet security protocols and applications. In this paper, we present our analytical study on the implementation of NTRU encryption scheme which serves as a guideline for security practitioners who are novice to lattice-based cryptography or even cryptography. In particular, we show some non-trivial issues that should be considered towards a secure and efficient NTRU implementation.

Art and science as creative catalysts

Science, Art and Science Art collaborations are generally presented and understood in terms of their products. We argue that the process of Science art can be a significant, even principal benefit of these collaborations, even though it may be largely invisible to anyone other than the collaborators. Hosting the Centenary of Canberra Science Art Commission at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) has shown us that while Science and Art pursue orthogonal dimensions of creativity and innovation, collaborators can combine these directions to access new areas of imagination and ideas.