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Prospective authors are requested to submit new, unpublished manuscripts for inclusion in the upcoming event described in this call for papers. [ABSTRACT FROM AUTHOR]

An $(r, \delta)$ -locally repairable code ($(r, \delta)$ -LRC for short) was introduced by Prakash et al. for tolerating multiple failed nodes in distributed storage systems, which was a generalization of the concept of $r$ -LRCs produced by Gopalan et al.. An $(r, \delta)$ -LRC is said to be optimal if it achieves the Singleton-like bound. Recently, Chen et al. generalized the construction of cyclic $r$ -LRCs proposed by Tamo et al. , and constructed several classes of optimal $(r, \delta)$ -LRCs of length $n$ for $n\, |\, (q-1)$ or $n\,|\, (q+1)$ , respectively in terms of a union of the set of zeros controlling the minimum distance and the set of zeros ensuring the locality. Following the work of , , this paper first characterizes $(r, \delta)$ -locality of a cyclic code via its zeros. Then we construct several classes of optimal cyclic $(r, \delta)$ -LRCs of length $n$ for $n\, |\, (q-1)$ or $n\,|\, (q+1)$ , respectively from the product of two sets of zeros. Our constructions include all optimal cyclic $(r,\delta)$ -LRCs proposed in , , and our method seems more convenient to obtain optimal cyclic $(r, \delta)$ -LRCs with flexible parameters. Moreover, many optimal cyclic $(r,\delta)$ -LRCs of length $n$ for $n\, |\, (q-1)$ or $n\,|\, (q+1)$ , respectively with $(r+\delta -1)\nmid n$ can be obtained from our method. [ABSTRACT FROM AUTHOR]

Consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes. Recent work by Avestimehr has approximated the capacity of this network up to an additive gap. The communication scheme achieving this capacity approximation is based on compress-and-forward, resulting in noise accumulation as the messages traverse the network. As a consequence, the approximation gap increases linearly with the network depth. This paper develops a computation alignment strategy that can approach the capacity of a class of layered, time-varying wireless relay networks up to an approximation gap that is independent of the network depth. This strategy is based on the compute-and-forward framework, which enables relays to decode deterministic functions of the transmitted messages. Alone, compute-and-forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex-valued coefficients by a channel with integer coefficients. Here, this penalty is circumvented by carefully matching channel realizations across time slots to create integer-valued effective channels that are well suited to compute-and-forward. Unlike prior constant gap results, the approximation gap obtained in this paper also depends closely on the fading statistics, which are assumed to be i.i.d. Rayleigh. [ABSTRACT FROM PUBLISHER]

This paper studies the multiple-access channel (MAC) with rate-limited feedback. The channel output is encoded into one stream of bits, which is provided causally to the two users at the channel input. An achievable rate region for this setup is derived, based on superposition of information, block Markov coding, and coding with various degrees of side information for the feedback link. The suggested region coincides with the Cover–Leung inner bound for large feedback rates. The result is then extended for cases where there is only a feedback link to one of the transmitters, and for a more general case where there are two separate feedback links to both transmitters. We compute achievable regions for the Gaussian MAC and for the binary erasure MAC. The Gaussian region is computed for the case of common rate-limited feedback, whereas the region for the binary erasure MAC is computed for one-sided feedback. It is known that for the latter, the Cover–Leung region is tight, and we obtain results that coincide with the feedback capacity region for high feedback rates. [ABSTRACT FROM PUBLISHER]

This paper provides a link between matroid theory and locally repairable codes (LRCs) that are either linear or more generally almost affine. Using this link, new results on both LRCs and matroid theory are derived. The parameters $(n,k,d,r,\delta )$ of LRCs are generalized to matroids, and the matroid analog of the generalized singleton bound by Gopalan et al. for linear LRCs is given for matroids. It is shown that the given bound is not tight for certain classes of parameters, implying a nonexistence result for the corresponding locally repairable almost affine codes that are coined perfect in this paper. Constructions of classes of matroids with a large span of the parameters $(n,k,d,r,\delta )$ and the corresponding local repair sets are given. Using these matroid constructions, new LRCs are constructed with prescribed parameters. The existence results on linear LRCs and the nonexistence results on almost affine LRCs given in this paper strengthen the nonexistence and existence results on perfect linear LRCs given by Song et al. [ABSTRACT FROM AUTHOR]

Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model. [ABSTRACT FROM AUTHOR]

Different spreading processes in multiplex networks may interact with each other and display intertwined effects. In this paper, we propose a theoretical framework called infection-probability-dependent interlayer interaction propagation processes in multiplex networks with an arbitrary number of layers, to more precisely depict the intertwined effects which bring challenges to the existing state-dependent interlayer interaction models. Specifically, the spreading rate of each node is regulated by the proposed spreading rate function (SRF) which depends on both the intrinsic dynamics in its layer and the infection probabilities of its counterparts. We propose an algorithm to obtain the spreading threshold of each layer of the proposed theoretical framework. We analyze the three-layer tuberculosis-awareness-flu model with the SRF of each node being the expectation of infection-probability-dependent spreading rate. This paper gives a thorough and detailed numerical investigation of the impact and interaction of system settings and the spreading threshold of each layer. We find that for tuberculosis spreading which is in competing relation with awareness and cooperation relation with flu, the epidemic threshold is a constant when other layers’ intrinsic spreading rates are small. The cooperation layer has dramatic influence on the constant while the competing layer has no effect on it. [ABSTRACT FROM AUTHOR]

The state-dependent point-to-point Gaussian channel with a helper is first studied, in which a transmitter communicates with a receiver via a state-corrupted channel. The state is not known to the transmitter nor to the receiver, but known to a helper noncausally, which then wishes to assist the receiver to cancel the state. Differently from the previous work that characterized the capacity only in the infinite state power regime, this paper explores the general case with arbitrary state power. A lower bound on the capacity is derived based on an achievable scheme that integrates direct state subtraction and single-bin dirty paper coding. By analyzing this lower bound and further comparing it with the existing upper bounds, the capacity of the channel is characterized for a wide range of channel parameters. Such an idea of characterizing the capacity is further extended to study the two-user state-dependent multiple access channel with a helper. By comparing the derived inner and outer bounds, the channel parameters are partitioned into appropriate cases, and for each case, either segments on the capacity region boundary or the full capacity region are characterized. [ABSTRACT FROM PUBLISHER]

Maximum distance profile codes over finite non-binary fields have been introduced and thoroughly studied in the last decade. These codes have the property that their column distances are maximal among all codes of the same rate and degree. In this paper, we aim at studying this fundamental concept in the context of convolutional codes over a finite ring. We extensively use the concept of $p$ -encoder to establish the theoretical framework and derive several bounds on the column distances. In particular, a method for constructing (not necessarily free) maximum distance profile convolutional codes over ${\mathbb Z}_{p^{r}}$ is presented. [ABSTRACT FROM AUTHOR]

Linear codes with certain special properties have received renewed attention in recent years due to their practical applications. Among them, binary linear complementary dual (LCD) codes play an important role in implementations against side-channel attacks and fault injection attacks. Self-orthogonal codes can be used to construct quantum codes. In this paper, four classes of binary linear codes are constructed via a generic construction which has been intensively investigated in the past decade. Simple characterizations of these linear codes to be LCD or self-orthogonal are presented. Resultantly, infinite families of binary LCD codes and self-orthogonal codes are obtained. Infinite families of binary LCD codes from the duals of these four classes of linear codes are produced. Many LCD codes and self-orthogonal codes obtained in this paper are optimal or almost optimal in the sense that they meet certain bounds on general linear codes. In addition, the weight distributions of two sub-families of the proposed linear codes are established in terms of Krawtchouk polynomials. [ABSTRACT FROM AUTHOR]

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arıkan style constructions. This paper, which is presented in two parts, solves this problem by providing a necessary and sufficient condition for a binary operation to be polarizing. This (first) part of this paper introduces the mathematical framework that we will use in the second part to characterize the polarizing operations. We define uniformity preserving, irreducible, ergodic, and strongly ergodic operations, and we study their properties. The concepts of a stable partition and the residue of a stable partition are introduced. We show that an ergodic operation is strongly ergodic if and only if all its stable partitions are their own residues. We also study the products of binary operations and the structure of their stable partitions. We show that the product of a sequence of binary operations is strongly ergodic if and only if all the operations in the sequence are strongly ergodic. In the second part of this paper, we provide a foundation of polarization theory based on the ergodic theory of binary operations that we develop in this part. [ABSTRACT FROM PUBLISHER]

Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of BCH codes $\mathcal {C}_{(q,q+1,4,1)}$ and their dual codes with $q=2^{m}$ and established that the codewords of the minimum (or the second minimum) weight in these codes support 4-designs or 3-designs. Motivated by this, we further investigate the codewords of the next adjacent weight in such codes and discover more infinite classes of $t$ -designs with $t=3,4$. In particular, we prove that codewords of weight 7 in $\mathcal {C}_{(q,q+1,4,1)}$ support 4-designs for odd $m \geqslant 5$ and they support 3-designs for even $m \geqslant 4$ , which provide infinite classes of simple $t$ -designs with new parameters. Another significant class of $t$ -designs we produce in this paper has complementary designs with parameters 4- $(2^{2s+1}+ 1,5,5)$ ; these designs have the smallest index among all the known simple 4- $(q+1,5,\lambda)$ designs derived from codes for prime powers $q$ ; and they are further proved to be isomorphic to the 4-designs admitting the projective general linear group PGL $(2,2^{2s+1})$ as the automorphism group constructed by Alltop in 1969. [ABSTRACT FROM AUTHOR]

Linear codes generated by component functions of perfect nonlinear (PN for short) and almost perfect nonlinear (APN for short) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper is to investigate some binary shortened codes of two families of linear codes from APN functions and some $p$ -ary shortened codes associated with PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and $p$ -ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal. The results of this paper show that the shortening technique is very promising for constructing good codes. [ABSTRACT FROM AUTHOR]

A function computation problem over a directed acyclic network has been considered in the literature, where a sink node is required to compute a target function correctly with the inputs arbitrarily generated at multiple source nodes. The network links are error free but capacity limited, and the intermediate nodes perform network coding. The computing rate of a network code is the average number of times that the target function is computed for one use of the network, i.e., each link in the network is used at most once. In the existing papers, two cut-set bounds were proposed on the computing rate. However, we in this paper show that these bounds are not valid for general network function computation problems. We analyze the reason of the invalidity and propose a general cut-set bound by using a new equivalence relation associated with the inputs of the target function. Moreover, some results in the existing papers were proved by applying the invalid upper bound. We also justify the validity of these results. [ABSTRACT FROM AUTHOR]

It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH codes are given. The BCH codes presented in this paper have good parameters in general, containing many optimal linear codes. In particular, two open problems about the minimum distance of BCH codes of this type are partially solved in this paper. [ABSTRACT FROM AUTHOR]

Several continuous manufacturing processes use stochastic texture images for quality control and monitoring. Large amounts of pictorial data are acquired, providing important information about both the materials produced and the manufacturing processes involved. However, it is often difficult to measure objectively the similarity among such industrial stochastic images or to discriminate between the texture images of stochastic materials with distinct properties. Nowadays, the degree of discrimination required by industrial processes often goes beyond the limits of human visual perception. This paper proposes a new approach for multiresolution stochastic texture discrimination in the industry (e.g., nonwoven textiles and paper), which is focused on sheet formation properties. The wavelet transform is used to represent stochastic texture images in multiple resolutions and to describe them using local density variability as features. At each resolution, the wavelet subbands approximate image gradients. The image gradients are modeled as Gaussian colored noise, and the gradient magnitudes, as Rayleigh probability density functions. Based on this representation, a multiresolution distance measure for stochastic textures is proposed. Some experimental results are reported, and ideas for future work are presented with the conclusions. [ABSTRACT FROM AUTHOR]

This article comments on a research paper "A Noncoherent Tracking Loop With Diversity and Multipath Interference Cancellationfor Direct-Sequence Spread-Spectrum Systems." Researchers presented a noncoherent tracking loop with diversity and multipath interference cancellation to improve the loop performance on frequency-selective fading channels. Actually, such effects can change the error characteristic, at least in the mean sense, and thus make the analyses of jitter performance improper. The mathematical derivation of the research has been provided in the article.

Cyclic codes are widely employed in communication systems, storage devices, and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. A subclass of good BCH codes are the narrow-sense BCH codes over \mathrm GF(q) with length n=(q^m-1)/(q-1) . Little is known about this class of BCH codes when $q>2$ . The objective of this paper is to study some of the codes within this class. In particular, the dimension, the minimum distance, and the weight distribution of some ternary BCH codes with length n=(3^{m}-1)/2 are determined in this paper. A class of ternary BCH codes meeting the Griesmer bound is identified. An application of some of the BCH codes in secret sharing is also investigated. [ABSTRACT FROM PUBLISHER]

The ability to cohere the wireless operations between separate, moving microwave systems enables significant increases in capability for remote sensing, radar, communications, and other microwave wireless applications. Open-loop coherent distributed arrays, which are distributed systems of nodes that coherently coordinate without external signal inputs from the destination, are introduced in this paper. A model of the signal received from a coherent distributed array is derived, and a statistical analysis of the variation in signal power in the presence of coordination errors is presented. Requirements on the tolerable errors for internode range measurement, beamsteering angle measurement, and internode clock phase synchronization are given as a function of the probability of achieving a given signal power. Approaches for achieving the necessary internode range and angle measurements are presented, and the experimental results of a novel one-way clock transfer approach to phase synchronization are shown. These examples demonstrate the feasibility of implementing coherent distributed arrays on moving platforms operating at frequencies extending into the microwave region. [ABSTRACT FROM AUTHOR]

Electromagnetic scattering characteristics highly depend on the geometry and material property of the scatterers. In particular, electromagnetic wave scattering occurs at the discontinuity of the propagation path, such as the edge of a scatterer. In this paper, the edge scattering from a triangular object is largely reduced by patterning the triangular surface with inhomogeneous and anisotropic impedance surface. Because surface waves propagate toward the direction with the lower surface refractive index on an anisotropic surface, the direction of the wave propagation can be controlled by designing the distribution of the refractive index. Consequently, the proposed anisotropic impedance surfaces can make the current flows toward or away from the edge so that the edge scattering can be reduced or redirected to a different angle. For demonstration, anisotropic unit cells are analyzed and designed. Also, the anisotropic impedance surfaces are simulated, fabricated, and measured. Here we propose two types of impedance profiles, which are capable of changing the surface current direction either toward or away from the scattering edge. The experimental measurement demonstrates a 7–10 dB edge scattering reduction. [ABSTRACT FROM AUTHOR]

This paper is concerned with the topological structure, reachability, and stabilization for Boolean control networks (BCNs) with state constraints via event-triggered control (ETC) scheme. In the first part, the topological structure of BCNs with state constraints is studied. Under the framework of state constrain, the definitions of fixed point and cycle are first defined. A novel phenomenon is that there may exist two kinds constrained fixed points, which are, respectively, named as the livelock and deadlock ones. It is different with the traditional fixed point. Accordingly, a formula is presented to calculate the number of constrained fixed points and constrained cycles. In the second part, the constrained reachability and stabilization problem of the event-triggered controlled BCNs are investigated. Two necessary and sufficient criteria are, respectively, obtained. Furthermore, an algorithm is developed to design all feasible controllers. Finally, a reduced model of the lac operon in the Escherichia coli is shown to illustrate the efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

Symbol-pair codes were introduced by Cassuto and Blaum in 2010 to protect pair errors in symbol-pair read channels. Recently Yaakobi, Bruck and Siegel (2016) generalized this notion to b-symbol codes in order to consider consecutive b errors for a prescribed integer b ≥ 2, and they gave constructions and decoding algorithms. Cyclic codes were considered by various authors as candidates for symbol-pair codes and they established minimum distance bounds on (certain) cyclic codes. In this paper we use algebraic curves over finite fields in order to obtain tight lower and upper bounds on b-symbol Hamming weights of arbitrary cyclic codes over Fq. Here b ≥ 2 is an arbitrary prescribed positive integer and Fq is an arbitrary finite field. We also present a stability theorem for an arbitrary cyclic code C of dimension k and length n: the b-symbol Hamming weight enumerator of C is the same as the k-symbol Hamming weight enumerator of C if k ≤ b ≤ n−1. Moreover, we give improved tight lower and upper bounds on b-symbol Hamming weights of some cyclic codes related to irreducible cyclic codes. Throughout the paper the length n is coprime to q. [ABSTRACT FROM AUTHOR]

The binary quadratic-residue codes and the punctured Reed-Muller codes ${\mathcal {R}}_{2}((m-1)/2, m))$ are two families of binary cyclic codes with parameters $[n, (n+1)/2, d \geq \sqrt {n}]$. These two families of binary cyclic codes are interesting partly due to the fact that their minimum distances have a square-root bound. The objective of this paper is to construct two families of binary cyclic codes of length $2^{m}-1$ and dimension near $2^{m-1}$ with good minimum distances. When $m \geq 3$ is odd, the codes become a family of duadic codes with parameters $[2^{m}-1, 2^{m-1}, d]$ , where $d \geq 2^{(m-1)/2}+1$ if $m \equiv 3 \pmod {4}$ and $d \geq 2^{(m-1)/2}+3$ if $m \equiv 1 \pmod {4}$. The two families of binary cyclic codes contain some optimal binary cyclic codes. [ABSTRACT FROM AUTHOR]

In the last ten years, cloud services provided many applications in various areas. Most of them are hosted in a heterogeneous distributed large-scale cloud computing environment and face inherent uncertainty, unreliability, and malicious attacks that trouble both service users and providers. To solve the problems of malicious attacks (including solo and collusion deception ones) in a public cloud computing environment, we for the first time propose a double-blind anonymous evaluation-based trust model. Based on it, cloud service providers and users are anonymously matched according to user requirements. It can be used to effectively handle some malicious attacks that intend to distort trust evaluations. Providers may secretly hide gain-sharing information into service results and send the results to users to ask for higher trust evaluations than their deserved ones. This paper proposes to adopt checking nodes to help detect such behavior. It then conducts gain–loss analysis for providers who intend to perform provider–user collusion deception. The proposed trust model can be used to effectively help one recognize collusion deception behavior and allow policy-makers to set suitable loss to punish malicious providers. Consequently, provider-initiated collusion deception behavior can be greatly discouraged in public cloud computing systems. Simulation results show that the proposed method outperform two updated methods, i.e., one based on fail-stop signature and another based on fuzzy mathematics in terms of malicious node detection ratio and speed. [ABSTRACT FROM AUTHOR]

Emergency Remote Teaching (ERT) can be defined as a shift of instructional delivery to a substitute delivery approach during a crisis. Such a shift poses several challenges for students at Higher Education Institutes. This paper presents a taxonomy of such challenges faced by first-year mathematics students in the Pacific region during the ERT dictated by the COVID-19 pandemic. First, a list of 44 challenges was assembled based on a university’s in-house monitoring report, literature review and the authors’ experiences of challenges faced by students. Next, the open card sorting technique involving 32 participants was used to classify these challenges. Open card sorting is a well-established method for discovering how people understand and categorize information. This paper employed a recently proposed algorithm to quantitatively analyze open card sorting data using the Best Merge Method, Category Validity Technique and Multidimensional Scaling. Analysis of the collected card sort data produced the initial taxonomy of challenges. Finally, the participants were asked to answer a questionnaire so that we could validate and further refine the taxonomy. The proposed taxonomy includes seven challenges: i) lack of online learning support; ii) problem with online course delivery; iii) time and workload management; iv) learning management system issues; v) lack of face-to-face interaction; vi) financial hardship; vii) internet challenge. Such a taxonomy might be particularly useful in designing and evaluating an ERT approach.

High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and degradation of several transmission performances. We continue the theoretical contributions made by Boche and Farell toward the understanding of peak value reduction, using the strategy known as tone reservation for orthogonal transmission schemes. There it was shown that for orthogonal frequency-division multiplexing (OFDM) systems, the combinatorial object called arithmetic progression plays an important role in setting limitations for the applicability of the tone reservation method. In this paper, we show that the combinatorial object introduced as perfect Walsh sum (PWS) plays a similar role for code-division multiple access (CDMA) systems as arithmetic progression for OFDM systems. By specific construction, we show that for a chosen numbers $m$ and $n$ , all subsets $\mathcal {I} $ of the set $[N]$ of the first $N=2^{n}$ natural numbers, which has the density in $[N]$ larger than a given $\delta \in (0,1)$ , i.e., $\left |{ \mathcal {I} }\right |/N\geq \delta $ , and which is sufficiently large enough, in the sense that $\left |{ I }\right |\geq 2(2/\delta)^{2^{m}-1}$ , contains a PWS of size $2^{m}$. By means of this result, and motivated by the previously mentioned connection between arithmetic progression and PWS, we show results for the PWS which are analogous to the famous Szemerédi theorem on arithmetic progressions, Conlon-Gower’s theorem on probabilistic construction of “sparse” sets containing an arithmetic progression, and even a solution of an analogon to the Erdős’ conjecture on arithmetic progressions. Those results give in particular an insight into the asymptotic limitations of tone reservation method for the CDMA systems. Besides, we show that a subset $I$ of $[N]$ is a PWS if and only if the embedding inequality of the subspace of $L^{1}([{0,1}])$ , containing linear combinations of Walsh functions indexed by elements of $\mathcal {I} $ , holds with the minimum possible embedding constant $\sqrt { \left |{ \mathcal {I} }\right |}$. The corresponding approach based in particular by the fact that the PWSs are the only Walsh sums having unit $L^{1}$ -norm, proven in this paper. By means of that results, we show that the minimum possible threshold constant for which the tone reservation method is applicable yields $\sqrt { \left |{ \mathcal {I} }\right |}$ if and only if the information set $\mathcal {I} $ is a PWS. [ABSTRACT FROM AUTHOR]

This paper presents, in development in Brazil, a research for an ac three-phase cold dielectric (CD) high-temperature superconducting (HTS) power cable. That cable was rated to operate mainly at 69 kV/300 A. The first phase of research was part of a National Strategic Project for power transfer in Brazil. The research over the last two years included an improvement in design in order to enable operation also at higher voltages. The cable design changed and now each phase is inside its own cryostat. The electric isolation also changed. It was selected a laminated dielectric material not yet used (to our knowledge) in any other HTS power cable project. The main outcomes and results presented here are i) the improved cable design, ii) the characterizations of the new isolating material, iii) the facilities for cable construction and high-current tests, iv) one demonstrative model for one phase of the cable, and v) the validation of the new cable geometry by numerical simulation of electromagnetic and thermal behaviors of one of its phases at the rated voltage and current. As a conclusion, the results allowed to improve and disseminate the feasibility of the CD HTS cable technology in Brazil. Some details are not shown because they are patent pending. [ABSTRACT FROM AUTHOR]

This paper defines a generalization of the recursive Bayesian estimate (RBE), within the mathematical possibility theory. This generalization is motivated by the fact that the classical RBE, by design, deals only with random variables and can only provide closed-form solution for a few cases. The possibilistic generalization is based on the random-fuzzy variables, thus allowing one to take into account, in a very natural way, both random and systematic contributions to the uncertainty and to implement the RBE for any distribution of system state variables in a simple way. This paper illustrates the advantages of the proposed generalization, by presenting both the theoretical development, and a detailed application example. [ABSTRACT FROM AUTHOR]