Discrete Chaos-I: Theory

We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent approaches the largest Lyapunov exponent of a chaotic map when M/spl rarr//spl infin/, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has discrete chaos if its discrete Lyapunov exponent tends to a positive number, when M/spl rarr//spl infin/. We present several examples to illustrate the concepts being introduced.     

Estimating and reducing the memory requirements of signal processing codes for embedded systems

Most embedded systems have limited amount of memory. In contrast, the memory requirements of the digital signal processing (DSP) and video processing codes (in nested loops, in particular) running on embedded systems is significant. This paper addresses the problem of estimating and reducing the amount of memory needed for transfers of data in embedded systems. First, the problem of estimating the region associated with a statement or the set of elements referenced by a statement during the execution of nested loops is analyzed. For a fixed execution ordering, a quantitative analysis of the number of elements referenced is presented; exact expressions for uniformly generated references and a close upper and lower bound for nonuniformly generated references are derived. Second, in addition to presenting an algorithm that computes the total memory required, this paper also discusses the effect of transformations (that change the execution ordering) on the lifetimes of array variables, i.e., the time between the first and last accesses to a given array location. The term maximum window size is introduced, and quantitative expressions are derived to compute the maximum window size. A detailed analysis of the effect of unimodular transformations on data locality, including the calculation of the maximum window size, is presented.     

Bandpass filters with reconfigurable transmission zeros using varactor-tuned tapped stubs

In this letter, bandpass filters with one or two tunable transmission zeros are proposed. The reconfigurable transmission zeros are implemented through varactors in combination with tapped quarter-wavelength stubs. Based on mixed mode simulations including EM simulation and circuit simulation, the proposed filters were designed and fabricated on low-cost FR4 board. The measurement results verified the design concepts.     

Nash equilibria of packet forwarding strategies in wireless ad hoc networks

In self-organizing ad hoc networks, all the networking functions rely on the contribution of the participants. As a basic example, nodes have to forward packets for each other in order to enable multihop communication. In recent years, incentive mechanisms have been proposed to give nodes incentive to cooperate, especially in packet forwarding. However, the need for these mechanisms was not formally justified. In this paper, we address the problem of whether cooperation can exist without incentive mechanisms. We propose a model,based on game theory and graph theory to investigate equilibrium conditions of packet forwarding strategies. We prove theorems about the equilibrium conditions for both cooperative and noncooperative strategies. We perform simulations to estimate the probability that the conditions for a cooperative equilibrium hold in randomly generated network scenarios.. As the problem is involved, we deliberately restrict ourselves to a static configuration. We conclude that in static ad hoc networks where the relationships between the nodes are likely to be stab le-cooperation needs to be encouraged.     

Computation of Running Averages

This brief presents and compares several recursive and nonrecursive techniques for the efficient computation of the running average of discrete signals. First of all, the standard recursive algorithm is considered and its long-term accuracy is assessed when the floating-point arithmetic is employed. A cheap refreshing strategy is proposed as a means of keeping the computed value close enough to the exact one. Then, two alternative nonrecursive algorithms, requiring only log₂N additions, are developed, which are as reliable and accurate as the direct implementation     

Equivalent electrical network of the DNA molecule

The variation of current density with bias or temperature is examined for DNA molecules of different configuration. To this end, the DNA molecule is represented as an equivalent electrical network whose behavior is then simulated with PSPICE. The results are found to be in close agreement with ones obtained within a physical model. It is established that the electrical response of a DNA molecule to an applied electric field depends on the boundary conditions and the potential profile along the molecule. This finding should contribute to the creation of a complete library of DNA-molecule configurations with prescribed electrical properties.     

The colored revolution of bioimaging

This paper provides an overview of the main aspects of modern fluorescence microscopy. It covers the principles of fluorescence and highlights the key discoveries in the history of fluorescence microscopy. The paper also discusses the optics of fluorescence microscopes and examines the various types of detectors. It also discusses the signal and image processing challenges in fluorescence microscopy and highlights some of the present developments and future trends in the field.     

Three takes on telecom's troubles

Spectrum asked three IEEE members from the telecommunications sector to comment on the industry's current woes and prospects. Roch Guerin discusses bandwidth as a commodity and how to deal with it. The impact of technological change on telecommunications is enormous and calls for a shift in business models. Technology is making bandwidth a commodity and it should not matter who supplies it. Competition is vital and commodity providers must be decoupled from value providers. Frank Ferrante points out that the Year 2000 crisis resulted in manufacturers being deluged with orders for new upgraded systems. Vast sums were spent to meet the demand in time. However, when Y2K was over, production stayed high and inventories continued to build, while demand effectively stopped overnight. Dazzling new innovations are needed to compel the masses to spend and manufacturers must apply their resources to deliver quickly and efficiently. Jules A. Bellisio discusses the role of engineers in bringing new ideas to the market place. Many engineers have put together ventures for the sole purpose of attracting capital. The underlying technology and business propositions were there solely to lure the unsuspecting. By allowing engineers to use technology simply to cover for a scam, then the profession is also to blame for the current problems.     

The rank and kernel of extended 1-perfect /spl Zopf//sub 4/-linear and additive non-/spl Zopf//sub 4/-linear codes

A binary extended 1-perfect code of length n + 1 = 2/sup t/ is additive if it is a subgroup of /spl Zopf//sub 2//sup /spl alpha// /spl times/ /spl Zopf//sub 4//sup /spl beta//. The punctured code by deleting a /spl Zopf//sub 2/ coordinate (if there is one) gives a perfect additive code. 1-perfect additive codes were completely characterized and by using that characterization we compute the possible parameters /spl alpha/, /spl beta/, rank, and dimension of the kernel for extended 1-perfect additive codes. A very special case is that of extended 1-perfect /spl Zopf//sub 4/-linear codes.     

Parameterisation of slant-Haar transforms

A parameterisation of the slant-Haar transform is presented, which includes an existing version of the slant-Haar transform. An efficient algorithm for the slant-Haar transform is developed and its computational complexity is estimated. The parametric slant-Haar transforms are compared to the Karhunen-Loeve transform. The parametric slant-Haar is shown to perform better than the commonly used slant-Haar and slant-Hadamard transforms for the first-order Markov model and also performs better than the discrete cosine transform for images approximated by the generalised image correlation model