There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Time reversal of ultrasonic fields represents a way to focus through an inhomogeneous medium. This may be accomplished by a time-reversal mirror (TRM) made from an array of transmit-receive transducers that respond linearly and allow the incident acoustic pressure to be sampled. The pressure field is then time-reversed and re-emitted. This process can be used to focus through inhomogeneous media on a reflective target that behaves as an acoustic source after being insonified. The time-reversal approach is introduced in a discussion of the classical techniques used for focusing pulsed waves through inhomogeneous media (adaptive time-delay techniques). Pulsed wave time-reversal focusing is shown using reciprocity valid in inhomogeneous medium to be optimal in the sense that it realizes the spatial-temporal matched filter to the inhomogeneous propagation transfer function between the array and the target. The research on time-reversed wave fields has also led to the development of new concepts that are described: time-reversal cavity that extends the concept of the TRM, and iterative time-reversal processing for automatic sorting of targets according to their reflectivity and resonating of extended targets. >

Time reversal of ultrasonic fields. I. Basic principles

Most current Artificial Neural Network (ANN) models are based on highly simplified brain dynamics. They have been used as powerful computational tools to solve complex pattern recognition, function estimation, and classification problems. ANNs have been evolving towards more powerful and more biologically realistic models. In the past decade, Spiking Neural Networks (SNNs) have been developed which comprise of spiking neurons. Information transfer in these neurons mimics the information transfer in biological neurons, i.e., via the precise timing of spikes or a sequence of spikes. To facilitate learning in such networks, new learning algorithms based on varying degrees of biological plausibility have also been developed recently. Addition of the temporal dimension for information encoding in SNNs yields new insight into the dynamics of the human brain and could result in compact representations of large neural networks. As such, SNNs have great potential for solving complicated time-dependent pattern recognition problems because of their inherent dynamic representation. This article presents a state-of-the-art review of the development of spiking neurons and SNNs, and provides insight into their evolution as the third generation neural networks.

Spiking neural networks.

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.

/pdf/modeling-nonlinear-ultrasound-propagation-in-heterogeneous-4mrm4bt7mx.pdf

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.

Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency.

An equation for acoustic propagation in an inhomogeneous medium with relaxation loss is systematically derived from the classical dynamic equations together with an equation of state for relaxation. The derivation assumes small acoustic perturbations but accommodates arbitrary spatial inhomogeneities in material compressibility, density, and parameters of relaxation. The linearized wave equation obtained for n relaxation mechanisms has order n + 2, is causal, and yields the expected dependence of attenuation on frequency. Exact analytic expressions valid at all frequencies are given for the spatially varying attenuation coefficient, as well as phase velocity. A Green's function is calculated for the equation. The results may be used to model scattering for image reconstruction and the determination of statistical properties, such as average differential scattering cross section.

An equation for acoustic propagation in inhomogeneous media with relaxation losses

A quantum entangled radar uses entangled photons instead of separate photons. It has been shown that for quantum
entangled interferometers that the value of quantum entanglement deteriorates in an environment with attenuation. This
paper introduces a correction method that allows the quantum radar to maintain excellent performance even when
dealing with an environment with attenuation. The correction method is analogous to techniques used in adaptive optics
to improve images. Correction approaches based on signal sources deliberately introduced into the environment and
electromagnetic sources already present in the environment are considered. Closed form expressions for estimating the
range error are derived for the cases when the radar uses N entangled photons for imaging or N separate imaging
photons. Simulations of radar range error estimates for entangled and separate photon cases for propagation media with
widely varying attenuation properties are provided. Comparisons of estimates with and without atmospheric correction
are given. The atmospheric correction method extends the range of the beneficial effects of entanglement by a factor of
82, i.e. to 5000 km for a slowly varying propagation medium. For a propagation medium with 50 times as much
variation, the atmospheric correction method offers super sensitivity for three times the range of the uncorrected case.

Quantum entangled radar theory and a correction method for the effects of the atmosphere on entanglement

A Resource Manager for Distributed Resources: Fuzzy Decision Trees and Genetic Optimization.

A recursive multisensor association algorithm has been developed based on fuzzy logic. It simultaneously determines fuzzy grades of membership and fuzzy cluster centers. It is capable of associating data from various sensor types and in its simplest form makes no assumption about noise statistics as many association algorithms do. The algorithm is capable of performing without operator intervention, i.e., it is unsupervised. It associates data from the same target for multiple sensor types. The algorithm also provides an estimate of the number of targets present, reduced noise estimates of the quantities being measured, and a measure of confidence to assign to the data association. The fuzzy logic formalism used offers the opportunity to incorporate additional information or heuristic rules easily. A comparison of the algorithm to a more conventional Bayesian association algorithm is provided. Also, procedures for defuzzification, i.e, mapping fuzzy results to hard results are discussed as well as the method of determining target validity. Various simulated and experimentally measured real-time data sets are analyzed and provide a basis for comparison of the fuzzy and Bayesian association algorithms.

Fuzzy logic multisensor association algorithm

With the goal in mind of designing radars, interferometers and other sensors based on quantum entanglement the virtues of N00N states, plain M and M states (PMMSs) and linear co mbinations of M and M states (LCMMS) are considered. A derivation of the closed form expression for the detection operator that is optimal subject to constraints is provided. The raising and lowering properties of the detection operator and its square are developed. The expectations of the optimal detection operator and its square are derived. The expression for the visibility, the maximum expectation of the optimal detection operator, is developed. From the expectation of the square of the detection operator and the visibility, the phase error and the minimum phase error for the detection operator are derived. The optimal resolution for the maximum visibility and minimum phase error are found. For the visibility, comparisons between PMMSs, LCMMS and N00N states are provided. For the minimum phase error comparisons between LCMMS, PMMSs, N00N states, separate photon states (SPSs), the shot noise limit (SNL), and the Heisenberg limit (HL) are provided. A representative collection of computational results illustrating the superiority of LCMMS when compared to PMMSs and N00N states is given. It is found for a resolution 12 times the classical result LCMMS has visibility 11 times that of N00N states and four times that of PMMSs. For the same case, the minimum phase error for LCMMS is 10.7 times smaller than that of PMMS and 29.7 times smaller than that of N00N states. Keywords: quantum radar, quantum sensors, super resolution, super sensitivity, quantum entanglement, quantum metrology, quantum imaging, N00N states, M and M states, quantum interferometer

Quantum interferometer and radar theory based on N00N, M and M or linear combinations of entangled states

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