Algebraic Collision Attacks on Keccak

The goal of reconstruction or tomographic techniques is to solve for material parameters from boundary information. Linear reconstruction techniques such as ART or SIRT are desirable because of their efficient performance. The derivation of these methods do not take into account scattering media, which is non-linear in nature. We present a summary of linear reconstruction techniques applied to scattering media. We also evaluate using photon distributions as a novel algebraic reconstruction technique matrix. We show the clear benefit of using the randomized reconstruction techniques with many passes over their non-randomized counterparts. We show a marginal improvement in all linear reconstruction techniques with a moderate amount of scattering. We also demonstrate the poor performance of the linear techniques with scattering media, even when using known photon distributions.

This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller.

The application of linear reconstruction techniques, namely, the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), to the reconstruction of the microwave attenuation coefficient distribution of 2D and 3D lossy dielectric objects is investigated. The reconstructed 2D and 3D images using both techniques are compared for noiseless data and for data with a finite signal-to-noise ratio. It shows that the ART generally produces better images. However, the SART has a less effect from the noise.

Mathematically, the complex reactions can be simplified through different linear/non-linear algebraic techniques that are the easiest way to balance the complex models. Furthermore, the complex chemical equations can be balanced with the linear algebraic technique based on matrix-inversion applications. That is the other way for the researchers and chemists to balance the complex chemical equation. In this article, we provide information about coefficients that balance the chemical equations through null-space methodology and the steady-state approximation by applying linear algebra technique. The purpose is not only to identify the undetermined coefficients but also to compute the kernel matrix or null spaces. Furthermore, the steady state for a two-step reaction mechanism is established.

Linear-based gain-determining method for adaptive backstepping controller

From Bayes to Tarantola: New insights to understand uncertainty in inverse problems

This paper proposes a novel integrated navigation filter based on a combined long baseline/ultra short baseline acoustic positioning system with application to underwater vehicles. With a tightly coupled structure, the position, linear velocity, attitude, and rate gyro bias are estimated, considering the full nonlinear system dynamics without resorting to any algebraic inversion or linearisation techniques. The resulting solution ensures convergence of the estimation error to zero for all initial conditions, exponentially fast. Finally, it is shown, under simulation environment, that the filter achieves very good performance in the presence of sensor noise.

Fast reconstruction of computerized tomography images based on the cross-entropy method

We compare, through simulations, the performance of four linear algorithms for diffuse optical tomographic reconstruction of the three-dimensional distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave approximation. The simulation geometry consisted of a coplanar array of sources and detectors at the boundary of a half-space medium. The forward solution matrix is both underdetermined, because we estimate many more absorption coefficient voxels than we have measurements, and ill-conditioned, due to the ill-posedness of the inverse problem. We compare two algebraic techniques, ART and SIRT, and two subspace techniques, the truncated SVD and CG algorithms. We compare three-dimensional reconstructions with two-dimensional reconstructions which assume all inhomogeneities are confined to a known horizontal slab, and we consider two `object-based' error metrics in addition to mean square reconstruction error. We include a comparison using simulated data generated using a different FDFD method with the same inversion algorithms to indicate how our conclusions are affected in a somewhat more realistic scenario. Our results show that the subspace techniques are superior to the algebraic techniques in localization of inhomogeneities and estimation of their amplitude, that two-dimensional reconstructions are sensitive to underestimation of the object depth, and that an error measure based on a location parameter can be a useful complement to mean squared error.

An informal personal survey of some major outstanding questions in matrix theory is given. These are grouped into several categories and illustrate the faci that modern work in matrix theory relies predominantly on neither linear nor algebraic techniques. Occasional references are given. Category 1 involves simultaneous conditions on sets of parameters associated with a matrix; category 2 includes restricted similarity questions, and category 3 is represented by the D-stability problem. In category 4 are questions associated with the geometry of major classes of matrices and category 5 is that of determinant optimization and inequality problems. Finallycategory 6 recognizes an area of rapidly growing interest, that of combinatorial aspects of matrix problems.

Algebraic reconstruction algorithms are a better choice compared to transform-based algorithms whenever projection data is limited in nature. High computational cost and huge memory requirements are two major downsides of iterative reconstruction methods. Among all algebraic techniques, the Multiplicative Algebraic Reconstruction Technique (MART) is most popular because it maximizes the entropy (of the image) in the limiting case. In the present work, our ultimate goal is to reduce computational complexity and cope with the huge storage scenario of the MART algorithm. We propose a new sparse MART algorithm (Sp-MART) and test it with two-dimensional and three-dimensional (2D/3D) numerical data. A more accurate and efficient geometrical formula for calculating intersection length is also presented. Experimental projection data of human tooth and drip irrigation pipe is processed for further validation of the Sp-MART algorithm. Reconstructions of real specimens are also done using the FDK algorithm. The difference between two algorithms are investigated by calculating the structural similarity index (SSIM) and the L2 error of the results.

Existing data collections can be large in both number of samples and in number of attributes per sample. In either case, we have found that many advanced techniques in numerical linear algebra can be used to design efficient algorithms for clustering and exploring these datasets. We illustrate this point with the method of Principal Direction Divisive Partitioning, a scalable unsupervised clustering algorithm which has been found to give high quality clusters. We show how the scalability to large sizes is achieved using those advanced linear algebra techniques. These techniques also lead to an alternate representation of the dataset which is close enough to the original for the purposes of clustering while occupying a much smaller memory footprint.

Non-orthogonal multiple access (NOMA) is one of the potential candidates for future radio access to address the increasing demands of mobile traffic. NOMA-based systems employ orthogonal frequency division multiplexing (OFDM) for multicarrier modulation which induces peak-to-average power ratio (PAPR). High PAPR makes conventional NOMA systems spectrally and energy inefficient. Thus, in this paper, precoded NOMA system is proposed to overcome the PAPR problem in downlink NOMA. Different unitary transforms such as Walsh Hadamard transform (WHT), Zadoff chu transform (ZCT), and discrete Hartley transform are applied as linear precoding techniques to overcome the PAPR problem in NOMA. Moreover, a new precoding technique -transform is also proposed which is a hybrid combination of WHT and ZCT. Link-level performance of power domain NOMA is analysed in terms of PAPR, spectral efficiency, bit error rate, and computational complexity. Simulation results show that in the presence of linear precoding techniques, performance of classic NOMA systems improve at the cost of slight increment in complexity.

Integrated Class D audio amplifiers are very power efficient, but require an external filter which prevents further integration. Also due to this filter, large feedback factors are hard to realise, so that the load influences the distortion- and transfer characteristics. The amplifier presented in this paper consists of a switching part that contains a much simpler filter, and a linear part that ensures a low distortion and flat frequency response. A 30W version was realised. The switching part of the amplifier was integrated in a BCD process. Together with a linear part and with a loudspeaker as load, it has a flat frequency response +/- 0.3dB, a dissipation that is up to 5 times lower than a traditional class AB audio amplifier, and a distortion of <0.02% over power and frequency range.

ObjectivesHeightened inflammatory state, as measured by circulating C‐reactive protein (CRP) levels, can promote inflammation‐mediated disease risk. It is important to account for population fluctuation and sex variation in serum CRP concentrations on overall time trends.MethodsUsing the National Health and Nutrition Examination Survey data, we specify linear and algebraic decomposition models separately by sex to identify the drivers of the changing trends in the distribution of CRP values in the population.ResultsWe found a nonsignificant overall increase in CRP, but a significant decrease among women and increase among men, over a 10‐year period. We then used linear and algebraic decomposition techniques to identify the sources of change in CRP over time, separately for women and men. CRP increased among men mainly because lifestyle/health characteristics worsened over time, and because the size of socioeconomic/demographic groups with higher CRP increased and the size of groups with lower CRP decreased. The downward shift in CRP among women occurred because the typical woman across all cohorts had lower CRP levels.ConclusionsWe identified two fundamentally different processes of change driving the decline and rise in CRP values among women and men, respectively.