A Pseudo Random Number Generator (PRNG) produces a sequence whose randomness is evaluated by statistical tests like NIST and TestU01. The random sequences are deterministic and reproducible when using the same seed value. In this manner, and for cryptographic applications, the key size of a PRNG must be increased to resist brute force attacks. Henceforth, a fractional-order chaotic system, like the Lorenz one, is suitable to be used to design a PRNG, which implementation can be performed by using embedded devices such as the low-cost EPS32 (32-bit LX6 microprocessor) and field-programmable gate array (FPGA). To increase the throughput, the fractional Lorenz system is integrated with an approximated two steps Runge–Kutta method. An analysis in performed to find the domain of attraction for each state variable, and to verify that the PRNG produces non-correlated sequences. The hardware implementation is detailed by establishing the number of bits (or keys) required for the PRNG to guarantee its suitability for cryptographic applications. Finally, the hardware design of a PRNG using the fractional Lorenz system provides a throughput of 4.99 Mbits/sec in the EPS32 platform, and 112.96 Mbits/sec in the FPGA.

This work presents an optimized Field-Programmable Gate Array (FPGA) implementation of an Echo State Network (ESN), a type of Recurrent Neural Network (RNN), to predict the chaotic signal of the Lorenz system. The focus is on executing AI models efficiently on resource-limited devices like those in the Internet of Things (IoT). In contrast to previous state-of-the-art works that used the tanh activation function (which required complex hardware approximations), this proposal employs the simpler ReLU function. This choice eliminates the need for approximations and, when combined with an optimized network architecture, enables a drastic reduction in resource usage. Specifically, the optimization achieved three key reductions: a) The reservoir size, decreased from 50 to 3; b) The connectivity matrix, transitioned from a dense matrix of 2500 values to a diagonal matrix with only 3 non-zero values; and c) Precision, reducing the operational bit-width from 32 to 23 bits. As a result, the optimized ESN is significantly more efficient on FPGA hardware, successfully reducing utilized resources while simultaneously achieving improved performance compared to prior state-of-the-art implementations. • We apply a Network Search Architecture with Echo State Networks (ESN) to predict the chaotic signal of Lorenz system. • A very small network with a size of 3 neurons in the reservoir is ob- tained. • An implementation of the obtained ESN in FPGA is presented.

It is well known that Pareto based algorithms do not scale when the number of objectives is greater than three. That way, it is an open problem in integrated circuit design because optimizing amplifiers by multi-objective evolutionary algorithms requires evaluating many objectives with many constraints. In this manner, we show the usefulness of MOMBI, an algorithm based on R2 indicator, for improving the optimal sizing of amplifiers designed with MOSFETs. It is highlighted that such kind of algorithms could lead to solve problems in analog integrated circuit optimization when considering many objectives. In addition, a handling constraint scheme is incorporated to MOMBI. The optimization algorithm based on R2 indicator is applied herein to an amplifier that is used to implement a universal active filter showing good SPICE simulations results.

An strategy based on the optimal computing budget allocation (OCBA) approach is presented to reduce the simulation cost in the yield optimization of analog integrated circuits (ICs), when it is performed on classical Monte Carlo simulations. OCBA is applied to distribute the large portion of the budget simulations among critical IC sizing optimization cases, while limiting the simulations for the non-critical cases. The optimal sizing is performed by applying three evolutionary algorithms, namely: non-dominated sorting genetic algorithm (NSGA-II), multi-objective evolutionary algorithm with decomposition (MOEA/D), and particle swarm optimization (PSO). They are executed within the OCBA-based strategy to enhance the yield of an operational transconductance amplifier using IC technology of 90 nm.

A multi-parameter sensitivity approach based on Richardson extrapolation, and applied to the optimal sizing of analog integrated circuits (ICs), is presented. First, the multiobjective evolutionary algorithm (EA) called non-dominated sorting genetic algorithm (NSGA-II), is applied to compute the feasible sizes of analog ICs, i.e. the optimal width and length (W/L) of every metal-oxide-semiconductor field-effect-transistor (MOSFET) is found. At this stage, the simulation program with integrated circuits emphasis (SPICE) is used to evaluate the electrical characteristics of analog ICs. Second, the multiparameter sensitivity analysis based on Richardson extrapolation, is applied to approximate the partial derivatives associated to the sensitivities on the performances of the ICs with respect to W/L of every MOSFET. The cases of study are three analog ICs, namely: voltage follower (VF), positive-type second generation current conveyor (CCII+), and current-feedback operational amplifier (CFOA). The proposed approach selects W/L feasible sizes presenting the lower sensitivities that are computed from the corresponding Pareto sets. Finally, 18 feasible (W/L sizes) solutions accomplishing 18 performance objectives and guaranteeing low W/L sensitivities for a complementary metal-oxide-semiconductor (CMOS) CFOA, are listed in Table I.

In this article we present a new approach to extract points that belongs to several ellipses or circles presented on a same image and with the presence of outliers. Each geometric form is extracted by means of a robust fitting, that is a nonlinear optimization problem, solved with two different heuristics: differential evolution and RANSAC. Once the geometric form is fitted, its points are extracted by calculating their statistics. Several tests with synthetic and real images are performed to show its effectiveness.

In this paper we solve the problem of robust fitting of ellipses to a set of points under condition of very high noise (when more than 50% of the points are outliers), using the sum of the orthogonal distances (instead of the sum of the squares of the distances) from the given points to the fitted ellipse. The fitting problem now is nonlinear and is solved using Differential Evolution. We demonstrate by simulations that one or several ellipses can be extracted from the data set of points. The proposed method is compared with the least median of squares solved with RANSAC.

To obtain a 3D metric reconstruction from two images taken with a same camera without previous calibration, it is necessary to estimate the intrinsic camera parameters and the orientation and position of the two views with respect to the camera. At the present time, there are several algorithms to estimate camera parameters from two views, all of them are based on the epipolar geometry and the estimation of the fundamental matrix. However, it is well known there are some configurations where the fundamental matrix can not be estimated, called critical configurations. In this article we present a novel method to retrieve directly the camera parameters, and orientation and position parameters for two views, from points taken over the two images, using the Differential Evolution (DE) algorithm. This method exploits the reprojection error as the cost function for DE, instead of computing the fundamental matrix. Experimental results show our method recovers 3D points, intrinsic, and orientation and position parameters on non-critical configurations and in the critical configuration of pure translation.We used simulated and real images to prove its effectiveness and robustness.