Luis Gerardo de la Fraga

A variant to the “random approximation” of the reference-free alignment algorithm

Abstract Single-particle averaging from electron microscope images strongly depends on alignment. Most alignment procedures are based on cross-correlation of an initial reference image with the rest of the population, leading to a clear pattern dependence. Among the different approaches that have been proposed to minimize this problem, one of the most widely used is the so-called iterative reference-free alignment algorithm (RFAA), proposed by Penczek et al. [Ultramicroscopy 40 (1992) 33]. To avoid the pattern dependence shown by the initial “random approximation” step of this method, we propose a variant of the algorithm that is more independent of the input order of the initial images and which could substitute the random initialization of the RFAA.

Binary Genetic Encoding for the Synthesis of Mixed-Mode Circuit Topologies

A binary genetic encoding (BGE) representation for the automatic synthesis of mixed-mode circuit topologies, is introduced. First, the genetic encoding of unity-gain cells (UGCs), such as voltage (VF) and current followers (CF), and voltage (VM) and current mirrors (CM), is presented. New BGEs for the VM and CM are introduced. Second, the UGC’s chromosomes are combined to synthesize mixed-mode circuit-topologies, namely current conveyors and current-feedback operational amplifiers (CFOA). Five strategies for the combination or superimposing of UGCs are introduced. The proposed BGE has been implemented in MATLABTM, and links SPICE to evaluate the populations with different integrated circuit technologies. Some new synthesized circuit topologies are shown along with their chromosome description.

Richardson extrapolation-based sensitivity analysis in the multi-objective optimization of analog circuits

The feasible solutions provided by a multi-objective evolutionary algorithm (MOEA) in the optimal sizing of analog integrated circuits (ICs) can be very sensitive to process variations. Therefore, to select the optimal sizes of metal-oxide-semiconductor field-effect-transistors (MOSFETs) but with low sensitivities, we propose to perform multi-parameter sensitivity analysis. However, since MOEAs generate feasible solutions without an explicit equation, then we show the application of Richardson extrapolation to approximate the partial derivatives associated to the sensitivities of the performances of an amplifier with respect to the sizes of every MOSFET. The proposed multi-parameter sensitivity analysis is verified through the optimization of a recycled folded cascode (RFC) operational transconductance amplifier (OTA). We show the behavior of the multi-parameter sensitivity approach versus generations. The final results show that the optimal sizes, selected after executing the sensitivity approach, guarantee the lowest sensitivities values while improving the performances of the RFC OTA.

Confidence limits for resolution estimation in image averaging by random subsampling

Abstract In this communication we present an empirical approach to the task of estimating the reproducible limit of resolution that can be achieved when a set of images is averaged. The proposed solution is based on a random subsampling method. We derive confidence limits for two of the most widely used measures of reproducibility in this field, the differential phase residual (DPR) and the Fourier ring correlation (FRC). Results both for negatively stained specimens and for those embedded in ice are presented. Our results provide a common framework that allows a number of previous observations and suggestions regarding these measures to be further analyzed.

Optimal Triangulation in 3D Computer Vision Using a Multi-objective Evolutionary Algorithm

The triangulationis a process by which the 3D point position can be calculated from two images where that point is visible. This process requires the intersection of two known lines in the space. However, in the presence of noise this intersection does not occur, then it is necessary to estimate the best approximation. One option towards achieving this goal is the usage of evolutionary algorithms. In general, evolutionary algorithms are very robust optimization techniques, however in some cases, they could have some troubles finding the global optimum getting trapped in a local optimum. To overcome this situation some authors suggested removing the local optima in the search space by means of a single-objective problem to a multi-objective transformation. This process is called multi-objectivization. In this paper we successfully apply this multi-objectivizationto the triangulation problem.

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators.

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.

Evolutionary Algorithms in the Optimal Sizing of Analog Circuits

Analog signal processing applications such as filter design and oscillators, require the use of different kinds of amplifiers, namely: voltage follower, current conveyors, operational amplifiers and current feedback operational amplifiers. To improve the performances on these applications, it is very much needed to optimize the behavior of the amplifiers. That way, this work shows their optimization by applying two evolutionary algorithms: the Non-Sorting Genetic Algorithm (NSGA-II), and the Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D). The analog circuits are sized taking into account design constraints, and linking HSPICE like circuit simulator to evaluate their electrical characteristics. Additionally, we show that differential evolution (DE) enhances the convergence to the Pareto front and controls the evolution of the objectives among different runs. DE also preserves the same time efficiency and increases the dominance on NSGA-II and MOEA/D compared with the one point crossover genetic operator.

Direct Calibration by Fitting of Cuboids to a Single Image Using Differential Evolution

In this article we propose a new method to calibrate directly the camera by which it was taken an image of a cuboid, and to find at the same time the orientation and side lengths of the cuboid. This is a highly non-linear optimization problem that is solved directly using a heuristic called differential evolution. We show in this paper that this problem is very difficult if one tries to solve it with a conventional scalar optimization procedure. Although differential evolution is a heuristic, we find valid results in 100% of the executions. We test our method with synthetic and real images.

Euclidean Distance Fit of Ellipses with a Genetic Algorithm

We use a genetic algorithm to solve the problem, widely treated in the specialized literature, of fitting an ellipse to a set of given points. Our proposal uses as the objective function the minimization of the sum of orthogonal Euclidean distances from the given points to the curve; this is a non-linear problem which is usually solved using the minimization of the quadratic distances that allows to use the gradient and the numerical methods based on it, such as Gauss-Newton. The novelty of the proposed approach is that as we are using a GA, our algorithm does not need initialization, and uses the Euclidean distance as the objective function. We will also show that in our experiments, we are able to obtain better results than those previously reported. Additionally our solutions have a very low variance, which indicates the robustness of our approach.

CDCTA and OTA Realizations of a Multi-phase Sinusoidal Oscillator

ABSTRACT A new topology for a current-mode multi-phase sinusoidal oscillator (MSO) is introduced. It is designed using current-differencing cascaded transconductance amplifiers (CDCTAs) and operational transconductance amplifiers (OTA). Both designs realize odd and even numbers of phase oscillators. The MSO is implemented by cascading first-order all-pass filter stages that are designed with CDCTAs or OTAs and show the same transfer function. The MSO includes n grounded resistors and n grounded capacitors to generate n phases. We highlight the advantage of using OTAs because the resulting MSO circuitry is greatly reduced compared to using CDCTAs, while in both designs the high output impedances facilitate easy driving an external load without additional current buffers. The condition of oscillation and the frequency of oscillation are orthogonal and can be adjusted by varying a bias current. Finally, SPICE simulation results using integrated circuit technology of 0.35 µm show that the designed MSO provides odd/even phase signals that are equally spaced in phase and with equal amplitude.