Integrated program debugging, verification, and optimization using abstract interpretation (and the Ciao system preprocessor)

The technique of Abstract Interpretation has allowed the development of very sophisticated global program analyses which are at the same time provably correct and practical. We present in a tutorial fashion a novel program development framework which uses abstract interpretation as a fundamental tool. The framework uses modular, incremental abstract interpretation to obtain information about the program. This information is used to validate programs, to detect bugs with respect to partial specifications written using assertions (in the program itself and/or in system libraries), to generate and simplify run-time tests, and to perform high-level program transformations such as multiple abstract specialization, parallelization, and resource usage control, all in a provably correct way. In the case of validation and debugging, the assertions can refer to a variety of program points such as procedure entry, procedure exit, points within procedures, or global computations. The system can reason with much richer information than, for example, traditional types. This includes data structure shape (including pointer sharing), bounds on data structure sizes, and other operational variable instantiation properties, as well as procedure-level properties such as determinacy, termination, nonfailure, and bounds on resource consumption (time or space cost). CiaoPP, the preprocessor of the Ciao multi-paradigm programming system, which implements the described functionality, will be used to illustrate the fundamental ideas.

Practical case with regard to applying the functional and environmental method to low crest level, detached breakwaters

The research work as presented in this article covers the design of detached breakwaters since they constitute a type of coastal defence work with which to combat many of the erosion problems found on beaches in a stable, sustainable fashion. The main aim of this work is to formulate a functional and environmental (but not structural) design method, enabling the fundamental characteristics of a detached breakwater to be defined as a function of the effect it is wished to induce on the coast, and taking into account variables of a different nature (climate, geomorphology and geometry) influencing the changes the shoreline undergoes after its construction. With this article, it is intended to submit the final result of the investigation undertaken, applying the detached breakwater design method as developed to solving a practical case. Thus it may be shown how the method enables a detached breakwater’s geometric pre-sizing to be tackled at a place on the coast with certain climate, geomorphology and littoral dynamic characteristics, first setting the final state of equilibrium it is wanted to obtain therein after its construction.

The lead salt quantum dot intermediate band solar cell

We propose a new kind of quantum dot (QD) materials for the implementation of the intermediate band solar cell (IBSC) [1]. The materials are formed by lead salt QDs of the family IV-VI (PbTe, PbSe or PbS) embedded in a semiconductor of the family II-VI (Cd1-xMgxTe, CdxZn1-xTe, and CdS1-xSex or ZnSe1-xTex, respectively). These QDs are not nucleated due to lattice mismatch, as it is the case of the InAs/GaAs QD material system grown by the Stranski-Krastanov (S-K) mode. In these materials, the QDs precipitate due to the difference in lattice type: the QD lead salt material crystallizes in the rocksalt structure, while the II-VI host material has the zincblende structure [2]. Therefore, it is possible to use lattice-matched QD/host combinations, avoiding all the strain-related problems found in previous QD-IBSC developments. In this paper we discuss the properties of the lead salt QD materials and propose that they are appropriate to overcome the fundamental drawbacks of present III-V-based QD-IBSC prototypes. We also calculate the band diagram for some examples of IV-VI/II-VI QD materials. The detailed balance efficiency limit of QD-IBSCs based on the studied materials is found to be over 60% under maximum concentration.

Image Processing Challenges in the Creation of Spatiotemporal Gene Expression Atlases of Developing Embryos

To properly understand and model animal embryogenesis it is crucial to obtain detailed measurements, both in time and space, about their gene expression domains and cell dynamics. Such challenge has been confronted in recent years by a surge of atlases which integrate a statistically relevant number of different individuals to get robust, complete information about their spatiotemporal locations of gene patterns. This paper will discuss the fundamental image analysis strategies required to build such models and the most common problems found along the way. We also discuss the main challenges and future goals in the field.

Image Processing Challenges in the Creation of Spatiotemporal Gene Expression Atlases of Developing Embryos

To properly understand and model animal embryogenesis it is crucial to obtain detailed measurements, both in time and space, about their gene expression domains and cell dynamics. Such challenge has been confronted in recent years by a surge of atlases which integrate a statistically relevant number of different individuals to get robust, complete information about their spatiotemporal locations of gene patterns. This paper will discuss the fundamental image analysis strategies required to build such models and the most common problems found along the way. We also discuss the main challenges and future goals in the field.

A portable NIR device for the optical supervision of milk coagulation process

The coagulation of milk is the fundamental process in cheese-making, based on a gel formation as consequence of physicochemical changes taking place in the casein micelles, the monitoring the whole process of milk curd formation is a constant preoccupation for dairy researchers and cheese companies (Lagaude et al., 2004). In addition to advances in composition-based applications of near infrared spectroscopy (NIRS), innovative uses of this technology are pursuing dynamic applications that show promise, especially in regard to tracking a sample in situ during food processing (Bock and Connelly, 2008). In this way the literature describes cheese making process applications of NIRS for curd cutting time determination, which conclude that NIRS would be a suitable method of monitoring milk coagulation, as shown i.e. the works published by Fagan et al. (Fagan et al., 2008; Fagan et al., 2007), based in the use of the commercial CoAguLite probe (with a LED at 880nm and a photodetector for light reflectance detection).

Mathematical models for the arrangement and the cleaning of the river basin and surroundings of the river sandy grounds to its passage by the city of Salta (Argentina)

The province of Salta is located the Northwest of Argentina in the border with Bolivia, Chile and Paraguay. Its Capital is the city of Salta that concentrates half of the inhabitants of the province and has grown to 600000 hab., from a small active Spanish town well founded in 1583. The city is crossed by the Arenales River descending from close mountains at North, source of water and end of sewers. But with actual growing it has become a focus of infection and of remarkable unhealthiness. It is necessary to undertake a plan for the recovery of the river, directed to the attainment of the well-being and to improve the life?s quality of the Community. The fundamental idea of the plan is to obtain an ordering of the river basin and an integral management of the channel and its surroundings, including the cleaning out. The improvement of the water?s quality, the healthiness of the surroundings and the improvement of the environment, must go hand by hand with the development of sport activities, of relaxation, tourism, establishment of breeding grounds, kitchen gardens, micro enterprises with clean production and other actions that contribute to their benefit by the society, that being a basic factor for their care and sustainable use. The present pollution is organic, chemical, industrial, domestic, due to the disposition of sweepings and sewer effluents that affects not only the flora and small fauna, destroying the biodiversity, but also to the health of people living in their margins. Within the plan it will be necessary to consider, besides hydric and environmental cleaning and the prevention of floods, the planning of the extraction of aggregates, the infrastructure and consolidation of margins works and the arrangement of all the river basin. It will be necessary to consider the public intervention at state, provincial and local level, and the private intervention. In the model it has been necessary to include the sub-model corresponding to the election of the entity to be the optimal instrument to reach the proposed objectives, giving an answer to the social, environmental and economic requirements. For that the authors have used multi-criteria decision methods to qualify and select alternatives, and for the programming of their implementation. In the model the authors have contemplated the short, average and long term actions. They conform a Paretooptimal alternative which secures the ordering, integral and suitable management of the basin of the Arenales River, focusing on its passage by the city of Salta.

Program development using abstract interpretation (and the ciao system preprocessor)

The technique of Abstract Interpretation has allowed the development of very sophisticated global program analyses which are at the same time provably correct and practical. We present in a tutorial fashion a novel program development framework which uses abstract interpretation as a fundamental tool. The framework uses modular, incremental abstract interpretation to obtain information about the program. This information is used to validate programs, to detect bugs with respect to partial specifications written using assertions (in the program itself and/or in system librarles), to genérate and simplify run-time tests, and to perform high-level program transformations such as múltiple abstract specialization, parallelization, and resource usage control, all in a provably correct way. In the case of validation and debugging, the assertions can refer to a variety of program points such as procedure entry, procedure exit, points within procedures, or global computations. The system can reason with much richer information than, for example, traditional types. This includes data structure shape (including pointer sharing), bounds on data structure sizes, and other operational variable instantiation properties, as well as procedure-level properties such as determinacy, termination, non-failure, and bounds on resource consumption (time or space cost). CiaoPP, the preprocessor of the Ciao multi-paradigm programming system, which implements the described functionality, will be used to illustrate the fundamental ideas.

Why Ciao? An overview of the ciao system's design philosophy

Our intention in this note is not to provide a listing of the many features of the Ciao system: this can be found in part for example in the brochures announcing upcoming versions, in the Ciao website, or in more feature-oriented descriptions such as. Instead in this document we would like to describe the objectives and reasoning followed in our design as well as the fundamental characteristics that in our opinion make Ciao quite unique and hopefully really useful to you as a Ciao user.

Boundary element approach to the dynamic stiffness functions of circular foundations

A boundary element approach for time harmonic axisymmetric problems using the complete space point load fundamental solution is presented. The fundamental solution is integrated numerically along the azimuthal co-ordinate of each axisymmetric element. To increase the accuracy of the numerical integration a simple co-ordinate transformation is proposed. The approach is applied to the computation of the dynamic stiffness functions of rigid circular foundations on layered viscoelastic soils. Three different sites are considered: a uniform half-space, a soil layer on a half-space, and a soil consisting of four horizontal layers and a compliant half-space. The numerical results obtained by the proposed approach for surface circular foundations are very close to corresponding published results obtained by different procedures.

An integral model for natural regeneration of Pinus pinea L. in the Northern Plateau (Spain) = Modelo integral de regeneración natural para Pinus pinea L. en la Meseta Norte (España)

Natural regeneration is an ecological key-process that makes plant persistence possible and, consequently, it constitutes an essential element of sustainable forest management. In this respect, natural regeneration in even-aged stands of Pinus pinea L. located in the Spanish Northern Plateau has not always been successfully achieved despite over a century of pine nut-based management. As a result, natural regeneration has recently become a major concern for forest managers when we are living a moment of rationalization of investment in silviculture. The present dissertation is addressed to provide answers to forest managers on this topic through the development of an integral regeneration multistage model for P. pinea stands in the region. From this model, recommendations for natural regeneration-based silviculture can be derived under present and future climate scenarios. Also, the model structure makes it possible to detect the likely bottlenecks affecting the process. The integral model consists of five submodels corresponding to each of the subprocesses linking the stages involved in natural regeneration (seed production, seed dispersal, seed germination, seed predation and seedling survival). The outputs of the submodels represent the transitional probabilities between these stages as a function of climatic and stand variables, which in turn are representative of the ecological factors driving regeneration. At subprocess level, the findings of this dissertation should be interpreted as follows. The scheduling of the shelterwood system currently conducted over low density stands leads to situations of dispersal limitation since the initial stages of the regeneration period. Concerning predation, predator activity appears to be only limited by the occurrence of severe summer droughts and masting events, the summer resulting in a favourable period for seed survival. Out of this time interval, predators were found to almost totally deplete seed crops. Given that P. pinea dissemination occurs in summer (i.e. the safe period against predation), the likelihood of a seed to not be destroyed is conditional to germination occurrence prior to the intensification of predator activity. However, the optimal conditions for germination seldom take place, restraining emergence to few days during the fall. Thus, the window to reach the seedling stage is narrow. In addition, the seedling survival submodel predicts extremely high seedling mortality rates and therefore only some individuals from large cohorts will be able to persist. These facts, along with the strong climate-mediated masting habit exhibited by P. pinea, reveal that viii the overall probability of establishment is low. Given this background, current management –low final stand densities resulting from intense thinning and strict felling schedules– conditions the occurrence of enough favourable events to achieve natural regeneration during the current rotation time. Stochastic simulation and optimisation computed through the integral model confirm this circumstance, suggesting that more flexible and progressive regeneration fellings should be conducted. From an ecological standpoint, these results inform a reproductive strategy leading to uneven-aged stand structures, in full accordance with the medium shade-tolerant behaviour of the species. As a final remark, stochastic simulations performed under a climate-change scenario show that regeneration in the species will not be strongly hampered in the future. This resilient behaviour highlights the fundamental ecological role played by P. pinea in demanding areas where other tree species fail to persist.

Seismic Hazard and Ground Motion Characterization at the Itoiz Dam (Northern Spain).

This paper presents a new hazard-consistent ground motion characterization of the Itoiz dam site, located in Northern Spain. Firstly, we propose a methodology with different approximation levels to the expected ground motion at the dam site. Secondly, we apply this methodology taking into account the particular characteristics of the site and of the dam. Hazard calculations were performed following the Probabilistic Seismic Hazard Assessment method using a logic tree, which accounts for different seismic source zonings and different ground-motion attenuation relationships. The study was done in terms of peak ground acceleration and several spectral accelerations of periods coinciding with the fundamental vibration periods of the dam. In order to estimate these ground motions we consider two different dam conditions: when the dam is empty (T = 0.1 s) and when it is filled with water to its maximum capacity (T = 0.22 s). Additionally, seismic hazard analysis is done for two return periods: 975 years, related to the project earthquake, and 4,975 years, identified with an extreme event. Soil conditions were also taken into account at the site of the dam. Through the proposed methodology we deal with different forms of characterizing ground motion at the study site. In a first step, we obtain the uniform hazard response spectra for the two return periods. In a second step, a disaggregation analysis is done in order to obtain the controlling earthquakes that can affect the dam. Subsequently, we characterize the ground motion at the dam site in terms of specific response spectra for target motions defined by the expected values SA (T) of T = 0.1 and 0.22 s for the return periods of 975 and 4,975 years, respectively. Finally, synthetic acceleration time histories for earthquake events matching the controlling parameters are generated using the discrete wave-number method and subsequently analyzed. Because of the short relative distances between the controlling earthquakes and the dam site we considered finite sources in these computations. We conclude that directivity effects should be taken into account as an important variable in this kind of studies for ground motion characteristics.

The neocortical column

In the middle of the twentieth century, Rafael Lorente de Nó (1902?1990) introduced the fundamental concept of the ?elementary cortical unit of operation,? proposing that the cerebral cortex is formed of small cylinders containing vertical chains of neurons (Lorente de Nó, 1933, 1938). On the basis of this idea, the hypothesis was later developed of the columnar organization of the cerebral cortex, primarily following the physiological and anatomical studies of Vernon Mountcastle, David Hubel, Torsten Wiesel, János Szentágothai, Ted Jones, and Pasko Rakic (for a review of these early studies, see Mountcastle, 1998). The columnar organization hypothesis is currently the most widely adopted to explain the cortical processing of information, making its study of potential interest to any researcher interested in this tissue, both in a healthy and pathological state. However, it is frequently remarked that the nomenclature surrounding this hypothesis often generates problems, as the term ?Column? is used freely and promiscuously to refer to multiple, distinguishable entities, such as cellular or dendritic minicolumns or afferent macrocolumns, with respective diameters of menor que50 and 200?500 ?m. Another problem is the degree to which classical criteria may need to be modified (shared response properties, shared input, and common output) and if so, how. Moreover, similar problems arise when we consider the need to define area-specific and species-specific variations. Finally, and what is more an ultimate goal than a problem, it is still necessary to achieve a better fundamental understanding of what columns are and how they are used in cortical processes. Accordingly, it is now very important to translate recent technical advances and new findings in the neurosciences into practical applications for neuroscientists, clinicians, and for those interested in comparative anatomy and brain evolution.

Influence of the Second Flexural Mode on the Response of High-Speed Bridges

This paper deals with the assessment of the contribution of the second flexural mode to the dynamic behaviour of simply supported railway bridges. Alluding to the works of other authors, it is suggested in some references that the dynamic behaviour of simply supported bridges could be adequately represented taking into account only the contribution of the fundamental flexural mode. On the other hand, the European Rail Research Institute (ERRI) proposes that the second mode should also be included whenever the associated natural frequency is lower than 30 Hz]. This investigation endeavours to clarify the question as much as possible by establishing whether the maximum response of the bridge, in terms of displacements, accelerations and bending moments, can be computed accurately not taking account of the contribution of the second mode. To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed $ \alpha$=VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed high-speed bridges, a parametric analysis is conducted over realistic ranges of values of $ \alpha$ and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the so-called Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twenty-one different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode.

Optical systems design using the SMS method and optimizations

Resumen El diseño de sistemas ópticos, entendido como un arte por algunos, como una ciencia por otros, se ha realizado durante siglos. Desde los egipcios hasta nuestros días los sistemas de formación de imagen han ido evolucionando así como las técnicas de diseño asociadas. Sin embargo ha sido en los últimos 50 años cuando las técnicas de diseño han experimentado su mayor desarrollo y evolución, debido, en parte, a la aparición de nuevas técnicas de fabricación y al desarrollo de ordenadores cada vez más potentes que han permitido el cálculo y análisis del trazado de rayos a través de los sistemas ópticos de forma rápida y eficiente. Esto ha propiciado que el diseño de sistemas ópticos evolucione desde los diseños desarrollados únicamente a partir de la óptica paraxial hasta lo modernos diseños realizados mediante la utilización de diferentes técnicas de optimización multiparamétrica. El principal problema con el que se encuentra el diseñador es que las diferentes técnicas de optimización necesitan partir de un diseño inicial el cual puede fijar las posibles soluciones. Dicho de otra forma, si el punto de inicio está lejos del mínimo global, o diseño óptimo para las condiciones establecidas, el diseño final puede ser un mínimo local cerca del punto de inicio y lejos del mínimo global. Este tipo de problemática ha llevado al desarrollo de sistemas globales de optimización que cada vez sean menos sensibles al punto de inicio de la optimización. Aunque si bien es cierto que es posible obtener buenos diseños a partir de este tipo de técnicas, se requiere de muchos intentos hasta llegar a la solución deseada, habiendo un entorno de incertidumbre durante todo el proceso, puesto que no está asegurado el que se llegue a la solución óptima. El método de las Superficies Múltiples Simultaneas (SMS), que nació como una herramienta de cálculo de concentradores anidólicos, se ha demostrado como una herramienta también capaz utilizarse para el diseño de sistemas ópticos formadores de imagen, aunque hasta la fecha se ha utilizado para el diseño puntual de sistemas de formación de imagen. Esta tesis tiene por objeto presentar el SMS como un método que puede ser utilizado de forma general para el diseño de cualquier sistema óptico de focal fija o v afocal con un aumento definido así como una herramienta que puede industrializarse para ayudar al diseñador a afrontar de forma sencilla el diseño de sistemas ópticos complejos. Esta tesis está estructurada en cinco capítulos: El capítulo 1, es un capítulo de fundamentos donde se presentan los conceptos fundamentales necesarios para que el lector, aunque no posea una gran base en óptica formadora de imagen, pueda entender los planteamientos y resultados que se presentan en el resto de capítulos El capitulo 2 aborda el problema de la optimización de sistemas ópticos, donde se presenta el método SMS como una herramienta idónea para obtener un punto de partida para el proceso de optimización. Mediante un ejemplo aplicado se demuestra la importancia del punto de partida utilizado en la solución final encontrada. Además en este capítulo se presentan diferentes técnicas que permiten la interpolación y optimización de las superficies obtenidas a partir de la aplicación del SMS. Aunque en esta tesis se trabajará únicamente utilizando el SMS2D, se presenta además un método para la interpolación y optimización de las nubes de puntos obtenidas a partir del SMS3D basado en funciones de base radial (RBF). En el capítulo 3 se presenta el diseño, fabricación y medidas de un objetivo catadióptrico panorámico diseñado para trabajar en la banda del infrarrojo lejano (8-12 μm) para aplicaciones de vigilancia perimetral. El objetivo presentado se diseña utilizando el método SMS para tres frentes de onda de entrada utilizando cuatro superficies. La potencia del método de diseño utilizado se hace evidente en la sencillez con la que este complejo sistema se diseña. Las imágenes presentadas demuestran cómo el prototipo desarrollado cumple a la perfección su propósito. El capítulo 4 aborda el problema del diseño de sistemas ópticos ultra compactos, se introduce el concepto de sistemas multicanal, como aquellos sistemas ópticos compuestos por una serie de canales que trabajan en paralelo. Este tipo de sistemas resultan particularmente idóneos para él diseño de sistemas afocales. Se presentan estrategias de diseño para sistemas multicanal tanto monocromáticos como policromáticos. Utilizando la novedosa técnica de diseño que en este capítulo se presenta el diseño de un telescopio de seis aumentos y medio. En el capítulo 5 se presenta una generalización del método SMS para rayos meridianos. En este capítulo se presenta el algoritmo que debe utilizarse para el diseño de cualquier sistema óptico de focal fija. La denominada optimización fase 1 se vi introduce en el algoritmo presentado de forma que mediante el cambio de las condiciones iníciales del diseño SMS que, aunque el diseño se realice para rayos meridianos, los rayos skew tengan un comportamiento similar. Para probar la potencia del algoritmo desarrollado se presenta un conjunto de diseños con diferente número de superficies. La estabilidad y potencia del algoritmo se hace evidente al conseguirse por primera vez el diseño de un sistema de seis superficies diseñado por SMS. vii Abstract The design of optical systems, considered an art by some and a science by others, has been developed for centuries. Imaging optical systems have been evolving since Ancient Egyptian times, as have design techniques. Nevertheless, the most important developments in design techniques have taken place over the past 50 years, in part due to the advances in manufacturing techniques and the development of increasingly powerful computers, which have enabled the fast and efficient calculation and analysis of ray tracing through optical systems. This has led to the design of optical systems evolving from designs developed solely from paraxial optics to modern designs created by using different multiparametric optimization techniques. The main problem the designer faces is that the different optimization techniques require an initial design which can set possible solutions as a starting point. In other words, if the starting point is far from the global minimum or optimal design for the set conditions, the final design may be a local minimum close to the starting point and far from the global minimum. This type of problem has led to the development of global optimization systems which are increasingly less sensitive to the starting point of the optimization process. Even though it is possible to obtain good designs from these types of techniques, many attempts are necessary to reach the desired solution. This is because of the uncertain environment due to the fact that there is no guarantee that the optimal solution will be obtained. The Simultaneous Multiple Surfaces (SMS) method, designed as a tool to calculate anidolic concentrators, has also proved useful for the design of image-forming optical systems, although until now it has occasionally been used for the design of imaging systems. This thesis aims to present the SMS method as a technique that can be used in general for the design of any optical system, whether with a fixed focal or an afocal with a defined magnification, and also as a tool that can be commercialized to help designers in the design of complex optical systems. The thesis is divided into five chapters. Chapter 1 establishes the basics by presenting the fundamental concepts which the reader needs to acquire, even if he/she doesn‟t have extensive knowledge in the field viii of image-forming optics, in order to understand the steps taken and the results obtained in the following chapters. Chapter 2 addresses the problem of optimizing optical systems. Here the SMS method is presented as an ideal tool to obtain a starting point for the optimization process. The importance of the starting point for the final solution is demonstrated through an example. Additionally, this chapter introduces various techniques for the interpolation and optimization of the surfaces obtained through the application of the SMS method. Even though in this thesis only the SMS2D method is used, we present a method for the interpolation and optimization of clouds of points obtained though the SMS3D method, based on radial basis functions (RBF). Chapter 3 presents the design, manufacturing and measurement processes of a catadioptric panoramic lens designed to work in the Long Wavelength Infrared (LWIR) (8-12 microns) for perimeter surveillance applications. The lens presented is designed by using the SMS method for three input wavefronts using four surfaces. The powerfulness of the design method used is revealed through the ease with which this complex system is designed. The images presented show how the prototype perfectly fulfills its purpose. Chapter 4 addresses the problem of designing ultra-compact optical systems. The concept of multi-channel systems, such as optical systems composed of a series of channels that work in parallel, is introduced. Such systems are especially suitable for the design of afocal systems. We present design strategies for multichannel systems, both monochromatic and polychromatic. A telescope designed with a magnification of six-and-a-half through the innovative technique exposed in this chapter is presented. Chapter 5 presents a generalization of the SMS method for meridian rays. The algorithm to be used for the design of any fixed focal optics is revealed. The optimization known as phase 1 optimization is inserted into the algorithm so that, by changing the initial conditions of the SMS design, the skew rays have a similar behavior, despite the design being carried out for meridian rays. To test the power of the developed algorithm, a set of designs with a different number of surfaces is presented. The stability and strength of the algorithm become apparent when the first design of a system with six surfaces if obtained through the SMS method.