Electric power distribution networks face increasing factors for power-quality (PQ) deterioration, such as distributed, renewable-energy generation units and countless high-end electronic devices loaded as controllers or in standalone... more
Electric power distribution networks face increasing factors for power-quality (PQ) deterioration, such as distributed, renewable-energy generation units and countless high-end electronic devices loaded as controllers or in standalone mode. Consequently, government regulations are issued worldwide to set up strict PQ distribution standards; the distribution grids must comply with those regulations. This situation drives research towards PQ forecasting as a crucial part of early-warning systems. However, most of the approaches in the literature disregard the big-data nature of the problem by working on small datasets. These datasets come from short-scale off-grid configurations or selected portions of a larger power grid. This article addresses a study case from a region-sized state-owned Mexican distribution grid, where the company must preserve essential PQ standards in approximately 700 distribution circuits and 150 quality-control nodes. We implemented a machine-learning pipeline...
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Experience shows that solar resource prediction is a difficult task. The available solar irradiance where a photovoltaic plant is located or is planned to be installed depends mainly on the cloud incidence at the site. This incidence of... more
Experience shows that solar resource prediction is a difficult task. The available solar irradiance where a photovoltaic plant is located or is planned to be installed depends mainly on the cloud incidence at the site. This incidence of clouds depends on the climate system of the region, which is well known to be a non-linear, chaotic, and extremely complex, for which there is no exact mathematical model. In fact, the chaos level has been determined for various time series of wind and solar irradiance, and it turns out that the chaos level of the solar time series is greater than that of the wind series. This indicates that the complexity of solar irradiance prediction is considerable. In previous works of solar irradiance prediction, using Artificial Neural Networks, it has been observed that the trained models fail to predict irradiance spikes in conditions of intermittent cloudiness. By conducting a study in this area, we have found that, for a given date, there exist a model to determine the ideal solar irradiance in any geographical location of the planet. These models, so-called clear sky models, have been taken as a reference to predict not the solar irradiance, but the amount of irradiance occluded by the clouds. That is, the difference between ideal irradiance and that measured by the weather station. The proposed model is called SolarDiff, which predicts this difference using Artificial Neural Networks. This article empirically demonstrates that the SolarDiff model exhibits better behavior than models based on direct data. The performance, as in most forecast models, is measured by quantifying the forecast error. In this case the symmetric MAPE error is used.
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The integration of photovoltaic systems (PVS) in electric vehicles (EV) increases the vehicle’s autonomy by providing an additional energy source other than the battery. However, current solar cell technology generates around 200 W for a... more
The integration of photovoltaic systems (PVS) in electric vehicles (EV) increases the vehicle’s autonomy by providing an additional energy source other than the battery. However, current solar cell technology generates around 200 W for a 1.4 m2 panel (to be installed on the roof of the EV) at stable irradiance conditions. This limitation in production and the sudden changes in irradiance produced by shadows of clouds, buildings, and other structures make developing a fast and efficient maximum power point tracking (MPPT) technique in this area necessary. This article proposes an artificial neural network (ANN)-based MPPT, called DS-ANN, that uses manufacturer datasheet parameters as inputs to the network to address this problem. The Bayesian backpropagation-regularization performs the training, ensuring that the MPPT technique operates satisfactorily on different PVS without retraining. We simulated the response of 20 commercial modules against actual irradiance data to validate the...
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It has been shown that the emotional state of students has an important relationship with learning; for instance, engaged concentration is positively correlated with learning. This paper proposes the Inductive Control (IC) for educational... more
It has been shown that the emotional state of students has an important relationship with learning; for instance, engaged concentration is positively correlated with learning. This paper proposes the Inductive Control (IC) for educational games. Unlike conventional approaches that only modify the game level, the proposed technique also induces emotions in the player for supporting the learning process. This paper explores a fuzzy system that analyzes the players' performance and their emotional state for controlling the level and aesthetic content of an educational video game. The emotional state of the player is recognized through voice analysis. A total of 20 subjects played a video game designed to practice basic math skills; for each trial, a student plays two times in a row the same game but each time the game was controlled by one of the two approaches ---Dynamic Difficulty Adjustment (DDA) and IC, the playing order was assigned randomly. Results show that when the propose...
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ABSTRACT The design of models for time series prediction has found a solid foundation on statistics. Recently, artificial neural networks have been a good choice as approximators to model and forecast time series. Designing a neural... more
ABSTRACT The design of models for time series prediction has found a solid foundation on statistics. Recently, artificial neural networks have been a good choice as approximators to model and forecast time series. Designing a neural network that provides a good approximation is an optimization problem. Given the many parameters to choose from in the design of a neural network, the search space in this design task is enormous. When designing a neural network by hand, scientists can only try a few of them, selecting the best one of the set they tested. In this paper we present a hybrid approach that uses evolutionary computation to produce a complete design of a neural network for modeling and forecasting time series. The resulting models have proven to be better than the ARIMA models produced by a statistical analysis procedure and than hand-made artificial neural networks.
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Calcium signaling is an intensively studied area, which establishes calcium ion (Ca2+) as a key player in the control of cell's basic functions. Calcium is a highly versatile intracellular signal present throughout the cell's life... more
Calcium signaling is an intensively studied area, which establishes calcium ion (Ca2+) as a key player in the control of cell's basic functions. Calcium is a highly versatile intracellular signal present throughout the cell's life cycle as birth, life, and death, regulating many cellular functions. In this work, we study a mathematical model previously reported called Standard Kinetics (SK), which tries to explain the apparent paradox in ryanodine receptors (RyR) driven calcium release from the sarcoplasmic reticulum (SR), where the relation between free and total calcium concentration in the SR is calculated according to the basic chemical reaction for Ca2+ buffering proposed by Nobel Prize Erwin Neher. We prove the generalization of the SK model by identifying the model parameters with Differential Evolution (DE) solving a bi-objective function to fit simultaneously and independently the recording of the two states variables representing the intracellular calcium concentration [Ca2+]i and the Ca2+ level in the SR in smooth muscle cells (SMC).
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Breast cancer is one of the leading causes of death in women. Temperature measurement by means of thermography has several advantages; It is non-invasive, non-destructive and it is profitable. The measurement of breast temperature by... more
Breast cancer is one of the leading causes of death in women. Temperature measurement by means of thermography has several advantages; It is non-invasive, non-destructive and it is profitable. The measurement of breast temperature by infrared thermography is useful for detecting changes in blood perfusion that may occur due to inflammation, angiogenesis or other pathological causes. In this work, 206 thermograms of patients with suspected breast cancer were analyzed, using a classification method, in which thermal asymmetries were calculated. The most vascularized areas of each breast were extracted and compared; these two metrics were then added to obtain a thermal score, indicative of thermal anomalies. The classification method based on this thermal score allowed us to evaluate the effectiveness of the test, obtaining a sensitivity of 100%, specificity of 68.68%; a positive predictive value of 11.42% and a negative predictive value of 100%. These results highlight the potential o...
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In this paper, we present a framework for performing incremental design in the domain of linear circuits (Kerr 1977 ; Lancaster 1974 ; Walton 1987) . By incremental design, we mean the modification of an existing design to meet additional... more
In this paper, we present a framework for performing incremental design in the domain of linear circuits (Kerr 1977 ; Lancaster 1974 ; Walton 1987) . By incremental design, we mean the modification of an existing design to meet additional design goals while not denying certain design constraints . We start with a given circuit and want to modify aspects of its behavior while not changing others . Through means-ends search, we add components to the circuit to achieve the desired behavior without violating given constraints . The means-ends solution is based on a constraint-based model derived from circuit theory . A given design problem is first solved in terms of a qualitative model of the circuit . The framework we present is also capable of determining numerical values of parameters associated with the components added by the design process . This is accomplished by using the operating conditions of the circuit as input and the values of the parameters as output and running our co...
DiagnosisofLinearCircuitsJuanFloresFacultaddeIngenieriaElectricaUniversidadMichoacanaMorelia,Michoacan,58030juanf@zeus.ccu.umich.mxABSTRACTThequalitativereasoningcommunityhasstud-iedandmo deledelectricalcircuitssinceearly80's[13 ,3... more
DiagnosisofLinearCircuitsJuanFloresFacultaddeIngenieriaElectricaUniversidadMichoacanaMorelia,Michoacan,58030juanf@zeus.ccu.umich.mxABSTRACTThequalitativereasoningcommunityhasstud-iedandmo deledelectricalcircuitssinceearly80's[13 ,3 ,14 ,4,9].Also,thediagnosiscommunity,hasdevelop edseveraltechniquesfordiagnosisofelectricalcircuits,ofdi erentsortsandunderdif-ferentconditions[2 ,12 ,1,5,6,10 ].ThesystemIampresentinginthispap erp erformsdiagnosisanddesignoflinearcircuitsinsinusoidalsteadystate.Diagnosiscanb eseenasthepro cessofmea-surementinterpretation,wherethecircuitisob-servedandtheobservationscomparedtoitswork-ingmo del.If,atanytime,wedetectinconsis-tencyinitsb ehavior,wecantellthereisap ossi-blefaultandpro ceedtodiagnosethecircuit.Thecircuit'sworkingmo delrepresentsthesetofvalidb ehaviorsforthecircuitunderworkingcondi-tions.Thismo delispro ducedbyourcircuitsolverQPA(aconstraintbasedcircuitsolver)[8].Faultsarefoundbyapplyingasetofrulestoeachcomp onentorclusterinthecircuit.Un...
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Load forecasting provides essential information for engineers and operators of an electric system. Using the forecast information, an electric utility company’s engineers make informed decisions in critical scenarios. The deregulation of... more
Load forecasting provides essential information for engineers and operators of an electric system. Using the forecast information, an electric utility company’s engineers make informed decisions in critical scenarios. The deregulation of energy industries makes load forecasting even more critical. In this article, the work we present, called Nearest Neighbors Load Forecasting (NNLF), was applied to very short-term load forecasting of electricity consumption at the national level in Mexico. The Energy Control National Center (CENACE—Spanish acronym) manages the National Interconnected System, working in a Real-Time Market system. The forecasting methodology we propose provides the information needed to solve the problem known as Economic Dispatch with Security Constraints for Multiple Intervals (MISCED). NNLF produces forecasts with a 15-min horizon to support decisions in the following four electric dispatch intervals. The hyperparameters used by Nearest Neighbors are tuned using Di...
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Aromatic compounds have been hydrogenated in water using recoverable catalysts based on water-soluble platinum nanoparticles capped with NHC ligands.
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En este artículo presentamos el Algoritmo Combinación Lineal de Imágenes con Ventanas Variables (CLI-VV) para la fusión de imágenes multi-foco. A diferencia del Algoritmo CLI-S presentado en un trabajo anterior, el algoritmo CLI-VV... more
En este artículo presentamos el Algoritmo Combinación Lineal de Imágenes con Ventanas Variables (CLI-VV) para la fusión de imágenes multi-foco. A diferencia del Algoritmo CLI-S presentado en un trabajo anterior, el algoritmo CLI-VV permite determinar automáticamente el tamaño óptimo de la ventana en cada píxel para la segmentación de las regiones con la mayor nitidez. También presentamos la generalizado el Algoritmo CLI-VV para la fusión de conjuntos de imágenes multi-foco con más de dos imágenes. A este nuevo algoritmo lo denominamos Fusión Multi-foco con Ventanas Variables (FM-VV). El Algoritmo CLI-VV se probó con 21 pares de imágenes sintéticas y 29 pares de imágenes multi-foco reales, y el Algoritmo FM-VV sobre 5 tríos de imágenes multi-foco. En todos los ejemplos se obtuvo un porcentaje de acierto competitivos, producidos en tiempos de ejecución menores a los reportados en la literatura.
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Computer Science and Art
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This article presents a comparison of wind speed forecasting techniques, starting with the Auto-regressive Integrated Moving Average, followed by Artificial Intelligence-based techniques. The objective of this article is to compare these... more
This article presents a comparison of wind speed forecasting techniques, starting with the Auto-regressive Integrated Moving Average, followed by Artificial Intelligence-based techniques. The objective of this article is to compare these methods and provide readers with an idea of what method(s) to apply to solve their forecasting needs. The Artificial Intelligence-based techniques included in the comparison are Nearest Neighbors (the original method, and a version tuned by Differential Evolution), Fuzzy Forecasting, Artificial Neural Networks (designed and tuned by Genetic Algorithms), and Genetic Programming. These techniques were tested against twenty wind speed time series, obtained from Russian and Mexican weather stations, predicting the wind speed for 10 days, one day at a time. The results show that Nearest Neighbors using Differential Evolution outperforms the other methods. An idea this article delivers to the reader is: what part of the history of the time series to use a...
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The synthesis of metal nanoparticles (NPs) under controlled conditions in water remains a challenge in nanochemistry. Two different approaches to obtain platinum NPs, which involve the treatment of aqueous solutions of preformed... more
The synthesis of metal nanoparticles (NPs) under controlled conditions in water remains a challenge in nanochemistry. Two different approaches to obtain platinum NPs, which involve the treatment of aqueous solutions of preformed sulfonated (NHC)Pt(ii) dimethyl complexes with carbon monoxide, and of (NHC)Pt(0) diolefin complexes with dihydrogen (NHC = N-heterocyclic carbene), are disclosed here. The resulting NPs were found to be highly stable in water under air for an indefinite time period. Coordination of the NHC ligands to the platinum surface via the carbenic carbon was monitored by solid-state NMR spectroscopy, and the presence of a platinum-carbon bond was unambiguously evidenced by the determination of aC-Pt coupling constant (1106 and 1050 Hz for NPs containingC labeled-NHC ligands and prepared under CO and H, respectively). The coordination of CO to the (NHC)Pt(ii) precursors prior to formation of the NPs was confirmed by NMR spectroscopy. When using a disulfonated NHC liga...
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Efficient management of a drinking water network reduces the economic costs related to water production and transport (pumping). Model predictive control (MPC) is nowadays a quite well-accepted approach for the efficient management of the... more
Efficient management of a drinking water network reduces the economic costs related to water production and transport (pumping). Model predictive control (MPC) is nowadays a quite well-accepted approach for the efficient management of the water networks because it allows formulating the control problem in terms of the optimization of the economic costs. Therefore, short-term forecasts are a key issue in the performance of MPC applied to water distribution networks. However, the short-term horizon demand forecast in a horizon of 24 hours in an hourly based scale presents some challenges as the water consumption can change from one day to another, according to certain patterns of behavior (e.g., holidays and business days). This paper focuses on the problem of forecasting water demand for the next 24 hours. In this work, we propose to use a bank of models instead of a single model. Each model is designed for forecasting one particular hour. Hourly models use artificial neural networks...
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Noise is ubiquitous in the production of time series; we cannot assume that our source data is clean, data is always (most of the time) contaminated with noise. Noise may come from different sources: measuring devices, transmission means,... more
Noise is ubiquitous in the production of time series; we cannot assume that our source data is clean, data is always (most of the time) contaminated with noise. Noise may come from different sources: measuring devices, transmission means, etc. This article presents an analysis and comparison of how the presence of noise affects different forecasting techniques. Since chaotic time series are the most difficult to predict, we base our study on this kind of time series. Furthermore, there exist several small mathematical models that exhibit chaotic behavior. We can produce clean data by integrating those models over time. We then add noise at different levels of Noise to Signal Ratios, and measure the performance of the models produced by different forecasting techniques. The forecasting techniques included in this comparison are Nearest Neighbors, Artificial Neural Networks, ARIMA, Fuzzy Neural Networks, and Nearest Neighbors combined with Differential Evolution. Among all of them, the technique that performs better and is less affected by noise is Nearest Neighbors combined with Differential Evolution.
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Pre-synthesized mono- and bis(NHC) palladium complexes have been grafted onto magnetic core/shell γ-Fe2O3/silica particles and tested as catalysts in model Suzuki-Miyaura coupling reactions. The bis(NHC) immobilized complex was found to... more
Pre-synthesized mono- and bis(NHC) palladium complexes have been grafted onto magnetic core/shell γ-Fe2O3/silica particles and tested as catalysts in model Suzuki-Miyaura coupling reactions. The bis(NHC) immobilized complex was found to be a robust catalyst that can operate under mild conditions in aqueous media, even for the activation of chloroarene, whereas the mono(NHC) counterpart rapidly deactivates. Moreover, it can be readily recovered by magnetic separation and reused many times, providing very high productivities, and with so low leaching of palladium that the crude products obtained contain ≤10 ppm Pd.
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The University Course Timetabling Problem (UCTP) is a well known optimization problem. Literature reports different methods and techniques to solve it, being Evolutionary Algorithms (EA) one of the most successful. In the EA field, the... more
The University Course Timetabling Problem (UCTP) is a well known optimization problem. Literature reports different methods and techniques to solve it, being Evolutionary Algorithms (EA) one of the most successful. In the EA field, the selection of the best algorithm and its parameters to solve a particular problem, is a difficult problem; would be helpful to know a priori the performance related to that algorithm. Fitness Landscape Analysis (FLA) is a set of tools to describe optimization problems and for the prediction of the performance related with EA. FLA uses a set of metrics to characterize the landscape depicted by a cost function, aiming to understand the behaviour of search algorithms. This work presents an empirical study to characterize some instances of UCTP, and for the prediction of difficulty exhibited by Real-Coded Genetic Algorithms (RCGA) to solve the instances. We used FLA as characterization schema; neutrality, ruggedness, and negative slope coefficient are the metrics used in the analysis. To test and validate the proposal, we use three UCTP instances based on Mexican universities. Incipient results suggest an correlation between the negative slope coefficient and the difficulty exhibited by RCGA in the solution of UCTP instances. Ruggedness and neutrality provide the global structure of the instances’s landscape.
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An application of a nonlinear simple filter in a Multi-Model Predictor based on the decomposition of its qualitative and quantitative components is proposed. We propose a filter that increases the prediction accuracy when a nonlinear... more
An application of a nonlinear simple filter in a Multi-Model Predictor based on the decomposition of its qualitative and quantitative components is proposed. We propose a filter that increases the prediction accuracy when a nonlinear structure is found in the residuals of the qualitative component. The residuals are the mismatch between the real and the predicted qualitative component of the time series. The information given by these residuals is used to find unmodeled structures to correct a new prediction. The proposed implementation is applied to predict the next 24 hours ahead of hourly water demand for control purposes.
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In this work we compare the performance of Repair Heuristics using Genetic Algorithms (GA) results of the solution to the Circle Packing Problem to a set of unit circle problems. The Circle Packing Problem consists of placing a set of... more
In this work we compare the performance of Repair Heuristics using Genetic Algorithms (GA) results of the solution to the Circle Packing Problem to a set of unit circle problems. The Circle Packing Problem consists of placing a set of circles into a larger containing circle without overlaps, this problem is known to be NP-hard. Given the impossibility to solve this problem efficiently, traditional and metaheuristic methods have been proposed to solve it. A naive representation for chromosomes in a population-based heuristic search leads to high probabilities of violation of the problem constraints. To convert solutions that violate constraints into ones that do not, in this paper we propose and compare three repair heuristics (Repulsion, Delaunay Triangulation-"DT" and Hybrid) that lead the circles to positions where the overlaps are resolved. The experiments show that the Delaunay Triangulation-based repair can produce better solutions than the other two repair heuristics. Further, the Delaunay Triangulation has the lowest computational complexity of the three heuristics proposed.
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Novel water-soluble (NHC)Pt(0)(1,6-diene) complexes are presented, along with details of their preparation, stability, and use as catalysts for the hydrosilylation of acetylenes in water.
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How does sovereign debt emerge and become sustainable? This paper provides a new answer to this unsolved puzzle. Focusing on the early 19th century, we argue that intermediaries' market power served to overcome information asymmetries... more
How does sovereign debt emerge and become sustainable? This paper provides a new answer to this unsolved puzzle. Focusing on the early 19th century, we argue that intermediaries' market power served to overcome information asymmetries and sustained the development of sovereign debt. Relying on insights from corporate finance, we argue that capitalists turned to intermediaries' reputations to guide their investment strategies. The outcome was a two-tier global bond market, which was sustained by hierarchical relations among intermediaries. This novel theoretical perspective is backed by new archival evidence and empirical data that have never been gathered so far.
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We address the problem of finding the boundaries of a set of points by using a limited range-cyclic order detector. This sensor, denoted by lrcod, is able to detect nearby objects and enumerate them by their cyclic order; neither distance... more
We address the problem of finding the boundaries of a set of points by using a limited range-cyclic order detector. This sensor, denoted by lrcod, is able to detect nearby objects and enumerate them by their cyclic order; neither distance nor the angular position of each object is provided. Boundaries are important in many applications such as detecting the breakdown of networks, insufficient coverage or connectivity, abnormal functioning sensors, and virtual coordinates for routing. We studied the information space of the lrcod sensors and established their capabilities to find inner and outer boundaries. Our proposed approach uses local information to recognize points on the boundary. To discover the complete boundary we define the Right Hand Without Crossings (RHWoC) rule. We also provide a correctness proof of this rule. The experimental evaluation confirms the effectiveness to find the boundary of large sensor networks.
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This work presents a theoretical extension to the inventory model EOQ with and without production, representing all variables as fuzzy quantities. The model is compared against the classical EOQ model with and without production. In this... more
This work presents a theoretical extension to the inventory model EOQ with and without production, representing all variables as fuzzy quantities. The model is compared against the classical EOQ model with and without production. In this comparison, crisp and fuzzy data were used, and the results and conclusions were contrasted. We present the advantages of the fuzzy theory vs. classical theory in decision-making in the enterprise.
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The kNN time series forecasting method is based on a very simple idea. kNN forecasting is base on the idea that similar training samples most likely will have similar output values. One has to look for a certain number of nearest... more
The kNN time series forecasting method is based on a very simple idea. kNN forecasting is base on the idea that similar training samples most likely will have similar output values. One has to look for a certain number of nearest neighbors, according to some distance. The first idea that comes to mind when we see the nearest neighbor time series forecasting technique is to weigh the contribution of the different neighbors according to distance to the present observation. The fuzzy version of the nearest neighbor time series forecasting technique implicitly weighs the contribution of the different neighbors to the prediction, using the fuzzy membership of the linguistic terms as a kind of distance to the current observation. The training phase compiles all different scenarios of what has been observed in the time series’ past as a set of fuzzy rules. When we encounter a new situation and need to predict the future outcome, just like in normal fuzzy inference systems, the current observation is fuzzyfied, the set of rules is traversed to see which ones of them are activated (i.e., their antecedents are satisfied) and the outcome of the forecast is defuzzyfied by the common center of gravity rule.
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There is a great interest in the Genetic Programming (GP) community to develop semantic genetic operators. Most recent approaches includes the genetic programming framework for symbolic regression called Error Space Alignment GP, the... more
There is a great interest in the Genetic Programming (GP) community to develop semantic genetic operators. Most recent approaches includes the genetic programming framework for symbolic regression called Error Space Alignment GP, the geometric semantic operators, and our previous work the semantic crossover based on the partial derivative error. To the best of our knowledge, there has not been a semantic genetic operator similar to the point mutation. In this contribution, we start filling this gap by proposing a semantic point mutation based on the derivative of the error. This novel operator complements our previous semantic crossover and, as the results show, there is an improvement in performance when this novel operator is used, and, furthermore, the best performance in our setting is the system that uses the semantic crossover and the semantic point mutation.
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ABSTRACT A bifurcation occurs in a dynamic system when the structure of the system itself and therefore also its qualitative behavior change as a result of changes in one of the system’s parameters. In most cases, an infinitesimal change... more
ABSTRACT A bifurcation occurs in a dynamic system when the structure of the system itself and therefore also its qualitative behavior change as a result of changes in one of the system’s parameters. In most cases, an infinitesimal change in one of the parameters make the dynamic system exhibit dramatic changes. In this paper, we present a framework (QRBD) for performing qualitative analysis of dynamic systems exhibiting bifurcations. QRBD performs a simulation of the system with bifurcations, in the presence of perturbations, producing accounts for all events in the system, given a qualitative description of the changes it undergoes. In such a sequence of events, we include catastrophic changes due to perturbations and bifurcations, and hysteresis. QRBD currently works with first-order systems with only one varying parameter. We propose the qualitative representations and algorithm that enable us to reason about the changes a dynamic system undergoes when exhibiting bifurcations, in the presence of perturbations.
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El objetivo de este trabajo fue evaluar el efecto de la inoculacion de Pinus pinea, con las bacterias PGPRs Bacillus licheniformis y Bacillus pumilus, en combinacion con la ectomicorriza Pisolithus tinctorius sobre parametros biometricos... more
El objetivo de este trabajo fue evaluar el efecto de la inoculacion de Pinus pinea, con las bacterias PGPRs Bacillus licheniformis y Bacillus pumilus, en combinacion con la ectomicorriza Pisolithus tinctorius sobre parametros biometricos de las plantas y actividad biologica rizosferica. La produccion de fitohormonas (auxinas y giberelinas) por parte de las PGPRs mencionadas, produjeron un incremento significativo en la superficie y longitud aerea y radical, asi como tambien el en peso seco de las plantas tratadas. Respecto a la actividad biologica rizosferica se evaluo mediante la incorporacion de 3H-timidina y 14C-Leucina, encontrandose que esta fue mayor en las plantas tratadas, debido a que las plantas inoculadas exudaron mayores cantidades de amonio, nitratos y azucares, los cuales quedan disponibles para las bacterias rizosfericas las que a su vez, intervienen en el reciclado de nutrientes.