Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse-engineering and a colonization-competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co-occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio-temporal samples of assemblages in homogenous environments or environmental gradients.

gems: An R Package for Simulating from Disease Progression Models

Mathematical models of disease progression predict disease outcomes and are useful epidemiological tools for planners and evaluators of health interventions. The R package gems is a tool that simulates disease progression in patients and predicts the effect of different interventions on patient outcome. Disease progression is represented by a series of events (e.g., diagnosis, treatment and death), displayed in a directed acyclic graph. The vertices correspond to disease states and the directed edges represent events. The package gems allows simulations based on a generalized multistate model that can be described by a directed acyclic graph with continuous transition-specific hazard functions. The user can specify an arbitrary hazard function and its parameters. The model includes parameter uncertainty, does not need to be a Markov model, and may take the history of previous events into account. Applications are not limited to the medical field and extend to other areas where multistate simulation is of interest. We provide a technical explanation of the multistate models used by gems, explain the functions of gems and their arguments, and show a sample application.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

Estudio experimental sobre la reacción álcali-sílice en el hormigón producida por áridos de reacción lenta

La finalidad de esta investigación se enmarca dentro de los estudios sobre hormigones de presas llevados a cabo en el Laboratorio Central de Estructuras y Materiales del CEDEX. En España se han diagnosticado 18 obras afectadas tanto por la reacción álcali-sílice de tipo rápido como por la de tipo lento. Dos de de las obras, fabricadas con áridos graníticos, no presentan signos de deterioro pero en laboratorio se han hallado productos expansivos. En las 16 presas españolas restantes, el hormigón de 10 de ellas estaba fabricado con áridos graníticos, de las cuales, 7 están afectadas por la reacción de tipo lento. Sin embargo, en las clasificaciones internacionales de las rocas potencialmente reactivas se establece habitualmente que las rocas graníticas son inocuas o de reactividad muy baja. En los casos puntuales encontrados en la literatura, la reactividad de este tipo de áridos se encuentra frecuentemente asociada al cuarzo microcristalino que contienen y ocasionalmente se asocia esta reactividad también al cuarzo deformado y/o microfisurado. En la tesis doctoral de Víctor Daniel Lanza Fernández, también realizada en el CEDEX, se han tratado los áridos de reacción rápida, dando una descripción detallada de los componentes que intervienen en este tipo de reacción y presentando un ensayo eficaz para su detección en el laboratorio. La investigación desarrollada en la presente tesis doctoral se ha centrado en los áridos de reacción lenta, mucho menos estudiados. A partir del estudio bibliográfico realizado sobre este tipo de reacción se ha detectado ciertas lagunas, basadas principalmente en la falta de un método de detección en el laboratorio para los áridos de reacción lenta. No se ha encontrado un procedimiento en el estudio petrográfico que sea fiable y cuantificable para este tipo de áridos. El ensayo acelerado de barras de mortero, que para los áridos de reacción rápida supone un método rápido y fiable, falla en la detección de los áridos de reacción lenta al aplicar los límites normalizados. Si bien en publicaciones recientes se ha propuesto la posibilidad de ampliar el tiempo de tratamiento hasta los 90 días, la duración del ensayo es más larga de lo deseado. Para resolver estas lagunas, se han tomado áridos de obras reales afectadas por la reacción álcali-sílice (en algún caso también de las canteras de donde se extrajeron los áridos para la ejecución), con lo que la reactividad de estos áridos queda demostrada por su comportamiento en obra. Al objeto de aumentar la muestra de ensayo y utilizar también áridos inocuos, se han tomado muestras de canteras, tanto en uso como abandonadas. Sobre estos áridos se ha realizado una caracterización completa con los ensayos actualmente disponibles para el estudio de su reactividad con los álcalis del cemento: estudio petrográfico, ensayo acelerado de barras de mortero y Gel-Pat modificado. En la investigación se ha desarrollado una metodología de tinción de geles álcali-sílice para la cuantificación de los mismos en el interior de las barras de mortero. Se ha relacionado el volumen de gel generado en la reacción con la expansión producida, tanto para áridos lentos, como rápidos, estableciendo analogías y diferencias en el comportamiento de ambos. La cuantificación de este tipo de compuestos realizada en las barras de mortero, abre la posibilidad de estudiar la capacidad expansiva que presentan en testigos de hormigón de obras afectadas. Este dato podría ser una herramienta importante para el desarrollo de modelos matemáticos que puedan predecir el futuro comportamiento de las estructuras afectadas por la reacción álcali-sílice. La tinción ha sido asimismo utilizada para establecer un método de detección de áridos reactivos basado en el ensayo de Gel-Pat modificado. La metodología de detección propuesta para estos áridos es cuantitativa y proporciona los resultados en 14 días, suponiendo una ventaja importante sobre los métodos actuales, que permiten detectarlos en 90 días (de forma orientativa en 56 días). This research is part of the studies on durability of concrete dams carried out in the Laboratorio Central de Estructuras y Materiales of CEDEX during the last years. At the present time, 18 public works affected by alkali-silica reaction have been diagnosed in Spain. In 12 of them the concrete was mixed with granitic aggregates, 7 of which were damaged by the slow alkali-silica reaction, 3 by the rapid alkali-silica reaction and in the other 2 cases, although there was no visual evidence of the reaction in field, the laboratory tests showed the presence of expansive products inside the concrete. However, in the international classifications of potentially reactive aggregates granitic rocks are pointed out as innocuous or as low reactivity and usually their reactivity is attributed to the presence of microcrystalline quartz and occasionally with the strained and microcracked quartz. The rapid reactive aggregates were deeply studied in a previous research (Víctor Daniel Lanza’s Thesis) also carried out in CEDEX. In this research, a detailed description of the components involved in the rapid alkali-silica reaction was given. Also, a fast method to detect them in the laboratory was developed. The research of the present PhD Thesis is focused in the slow-reactive aggregates, much less studied. The state of the art has shown some gaps in the knowledge about this reaction, mainly the absence of a reliable method to detect slow-reactive aggregates. On one side, there is no systematic and quantitative petrographic test for these aggregates. On the other side, the accelerated mortar bar test has been proved to be effective to detect rapid reactive aggregates but the standard limits fail in the detection of the slowreactive aggregates. In recent investigations it has been proposed extending the test until 90 days, but this period is considered too long. In this research, aggregates taken from affected structures have been used in the test, so their reactivity has been shown in practice. With the aim of increasing the number of samples aggregates from quarries have been also used. A method to stain alkali-silica gels has been applied to mortar bars, thereby quantifying the volume of gel generated inside. This volume has been related to the expansion of the bars, both for rapid for slow reactive aggregates, establishing similarities and differences. The quantification of the gel volume, applied to concrete cores extracted from affected structures, could be an important tool in mathematical models to predict the future behaviour of the structures affected by the alkali-silica reaction. The staining method has been also used to develop a method to detect slow reactive aggregates, based on the optimised Gel-Pat test, obtaining results in 14 days. This represents a major improvement compared to the actual methods (accelerated mortar bar test) which give an indicative value of reactivity at 56 days, and a final result at 90 days.

Two-dimensional direct rainfall hydraulic models applied to direct calculation of hydrologic events in dams to prevent overtopping

One of the main concerns when conducting a dam test is the acute determination of the hydrograph for a specific flood event. The use of 2D direct rainfall hydraulic mathematical models on a finite elements mesh, combined with the efficiency of vector calculus that provides CUDA (Compute Unified Device Architecture) technology, enables nowadays the simulation of complex hydrological models without the need for terrain subbasin and transit splitting (as in HEC-HMS). Both the Spanish PNOA (National Plan of Aereal Orthophotography) Digital Terrain Model GRID with a 5 x 5 m accuracy and the CORINE GIS Land Cover (Coordination of INformation of the Environment) that allows assessment of the ground roughness, provide enough data to easily build these kind of models

Modelización del proceso de eliminación de la contaminación de suelos con hidrocarburos mediante desorción térmica “in situ” Comprobación de Modelo

El objetivo definitivo de esta investigación es contribuir con la profundización del conocimiento en las tecnologías de remediación, específicamente las térmicas, debido a que la contaminación de suelos es motivo de preocupación por ser uno de los graves impactos ambientales que origina el hombre con sus actividades, especialmente las industriales, afectando a la salud de los seres humanos, y el medio ambiente, representando elevados costes de saneamiento y en ocasiones problemas graves de salud de las comunidades aledañas. Se establecen tres fases de investigación. En la primera se diseña el sistema de termodesorción a escala piloto, se desarrolla las corridas experimentales, la segunda con corridas en laboratorio para investigar sobre los parámetros que intervienen en el proyecto. Se hacen las corridas respectivas para determinar la eficacia del sistema, y la tercera fase que consiste en comparar los modelos teóricos de Hartley, con los de Hartley Graham –Bryce y el de Hamaker para determinar su aproximación con los resultados reales. Apoyado en investigaciones anteriores, se diseñó y construyó un sistema de desorción térmica, el cual consiste en un horno tipo caja con 4 calentadores (resistencias), y una campana con un filtro para evitar la contaminación atmosférica, así mismo, se diseñó un sistema de control que permitió hacer las corridas con 1/3 de la potencia, con una relación de encendido apagado 3:1 respectivamente. Para validar los resultados obtenidos en el estudio matemático, se compararon dos modelos con la finalidad cuál de ellos se aproxima más a la realidad, se tomaron los ensayos con sus tiempos de operación a las temperaturas y se trabajó a distintas bandas de temperaturas para verificar la fiabilidad del proceso matemático. La temperatura es un variable importante en los procesos de desorción, como los son también la humedad del suelo, pues esta va influir directamente en el tiempo de remediación, por lo que es importante tomarla en cuenta. De igual forma el tipo de suelo va influir en los resultados, siendo las arenas más aptas para este tipo de remediación. Los resultados de la modelización son presentados para temperaturas constantes, el cual difiere de la realidad, pues el proceso de calentamiento es lento y va en accenso dependiendo del contenido de humedad y de las propiedades del suelo. La experimentación realizada concluye con buenos resultados de la aplicación de sistemas de desorción de acuerdo a las variables de Panamá. Con relación al grado de cumplimiento respecto a las normativas actuales relacionadas a los límites máximos permitidos. Los resultados garantizan las posibilidades del proceso de remediación térmica de suelos contaminados con combustibles en rango de diésel, garantizando niveles aceptables de limpieza en un tiempo menor a otras metodologías no destructivas pudieran tomar. ABSTRACT The ultimate goal of this investigation is to enhance the pool of knowledge related to remediation technologies, specifically thermal desorption. The motivation for this study is based on concerns due to pollution of land as one of the most serious environmental impacts caused by anthropogenic effects, specially industrial activities, affecting human health and the environment in general, which represents high reclamation costs, and in some cases, serious health issues in nearby communities. Three phases have been established for this study. The first phase involves the design of a thermal desorption system as a pilot experiment, and associated tests. The second phase consists of laboratory testing to investigate the parameters that affect the investigation, as well as to determine the efficacy of the system. The third phase covers the comparison of theorical models as proposed by Hartley, Hartley Graham – Bryce, and Hamaker, as well as the evaluation of these models versus the laboratory results. Supported by previous researches, the thermal desorption system was designed and installed as a “box” type oven with four heaters (resistances) and one absorption hood with a filter to avoid atmospheric contamination. In the same way, a control system was designed allowing testing with 1/3 of the power, with an on/off rate of 3:1 respectively. In order to validate the results, two mathematical models were compared to identify which model is closer to the experimental results; test results were documented with respective durations and temperatures; and experiments were executed using different ranges of temperature to validate the consistency of the mathematical process. Temperature is an important variable that should be considered for the desorption processes, as well as the humidity content within the soil, that has direct influence over the required duration to achieve remediation. In the same manner, the type of soil also influences the results, where sands are more efficient for this type of remediation process. The results from this experiment are according to constant temperatures, which is not a complete representation of the reality, as the heating process is slow and the temperature gradually increases according to the humidity content and other properties of the soil. The experiment shows good results for the application of thermal desorption systems according to the variables in Panama, as well as the level of compliance required to fulfill current regulations and mandatory maximum limits. The results guarantee the possibility of soil thermo-remediation as a resource to clean sites that have been polluted with diesel-like combustibles, allowing acceptable levels in a period of time that is lower than with other non-destructive remediation technics.

Application of the dynamic models to the detection of imperfections in plate Structures

This paper is part of a set of publications related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. The first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment, particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection of the first class of imperfections, i.e. cracks and it is the object of the present paper. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With this group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally, in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present and a numerical application has been shown.

Models of immune memory: On the role of cross-reactive stimulation, competition, and homeostasis in maintaining immune memory

There has been much debate on the contribution of processes such as the persistence of antigens, cross-reactive stimulation, homeostasis, competition between different lineages of lymphocytes, and the rate of cell turnover on the duration of immune memory and the maintenance of the immune repertoire. We use simple mathematical models to investigate the contributions of these various processes to the longevity of immune memory (defined as the rate of decline of the population of antigen-specific memory cells). The models we develop incorporate a large repertoire of immune cells, each lineage having distinct antigenic specificities, and describe the dynamics of the individual lineages and total population of cells. Our results suggest that, if homeostatic control regulates the total population of memory cells, then, for a wide range of parameters, immune memory will be long-lived in the absence of persistent antigen (T1/2 > 1 year). We also show that the longevity of memory in this situation will be insensitive to the relative rates of cross-reactive stimulation, the rate of turnover of immune cells, and the functional form of the term for the maintenance of homeostasis.

Stable isotope evidence for increasing dietary breadth in the European mid-Upper Paleolithic

New carbon and nitrogen stable isotope values for human remains dating to the mid-Upper Paleolithic in Europe indicate significant amounts of aquatic (fish, mollusks, and/or birds) foods in some of their diets. Most of this evidence points to exploitation of inland freshwater aquatic resources in particular. By contrast, European Neandertal collagen carbon and nitrogen stable isotope values do not indicate significant use of inland aquatic foods but instead show that they obtained the majority of their protein from terrestrial herbivores. In agreement with recent zooarcheological analyses, the isotope results indicate shifts toward a more broad-spectrum subsistence economy in inland Europe by the mid-Upper Paleolithic period, probably associated with significant population increases.

Dynamics of maize endosperm development and DNA endoreduplication.

Endosperm development in Zea mays is characterized by a period of intense mitotic activity followed by a period in which mitosis is essentially eliminated and the cell cycle becomes one of alternating S and G phases, leading to endoreduplication of the nuclear DNA. The endosperm represents a significant contribution to the grain yield of maize; thus, methods that facilitate the study of cellular kinetics may be useful in discerning cellular and molecular components of grain yield. Two mathematical models have been developed to describe the kinetics of endosperm growth. The first describes the kinetics of mitosis during endosperm development; the second describes the kinetics of DNA endoreduplication during endosperm development. The mitotic model is a modification of standard growth curves. The endoreduplication model is composed of six differential equations that represent the progression of nuclei from one DNA content to another during the endoreduplication process. Total nuclei number per endosperm and the number of 3C, 6C, 12C, 24C, 48C, and 96C nuclei per endosperm (C is the haploid DNA content per nucleus) for inbred W64A from 8 to 18 days after pollination were determined by flow cytometry. The results indicate that the change in number of nuclei expressed as a function of the number of days after pollination is the same from one yearly crop to another. These data were used in the model to determine the endosperm growth rate, the maximum nuclei number per endosperm, and transition rates from one C value to the next higher C value. The kinetics of endosperm development are reasonably well represented by the models. Thus, the models provide a means to quantify the complex pattern of endosperm development.

USLE and WEPP Soil Erosion Models: Their Applicability and Use in Generating Cover Values to Stabilize Soil in the Los Alamos, New Mexico Area

Soil erosion is a naturally occurring process that involves the detachment, transport, and deposition of soil particles. Disturbances such as thinning and wildfire can reduce cover greatly and increase erosion rates. Forest managers may use erosion prediction tools, such as the Universal Soil Loss Equation (USLE) and Water Erosion Prediction Project (WEPP) to estimate erosion rates and develop techniques to manage erosion. However, it is important to understand the differences and the applications of each model. Erosion rates were generated by each model and the model most applicable to the study site, Los Alamos, New Mexico was determined. It was also used to find the amount of cover needed to stabilize soil. The USLE is a simpler model and less complicated than a computer model like WEPP, and thus easier to manipulate to estimate cover values. Predicted cover values were compared to field cover values. Cover is necessary to establish effective erosion control guidelines.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

Comparisons of models predicting ambient lake phosphorus concentrations /

Mode of access: Internet.

Comparison of numerical and physical hydraulic models, Masonboro Inlet, North Carolina /

"June 1977."