The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

An empirical test of the gravity p-median model

A customer is presumed to gravitate to a facility by the distance to it and the attractiveness of it. However regarding the location of the facility, the presumption is that the customer opts for the shortest route to the nearest facility.This paradox was recently solved by the introduction of the gravity p-median model. The model is yet to be implemented and tested empirically. We implemented the model in an empirical problem of locating locksmiths, vehicle inspections, and retail stores ofv ehicle spare-parts, and we compared the solutions with those of the p-median model. We found the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Superspace approach to the renormalization of the O'Raifeartaigh model up to the second order in the linear delta expansion parameter

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The STATFLUX code: a statistical method for calculation of flow and set of parameters, based on the Multiple-Compartment Biokinetical Model

The code STATFLUX, implementing a new and simple statistical procedure for the calculation of transfer coefficients in radionuclide transport to animals and plants, is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. Flow parameters were estimated by employing two different least-squares procedures: Derivative and Gauss-Marquardt methods, with the available experimental data of radionuclide concentrations as the input functions of time. The solution of the inverse problem, which relates a given set of flow parameter with the time evolution of concentration functions, is achieved via a Monte Carlo Simulation procedure.Program summaryTitle of program: STATFLUXCatalogue identifier: ADYS_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYS_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer for which the program is designed and others on which it has been tested: Micro-computer with Intel Pentium III, 3.0 GHzInstallation: Laboratory of Linear Accelerator, Department of Experimental Physics, University of São Paulo, BrazilOperating system: Windows 2000 and Windows XPProgramming language used: Fortran-77 as implemented in Microsoft Fortran 4.0. NOTE: Microsoft Fortran includes non-standard features which are used in this program. Standard Fortran compilers such as, g77, f77, ifort and NAG95, are not able to compile the code and therefore it has not been possible for the CPC Program Library to test the program.Memory, required to execute with typical data: 8 Mbytes of RAM memory and 100 MB of Hard disk memoryNo. of bits in a word: 16No. of lines in distributed program, including test data, etc.: 6912No. of bytes in distributed Program, including test data, etc.: 229 541Distribution format: tar.gzNature of the physical problem: the investigation of transport mechanisms for radioactive substances, through environmental pathways, is very important for radiological protection of populations. One such pathway, associated with the food chain, is the grass-animal-man sequence. The distribution of trace elements in humans and laboratory animals has been intensively studied over the past 60 years [R.C. Pendlenton, C.W. Mays, R.D. Lloyd, A.L. Brooks, Differential accumulation of iodine-131 from local fallout in people and milk, Health Phys. 9 (1963) 1253-1262]. In addition, investigations on the incidence of cancer in humans, and a possible causal relationship to radioactive fallout, have been undertaken [E.S. Weiss, M.L. Rallison, W.T. London, W.T. Carlyle Thompson, Thyroid nodularity in southwestern Utah school children exposed to fallout radiation, Amer. J. Public Health 61 (1971) 241-249; M.L. Rallison, B.M. Dobyns, F.R. Keating, J.E. Rall, F.H. Tyler, Thyroid diseases in children, Amer. J. Med. 56 (1974) 457-463; J.L. Lyon, M.R. Klauber, J.W. Gardner, K.S. Udall, Childhood leukemia associated with fallout from nuclear testing, N. Engl. J. Med. 300 (1979) 397-402]. From the pathways of entry of radionuclides in the human (or animal) body, ingestion is the most important because it is closely related to life-long alimentary (or dietary) habits. Those radionuclides which are able to enter the living cells by either metabolic or other processes give rise to localized doses which can be very high. The evaluation of these internally localized doses is of paramount importance for the assessment of radiobiological risks and radiological protection. The time behavior of trace concentration in organs is the principal input for prediction of internal doses after acute or chronic exposure. The General Multiple-Compartment Model (GMCM) is the powerful and more accepted method for biokinetical studies, which allows the calculation of concentration of trace elements in organs as a function of time, when the flow parameters of the model are known. However, few biokinetics data exist in the literature, and the determination of flow and transfer parameters by statistical fitting for each system is an open problem.Restriction on the complexity of the problem: This version of the code works with the constant volume approximation, which is valid for many situations where the biological half-live of a trace is lower than the volume rise time. Another restriction is related to the central flux model. The model considered in the code assumes that exist one central compartment (e.g., blood), that connect the flow with all compartments, and the flow between other compartments is not included.Typical running time: Depends on the choice for calculations. Using the Derivative Method the time is very short (a few minutes) for any number of compartments considered. When the Gauss-Marquardt iterative method is used the calculation time can be approximately 5-6 hours when similar to 15 compartments are considered. (C) 2006 Elsevier B.V. All rights reserved.

Applying a new methodology to verify transmission line model performance - the equivalent impedance test

The objective of this paper is to present a methodology to analyze a transmission line model used in electromagnetic transitory simulators, called equivalent impedance test. Initially the definition of equivalent impedance reference test is shown. Soon after this methodology is applied to a transmission line model, the Quasi-Modes model. The studies were accomplished in a hypothetical non-transposed three-phase transmission fine of 440 kV. The line length is 500 km, and it was modeled through cascades of pi-circuits (with 50 pi's circuits, each with 10 km length).

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Anaerobic running capacity determined from the critical velocity model is not significantly associated with maximal accumulated oxygen deficit in army runners

Purpose: The aim of this study was to verify whether there is an association between anaerobic running capacity (ARC) values, estimated from two-parameter models, and maximal accumulated oxygen deficit (MAOD) in army runners. Methods: Eleven, trained, middle distance runners who are members of the armed forces were recruited for the study (20 ± 1 years). They performed a critical velocity test (CV) for ARC estimation using three mathematical models and an MAOD test, both tests were applied on a motorized treadmill. Results: The MAOD was 61.6 ± 5.2 mL/kg (4.1 ± 0.3 L). The ARC values were 240.4 ± 18.6 m from the linear velocity-inverse time model, 254.0 ± 13.0 m from the linear distance-time model, and 275.2 ± 9.1 m from the hyperbolic time-velocity relationship (nonlinear 2-parameter model), whereas critical velocity values were 3.91 ± 0.07 m/s, 3.86 ± 0.08 m/s and 3.80 ± 0.09 m/s, respectively. There were differences (P < 0.05) for both the ARC and the CV values when compared between velocity-inverse time linear and nonlinear 2-parameter mathematical models. The different values of ARC did not significantly correlate with MAOD. Conclusion: In conclusion, estimated ARC did not correlate with MAOD, and should not be considered as an anaerobic measure of capacity for treadmill running. © 2013 Elsevier Masson SAS. All rights reserved.

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

Development of an adequate model for verification of design safety-margins of the HTTR nuclear test facility

This work is based on the prototype High Engineering Test Reactor (HTTR) of the Japan Agency of Energy Atomic (JAEA). Its objective is to describe an adequate deterministic model to be used in the assessment of its design safety margins via damage domains. The concept of damage domain is defined and it is shown its relevance in the ongoing effort to apply dynamic risk assessment methods and tools based on the Theory of Stimulated Dynamics (TSD). To illustrate, we present results of an abnormal control rod (CR) withdrawal during subcritical condition and its comparison with results obtained by JAEA. No attempt is made yet to actually assess the detailed scenarios, rather to show how the approach may handle events of its kind

Desintegración vertical en la industria del automóvil en España: un caso de estudio = Vertical disintegration in the automotive industry in Spain: a case study

En los años recientes se ha producido un rápido crecimiento del comercio internacional en productos semielaborados que son diseñados, producidos y ensamblados en diferentes localizaciones a lo largo de diferentes países, debido principalmente a los siguientes motivos: el desarrollo de las tecnologías de la información, la reducción de los costes de transporte, la liberalización de los mercados de capitales, la armonización de factores institucionales, la integración económica regional que implica la reducción y la eliminación de las barreras al comercio, el desarrollo económico de los países emergentes, el uso de economías de escala, así como una desregulación del comercio internacional. Todo ello ha incrementado la competencia a nivel mundial en los mercados y ha posibilitado a las compañías tener más facilidad de acceso a potenciales mercados, así como a la adquisición de capacidades y conocimientos en otros países y a la realización de alianzas estratégicas internacionales con terceros, creando un entorno con mayor incertidumbre y más exigente para las compañías que componen una industria, y que tiene consecuencias directas en las operaciones de las compañías y en la organización de su producción. Las compañías, para adaptarse, ser competitivas y beneficiarse de este nuevo escenario globalizado y más competitivo, han externalizado partes del proceso productivo hacia proveedores especializados, creando un nuevo mercado intermedio que divide el proceso productivo, anteriormente integrado en las compañías que conforman una industria, entre dos conjuntos de empresas especializadas en esa industria. Dicho proceso suele ocurrir conservando la industria en que tiene lugar, los mismos servicios y productos, la tecnología empleada y las compañías originales que la conformaban previamente a la desintegración vertical. Todo ello es así debido a que es beneficioso tanto para las compañías originales de la industria como para las nuevas compañías de este mercado intermedio por diversos motivos. La desintegración vertical en una industria tiene unas consecuencias que la transforman completamente, así como la forma de operar de las compañías que la integran, incluso para aquellas que permanecen verticalmente integradas. Una de las características más importantes de esta desintegración vertical en una industria es la posibilidad que tiene una compañía de adquirir a una tercera la primera parte del proceso productivo o un bien semielaborado, que posteriormente será finalizado por la compañía adquiriente con la práctica del outsourcing; así mismo, una compañía puede realizar la primera parte del proceso productivo o un bien semielaborado, que posteriormente será finalizado por una tercera compañía con la práctica de la fragmentación. El principal objetivo de la presente investigación es el estudio de los motivos, los facilitadores, los efectos, las consecuencias y los principales factores significativos, microeconómicos y macroeconómicos, que desencadenan o incrementan la práctica de la desintegración vertical en una industria; para ello, la investigación se divide en dos líneas completamente diferenciadas: el estudio de la práctica del outsourcing y, por otro lado, el estudio de la fragmentación por parte de las compañías que componen la industria del automóvil en España, puesto que se trata de una de las industrias más desintegradas verticalmente y fragmentadas, y este sector posee una gran importancia en la economía del país. En primer lugar, se hace una revisión de la literatura existente relativa a los siguientes aspectos: desintegración vertical, outsourcing, fragmentación, teoría del comercio internacional, historia de la industria del automóvil en España y el uso de las aglomeraciones geográficas y las tecnologías de la información en el sector del automóvil. La metodología empleada en cada uno de ellos ha sido diferente en función de la disponibilidad de los datos y del enfoque de investigación: los factores microeconómicos, utilizando el outsourcing, y los factores macroeconómicos, empleando la fragmentación. En el estudio del outsourcing, se usa un índice basado en las compras externas sobre el valor total de la producción. Así mismo, se estudia su correlación y significación con las variables económicas más importantes que definen a una compañía del sector del automóvil, utilizando la técnica estadística de regresión lineal. Aquellas variables relacionadas con la competencia en el mercado, la externalización de las actividades de menor valor añadido y el incremento de la modularización de las actividades de la cadena de valor, han resultado significativas con la práctica del outsourcing. En el estudio de la fragmentación se seleccionan un conjunto de factores macroeconómicos, comúnmente usados en este tipo de investigaciones, relacionados con las principales magnitudes económicas de un país, y un conjunto de factores macroeconómicos, no comúnmente usados en este tipo de investigaciones, relacionados con la libertad económica y el comercio internacional de un país. Se emplea un modelo de regresión logística para identificar qué factores son significativos en la práctica de la fragmentación. De entre todos los factores usados en el modelo, los relacionados con las economías de escala y los costes de servicio han resultado significativos. Los resultados obtenidos de los test estadísticos realizados en el modelo de regresión logística han resultado satisfactorios; por ello, el modelo propuesto de regresión logística puede ser considerado sólido, fiable y versátil; además, acorde con la realidad. De los resultados obtenidos en el estudio del outsourcing y de la fragmentación, combinados conjuntamente con el estado del arte, se concluye que el principal factor que desencadena la desintegración vertical en la industria del automóvil es la competencia en el mercado de vehículos. Cuanto mayor es la demanda de vehículos, más se reducen los beneficios y la rentabilidad para sus fabricantes. Estos, para ser competitivos, diferencian sus productos de la competencia centrándose en las actividades que mayor valor añadido aportan al producto final, externalizando las actividades de menor valor añadido a proveedores especializados, e incrementando la modularidad de las actividades de la cadena de valor. Las compañías de la industria del automóvil se especializan en alguna o varias de estas actividades modularizadas que, combinadas con el uso de factores facilitadores como las economías de escala, las tecnologías de la información, las ventajas de la globalización económica y la aglomeración geográfica de una industria, incrementan y motivan la desintegración vertical en la industria del automóvil, desencadenando la coespecialización en dos sectores claramente diferenciados: el sector de fabricantes de vehículos y el sector de proveedores especializados. Cada uno de ellos se especializa en unas actividades y en unos productos o servicios específicos de la cadena de valor, lo cual genera las siguientes consecuencias en la industria del automóvil: se reducen los costes de transacción en los productos o servicios intercambiados; se incrementan la relación de dependencia entre fabricantes de vehículos y proveedores especializados, provocando un aumento en la cooperación y la coordinación, acelerando el proceso de aprendizaje, posibilitando a ambos adquirir nuevas capacidades, conocimientos y recursos, y creando nuevas ventajas competitivas para ambos; por último, las barreras de entrada a la industria del automóvil y el número de compañías se ven alteradas cambiando su estructura. Como futura línea de investigación, los fabricantes de vehículos tenderán a centrarse en investigar, diseñar y comercializar el producto o servicio, delegando el ensamblaje en manos de nuevos especialistas en la materia, el contract manufacturer; por ello, sería conveniente investigar qué factores motivantes o facilitadores existen y qué consecuencias tendría la implantación de los contract manufacturer en la industria del automóvil. 1.1. ABSTRACT In recent years there has been a rapid growth of international trade in semi-finished products designed, produced and assembled in different locations across different countries, mainly due to the following reasons: development of information technologies, reduction of transportation costs, liberalisation of capital markets, harmonisation of institutional factors, regional economic integration, which involves the reduction and elimination of trade barriers, economic development of emerging countries, use of economies of scale and deregulation of international trade. All these factors have increased competition in markets at a global level and have allowed companies to gain easier access to potential markets and to the acquisition of skills and knowledge in other countries, as well as to the completion of international strategic alliances with third parties, thus creating a more demanding and uncertain environment for these companies constituting an industry, which has a direct impact on the companies' operations and the organization of their production. In order to adapt, be competitive and benefit from this new and more competitive global scenario, companies have outsourced some parts of their production process to specialist suppliers, generating a new intermediate market which divides the production process, previously integrated in the companies that made up the industry, into two sets of companies specialized in that industry. This process often occurs while preserving the industry where it takes place, its same services and products, the technology used and the original companies that formed it prior to vertical disintegration. This is because it is beneficial for both the industry's original companies and the companies belonging to this new intermediate market, for various reasons. Vertical disintegration has consequences which completely transform the industry where it takes place as well as the modus operandi of the companies that are part of it, even of those who remain vertically integrated. One of the most important features of vertical disintegration of an industry is the possibility for a company to acquire from a third one the first part of the production process or a semi-finished product, which will then be finished by the acquiring company through the practice of outsourcing; also, a company can perform the first part of the production process or a semi-finish product, which will then be completed by a third company through the practice of fragmentation. The main objective of this research is to study the motives, facilitators, effects, consequences and major significant microeconomic and macroeconomic factors that trigger or increase the practice of vertical disintegration in a certain industry; in order to do so, research is divided into two completely differentiated lines: on the one hand, the study of the practise of outsourcing and, on the other, the study of fragmentation by companies constituting the automotive industry in Spain, since this is one of the most vertically disintegrated and fragmented industries and this particular sector is of major significance in this country's economy. First, a review is made of the existing literature, on the following aspects: vertical disintegration, outsourcing, fragmentation, international trade theory, history of the automobile industry in Spain and the use of geographical agglomeration and information technologies in the automotive sector. The methodology used for each of these aspects has been different depending on the availability of data and the research approach: the microeconomic factors, using outsourcing, and the macroeconomic factors, using fragmentation. In the study on outsourcing, an index is used based on external purchases in relation to the total value of production. Likewise, their significance and correlation with the major economic variables that define an automotive company are studied, using the statistical technique of linear regression. Variables related to market competition, outsourcing of lowest value-added activities and increased modularisation of the activities of the value chain have turned out to be significant with the practice of outsourcing. In the study of fragmentation, a set of macroeconomic factors commonly used for this type of research, is selected, related to the main economic indicators of a country, as well as a set of macroeconomic factors, not commonly used for this type of research, which are related to economic freedom and the international trade of a certain country. A logistic regression model is used to identify which factors are significant in the practice of fragmentation. Amongst all factors used in the model, those related to economies of scale and service costs have turned out to be significant. The results obtained from the statistical tests performed on the logistic regression model have been successful; hence, the suggested logistic regression model can be considered to be solid, reliable and versatile; likewise, it is in line with reality. From the results obtained in the study of outsourcing and fragmentation, combined with the state of the art, it is concluded that the main factor that triggers vertical disintegration in the automotive industry is competition within the vehicle market. The greater the vehicle demand, the lower the earnings and profitability for manufacturers. These, in order to be competitive, differentiate their products from the competition by focusing on those activities that contribute with the highest added value to the final product, outsourcing the lower valueadded activities to specialist suppliers, and increasing the modularity of the activities of the value chain. Companies in the automotive industry specialize in one or more of these modularised activities which, combined with the use of enabling factors such as economies of scale, information technologies, the advantages of economic globalisation and the geographical agglomeration of an industry, increase and encourage vertical disintegration in the automotive industry, triggering co-specialization in two clearly distinct sectors: the sector of vehicle manufacturers and the specialist suppliers sector. Each of them specializes in certain activities and specific products or services of the value chain, generating the following consequences in the automotive industry: reduction of transaction costs of the goods or services exchanged; growth of the relationship of dependency between vehicle manufacturers and specialist suppliers, which causes an increase in cooperation and coordination, accelerates the learning process, enables both to acquire new skills, knowledge and resources, and creates new competitive advantages for both; finally, barriers to entry the automotive industry and the number of companies are altered, changing their structure. As a future line of research, vehicle manufacturers will tend to focus on researching, designing and marketing the product or service, delegating the assembly in the hands of new specialists in the field, the contract manufacturer; for this reason, it would be useful to investigate what motivating or facilitating factors exist in this respect and what consequences would the implementation of contract manufacturers have in the automotive industry.

Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out on the citizen supercomputer Ibercivis. Upon dilution, the pure model’s first-order transition becomes of the second order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their random field Ising model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.

The Great Lakes as a test model for profile response to sea level changes /

"December 1984."