Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.

Symmetry-breaking in cumulative measures of shapes of polymer models.

Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.

Simultaneous estimation of indirect and interaction effects using structural equation models

Interaction effects are usually modeled by means of moderated regression analysis. Structural equation models with non-linear constraints make it possible to estimate interaction effects while correcting formeasurement error. From the various specifications, Jöreskog and Yang's(1996, 1998), likely the most parsimonious, has been chosen and further simplified. Up to now, only direct effects have been specified, thus wasting much of the capability of the structural equation approach. This paper presents and discusses an extension of Jöreskog and Yang's specification that can handle direct, indirect and interaction effects simultaneously. The model is illustrated by a study of the effects of an interactive style of use of budgets on both company innovation and performance

Modelling of non-linear viscoelastic tissues with bar elements

In this work we develop a viscoelastic bar element that can handle multiple rheo- logical laws with non-linear elastic and non-linear viscous material models. The bar element is built by joining in series an elastic and viscous bar, constraining the middle node position to the bar axis with a reduction method, and stati- cally condensing the internal degrees of freedom. We apply the methodology to the modelling of reversible softening with sti ness recovery both in 2D and 3D, a phenomenology also experimentally observed during stretching cycles on epithelial lung cell monolayers.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

Detection of Optimal Models in Parameter Space with Support Vector Machines

The paper proposes an approach aimed at detecting optimal model parameter combinations to achieve the most representative description of uncertainty in the model performance. A classification problem is posed to find the regions of good fitting models according to the values of a cost function. Support Vector Machine (SVM) classification in the parameter space is applied to decide if a forward model simulation is to be computed for a particular generated model. SVM is particularly designed to tackle classification problems in high-dimensional space in a non-parametric and non-linear way. SVM decision boundaries determine the regions that are subject to the largest uncertainty in the cost function classification, and, therefore, provide guidelines for further iterative exploration of the model space. The proposed approach is illustrated by a synthetic example of fluid flow through porous media, which features highly variable response due to the parameter values' combination.

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

A unifying approach to the empirical evaluation of asset pricing models

Two main approaches are commonly used to empirically evaluate linear factor pricingmodels: regression and SDF methods, with centred and uncentred versions of the latter.We show that unlike standard two-step or iterated GMM procedures, single-step estimatorssuch as continuously updated GMM yield numerically identical values for prices of risk,pricing errors, Jensen s alphas and overidentifying restrictions tests irrespective of the modelvalidity. Therefore, there is arguably a single approach regardless of the factors being tradedor not, or the use of excess or gross returns. We illustrate our results by revisiting Lustigand Verdelhan s (2007) empirical analysis of currency returns.

Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

Selecting statistical models to study the relationship between soybean yield and soil physical properties

Statistical models allow the representation of data sets and the estimation and/or prediction of the behavior of a given variable through its interaction with the other variables involved in a phenomenon. Among other different statistical models, are the autoregressive state-space models (ARSS) and the linear regression models (LR), which allow the quantification of the relationships among soil-plant-atmosphere system variables. To compare the quality of the ARSS and LR models for the modeling of the relationships between soybean yield and soil physical properties, Akaike's Information Criterion, which provides a coefficient for the selection of the best model, was used in this study. The data sets were sampled in a Rhodic Acrudox soil, along a spatial transect with 84 points spaced 3 m apart. At each sampling point, soybean samples were collected for yield quantification. At the same site, soil penetration resistance was also measured and soil samples were collected to measure soil bulk density in the 0-0.10 m and 0.10-0.20 m layers. Results showed autocorrelation and a cross correlation structure of soybean yield and soil penetration resistance data. Soil bulk density data, however, were only autocorrelated in the 0-0.10 m layer and not cross correlated with soybean yield. The results showed the higher efficiency of the autoregressive space-state models in relation to the equivalent simple and multiple linear regression models using Akaike's Information Criterion. The resulting values were comparatively lower than the values obtained by the regression models, for all combinations of explanatory variables.

Systematic trends in self-consistent calculations of linear quantum wires

Systematic trends in the properties of a linear split-gate heterojunction are studied by solving iteratively the Poisson and Schrödinger equations for different gate potentials and temperatures. A two-dimensional approximation is presented that is much simpler in the numerical implementation and that accurately reproduces all significant trends. In deriving this approximation, we provide a rigorous and quantitative basis for the formulation of models that assumes a two-dimensional character for the electron gas at the junction.

Do habitat suitability models reliably predict the recovery areas of threatened species?

1. Identifying those areas suitable for recolonization by threatened species is essential to support efficient conservation policies. Habitat suitability models (HSM) predict species' potential distributions, but the quality of their predictions should be carefully assessed when the species-environment equilibrium assumption is violated.2. We studied the Eurasian otter Lutra lutra, whose numbers are recovering in southern Italy. To produce widely applicable results, we chose standard HSM procedures and looked for the models' capacities in predicting the suitability of a recolonization area. We used two fieldwork datasets: presence-only data, used in the Ecological Niche Factor Analyses (ENFA), and presence-absence data, used in a Generalized Linear Model (GLM). In addition to cross-validation, we independently evaluated the models with data from a recolonization event, providing presences on a previously unoccupied river.3. Three of the models successfully predicted the suitability of the recolonization area, but the GLM built with data before the recolonization disagreed with these predictions, missing the recolonized river's suitability and badly describing the otter's niche. Our results highlighted three points of relevance to modelling practices: (1) absences may prevent the models from correctly identifying areas suitable for a species spread; (2) the selection of variables may lead to randomness in the predictions; and (3) the Area Under Curve (AUC), a commonly used validation index, was not well suited to the evaluation of model quality, whereas the Boyce Index (CBI), based on presence data only, better highlighted the models' fit to the recolonization observations.4. For species with unstable spatial distributions, presence-only models may work better than presence-absence methods in making reliable predictions of suitable areas for expansion. An iterative modelling process, using new occurrences from each step of the species spread, may also help in progressively reducing errors.5. Synthesis and applications. Conservation plans depend on reliable models of the species' suitable habitats. In non-equilibrium situations, such as the case for threatened or invasive species, models could be affected negatively by the inclusion of absence data when predicting the areas of potential expansion. Presence-only methods will here provide a better basis for productive conservation management practices.