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

Model-independent bounds for the potential and kinetic energy of liquid 4He at zero temperature

Using the experimental values of the chemical potentials of liquid 4He and of a 3He impurity in liquid 4He, we derive a model-independent lower (upper) bound to the kinetic (potential) energy per particle at zero temperature. The values of the bounds at the experimental saturation density are 13.42 K for the kinetic energy and -20.59 K for the potential energy. All the theoretical calculations based on the Lennard-Jones potential violate the upper-bound condition for the potential energy.

Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Discriminant ECOC: a heuristic method for application dependent design of error correcting output codes

We present a heuristic method for learning error correcting output codes matrices based on a hierarchical partition of the class space that maximizes a discriminative criterion. To achieve this goal, the optimal codeword separation is sacrificed in favor of a maximum class discrimination in the partitions. The creation of the hierarchical partition set is performed using a binary tree. As a result, a compact matrix with high discrimination power is obtained. Our method is validated using the UCI database and applied to a real problem, the classification of traffic sign images.

Subclass problem-dependent design for error-correcting output codes

A common way to model multiclass classification problems is by means of Error-Correcting Output Codes (ECOCs). Given a multiclass problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each subgroup of classes from each binary problem. However, we cannot guarantee that a linear classifier model convex regions. Furthermore, nonlinear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multiclass classification problems using subclass information in the ECOC framework. Complex problems are solved by splitting the original set of classes into subclasses and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceal the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

Les cegueses del coneixement: l'error i la il·lusió a partir de "El cónsul de sodoma"

Podeu consultar el document complet de la "XVI Setmana de Cinema Formatiu" a: http://hdl.handle.net/2445/22523

Subjetividad humana y "error" en la filosofía cartesiana

El presente trabajo, continuando la línea investigadora acerca de las nociones derazón, conciencia y subjetividad en Descartes, tal como se ha defendido en otros artículos ya publicados, aporta un nuevo argumento a una línea de trabajo previamente iniciada, poniendo de relieve que el problema gnoseológico del error viene condicionado por la misma noción cartesiana de racionalidad, y que ésta dista mucho de lo que tradicionalmente se ha entendido como una racionalidad abstracta y formal, libre de los imperativos humanos. Por otro lado, y a la inversa, también se intenta mostrar como el hecho del error contribuye, cartesianamente hablando, a definir un modelo de racionalidad profundamentehumanizada. El artículo, tras una introducción, se propone analizar las relaciones entre los conceptos básicos de racionalidad, dogma, y naturaleza, lo que permitirá a continuación dejar constancia de la copertenencia entre racionalidad y error, para acabar viendo como la libertad humana es la vez, y para ambos, su fundamento último.

Coocurrencia entre ansiedad y autismo: Las hipótesis del error social y de la carga alostática

Introducción. El concepto de comorbilidad en trastornos del neurodesarrollo como el autismo resulta, en ocasiones, ambiguo. La coocurrencia entre ansiedad y autismo es clínicamente signifi cativa; sin embargo, no siempre es fácil diferenciar si se trata de una comorbilidad"real", donde las dos condiciones comórbidas son fenotípica y etiológicamente idénticas a lo que supondría dicha ansiedad en personas con un desarrollo neurotípico; si se trata de una ansiedad fenotípicamente alterada por los procesos patogénicos de los trastornos del espectro autista, resultando en una variante específica de éstos, o si partimos de una comorbilidad falsa derivada de diagnósticos diferenciales poco exactos. Desarrollo. El artículo plantea dos hipótesis explicativas de dicha coocurrencia, que se retroalimentan entre sí y que no dejan de ser una refl exión en voz alta partiendo de las evidencias científi cas con las que contamos. La primera es la hipótesis del"error social", y considera que el desajuste en el comportamiento social de las personas con autismofruto de alteraciones en los procesos de cognición social contribuye a exacerbar la ansiedad en el autismo. La segunda hipótesis, la de la carga alostática, defi ende que la ansiedad es la respuesta a un estrés crónico, al desgaste o agotamiento que produce la hiperactivación de ciertas estructuras del sistema límbico. Conclusiones. Las manifestaciones prototípicas de la ansiedad presentes en la persona con autismo no siempre se relacionan con las mismas variables biopsicosociales evidenciadas en personas sin autismo. Las evidencias apuntan a respuestas hiperreactivas de huida o lucha (hipervigilancia) cuando la persona se encuentra fuera de su zona de confort, y apoyan la hipótesis del"error social" y de la descompensación del mecanismo de alostasis que permite afrontar el estrés.

Looking for Validity or Testing It? The Perils of Stepwise Regression, Extreme-Scores Analysis, Heteroscedasticity, and Measurement Error

When researchers introduce a new test they have to demonstrate that it is valid, using unbiased designs and suitable statistical procedures. In this article we use Monte Carlo analyses to highlight how incorrect statistical procedures (i.e., stepwise regression, extreme scores analyses) or ignoring regression assumptions (e.g., heteroscedasticity) contribute to wrong validity estimates. Beyond these demonstrations, and as an example, we re-examined the results reported by Warwick, Nettelbeck, and Ward (2010) concerning the validity of the Ability Emotional Intelligence Measure (AEIM). Warwick et al. used the wrong statistical procedures to conclude that the AEIM was incrementally valid beyond intelligence and personality traits in predicting various outcomes. In our re-analysis, we found that the reliability-corrected multiple correlation of their measures with personality and intelligence was up to .69. Using robust statistical procedures and appropriate controls, we also found that the AEIM did not predict incremental variance in GPA, stress, loneliness, or well-being, demonstrating the importance for testing validity instead of looking for it.

L'error com a forma de coneixement

" Has comes un error" . " Estas en un error" . " És un error votar aquest parti!" . " És un error votar" . " És un error afirmar que 2 + 3 = 9" . " És un error afirmar que és un error afirmar que 2 + 3 = 5" . " És un error afirmar que, quan dividim, sempre obtenim un nombre més petit" . " És un error que l'existencia precedeixi l'essencia" . " És un error que vulguis enganyar-me" . " És un error afirmar que a = a" ... i així fins a acomplir les il'limitades possibilitats del llenguatge. Qualsevol judici, en la mesura que té un significat, en la mesura que és assertori, és susceptible de ser erroni, de ser fals. Peró, l'error té sempre la mateixa qualitat? Us hem proposat un reguitzell d'exemples. És obvi (si excloem la mentida, que no és error, sinó mentida) que el significat d'" error" (o el seu valor) no és identic en tots els casos.

Sub- or intertrochanteric fracture following screw fixation of an intracapsular proximal femoral fracture: true complication or technical error?

PURPOSE: To review, retrospectively, the possible causes of sub- or intertrochanteric fractures after screw fixation of intracapsular fractures of the proximal femur. METHODS: Eighty-four patients with an intracapsular fracture of proximal femur were operated between 1995 and 1998 by using three cannulated 6.25 mm screws. The screws were inserted in a triangular configuration, one screw in the upper part of the femoral neck and two screws in the inferior part. Between 1999 and 2001, we use two screws proximally and one screw distally. RESULTS: In the first series, two patients died within one week after operation. Sixty-four fractures healed without problems. Four patients developed an atrophic non-union; avascular necrosis of the femoral head was found in 11 patients. Three patients (3.6%) suffered a sub- and/or intertrochanteric fracture after a mean postoperative time of 30 days, in one case without obvious trauma. In all three cases surgical revision was necessary. Between 1999 and 2001 we did not observe any fracture after screwing. CONCLUSION: Two screws in the inferior part of the femoral neck create a stress riser in the subtrochanteric region, potentially inducing a fracture in the weakened bone. For internal fixation for proximal intracapsular femoral fracture only one screw must be inserted in the inferior part of neck.

Evidence of systematic and proportional error in a widely used glucose oxidase analyser: Impact for clinical research?

Real time glycemia is a cornerstone for metabolic research, particularly when performing oral glucose tolerance tests (OGTT) or glucose clamps. From 1965 to 2009, the gold standard device for real time plasma glucose assessment was the Beckman glucose analyzer 2 (Beckman Instruments, Fullerton, CA), which technology couples glucose oxidase enzymatic assay with oxygen sensors. Since its discontinuation in 2009, today's researchers are left with few choices that utilize glucose oxidase technology. The first one is the YSI 2300 (Yellow Springs Instruments Corp., Yellow Springs, OH), known to be as accurate as the Beckman(1). The YSI has been used extensively for clinical research studies and is used to validate other glucose monitoring devices(2). The major drawback of the YSI is that it is relatively slow and requires high maintenance. The Analox GM9 (Analox instruments, London), more recent and faster, is increasingly used in clinical research(3) as well as in basic sciences(4) (e.g. 23 papers in Diabetes or 21 in Diabetologia). This article is protected by copyright. All rights reserved.

JPEG standard uniform quantization error modeling with applications to sequential and progressive operation modes

In this paper we propose a method for computing JPEG quantization matrices for a given mean square error or PSNR. Then, we employ our method to compute JPEG standard progressive operation mode definition scripts using a quantization approach. Therefore, it is no longer necessary to use a trial and error procedure to obtain a desired PSNR and/or definition script, reducing cost. Firstly, we establish a relationship between a Laplacian source and its uniform quantization error. We apply this model to the coefficients obtained in the discrete cosine transform stage of the JPEG standard. Then, an image may be compressed using the JPEG standard under a global MSE (or PSNR) constraint and a set of local constraints determined by the JPEG standard and visual criteria. Secondly, we study the JPEG standard progressive operation mode from a quantization based approach. A relationship between the measured image quality at a given stage of the coding process and a quantization matrix is found. Thus, the definition script construction problem can be reduced to a quantization problem. Simulations show that our method generates better quantization matrices than the classical method based on scaling the JPEG default quantization matrix. The estimation of PSNR has usually an error smaller than 1 dB. This figure decreases for high PSNR values. Definition scripts may be generated avoiding an excessive number of stages and removing small stages that do not contribute during the decoding process with a noticeable image quality improvement.