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Automatic Detection and Correction of Multiclass Classification Errors Using System Wholepart Relationships
"... Realworld dynamic systems such as physical and atmosphereocean systems often exhibit a hierarchical systemsubsystem structure. However, the paradigm of making this hierarchical/modular structure and the rich properties they encode a “firstclass citizen” of machine learning algorithms is largely a ..."
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Realworld dynamic systems such as physical and atmosphereocean systems often exhibit a hierarchical systemsubsystem structure. However, the paradigm of making this hierarchical/modular structure and the rich properties they encode a “firstclass citizen” of machine learning algorithms is largely absent from the literature. Furthermore, traditional data mining approaches focus on designing new classifiers or ensembles of classifiers, while there is a lack of study on detecting and correcting prediction errors of existing forecasting (or classification) algorithms. In this paper, we propose DETECTOR, a hierarchical method for detecting and correcting forecast errors by employing the wholepart relationships between the target system and nontarget systems. Experimental results show that DETECTOR can successfully detect and correct forecasting errors made by stateofart classifier ensemble techniques and traditional single classifier methods at an average rate of 22%, corresponding to a 11 % average forecasting accuracy increase, in seasonal forecasting of hurricanes and landfalling hurricanes in North Atlantic and North African rainfall. 1
Analysis of a Onedimensional Variational Model of the Equilibrium Shape of a Deformable Crystal*
"... Abstract. The equilibrium con gurations of a onedimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functio ..."
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Abstract. The equilibrium con gurations of a onedimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute minimum or only a minimizing sequence in which the term corresponding to the bulk energy is forced to zero by the production of a crack in the material. Key words. Equilibrium shape, nonconvex energy functional, variational problem AMS(MOS) subject classi cations (1985 revision). Primary 49S, 73V25 1. Introduction. The morphological instabilities of interfaces is a topic of primary interest in physics (e.g., see [4]). Currently, many branches of the natural sciences, including low temperature physics, fracture, crystal growth, epitaxy of nanoscale lms, metallurgy, geology, and materials science show a rapidly growing interest in the so called stress driven rearrangement
Accepted forP ublication in the Journal of the Mechanics andPd of Solids Chemically5Vk2k swelling of hydrogels
"... considera continuum model for chemicaqH100K9qa volume tra10#K#qH in hydrogels. Consistent with experimenta observaservq the theoryaeo ws fora sha1 interfa8 sepa82q ing swelleda ndcolla99q phaa of the underlying polymer network. The polymer cha81 a trea02 a a solute witha na ssociaz0 di#usion potenti ..."
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considera continuum model for chemicaqH100K9qa volume tra10#K#qH in hydrogels. Consistent with experimenta observaservq the theoryaeo ws fora sha1 interfa8 sepa82q ing swelleda ndcolla99q phaa of the underlying polymer network. The polymer cha81 a trea02 a a solute witha na ssociaz0 di#usion potentia a nd their concentranq9 is a90zK# to be discontinuousausqz the interfa02 Inaq11DB9 to the staB2KD bulka nd interfa9#q equaz01q imposing forcebaeqz0 a nd solutebauteq1 the model involvesa supplementa interfaD0q equaD0q imposingconfiguraqH1zB force ba12DK0 We presenta hybrid eXtendedFiniteElement/LevelSet Method (XFE/LSM) forobta90#q a pproximaK solutions to the governing equa2#1q of the model. As a a1z1B1qH1BK we consider the swelling ofa spherica specimen whose bounda9 istra182qHzDKD a nd is in conta1 witha reservoir of uniform chemica potentiaz Our numerica results exhibit goodqua22qHz# e compa2KqH with experimenta observaservas predict chaD199qHz01B swelling times thaaa proportiona to the squa# of the specimen raz8#B Our resultsaul suggest severa possible synthetic pat wa ystha might be pursued to engineer hydrogels withoptima response times. Keywords: A. Hydrogels; A. Pha2 tra1BqHz18K A. Chemomecha1#81 process; B. ConfigurazzzqH forces; B.ShaD interfa9 1
Pattern Formation in Solutal Convection: Vermiculated Rolls and Isolated Cells
"... Observations of the peculiar behaviour of a drink of liqueur topped with cream led us to perform experiments showing that the instability is a convection phenomenon that arises through destabilizing surfacetension forces. The convection is solutal: driven by gradients of concentration of a solute, ..."
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Observations of the peculiar behaviour of a drink of liqueur topped with cream led us to perform experiments showing that the instability is a convection phenomenon that arises through destabilizing surfacetension forces. The convection is solutal: driven by gradients of concentration of a solute, rather than by heat gradients as in the more commonly studied thermal convection. The convective patterns, vermiculated rolls and isolated cells, are quite unlike the usual planforms. They are associated with an elastic surface film, and the Marangoni number is high, characteristic of solutal convection. We have conducted further experiments that reproduce these patterns in simpler working fluids.
Regularized Wulff Flows, Nonconvex Energies and Backwards Parabolic Equations
, 2004
"... In this paper we propose a method of regularizing the backwards parabolic partial differential equations that arise from using gradient descent to minimize surface energy integrals within a level set framework in 2 and 3 dimensions. The proposed regularization energy is a functional of the mean cu ..."
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In this paper we propose a method of regularizing the backwards parabolic partial differential equations that arise from using gradient descent to minimize surface energy integrals within a level set framework in 2 and 3 dimensions. The proposed regularization energy is a functional of the mean curvature of the surface. Our method uses a local level set technique to evolve the resulting fourth order PDEs in time. Numerical results are shown, indicating stability and convergence to the asymptotic Wulff shape.
Thermal Expansion Models of Viscous Fluids Based On Limits of Free Energy
, 2002
"... Many viscous fluid flows are mechanically incompressible, yet thermally expand and shrink. Various approximations of the compressible NavierStokes equations have been proposed to resolve the diverse phenomena that arise in such fluid systems, with a primary goal to remove rapid timescales associ ..."
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Many viscous fluid flows are mechanically incompressible, yet thermally expand and shrink. Various approximations of the compressible NavierStokes equations have been proposed to resolve the diverse phenomena that arise in such fluid systems, with a primary goal to remove rapid timescales associated with sound waves. The Boussinesq model for laboratoryscale, buoyancydriven thermal convection patterns [20] and the anelastic model for atmosphericscale, densitystratification phenomena [7] are two important examples. Molten polymer and glass flows exhibit thermal expansion where mechanical compressibility is negligible, yet selfconsistent approximate models do not exist. With this motivation, we propose a systematic method to derive thermal expansion models based on mechanical incompressibility conditions applied directly on the free energy formulation of the compressible NavierStokes system. The method is distinct from other approaches in that the irreversible physics and second law are preserved, whereas the reversible physical mechanisms governed by the gradient and Hessian of the free energy function take special forms imposed by mechanical incompressibility.
WaterRock Interactions, Ore Deposits, and Environmental Geochemistry: A Tribute to David A. Crerar © The Geochemical Society, Special Publication No. 7, 2002
"... Abstract—To investigate pressure solution creep, chalk from the Paris basin (France) was deformed in a triaxial press with fluids. Experiments were conducted either under chemically closed (no fluid flow) or chemically open (fluid flow) conditions. In all experiments, the vertical stress (σ1) and th ..."
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Abstract—To investigate pressure solution creep, chalk from the Paris basin (France) was deformed in a triaxial press with fluids. Experiments were conducted either under chemically closed (no fluid flow) or chemically open (fluid flow) conditions. In all experiments, the vertical stress (σ1) and the lateral stress (σ3) were independently controlled, with 4.0 < σ1 ≤ 8.0 MPa and σ3 = 4.0 MPa; the pore fluid pressure was ≤ 0.3 MPa. In each experiment, axial strain (ε) was recorded as a function of time; experiments ranged from 30 to almost 700 days. The major goal of this investigation was to study the physicochemical reactions that occur when chalk is deformed under different differential stresses, in the presence of various fluids, and at temperatures ranging up to 80 °C. The results show that chalk deformation is characterized by viscous behavior, based on plots of log strain rate ( ) vs. log (σ1) with slopes of 12. The chemical nature of the pore fluid also plays a critical role in determining deformation rates; the strain rates decreased in the following order: saline solution> water> propanol. Thus, strain rate correlates with calcite solubility. The dependence of on grain diameter could not be evaluated. The temperature dependence of strain rates was found to be very low, with an activation energy estimated to be ≈ 12 kJ mol1. When all rateinfluencing parameters were kept constant, the material strain hardens, according to the relation ∝ε−2−5 ˙ε ˙ε ˙ε. The exact ratelimiting step (intergranular diffusion, dissolution, or precipitation) could not be determined based on the available data.
unknown title
, 2004
"... A numerical strategy for investigating the kinetic response of stimulusresponsive hydrogels ..."
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A numerical strategy for investigating the kinetic response of stimulusresponsive hydrogels
Full Paper Gibbs ’ Paradox and the Definition of Entropy
"... Abstract: Gibbs ’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adoptin ..."
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Abstract: Gibbs ’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adopting Boltzmann’s definition of the entropy, the violation of the second law is eliminated, the properties of colloids are correctly predicted, and Gibbs ’ Paradox vanishes. Keywords: Gibbs ’ Paradox, entropy, extensivity, Boltzmann. 1.