Did Schelling Misunderstand Fichte’s Transcendental Method?

The Fichte-Schelling Correspondence interweaves intriguing personal stories and philosophical combat. One of the sadder personal stories involves Schelling getting wind of Fichte’s remark to Friedrich Schlegel that he did not understand transcendental method. The letters document several clumsy attempts by Fichte to minimize the criticism only to have it surface again in a letter Fichte wrote to a former student, Jean Baptiste Schad, who showed the letter to Schelling. In it, Fichte claimed that Schelling understood Wissenschaftslehre no better than Friedrich Nicolai, whom Fichte had publicly excoriated for critiquing as “I-philosophy” a superficial assemblage of random quotes from mixed sources

The effect of irrigation method on the quality and shelf-life of strawberry fruit in organic production

The irrigation method did not affect either the shelf-life or the quality of fruit. In organic strawberry production grey mould is a major problem. Strawberry varieties differ from each other in disease susceptibility and the quality and shelf-life of the fruit is affected more by their properties and weather conditions than by the irrigation method

DID: Distributed Incremental Block Coordinate Descent for Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) has attracted much attention in the last decade as a dimension reduction method in many applications. Due to the explosion in the size of data, naturally the samples are collected and stored distributively in local computational nodes. Thus, there is a growing need to develop algorithms in a distributed memory architecture. We propose a novel distributed algorithm, called \textit{distributed incremental block coordinate descent} (DID), to solve the problem. By adapting the block coordinate descent framework, closed-form update rules are obtained in DID. Moreover, DID performs updates incrementally based on the most recently updated residual matrix. As a result, only one communication step per iteration is required. The correctness, efficiency, and scalability of the proposed algorithm are verified in a series of numerical experiments.Comment: Accepted by AAAI 201

Superconvergent interpolatory HDG methods for reaction diffusion equations I: An HDGk_{k} method

In our earlier work [8], we approximated solutions of a general class of scalar parabolic semilinear PDEs by an interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method. This method reduces the computational cost compared to standard HDG since the HDG matrices are assembled once before the time integration. Interpolatory HDG also achieves optimal convergence rates; however, we did not observe superconvergence after an element-by-element postprocessing. In this work, we revisit the Interpolatory HDG method for reaction diffusion problems, and use the postprocessed approximate solution to evaluate the nonlinear term. We prove this simple change restores the superconvergence and keeps the computational advantages of the Interpolatory HDG method. We present numerical results to illustrate the convergence theory and the performance of the method

Computer simulations of electrorheological fluids in the dipole-induced dipole model

We have employed the multiple image method to compute the interparticle force for a polydisperse electrorheological (ER) fluid in which the suspended particles can have various sizes and different permittivites. The point-dipole (PD) approximation being routinely adopted in computer simulation of ER fluids is shown to err considerably when the particles approach and finally touch due to multipolar interactions. The PD approximation becomes even worse when the dielectric contrast between the particles and the host medium is large. From the results, we show that the dipole-induced-dipole (DID) model yields very good agreements with the multiple image results for a wide range of dielectric contrasts and polydispersity. As an illustration, we have employed the DID model to simulate the athermal aggregation of particles in ER fluids both in uniaxial and rotating fields. We find that the aggregation time is significantly reduced. The DID model accounts for multipolar interaction partially and is simple to use in computer simulation of ER fluids.Comment: 22 pages, 7 figures, submitted to Phys. Rev.

Eigenvector Sky Subtraction

We develop a new method for estimating and removing the spectrum of the sky from deep spectroscopic observations; our method does not rely on simultaneous measurement of the sky spectrum with the object spectrum. The technique is based on the iterative subtraction of continuum estimates and Eigenvector sky models derived from Singular Value Decompositions (SVD) of sky spectra, and sky spectra residuals. Using simulated data derived from small telescope observations we demonstrate that the method is effective for faint objects on large telescopes. We discuss simple methods to combine our new technique with the simultaneous measurement of sky to obtain sky subtraction very near the Poisson limit.Comment: Accepted for publication in The Astrophysical Journal (Letters) 2000 March 7. Includes one extra figure which did not fit in a lette