Conservation laws, equivalence principle and forbidden radiation modes

There are standard proofs showing there can be no monopole electromagnetic radiation and no gravitational dipole radiation. We supplement these with a global topological argument for the former, and a local argument based directly on the equivalence principle for the latter

Error-tolerant Finite State Recognition with Applications to Morphological Analysis and Spelling Correction

Error-tolerant recognition enables the recognition of strings that deviate mildly from any string in the regular set recognized by the underlying finite state recognizer. Such recognition has applications in error-tolerant morphological processing, spelling correction, and approximate string matching in information retrieval. After a description of the concepts and algorithms involved, we give examples from two applications: In the context of morphological analysis, error-tolerant recognition allows misspelled input word forms to be corrected, and morphologically analyzed concurrently. We present an application of this to error-tolerant analysis of agglutinative morphology of Turkish words. The algorithm can be applied to morphological analysis of any language whose morphology is fully captured by a single (and possibly very large) finite state transducer, regardless of the word formation processes and morphographemic phenomena involved. In the context of spelling correction, error-tolerant recognition can be used to enumerate correct candidate forms from a given misspelled string within a certain edit distance. Again, it can be applied to any language with a word list comprising all inflected forms, or whose morphology is fully described by a finite state transducer. We present experimental results for spelling correction for a number of languages. These results indicate that such recognition works very efficiently for candidate generation in spelling correction for many European languages such as English, Dutch, French, German, Italian (and others) with very large word lists of root and inflected forms (some containing well over 200,000 forms), generating all candidate solutions within 10 to 45 milliseconds (with edit distance 1) on a SparcStation 10/41. For spelling correction in Turkish, error-tolerantComment: Replaces 9504031. gzipped, uuencoded postscript file. To appear in Computational Linguistics Volume 22 No:1, 1996, Also available as ftp://ftp.cs.bilkent.edu.tr/pub/ko/clpaper9512.ps.

The limits of conditionality and Europeanization: Turkey’s dilemmas in adopting the EU acquis on asylum

[From the introduction]. The purpose of this paper is to explore the impact of “uncertainty over ultimate membership” on Schimmelfening and Sedelmeier model of conditionality as a factor that explains Europeanization. It is with this in mind that this paper will examine the “limits of conditionality” with a particular emphasis on Turkish accession. Turkey constitutes a unique case. The prospect of Turkish membership has generated a debate in which a vocal group of actors in Europe resists eventual membership. This in turn is impacting on Turkish public policy makers cost-benefit analysis. At a time when academic interest in Turkish accession in general and Turkey’s “Europeanization” is increasing an effort to achieve a better understanding of the limits of conditionality is called for. The paper is divided into three sections. The first part offers a brief analysis of Turkey’s “Europeanization” under the influence of the EU’s political conditionality for starting accession negotiations. This was a period during which it is possible to argue that Schimmelfening and Sedelmeier “external incentive model” actually helps one to understand and explain the drastic transformation that Turkish domestic politics and foreign policy went through. The second section on the other hand focuses on how the model becomes inadequate to explain the manner in which policy makers in Turkey began to resist certain critical reforms once accession negotiations started. The paper looks in particular at the issue of asylum as a very specific area in which Turkey has to adopt EU rules and implement them. This section will offer a brief analysis of the evolution of the Turkish asylum system and show how Turkish decision makers have reached a point where they are ready to adopt EU rules and requirements but stop short of doing so. The final section attempts to demonstrate how in a very specific policy area the erosion of the EU’s credibility in respect to Turkey’s ultimate membership is actually weakening the capacity of “conditionality” to induce “rule adoption”. The paper will conclude that the uncertainty over eventual EU membership and mistrust is keeping public policy makers’ calculation of “governmental adoption costs” prohibitively high while at the same time the Turkish asylum system is itself going through a kind of “Europeanization”

Affine Dynamics with Torsion

In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schr\"{o}dinger, we construct and analyze different affine gravities based on the determinants of the Ricci tensor, the torsion tensor, the Riemann tensor and their combinations. In each case we reduce equations of motion to their simplest forms and give a detailed analysis of their solutions. Our analyses lead to the construction of the affine connection in terms of the curvature and torsion tensors. Our solutions of the dynamical equations show that the curvature tensors at different points are correlated via non-local, exponential rescaling factors determined by the torsion tensor.Comment: 25 pages, typos correcte

Optimal Column-Based Low-Rank Matrix Reconstruction

We prove that for any real-valued matrix $X \in \R^{m \times n}$, and positive integers $r \ge k$, there is a subset of $r$ columns of $X$ such that projecting $X$ onto their span gives a $\sqrt{\frac{r+1}{r-k+1}}$-approximation to best rank-$k$ approximation of $X$ in Frobenius norm. We show that the trade-off we achieve between the number of columns and the approximation ratio is optimal up to lower order terms. Furthermore, there is a deterministic algorithm to find such a subset of columns that runs in $O(r n m^{\omega} \log m)$ arithmetic operations where $\omega$ is the exponent of matrix multiplication. We also give a faster randomized algorithm that runs in $O(r n m^2)$ arithmetic operations.Comment: 8 page

On planar self-similar sets with a dense set of rotations

We prove that if $E$ is a planar self-similar set with similarity dimension $d$ whose defining maps generate a dense set of rotations, then the $d$-dimensional Hausdorff measure of the orthogonal projection of $E$ onto any line is zero. We also prove that the radial projection of $E$ centered at any point in the plane also has zero $d$-dimensional Hausdorff measure. Then we consider a special subclass of these sets and give an upper bound for the Favard length of $E(\rho)$ where $E(\rho)$ denotes the $\rho$-neighborhood of the set $E$.Comment: 16 page

How to Round Subspaces: A New Spectral Clustering Algorithm

A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different basis? In this paper, we propose a new spectral clustering algorithm. It can recover a $k$-partition such that the subspace corresponding to the span of its indicator vectors is $O(\sqrt{opt})$ close to the original subspace in spectral norm with $opt$ being the minimum possible ($opt \le 1$ always). Moreover our algorithm does not impose any restriction on the cluster sizes. Previously, no algorithm was known which could find a $k$-partition closer than $o(k \cdot opt)$. We present two applications for our algorithm. First one finds a disjoint union of bounded degree expanders which approximate a given graph in spectral norm. The second one is for approximating the sparsest $k$-partition in a graph where each cluster have expansion at most $\phi_k$ provided $\phi_k \le O(\lambda_{k+1})$ where $\lambda_{k+1}$ is the $(k+1)^{st}$ eigenvalue of Laplacian matrix. This significantly improves upon the previous algorithms, which required $\phi_k \le O(\lambda_{k+1}/k)$.Comment: Appeared in SODA 201