Instabilities in the nonsymmetric theory of gravitation

We consider the linearized nonsymmetric theory of gravitation (NGT) within the background of an expanding universe and near a Schwarzschild metric. We show that the theory always develops instabilities unless the linearized nonsymmetric lagrangian reduces to a particular simple form. This theory contains a gauge invariant kinetic term, a mass term for the antisymmetric metric-field and a coupling with the Ricci curvature scalar. This form cannot be obtained within NGT. Next we discuss NGT beyond linearized level and conjecture that the instabilities are not a relic of the linearization, but are a general feature of the full theory. Finally we show that one cannot add ad-hoc constraints to remove the instabilities as is possible with the instabilities found in NGT by Clayton.Comment: 29 page

Arithmetic coding revisited

Over the last decade, arithmetic coding has emerged as an important compression tool. It is now the method of choice for adaptive coding on multisymbol alphabets because of its speed, low storage requirements, and effectiveness of compression. This article describes a new implementation of arithmetic coding that incorporates several improvements over a widely used earlier version by Witten, Neal, and Cleary, which has become a de facto standard. These improvements include fewer multiplicative operations, greatly extended range of alphabet sizes and symbol probabilities, and the use of low-precision arithmetic, permitting implementation by fast shift/add operations. We also describe a modular structure that separates the coding, modeling, and probability estimation components of a compression system. To motivate the improved coder, we consider the needs of a word-based text compression program. We report a range of experimental results using this and other models. Complete source code is available

Abelian Anomalies in Nonlocal Regularization

Nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the barrier to quantizing the fully gauged chiral invariant theory, and consequences.Comment: 21 pages, UTPT-93-0

The Resolvent Average for Positive Semidefinite Matrices

We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given