Tate (co)homology via pinched complexes

For complexes of modules we study two new constructions, which we call the pinched tensor product and the pinched Hom. They provide new methods for computing Tate homology and Tate cohomology, which lead to conceptual proofs of balancedness of Tate (co)homology for modules over associative rings. Another application we consider is in local algebra. Under conditions of vanishing of Tate (co)homology, the pinched tensor product of two minimal complete resolutions yields a minimal complete resolution.Comment: Final version; 23 pp. To appear in Trans. Amer. Math. So

Towards Python-based Domain-specific Languages for Self-reconfigurable Modular Robotics Research

This paper explores the role of operating system and high-level languages in the development of software and domain-specific languages (DSLs) for self-reconfigurable robotics. We review some of the current trends in self-reconfigurable robotics and describe the development of a software system for ATRON II which utilizes Linux and Python to significantly improve software abstraction and portability while providing some basic features which could prove useful when using Python, either stand-alone or via a DSL, on a self-reconfigurable robot system. These features include transparent socket communication, module identification, easy software transfer and reliable module-to-module communication. The end result is a software platform for modular robots that where appropriate builds on existing work in operating systems, virtual machines, middleware and high-level languages.Comment: Presented at DSLRob 2011 (arXiv:1212.3308

On the Distribution of Random variables corresponding to Musielak-Orlicz norms

Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\| x \|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\mapsto tM'(t) - M(t)$ to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\ell_p$-norm by an arbitrary $N$-norm. This complements some deep results obtained by Gordon, Litvak, Sch\"utt, and Werner. We also prove a result in the spirit of their work which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces

Kim Emigh, Worldcom Whistleblower - A Case Study In Accounting Ethics At Worldcom

About two weeks before internal auditors at WorldCom began questioning capital expense adjustments, the Fort Worth Weekly (cite below) published the story of Kim Emigh, who was fired for questioning inappropriate accounting practices at WorldCom. The article first caught the attention of Mark Abide, the director of property accounting at WorldCom. On May 21, Mr. Abide forwarded the article to Glyn Smith on the internal audit staff, with a note saying that the allegations of the accounting misdeeds by Emigh were ‘worth looking into’ (Krim 2002). The internal auditing team, headed by Cynthia Cooper, met on May 29 to discuss the article and the results of a recent audit concerning overcharges by a group of contractors. At that meeting, the auditors focused on manipulations to the company\u27s capital expenses. The internal audit team resolved to make tracking down the adjustments a top priority. … Within a month the auditors had discovered that $3.9 billion in operating costs were improperly accounted for as capital expenses\u27\u27 (Malone 2002). Later, in a comment to the Fort Worth Weekly, Mr. Emigh is quoted as saying It\u27s a pretty amazing world. It just shows that a little bit of determination and standing up for what\u27s right can accomplish more than I ever imagined\u27\u27 (Malone 2002)

The generating hypothesis for the stable module category of a pp-group

Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C_2 or C_3. We also give various conditions which are equivalent to the generating hypothesis.Comment: 6 pages, fixed minor typos, to appear in J. Algebr

Isotropic magnetometry with simultaneous excitation of orientation and alignment CPT resonances

Atomic magnetometers have very high absolute precision and sensitivity to magnetic fields but suffer from a fundamental problem: the vectorial or tensorial interaction of light with atoms leads to "dead zones", certain orientations of magnetic field where the magnetometer loses its sensitivity. We demonstrate a simple polarization modulation scheme that simultaneously creates coherent population trapping (CPT) in orientation and alignment, thereby eliminating dead zones. Using $^{87}$Rb in a 10 Torr buffer gas cell we measure narrow, high-contrast CPT transparency peaks in all orientations and also show absence of systematic effects associated with non-linear Zeeman splitting.Comment: 4 pages, 4 figure