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

Whose Trojan Horse? The Dynamics of Resistance Against IFRS

The introduction of International Financial Reporting Standards (“IFRS”) has been debated in the United States since at least the accounting scandals of the early 2000s. While publicly traded firms around the world are increasingly switching to IFRS, often because they are required to do so by law or by their stock exchange, the Securities Exchange Com-mission (“SEC”) seems to have become more reticent in recent years. Only foreign issuers have been permitted to use IFRS in the United States since 2007. By contrast, the EU has mandated the use of IFRS in the consolidated financial statements of publicly traded firms since 2005. In the United States, IFRS, which are promulgated by the London-based Inter-national Accounting Standards Board (“IASB”), are often seen as an at-tempt by Europeans to colonize U.S. accounting standard setting, and as an element of a foreign legal system alien to U.S. capital markets and securities law. In this article, we suggest that this perception is actually a myth, which we attempt to debunk. In fact, the introduction of IFRS in Europe, particularly Continental Europe, was far from controversial. IFRS were promoted by Anglo-Saxon jurisdictions and strongly support-ed by the United States, particularly when capital markets internationalized in the 1990s. They were—and still are—in many ways at odds with the Continental European accounting cultures of countries such as France and Germany, on whose examples we draw. In spite of the EU mandate for publicly traded firms, accounting law in these jurisdictions has still not fully absorbed IFRS; nevertheless, for now a solution that reconciles traditional and international accounting has been found. In this article, we explore the problems and resistance of IFRS in Continental Europe and seek to draw lessons for the United States. We argue that given the shared heritage of U.S. Generally Accepted Accounting Principles (“GAAP”) and IFRS as investor-oriented accounting standards, their introduction in the United States should be considerably easier than it was on the other side of the Atlantic

The role of astrocyte-secreted matricellular proteins in central nervous system development and function

Matricellular proteins, such as thrombospondins (TSPs1-4), SPARC, SPARC-like1 (hevin) and tenascin C are expressed by astrocytes in the central nervous system (CNS) of rodents. The spatial and temporal expression patterns of these proteins suggest that they may be involved in important developmental processes such as cell proliferation and maturation, cell migration, axonal guidance and synapse formation. In addition, upon injury to the nervous system the expression of these proteins is upregulated, suggesting that they play a role in tissue remodeling and repair in the adult CNS. The genes encoding these proteins have been disrupted in mice. Interestingly, none of these proteins are required for survival, and furthermore, there are no evident abnormalities at the gross anatomical level in the CNS. However, detailed analyses of some of these mice in the recent years have revealed interesting CNS phenotypes. Here we will review the expression of these proteins in the CNS. We will discuss a newly described function for thrombospondins in synapse formation in the CNS in detail, and speculate whether other matricellular proteins could play similar roles in nervous system development and function

Hybrid 3D Localization for Visible Light Communication Systems

In this study, we investigate hybrid utilization of angle-of-arrival (AOA) and received signal strength (RSS) information in visible light communication (VLC) systems for 3D localization. We show that AOA-based localization method allows the receiver to locate itself via a least squares estimator by exploiting the directionality of light-emitting diodes (LEDs). We then prove that when the RSS information is taken into account, the positioning accuracy of AOA-based localization can be improved further using a weighted least squares solution. On the other hand, when the radiation patterns of LEDs are explicitly considered in the estimation, RSS-based localization yields highly accurate results. In order to deal with the system of nonlinear equations for RSS-based localization, we develop an analytical learning rule based on the Newton-Raphson method. The non-convex structure is addressed by initializing the learning rule based on 1) location estimates, and 2) a newly developed method, which we refer as random report and cluster algorithm. As a benchmark, we also derive analytical expression of the Cramer-Rao lower bound (CRLB) for RSS-based localization, which captures any deployment scenario positioning in 3D geometry. Finally, we demonstrate the effectiveness of the proposed solutions for a wide range of LED characteristics and orientations through extensive computer simulations.Comment: Submitted to IEEE/OSA Journal of Lightwave Technology (10 pages, 14 figures

Connectivity-Driven Coherence in Complex Networks

We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the coupling function. These findings predict that in random graphs, the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree, but rather on how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.Comment: 4 pages, 2 figure

A Software-Defined Multi-Element VLC Architecture

In the modern era of radio frequency (RF) spectrum crunch, visible light communication (VLC) is a recent and promising alternative technology that operates at the visible light spectrum. Thanks to its unlicensed and large bandwidth, VLC can deliver high throughput, better energy efficiency, and low cost data communications. In this article, a hybrid RF/VLC architecture is considered that can simultaneously provide light- ing and communication coverage across a room. Considered architecture involves a novel multi-element hemispherical bulb design, which can transmit multiple data streams over light emitting diode (LED) modules. Simulations considering various VLC transmitter configurations and topologies show that good link quality and high spatial reuse can be maintained in typical indoor communication scenarios