Projective Root-Locus: An Extension of Root-Locus Plot to the Projective Plane

In this paper we present an extension of the classical Root-Locus (RL) method where the points are calculated in the real projective plane instead of the conventional affine real plane; we denominate this extension of the Root-Locus as "Projective Root-Locus (PjRL)". To plot the PjRL we use the concept of "Gnomonic Projection" in order to have a representation of the projective real plane as a simi-sphere of radius one in ${\mathbb R}^3$. We will see that the PjRL reduces to the RL in the affine $XY$ plane, but also we can plot the RL onto another affine component of the projective plane, like $ZY$ affine plane for instance, to obtain what we denominate complementary plots of the conventional RL. We also show that with the PjRL the points at infinity of the RL can be computed as solutions of a set algebraic equations.Comment: 13 pages, 8 figure

Bettering Humanity through Biology

Biology is arguably referred to as the “science of the XXIth century”. This prestigious title intrinsically contains a huge responsibility. For many centuries, Biology has contributed directly or indirectly to bettering humankind, although its obvious and objective effects have only been made evident since the XIXth century. There are three main domains to which Biology has made significant contributions: Agriculture, Environment and Medicine. Several scientific disciplines connected to Biology have been involved such as Genetics (mendelian and molecular), Cell Biology, Ecology, Microbiology, and what was known for a long time as “Natural History” (today we would include these roughly within Botany and Zoology). Agronomy, a relatively recent science, has made a tremendous impact by providing knowledge on growing plants and animals, and developing new and better crops. One specific moment in time, following WW II, known as the “Green Revolution” benefitted humanity immensely, by combating hunger in countries such as India and Mexico. The “father” of the Green Revolution, Norman Borlaug, was awarded the 1970 Peace Nobel Prize for such achievements. In the XXIth century, biologists and agronomists are working hard to develop new and better crops to feed almost 8 billion people. In the medical field, the contributions are inumerable, from the discovery and development of vaccines (Jenner and Pasteur), to antibiotics (Fleming) and combatting diseases. This has increased the average life expectancy of humans from around 30-40 in the beginning of the XXth century, to a present value of around 75 (depending on the country). These achievements have been recognized by society, through dozens of Nobel Prizes in Medicine. All these successes have been made possible through Biology. In the past 30-40 years, numerous voices have been raised alerting for the environmental degradation of our planet, its land and oceans, its biomes and ecosystems. We have been depleting our planet at an incredible rate. But today, biologists and environmental scientists have the knowledge and tools to better the planet. We know how the ecosystems function and what causes harm them. There is still time, together with a strong public opinion, to halt the damage. Once again, Biology is a principal actor

Dear Students of Color

Why are we hated for the things that we cannot control? Why is the killing of a black man just another sequel? Why don’t black lives matter

Denying the Dream: How the Proposed Changes to the US Naturalization Test Would Prevent Immigrants from Becoming Citizens

This report details how (as of September 2003) efforts by the US Citizenship and Immigration Service (former Immigration and Naturalization Service) to redesign the citizenship test could threaten the aspirations of many immigrants, particularly Latinos and others with lower levels of education, to gain US citizenship

Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales

We explore the effects of a positive cosmological constant on astrophysical and cosmological configurations described by a polytropic equation of state. We derive the conditions for equilibrium and stability of such configurations and consider some astrophysical examples where our analysis may be relevant. We show that in the presence of the cosmological constant the isothermal sphere is not a viable astrophysical model since the density in this model does not go asymptotically to zero. The cosmological constant implies that, for polytropic index smaller than five, the central density has to exceed a certain minimal value in terms of the vacuum density in order to guarantee the existence of a finite size object. We examine such configurations together with effects of $\Lambda$ in other exotic possibilities, such as neutrino and boson stars, and we compare our results to N-body simulations. The astrophysical properties and configurations found in this article are specific features resulting from the existence of a dark energy component. Hence, if found in nature would be an independent probe of a cosmological constant, complementary to other observations.Comment: 23 pages, 11 figures, 2 tables. Reference added. Mon. Not. Roy. Astro. Soc in prin

Hide It or Unbundle It: A Comparison of the Antitrust Investigations Against Microsoft in the U.S. and the E.U.

[Excerpt] Microsoft Corporation, the world’s largest software company, has been facing antitrust scrutiny globally. In the U.S., after what’s been called the antitrust trial of the century, a consent decree was reached between Microsoft, the United States government, and several states, that closely resembled the litigated remedy that the remaining states received. Only Massachusetts appealed the litigated remedy, which was approved by the appeals court on June 30, 2004. In the United States, Microsoft was required to hide, but not remove, the Internet Explorer browser on the Windows Operating System. While antitrust litigation was ongoing in the United States against Microsoft, the European Union (“E.U.”) was also investigating Microsoft under E.U. antitrust law. In March, 2004, after a five year investigation, the European Union Commission fined Microsoft 497 million euros, required Microsoft to offer the Windows operating system without Windows Media Player, and required Microsoft to disclose interfaces to competitors. On December 22, 2004, the E.U.’s Court of First Instance denied Microsoft’s request for a stay of this order, and ordered Microsoft to comply; the full appeal is pending at the time of this publication. This article will examine, compare, and contrast the protracted antitrust litigation that Microsoft has faced in the U.S. and the E.U. This article will then examine what further antitrust problems Microsoft may be facing