We describe a variant of the Descartes algorithm for root isolation of polynomials with real coefficients. It is assumed that the coefficients of the polynomial can be approximated with arbitrary precision; exact computation in the field of coefficients is not required. We refer to such coefficients as bitstream coefficients. The algorithm is deterministic and has same asymptotic complexity as ...

Rene Descartes (1596-1650) stripped the sclera and choroid off the eye of an ox to perform a projection experiment onto a piece of paper. This proved that the retina initially sees an inverted image. Descartes thought of the brain as a machine with fibres running from the eyes like optical cables. These formed a rudimentary visual pathway. The inner soul within the brain then viewed the image t...

a Hôpital Européen Georges Pompidou, Paris Descartes University, Paris Sorbonne Cité, Paris, France b INSERM UMR 1138 Team 22: Information Sciences to support Personalized Medicine, Paris Descartes University, Sorbonne Paris Cité, Paris, France c Department of Radiation Medicine, Lowell General Hospital, Lowell, Massachusetts d Department of Radiation Oncology, Rutgers Cancer Institute of New J...

Sophie Mouillet-Richard* and Jean-Luc Vilotte 1 Toxicology, Pharmacology, and Cellular Signaling, Institut National de la Santé et de la Recherche Médicale Unité Mixtes de Recherche-S1124, Université Paris Descartes, Paris, France 2 Toxicology, Pharmacology, and Cellular Signaling, Sorbonne Paris Cité, Unité Mixtes de Recherche-S1124, Université Paris Descartes, Paris, France 3 Unité Mixtes de ...

APHP-Hôpital Necker-Enfants malades, Service de Maladies Infectieuses et Tropicales, Centre d’Infectiologie Necker-Pasteur, Paris, France; Université Paris Descartes, Sorbonne Paris Cité, Paris, France; IHU Imagine, Paris, France; AP-HP, Groupe Hospitalier Xavier Bichat-Claude Bernard, UF 301 Laboratoire de PharmacoToxicologie, F-75018 Paris, France; INSERM, IAME, UMR 1137, Université Paris Did...

Figure 1: An Apollonian Circle Packing Apollonius’s Theorem states that given three mutually tangent circles, there are exactly two circles which are tangent to all three. Apollonian circle packings are produced by repeating the construction of mutually tangent circles to fill all remaining spaces. A remarkable consequence of Descartes’ Theorem is if the initial four tangent circles have integr...