In what would turn out to be the twilight decades of early modern Edo, cracks appeared in the foundations of its society and politics. Scholars of Western medicine discovered that the Chinese philosophical ideas that underpinned not just scientific understanding but also morality and the political order could be wrong. The appearance of American warships at the mouth of Edo Bay in 1853 challenged the government and culminated in the signing of humiliating treaties with foreign powers, exacerbating concerns about the shogunate’s ability to govern. And two years later, the fierce Ansei earthquake depleted government coffers, further demonstrated the limits of shogunate power, and fueled popular desires for world renewal. After the Tokugawa regime was toppled in 1868, bringing an end to the early modern order and the very notion of a shogunate, Edo was renamed Tokyo and strategically remade into the capital of an emergent modern nation.

A gravitationally bound two-body system (if the two bodies are spheres of constant mass) shows simple periodic motion. We have seen that a three-body system, even if we install restrictions for computational simplicity, can show a rich variety of behaviors. Tadpole orbits, horseshoe orbits, and ZLK oscillations are just a sampling of what can happen.

Beyond the task of developing a realistic and workable propulsion system that would make interstellar travel possible and practical, there is the prior challenge of identifying an extrasolar planet that would be suitable for long-term human habitation. Any planet that is a candidate for human colonization has to satisfy a surprisingly large number of requirements stemming from the fact that human biology has evolved on Earth and nowhere else, and is therefore fit to survive only in an environment that is substantially similar to our own. As Daniel Deudney has said in his book Dark Skies, “Humans are sprung from the Earth, have never lived anywhere but on Earth, and the features of this planet have shaped every aspect of human life .… Life is not on Earth, it is of Earth.” And for that reason, a planet fit for human colonization elsewhere must be earthlike in several important respects.

Researchers proposed ever larger and yet more implausible designs for interstellar vehicles. And so in 1996, writing in the journal Nanotechnology, one Thomas L. McKendree discussed what would be possible if materials provided by molecular nanotechnology were used to build spacecraft in place of then current structural building materials such as aluminum, steel, and titanium. Molecular nanotechnology was the theoretical ability to design and build products to atomic precision. Such a technology, which does not exist as yet and might never, would allow the use of diamondoid materials that had much higher strength-to-density ratios than those that are now used to build structures. In his paper “Implications of Molecular Nanotechnology Technical Performance Parameters on Previously Defined Space System Architectures,” McKendree argued that the use of diamondoid structural materials would make possible extremely large space colonies. The classic cylindrical colony, for example, if made of diamondoid structural elements could have a radius of 461 kilometers and a length of 4,610 kilometers, or 2,865 miles.

This glycopeptide antibiotic, like vancomycin, has bactericidal activity against both aerobic and anaerobic Gram-positive bacteria: Staphylococcus aureus, including MRSA, Streptococcus spp., Listeria spp. and Clostridium spp. It is only bacteriostatic for most Enterococcus spp. It does not cause ‘red man’ syndrome through histamine release and is less nephrotoxic than vancomycin. However, due to the variation between patients, effective therapeutic levels for severe infections may not be reached for a number of days using the most commonly recommended dosage schedules. Serum monitoring of pre-dose levels can be undertaken, particularly for severe infections.

The prospect of human travel to the stars faces such an exceptionally wide and diverse assortment of obstacles, improbabilities, multiple risks, and inestimable costs, as to make any attempt to traverse the final frontier far more likely to end in tragedy than to succeed in getting human beings safely lodged on the surface of an extrasolar planet that is in all respects suitable for continued and sustained human life. There are, in general, seven separate categories of problems facing starflight: physical, biological, psychological, social, financial, ethical, and motivational. Starting with the physics of the enterprise, we have seen that none of the three icons of star travel embodies a realistic, practical, proven design that would be likely to work as advertised. Not the nuclear-powered Bernal sphere, nor the Bussard Interstellar Ramjet, nor the Project Daedalus rocket, which in any case was not even intended to carry passengers. Project Orion represented the high-watermark of deep space craziness, as many project members themselves realized afterward. As Freeman Dyson acknowledged much later, “We really were a bit insane, thinking that all these things would work.”

This chapter presents the theory of mixed-integer convex optimization, i.e., minimizing a convex function subject to convex constraints where some of the decision variables have to take integer values. State-of-the-art results on information and algorithmic complexity of mixed-integer convex optimization are established. The basics of continuous convex optimization are presented as the special case where no variable is integer constrained.

Information complexity of classical continuous optimization has been well understood since the 1970s. The information complexity in the presence of integer variables was not well developed until research work done in the past decade and is covered in complete detail here. On the algorithmic side, the best known upper bound of $2^{n\log(n)}$ on the complexity of deterministic algorithms for convex integer optimization is presented, which does not appear outside specialized, technical research articles. Moreover, a general mixed-integer complexity bound allowing for both integer and continuous variables is presented that does not explicitly appear anywhere in the literature. A complete theory of branch-and-cut methods is also covered.