The Long Road: An Analysis of the 1557 Book of Mirrors by Seydi Ali Reis

In 1552, Piri Reis was relieved from the Admiralty of the Ottoman Imperial Navy. Seydi Ali Reis was appointed to replace him and his assignment was to return fifteen galleys from Basra to Egypt. This should have been a relatively short journey. Seydi failed miserably, however. He lost most of the ships in battle with the Portuguese and bad weather, which he documents in his travelogue The Mirror of Countries. With nowhere left to turn, he sold the remaining ships in Surat on the west coast of India. To make matters worse, he took the long road home to Istanbul: a circuitous route which stretched his journey for two years. This path went as far north as Samarqand in modern Uzbekistan. The question which arises is why did Seydi take so long to return home

Rule-based Machine Learning Methods for Functional Prediction

We describe a machine learning method for predicting the value of a real-valued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision rules. A central objective of the method and representation is the induction of compact, easily interpretable solutions. This rule-based decision model can be extended to search efficiently for similar cases prior to approximating function values. Experimental results on real-world data demonstrate that the new techniques are competitive with existing machine learning and statistical methods and can sometimes yield superior regression performance.Comment: See http://www.jair.org/ for any accompanying file

Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may look like. This, then, has to be taken into account for effective equations which describe the evolution properly and can be used for further phenomenological investigations. Here, we provide the first analysis with interacting matter with new effective equations valid for weak self-interactions or small masses. They differ from the free scalar equations by crucial terms and have an important influence on the bounce and the space-time around it. Especially the role of squeezed states, which have often been overlooked in this context, is highlighted. The presence of a bounce is proven for uncorrelated states, but as squeezing is a dynamical property and may change in time, further work is required for a general conclusion.Comment: 26 page

Home Equity Insurance

Home equity insurance policies, policies insuring homeowners against declines in the price of their homes, would bear some resemblance both to ordinary insurance and to financial hedging vehicles. A menu of choices for the design of such policies is presented here, and conceptual issues are discussed. Choices include pass-through futures and options, in which the insurance company in effect serves as a retailer to homeowners of short positions in real estate futures markets or of put options on real estate. Another choice is a life-event-triggered insurance policy, in which the homeowner pays regular fixed insurance premia and is entitled to a claim if both there is a sufficient decline in the real estate price index and a specified life event (such as a move beyond a certain geographical distance) occurs. Pricing of the premia to cover loss experience is derived, and tables of break-even policy premia are shown, based on estimated models of Los Angeles housing prices 1971- 91.

Moral Hazard in Home Equity Conversion

Home equity conversion as presently constituted or proposed usually does not deal well with the potential problem of moral hazard. Once homeowners know that the risk of poor market performance of their homes is borne by investors, they have an incentive to neglect to take steps to maintain the homes' values. They may thus create serious future losses for the investors. A calibrated model for assessing this moral hazard risk is presented that is suitable for a number of home equity conversion forms: 1) reverse mortgages, 2) home equity insurance, 3) shared appreciation mortgages, 4) housing partnerships, 5) shared equity mortgages and 6) sale of remainder interest. Modifications of these forms involving real estate price indices are proposed that might deal better with the problem of moral hazard.Reverse mortgages, home equity insurance, shared appreciation mortgages, housing partnerships, shared equity mortgages, sale of remainder interest, moral hazard, real estate price indices, home maintenance, home improvements

Earth Albedo and the orbit of LAGEOS

The long-period perturbations in the orbit of the Lageos satellite due to the Earth's albedo have been found using a new analytical formalism. The Earth is assumed to be a sphere whose surface diffusely reflects sunlight according to Lambert's law. Specular reflection is not considered. The formalism is based on spherical harmonics; it produces equations which hold regardless of whether the terminator is seen by the satellite or not. Specializing to the case of a realistic zonal albedo shows that Lageos' orbital semimajor axis changes periodically by only the a few millimeters and the eccentricity by one part in 100,000. The longitude of the node increases secularly. The effect considered here can explain neither the secular decay of 1.1 mm/day in the semimajor axis nor the observed along-track variations in acceleration of order 2 x 10 to the minus 12 power/sq ms

Ground state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved rigorously that the commonly accepted leading order term of the ground state energy is correct in the zero-density-limit. Here, strong indications are given that also the next to leading term is correct. It is shown that the first terms obtained in a perturbative treatment provide contributions which are lost in the Bogoliubov approach.Comment: 6 pages, accepted for publication in Europhys. Lett. http://www.epletters.ch

The orbit of Lageos and solar eclipses

An eclipse of the Sun by the Moon as seen by the Lageos satellite can affect the orbital semimajor axis at the centimeter level. The weakened radiation pressure acting on Lageos perturbs the orbit differently from that due to full sunlight. This difference amounted to less than 2 mm in the semimajor axis for 23 of the 30 eclipses Lageos experienced between launch in 1976 and the end of 1983. However, it was 17.6 mm for the eclipses on 28 March 1979 and 11.2 mm for the one on 15 December 1982. Differences such as these generate large enough along-track errors to make it worthwhile to include eclipses in complex orbit determination programs such as GEODYN which integrate the orbit. Eclipses cannot explain the presently unmolded variations in along-track acceleration which have a magnitude of about 3 x 10(-12) ms(-2)