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

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

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.

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

Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond

We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\rightarrow\infty$, only the conventional large-$N$ limit is relevant for its {\it continuum} limit. We also give a mean--field analysis of the $N=2$ model in {\it any} $d$ and show that a saddle point always exists in the region $m^2>m_{\rm crit}^2(=d)$. In $d=1$ it exhibits critical behaviour as $m^2\rightarrow m_{\rm crit}^2$. However when $d$$>$$1$ there is no critical behaviour unless non--Gaussian terms are added to the scalar field action. We argue that similar behaviour should occur for any finite $N$ thus providing a simple explanation of a recent result of D. Gross. We show that critical behaviour at $d$$>$$1$ and $m^2>m^2_{\rm crit}$ can be obtained by adding a $logarithmic$ term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov--Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behaviour of the Gaussian model.Comment: 31 page