Risk of Death

When people face the risk of death, and when they ascribe no value to their wealth post-death, they over-invest in precautions in order to reduce that risk. There are two main reasons for such over-investment. First, people under risk of death discount their risk-reduction costs by the probability of death following precautions. Second, people facing the risk of death consider the consumption of their wealth when alive to be part of their benefit from risk-reduction. From a social perspective, people\u27s wealth does not cease to exist after death. Therefore, discounting costs by the probability of death and taking into account the benefit of wealth-consumption are socially inefficient. But more interestingly, even from the perspective of the individual facing the risk of death, the investment in risk reduction is only optimal as a second-best alternative. We show that if people could contract with reverse insurers , who would inherit their assets upon death while paying them a sum of money during their lifetimes, such contracts would make the insured individuals better off and, more importantly, would align the private and the social incentives to invest in risk reduction. Furthermore, we show how the insights developed in the paper should significantly change the application of Willingness to Pay (WTP) as a criterion for valuing life. In particular, we suggest that the WTP be discounted by the ex-post probability of death and that the value of life be determined irrespective of wealth. Finally, we argue that the results derived from traditional tort models for both unilateral and bilateral accidents should be substantially revised when applied to fatal accidents. In particular, we show that in bilateral accidents, contrary to conventional wisdom, negligence and strict liability rules lead to the same inefficient equilibrium. We also demonstrate how liability rules could be modified to increase efficiency

Decreasing Liability Contracts

Like constructing a building, performance on many contracts occurs in phases. As time passes, the promisor sinks more costs into performance and less expenditure remains. For phased performance, we show that optimal liability for the breaching party decreases as the remaining costs of completing performance decrease. In brief, efficiency requires a decreasing liability contract. To implement such a contract, we recommend deducting past expenditure on incomplete performance from liability. We show that progress payment contracts, which are commonplace in some industries, are materially equivalent to decreasing liability contracts. Our analysis should prove useful for elucidating progress payment contracts and for drafting and litigating phased contracts

Radiometric temperature analysis of the Hayabusa spacecraft re-entry

Hayabusa, an unmanned Japanese spacecraft, was launched to study and collect samples from the surface of the asteroid 25143 Itokawa. In June 2010, the Hayabusa spacecraft completed it’s seven year voyage. The spacecraft and the sample return capsule (SRC) re-entered the Earth’s atmosphere over the central Australian desert at speeds on the order of 12 km/s. This provided a rare opportunity to experimentally investigate the radiative heat transfer from the shock-compressed gases in front of the sample return capsule at true-flight conditions. This paper reports on the results of observations from a tracking camera situated on the ground about 100 km from where the capsule experienced peak heating during re-entry

Distance Oracles for Time-Dependent Networks

We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes $(1+\epsilon)-$approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and $(1+\sigma)-$approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network, for any constant $\sigma > \epsilon$. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An extended abstract also appeared in the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014, track-A

Attosecond time-resolved photoelectron holography

Ultrafast strong-field physics provides insight into quantum phenomena that evolve on an attosecond time scale, the most fundamental of which is quantum tunneling. The tunneling process initiates a range of strong field phenomena such as high harmonic generation (HHG), laser-induced electron diffraction, double ionization and photoelectron holography—all evolving during a fraction of the optical cycle. Here we apply attosecond photoelectron holography as a method to resolve the temporal properties of the tunneling process. Adding a weak second harmonic (SH) field to a strong fundamental laser field enables us to reconstruct the ionization times of photoelectrons that play a role in the formation of a photoelectron hologram with attosecond precision. We decouple the contributions of the two arms of the hologram and resolve the subtle differences in their ionization times, separated by only a few tens of attoseconds

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio