Cartesian Bicategories II

The notion of cartesian bicategory, introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories. It is shown that a cartesian bicategory is a symmetric monoidal bicategory

Online Differential Thermal Isotope Analysis of Hydration Water in Minerals by Cavity Ringdown Laser Spectroscopy.

We have developed a new method for measuring the isotopic composition (δ18O and δD) of different types of bonded water (e.g., molecular water, hydroxyl) contained in hydrated minerals by coupling a thermal gravimeter (TG) and a cavity ringdown laser spectrometer (CRDS). The method involves precisely step-heating a mineral sample, allowing the separation of the different types of waters that are released at different temperatures. Simultaneously, the water vapor evolved from the mineral sample is analyzed for oxygen and hydrogen isotopes by CRDS. Isotopic values for the separate peaks are calculated by integrating the product of the water amounts and its isotopic values, after correcting for background. We provide examples of the application of the differential thermal isotope analysis (DTIA) method to a variety of hydrous minerals and mineraloids including gypsum, clays, and amorphous silica (opal). The isotopic compositions of the total water evolved from a set of natural gypsum samples by DTIA are compared with the results of a conventional offline water extraction method followed by CRDS analysis. The results from both methods are in excellent agreement, and precisions (1σ) for δ18O (±0.12‰) and δD (±0.8‰) of the total gypsum hydration water from the DTIA method are comparable to that obtained by the offline method. A range of analytical challenges and solutions (e.g., spectroscopic interferences produced by VOCs in natural samples, isotopic exchange with structural oxygen, etc.) are discussed. The DTIA method has wide ranging applications for addressing fundamental problems across many disciplines in earth and planetary sciences, including paleoclimatology, sedimentology, volcanology, water exchange between the solid earth and hydrosphere, and water on Mars and other planetary bodies

Regulating Access to Adult Content (with Privacy Preservation)

In the physical world we have well-established mechanisms for keeping children out of adult-only areas. In the virtual world this is generally replaced by self declaration. Some service providers resort to using heavy-weight identification mechanisms, judging adulthood as a side effect thereof. Collection of identification data arguably constitutes an unwarranted privacy invasion in this context, if carried out merely to perform adulthood estimation. This paper presents a mechanism that exploits the adult's more extensive exposure to public media, relying on the likelihood that they will be able to recall details if cued by a carefully chosen picture. We conducted an online study to gauge the viability of this scheme. With our prototype we were able to predict that the user was a child 99% of the time. Unfortunately the scheme also misclassified too many adults. We discuss our results and suggest directions for future research

Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

Prediction of equilibrium isotopic fractionation of the gypsum/bassanite/water system using first-principles calculations

The stable isotopes (18O/16O, 17O/16O and 2H/1H) of structurally-bound water (also called hydration water) in gypsum (CaSO4•2H2O) and bassanite (CaSO4•0.5H2O) can be used to reconstruct the isotopic composition of paleo-waters. Understanding the variability of the isotope fractionation factors between the solution and the solid α17Omineral-water, α18Omineral-water and αDmineral-water) is crucial for applying this proxy to paleoclimatic research. Here we predict the theoretical equilibrium fractionation factors for triple oxygen and hydrogen isotopes in the gypsum-water and bassanite-water systems between 0 ⁰C and 60 ⁰C. We apply first-principles using density functional theory within the harmonic approximation. Our theoretical results for α18Ogypsum-water (1.00347±0.00037) are in agreement with previous experimental studies, whereas Dgypsum-water agrees only at temperatures above 25 ⁰C. At lower temperatures, the experimental values of αDgypsumwater are consistently higher than theoretical values (e.g. 0.9749 and 0.9782, respectively, at 3 ⁰C), which can be explained by kinetic effects that affect gypsum precipitation under laboratory conditions at low temperature. We predict that α18Obassanite-water is similar to α18Ogypsum-water in the temperature range of 0 ⁰C to 60 ⁰C. Both α18Ogypsum-water and α18Obassanite-water show a small temperature dependence of ~0.0000122 per ⁰C, which is negligible for most paleoclimate studies. The theoretical relationship between α17Ogypsumwater and α18Ogypsum-water from 0 °C to 60 °C is 0.5274±0.00063. The relationship is very insensitive to temperature (0.00002 per ⁰C). The fact that α18O values of gypsum hydration water are greater than free water (α18Ogypsum-water >1) whereas αD values of gypsum hydration water are less than free water (αDgypsum-water <1) is explained by phonon theory. We conclude that calculations from first-principles using density functional theory within the harmonic approximation can accurately predict fractionation factors between structurally-bound water of minerals and free water.ER

On three topical aspects of the N=28 isotonic chain

The evolution of single-particle orbits along the N=28 isotonic chain is studied within the framework of a relativistic mean-field approximation. We focus on three topical aspects of the N=28 chain: (a) the emergence of a new magic number at Z=14; (b) the possible erosion of the N=28 shell; and (c) the weakening of the spin-orbit splitting among low-j neutron orbits. The present model supports the emergence of a robust Z=14 subshell gap in 48Ca, that persists as one reaches the neutron-rich isotone 42Si. Yet the proton removal from 48Ca results in a significant erosion of the N=28 shell in 42Si. Finally, the removal of s1/2 protons from 48Ca causes a ~50% reduction of the spin-orbit splitting among neutron p-orbitals in 42Si.Comment: 12 pages with 5 color figure

Rigorous confidence intervals for critical probabilities

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases

Cellular automata and Lyapunov exponents

In this article we give a new definition of some analog of Lyapunov exponents for cellular automata . Then for a shift ergodic and cellular automaton invariant probability measure we establish an inequality between the entropy of the automaton, the entropy of the shift and the Lyapunov exponent