The fundamental group of reduced suspensions

We classify pointed spaces according to the first fundamental group of their reduced suspension. A pointed space is either of so-called totally path disconnected type or of horseshoe type. These two camps are defined topologically but a characterization is given in terms of fundamental groups. Among totally path disconnected spaces the fundamental group is shown to be a complete invariant for a notion of topological equivalence weaker than that of homeomorphism

Inverse optimal transport

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted by noise. In this paper we propose a systematic approach to infer unknown costs from noisy observations of optimal transportation plans. The algorithm requires only the ability to solve the forward optimal transport problem, which is a linear program, and to generate random numbers. It has a Bayesian interpretation, and may also be viewed as a form of stochastic optimization. We illustrate the developed methodologies using the example of international migration flows. Reported migration flow data captures (noisily) the number of individuals moving from one country to another in a given period of time. It can be interpreted as a noisy observation of an optimal transportation map, with costs related to the geographical position of countries. We use a graph-based formulation of the problem, with countries at the nodes of graphs and non-zero weighted adjacencies only on edges between countries which share a border. We use the proposed algorithm to estimate the weights, which represent cost of transition, and to quantify uncertainty in these weights

Interest rate convexity and the volatility smile

When pricing the convexity effect in irregular interest rate derivatives such as, e.g., Libor-in-arrears or CMS, one often ignores the volatility smile, which is quite pronounced in the interest rate options market. This note solves the problem of convexity by replicating the irregular interest flow or option with liquidly traded options with different strikes thereby taking into account the volatility smile. This idea is known among practitioners for pricing CMS caps. We approach the problem on a more general scale and apply the result to various examples. --interest rate options,volatility smile,convexity,,option replication

Notes on convexity and quanto adjustments for interest rates and related options

We collect simple and pragmatic exact formulae for the convexity adjustment of irregular interest rate cash flows as Libor-in-arrears or payments of a swap rate (CMS rate) at an irregular date. The results are compared with the results of an approximative approach available in the popular literature. For options on Libor-in-arrears or CMS rates like caps or binaries we derive an additional new convexity adjustment for the volatility to be used in a standard Black & Scholes model. We study the quality of the adjustments comparing the results of the approximative Black & Scholes formula with the results of an exact valuation formula. Further we investigate options to exchange interest rates which are possibly set at different dates or admit different tenors. We collect general quanto adjustments formulae for variable interest rates to be paid in foreign currency and derive valuation formulae for standard options on interest rates paid in foreign currency. --interest rate options,convexity,quanto adjustment,change of numeraire

Cross currency swap valuation

Cross currency swaps are powerful instruments to transfer assets or liabilities from one currency into another. The market charges for this a liquidity premium, the cross currency basis spread, which should be taken into account by the valuation methodology. We describe and compare two valuation methods for cross currency swaps which are based upon using two different discounting curves. The first method is very popular in practice but inconsistent with single currency swap valuation methods. The second method is consistent for all swap valuations but leads to mark-to-market values for single currency off market swaps, which can be quite different to standard valuation results. --interest rate swap,cross currency swap,basis spread

Stable isotope analysis of human hair and nail samples: the effects of storage on samples

When submitting samples for analysis, maintaining sample integrity is essential. Appropriate packaging must be used to prevent damage, contamination or loss of sample. This is particularly important for stable isotope analysis by isotope ratio mass spectrometry as this technique is capable of detecting subtle differences in isotopic composition with great precision. In a novel study, scalp hair and fingernail samples were placed in five different types of packaging, routinely used in forensic laboratories and stored for 6 weeks and 6 months. Samples were subsequently cleaned and submitted for 13C/12C, 15N/14N, 2H/1H and 18O/16O analysis. Results from 13C analysis indicate that type of packaging can cause slight changes in 13C abundance over time. Differences were noted in the 15N isotope signatures of both hair and nail samples after 6-week storage, but not after 6 months. This apparent discrepancy could be a result of the packaging not being properly sealed in the 6 weeks study. Fewer differences were noted when analyzing samples for 2H and 18O abundance

On computational irreducibility and the predictability of complex physical systems

Using elementary cellular automata (CA) as an example, we show how to coarse-grain CA in all classes of Wolfram's classification. We find that computationally irreducible (CIR) physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse-grained is irreducible and known to be a universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR

Dual two-state mean-field games

In this paper, we consider two-state mean-field games and its dual formulation. We then discuss numerical methods for these problems. Finally, we present various numerical experiments, exhibiting different behaviours, including shock formation, lack of invertibility, and monotonicity loss