Three implications of learning behaviour for price processes.

no abstract availableConsumers' preferences; Economics -- Psychological aspects;

Intersections on tropical moduli spaces

This article explores to which extent the algebro-geometric theory of rational descendant Gromov-Witten invariants can be carried over to the tropical world. Despite the fact that the tropical moduli-spaces we work with are non-compact, the answer is surprisingly positive. We discuss the string, divisor and dilaton equations, we prove a splitting lemma describing the intersection with a "boundary" divisor and we prove general tropical versions of the WDVV resp. topological recursion equations (under some assumptions). As a direct application, we prove that the toric varieties $\mathbb{P}^1$, $\mathbb{P}^2$, $\mathbb{P}^1 \times \mathbb{P}^1$ and with Psi-conditions only in combination with point conditions, the tropical and classical descendant Gromov-Witten invariants coincide (which extends the result for $\mathbb{P}^2$ in Markwig-Rau-2008). Our approach uses tropical intersection theory and can unify and simplify some parts of the existing tropical enumerative geometry (for rational curves).Comment: 40 pages, 17 Postscript figures; updated to fit the published versio

On the metric structure of space-time

I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a Lorentzian manifold is replaced by the weaker concept of an "event manifold", defined in terms of volume element, causal structure and affine connection(s). Exploiting properties of its structure group, I show that distinguishing Lorentzian manifolds from other classes of event manifolds requires the key idea of general relativity: namely that the manifold's physical structure, rather than being fixed, is itself a variable

Existence of graphs with sub exponential transitions probability decay and applications

In this paper, we present a complete proof of the construction of graphs with bounded valency such that the simple random walk has a return probability at time $n$ at the origin of order $exp(-n^{\alpha}),$ for fixed $\alpha \in [0,1[$ and with Folner function $exp(n^{\frac{2\alpha}{1-\alpha}})$. We begin by giving a more detailled proof of this result contained in (see \cite{ershdur}). In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on an infinite cluster on the percolation model.Comment: 46 page

Radio interferometric imaging of spatial structure that varies with time and frequency

The spatial-frequency coverage of a radio interferometer is increased by combining samples acquired at different times and observing frequencies. However, astrophysical sources often contain complicated spatial structure that varies within the time-range of an observation, or the bandwidth of the receiver being used, or both. Image reconstruction algorithms can been designed to model time and frequency variability in addition to the average intensity distribution, and provide an improvement over traditional methods that ignore all variability. This paper describes an algorithm designed for such structures, and evaluates it in the context of reconstructing three-dimensional time-varying structures in the solar corona from radio interferometric measurements between 5 GHz and 15 GHz using existing telescopes such as the EVLA and at angular resolutions better than that allowed by traditional multi-frequency analysis algorithms.Comment: 12 pages, 4 figures. SPIE Proceedings, Optical Engineering+Applications; Image Reconstruction from Incomplete Dat