The sources of Mill's views of ratiocination and induction

Steffen Ducheyne and John P. McCaskey (2014). “The Sources of Mill’s Views of Ratiocination and Induction,” in: Antis Loizides (ed.), John Stuart Mill’s ‘A System of Logic’: A Critical Guide (London, Routledge), pp. 63-8

Geometry of canonical self-similar tilings

We give several different geometric characterizations of the situation in which the parallel set $F_\epsilon$ of a self-similar set $F$ can be described by the inner $\epsilon$-parallel set $T_{-\epsilon}$ of the associated canonical tiling $\mathcal T$, in the sense of \cite{SST}. For example, $F_\epsilon=T_{-\epsilon} \cup C_\epsilon$ if and only if the boundary of the convex hull $C$ of $F$ is a subset of $F$, or if the boundary of $E$, the unbounded portion of the complement of $F$, is the boundary of a convex set. In the characterized situation, the tiling allows one to obtain a tube formula for $F$, i.e., an expression for the volume of $F_\epsilon$ as a function of $\epsilon$. On the way, we clarify some geometric properties of canonical tilings. Motivated by the search for tube formulas, we give a generalization of the tiling construction which applies to all self-affine sets $F$ having empty interior and satisfying the open set condition. We also characterize the relation between the parallel sets of $F$ and these tilings.Comment: 20 pages, 6 figure

Aggregation of Red Blood Cells: From Rouleaux to Clot Formation

Red blood cells are known to form aggregates in the form of rouleaux. This aggregation process is believed to be reversible, but there is still no full understanding on the binding mechanism. There are at least two competing models, based either on bridging or on depletion. We review recent experimental results on the single cell level and theoretical analyses of the depletion model and of the influence of the cell shape on the binding strength. Another important aggregation mechanism is caused by activation of platelets. This leads to clot formation which is life saving in the case of wound healing but also a major cause of death in the case of a thrombus induced stroke. We review historical and recent results on the participation of red blood cells in clot formation

Inflation convergence after the introduction of the Euro

Using the Johansen test for cointegration, we examine to which extent inflation rates in the Euro area have converged after the introduction of a single currency. Since the assumption of non-stationary variables represents the pivotal point in cointegration analyses we pay special attention to the appropriate identification of non-stationary inflation rates by the application of six different unit root tests. We compare two periods, the first ranging from 1993 to 1998 and the second from 1993 to 2002 with monthly observations. The Johansen test only finds partial convergence for the former period and no convergence for the latter.Unit root, Cointegration, Inflation convergence

Inflation Risk Analysis of European Real Estate Securities

The focus of this paper is the analysis of the inflation risk of European real estate securities. Following both a causal and a final understanding of risk, the analysis is twofold: First, to examine the causal influence of inflation on short- and long-term asset returns, we employ different regression approaches based on the methodology of Fama/Schwert 1977. Hedging capacities against expected inflation are found only for German open-end funds. Furthermore, different shortfall risk measures are used to study whether an investment in European real estate securities protects against a negative real return at the end of a given investment period.

Hedonic Price Indices for the Paris Housing Market

In this paper, we calculate a transaction-based price index for apartments in Paris (France). The heterogeneous character of real estate is taken into account using an hedonic model. The functional form is specified using a general Box-Cox function. The data basis covers 84 686 transactions of the housing market in 1990:01-1999:12, which is one of the largest samples ever used in comparable studies. Low correlations of the price index with stock and bond indices (first differences) indicate diversification benefits from the inclusion of real estate in a mixed asset portfolio

Kinetic induced phase transition

An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is completely eliminated and only an external field is taken into account the system offers a phase transition at a finite value of the applied field. The transition is realized due to a competition between the activation processes driven by the field and the dynamical rules for the spin-flips. The result is based on a master equation approach in a quantum formulation.Comment: 13 page

Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable

A long-standing conjecture of Lapidus claims that under certain conditions, self-similar fractal sets fail to be Minkowski measurable if and only if they are of lattice type. The theorem was established for fractal subsets of $\mathbb{R}$ by Falconer, Lapidus and v.~Frankenhuijsen, and the forward direction was shown for fractal subsets of $\mathbb{R}^d$, $d \geq 2$, by Gatzouras. Since then, much effort has been made to prove the converse. In this paper, we prove a partial converse by means of renewal theory. Our proof allows us to recover several previous results in this regard, but is much shorter and extends to a more general setting; several technical conditions appearing in previous versions of this result have now been removed.Comment: 20 pages, 6 figure

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

In a previous paper by the first two authors, a tube formula for fractal sprays was obtained which also applies to a certain class of self-similar fractals. The proof of this formula uses distributional techniques and requires fairly strong conditions on the geometry of the tiling (specifically, the inner tube formula for each generator of the fractal spray is required to be polynomial). Now we extend and strengthen the tube formula by removing the conditions on the geometry of the generators, and also by giving a proof which holds pointwise, rather than distributionally. Hence, our results for fractal sprays extend to higher dimensions the pointwise tube formula for (1-dimensional) fractal strings obtained earlier by Lapidus and van Frankenhuijsen. Our pointwise tube formulas are expressed as a sum of the residues of the "tubular zeta function" of the fractal spray in $\mathbb{R}^d$. This sum ranges over the complex dimensions of the spray, that is, over the poles of the geometric zeta function of the underlying fractal string and the integers $0,1,...,d$. The resulting "fractal tube formulas" are applied to the important special case of self-similar tilings, but are also illustrated in other geometrically natural situations. Our tube formulas may also be seen as fractal analogues of the classical Steiner formula.Comment: 43 pages, 13 figures. To appear: Advances in Mathematic

Minkowski measurability results for self-similar tilings and fractals with monophase generators

In a previous paper [arXiv:1006.3807], the authors obtained tube formulas for certain fractals under rather general conditions. Based on these formulas, we give here a characterization of Minkowski measurability of a certain class of self-similar tilings and self-similar sets. Under appropriate hypotheses, self-similar tilings with simple generators (more precisely, monophase generators) are shown to be Minkowski measurable if and only if the associated scaling zeta function is of nonlattice type. Under a natural geometric condition on the tiling, the result is transferred to the associated self-similar set (i.e., the fractal itself). Also, the latter is shown to be Minkowski measurable if and only if the associated scaling zeta function is of nonlattice type.Comment: 18 pages, 1 figur