Enumeration of PLCP-orientations of the 4-cube

The linear complementarity problem (LCP) provides a unified approach to many problems such as linear programs, convex quadratic programs, and bimatrix games. The general LCP is known to be NP-hard, but there are some promising results that suggest the possibility that the LCP with a P-matrix (PLCP) may be polynomial-time solvable. However, no polynomial-time algorithm for the PLCP has been found yet and the computational complexity of the PLCP remains open. Simple principal pivoting (SPP) algorithms, also known as Bard-type algorithms, are candidates for polynomial-time algorithms for the PLCP. In 1978, Stickney and Watson interpreted SPP algorithms as a family of algorithms that seek the sink of unique-sink orientations of $n$-cubes. They performed the enumeration of the arising orientations of the $3$-cube, hereafter called PLCP-orientations. In this paper, we present the enumeration of PLCP-orientations of the $4$-cube.The enumeration is done via construction of oriented matroids generalizing P-matrices and realizability classification of oriented matroids.Some insights obtained in the computational experiments are presented as well

New simplified molecular design for functional T cell receptor

We have produced a chimeric single-chain T cell receptor (TcR) that combines the specific antibody recognition function and TcR/CD3 signaling properties within the same polypeptide chain. This hybrid molecule consisted of a single-chain antibody combining site that was connected over a short spacer to the transmembrane and cytoplasmic region of CD3. When expressed on TcR- or TcR+ T cell hybridomas it could mediate recognition of relevent target cells and subsequent production of lymphokines; i.e. it could functionally replace the TcR/CD3 complex. Therefore, the single-chain TcR model presented here represents an interesting and useful means for the creation of T cells with new specificities

Combinatorial Characterizations of K-matrices

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids. As an application, we show that a simple principal pivot method applied to the linear complementarity problems with K-matrices converges very quickly, by a purely combinatorial argument.Comment: 17 pages; v2, v3: clarified proof of Thm 5.5, minor correction

Counting Unique-Sink Orientations

Unique-sink orientations (USOs) are an abstract class of orientations of the n-cube graph. We consider some classes of USOs that are of interest in connection with the linear complementarity problem. We summarise old and show new lower and upper bounds on the sizes of some such classes. Furthermore, we provide a characterisation of K-matrices in terms of their corresponding USOs.Comment: 13 pages; v2: proof of main theorem expanded, plus various other corrections. Now 16 pages; v3: minor correction

Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors

One of the most relevant weather regimes in the midlatitude atmosphere is the persistent deviation from the approximately zonally symmetric jet stream leading to the emergence of so-called blocking patterns. Such configurations are usually connected to exceptional local stability properties of the flow which come along with an improved local forecast skills during the phenomenon. It is instead extremely hard to predict onset and decay of blockings. Covariant Lyapunov Vectors (CLVs) offer a suitable characterization of the linear stability of a chaotic flow, since they represent the full tangent linear dynamics by a covariant basis which explores linear perturbations at all time scales. Therefore, we assess whether CLVs feature a signature of the blockings. As a first step, we examine the CLVs for a quasi-geostrophic beta-plane two-layer model in a periodic channel baroclinically driven by a meridional temperature gradient ΔT. An orographic forcing enhances the emergence of localized blocked regimes. We detect the blocking events of the channel flow with a Tibaldi-Molteni scheme adapted to the periodic channel. When blocking occurs, the global growth rates of the fastest growing CLVs are significantly higher. Hence, against intuition, the circulation is globally more unstable in blocked phases. Such an increase in the finite time Lyapunov exponents with respect to the long term average is attributed to stronger barotropic and baroclinic conversion in the case of high temperature gradients, while for low values of ΔT, the effect is only due to stronger barotropic instability. In order to determine the localization of the CLVs we compare the meridionally averaged variance of the CLVs during blocked and unblocked phases. We find that on average the variance of the CLVs is clustered around the center of blocking. These results show that the blocked flow affects all time scales and processes described by the CLVs

Ein Zwischenfall, dem Heinz Hopf 1939 in Karlsruhe ausgesetzt war

Zusammenfassung: Am 9. Januar 1939 wurde Heinz Hopf, damals ordentlicher Professor für Mathematik an der ETH in Zürich, auf der Rückreise aus Berlin in Karlsruhe von der Gestapo verhaftet und in Untersuchungshaft genommen. Die dramatischen Umstände dieser gefährlichen Verwicklung lassen sich dank der heute im Archiv der Bibliothek der ETH vorhandenen Unterlagen in großen Zügen rekonstruieren. Darunter befinden sich auch Unterlagen, die dem Archiv erst vor kurzer Zeit von Dr. Klaus Völlm zur Verfügung gestellt worden sind. Es ergibt sich daraus ein beklemmendes Bild der Umstände, in denen Personen und Institutionen damals Entscheidungen haben fällen müsse