Implementation of complex interactions in a Cox regression framework

The standard Cox proportional hazards model has been extended by functionally describable interaction terms. The first of which are related to neural networks by adopting the idea of transforming sums of weighted covariables by means of a logistic function. A class of reasonable weight combinations within the logistic transformation is described. Apart from the standard covariable product interaction, a product of logistically transformed covariables has also been included in the analysis of performance of the new terms. An algorithm combining likelihood ratio tests and AIC criterion has been defined for model choice. The critical values of the likelihood ratio test statistics had to be corrected in order to guarantee a maximum type I error of 5% for each interaction term. The new class of interaction terms allows interpretation of functional relationships between covariables with more flexibility and can easily be implemented in standard software packages

Flat Histogram Method of Wang-Landau and N-fold Way

We present a method for estimating the density of states of a classical statistical model. The algorithm successfully combines the Wang-Landau flat histogram method with the N-fold way in order to improve efficiency of the original single spin flip version. We test our implementation of the Wang-Landau method with the two-dimensional nearest neighbor Ising model for which we determine the tunneling time and the density of states. Furthermore, we show that our new algorithm performs correctly at right edges of an energy interval over which the density of states is computed. This removes a disadvantage of the original single spin flip Wang-Landau method where results showed systematically higher errors in the density of states at right boundaries. We compare our data with the detailed numerical tests presented in a study by Wang and Swendsen where the original Wang-Landau method was tested against various other methods. Finally, we apply our method to a thin Ising film of size $32\times 32\times 6$ with antisymmetric surface fields. With the density of states obtained from the simulations we calculate canonical averages related to the energy such as internal energy, Gibbs free energy and entropy, but we also sample microcanonical averages during simulations in order to determine canonical averages of the susceptibility, the order parameter and its fourth order cumulant. We compare our results with simulational data obtained from a conventional MC algorithm.Comment: Latex, 19 pages, 12 encapsulated Postscript figure

VISUELLE STATIK – I: Phänomenologische Betrachtungen zur Wahrnehmung von Gewicht und Last.

Kann man einem Gegenstand sein Gewicht "ansehen"? Es zeigt sich, dass es eine ganze Reihe visueller Kriterien für phänomenale Schwere gibt. Ein Objekt kann nur als schwer gesehen werden, wenn es in einen strukturellen Zusammenhang eingebettet ist, und zwar so, dass es als "lastend" erlebt wird; dies erfordert aber auch ein "Be-lastetes". Erst diese phänomenale Dualität macht es zumindest möglich, dass ein Objekt als "zu schwer" visuell erkannt wird. Neben der Dualität von Last und Träger bestimmen visuelle Eigenschaften der Objekte selbst deren anschauliche Schwere. Die relative Größe und Masse der Körper ist ein Kriterium. Fast ebenso wichtig ist die räumliche Proportionierung. Auch Helligkeit und Färbung der Körperoberfläche wirken sich auf die Schwere einer Last aus.Can you "see" the weight of an object? There are indeed many visual criteria of the phenomenon of weight. Only imbedded in a structural context an object can be determined as heavy with respect for weighting load. So a loaded object is also required. This duality enables an object to be recognized as too heavy. Furthermore some visual object-immanent characteristics define the phenomenal weight. These are the relative size and mass, the spatial proportions as well as brightness and colour of an object

VISUELLE STATIK – II

Das subjektive Einschätzen von Tragfähigkeit, also des Verhältnisses von Last und Belastetem, läuft meist intuitiv beim Betrachten von Bauwerken ab und steht oft im Widerspruch zur objektiv errechneten und realisierten Statik. An den Schnittstellen zwischen Ästhetik, Architektur und Psychologie angesiedelt, wird das Konzept einer visuellen Statik exemplarisch am anschaulichen Verhältnis von Last und Stütze untersucht. Die systematische Variation der Verhältnisse soll Aufschluss geben über interindividuelle Gemeinsamkeiten bei der wahrgenommenen Dimensionierung von lastenden und belasteten Strukturen. Nach einem hypothesenerkundenden Vorversuch wurde ein weiteres Bildschirmexperiment durchgeführt, wobei eine 16x16-Matrix von aufeinander stehenden Rechteckspaaren, systematisch variiert in ihren Dimensionierungen, zur Beurteilung vorgegeben wurde. Als Ergebnis kristallisierte sich eine ausgewogene Proportion von Last zu Stütze im Bereich von 1.0 - 1.66 heraus, bezogen auf den Quotienten aus Höhe der Last und Breite der Stütze. Die Grenzen des gefundenen Verhältnisbereichs entsprechen annähernd dem 1:1-Verhältnis und dem Goldenem Schnitt (1.618:1). Die Replikation mit greifbaren Modellen aus Holz stützte die Ergebnisse des Bildschirmexperiments nur zum Teil. Eine empirisch untermauerte Gültigkeit ist vorerst einzuschränken auf einfache und isolierte Last/Stütze-Muster.Individually biased estimation of load capacity, defined as proportion of loading to loaded elements, mostly occurs by intuition when looking at architectural structures and often seems incompatible with objective and calculated statics. Using the example of load and support in systematic variation, interindividual mutualities in the perception of the dimensions of loading and loaded structures shall be uncovered. After a prestudy, more for hypothesis generating purposes, another screen experiment was performed. A 16x16 matrix of systematically varied pairs of rectangles standing on each other was presented for estimation. As a result a ratio of 1.0 to 1.66 emerged, suggesting a harmonic proportion of load and support related on the ratio of the height of the load to the width of its support. The borders of the ratio are according rather exactly with the unity (1:1) and the golden section ratio (1.618:1). A replication with real wooden models partly confirmed the results of the screen experiment. Empirical validation so far is to be reduced on simple and single load/support patterns

Sensor for oxygen activity measurements in glass melts

Traditional oxygen activity measurement in glass melts is based on Y2O3-stabilized ZrO2 which, in continuous use in the glassworks, is subjected to considerable wear. The present paper describes an oxygen sensor that is not equipped with wear parts. The new sensor is far less sensitive to temperature gradients in the surrounding area than ZrO2 sensors; the oxygen measurement, however, is greatly disturbed at direct flame irradiation

Electrochemical measurements of oxygen activity of glass melts in glass melting furnaces

The electrochemical determination of the oxygen activity of a glass melt by a stabilized ZrO2 sensor was established as an online measurement in a working chamber and a feeder channel. Α method is described to take the temperature difference between the sensor's electrodes into account. In green glass a correlation between the oxygen activity and Fe2+/Fetot ratio, in amber glass a correlation between oxygen activity and Cr2O3 content are found

Interfaces in partly compatible polymer mixtures: A Monte Carlo simulation approach

The structure of polymer coils near interfaces between coexisting phases of symmetrical polymer mixtures (AB) is discussed, as well as the structure of symmetric diblock copolymers of the same chain length N adsorbed at the interface. The problem is studied by Monte Carlo simulations of the bond fluctuation model on the simple cubic lattice, using massively parallel computers (CRAY T3D). While homopolymer coils in the strong segregation limit are oriented parallel to the interface, the diblocks form ``dumbbells'' oriented perpendicular to the interface. However, in the dilute case (``mushroom regime'' rather than ``brush regime''), the diblocks are only weakly stretched. Distribution functions for monomers at the chain ends and in the center of the polymer are obtained, and a comparison to the self consistent field theory is made.Comment: to appear in Physica