Equation of motion approach to the Hubbard model in infinite dimensions

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, $G^{(n)}(\omega),\ n=2,3,\dots\$ . The first $n-1$ equations of motion are exactly fullfilled by $G^{(n)}(\omega)$ and the $n$'th equation of motion is decoupled following a simple set of decoupling rules. $G^{(2)}(\omega)$ corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for $n=2,3,4$.Comment: 10pager, REVTEX, 8-figures not available in postscript, manuscript may be understood without figure

Gait analysis by high school students

Human walking is a complicated motion. Movement scientists have developed various research methods to study gait. This article describes how a high school student collected and analysed high quality gait data in much the same way that movement scientists do, via the recording and measurement of motions with a video analysis tool and via electromyography, i.e., the measurement of muscle activity. Physics, biology, and mathematics come together in this practical investigation work at a rather high level. It shows that science learning at school can resemble science practice in research laboratories, provided that students have adequate tools

Change Mining in Adaptive Process Management Systems

The wide-spread adoption of process-aware information systems has resulted in a bulk of computerized information about real-world processes. This data can be utilized for process performance analysis as well as for process improvement. In this context process mining offers promising perspectives. So far, existing mining techniques have been applied to operational processes, i.e., knowledge is extracted from execution logs (process discovery), or execution logs are compared with some a-priori process model (conformance checking). However, execution logs only constitute one kind of data gathered during process enactment. In particular, adaptive processes provide additional information about process changes (e.g., ad-hoc changes of single process instances) which can be used to enable organizational learning. In this paper we present an approach for mining change logs in adaptive process management systems. The change process discovered through process mining provides an aggregated overview of all changes that happened so far. This, in turn, can serve as basis for all kinds of process improvement actions, e.g., it may trigger process redesign or better control mechanisms

Saccadic eye movements estimate prolonged time awake

Prolonged time awake increases the need to sleep. Sleep pressure increases sleepiness, impairs human alertness and performance and increases the probability of human errors and accidents. Human performance and alertness during waking hours are influenced by homeostatic sleep drive and the circadian rhythm. Cognitive functions, especially attentional ones, are vulnerable to circadian rhythm and increasing sleep drive. A reliable, objective and practical metrics for estimating sleepiness could therefore be valuable. Our aim is to study whether saccades measured with electro-oculography (EOG) outside the laboratory could be used to estimate the overall time awake without sleep of a person. The number of executed saccades was measured in 11 participants during an 8-min saccade task. The saccades were recorded outside the laboratory (Naval Academy, Bergen) using EOG every sixth hour until 54 hr of time awake. Measurements were carried out on two occasions separated by 10 weeks. Five participants participated in both measurement weeks. The number of saccades decreased during sustained wakefulness. The data correlated with the three-process model of alertness; performance differed between participants but was stable within individual participants. A mathematically monotonous relation between performance in the saccade task and time awake was seen after removing the circadian rhythm component from measured eye movement data. The results imply that saccades measured with EOG can be used as a time-awake metric outside the laboratory.Peer reviewe

Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions

In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T approx T_c/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.Comment: (5 pages, 3 figures, typeset with ReVTeX4