Truncating the loop series expansion for Belief Propagation

Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms to the BP free energy, one for each "generalized loop" in the factor graph, the exact partition sum is obtained. However, the usually enormous number of generalized loops generally prohibits summation over all correction terms. In this article we introduce Truncated Loop Series BP (TLSBP), a particular way of truncating the loop series of M. Chertkov and V.Y. Chernyak by considering generalized loops as compositions of simple loops. We analyze the performance of TLSBP in different scenarios, including the Ising model, regular random graphs and on Promedas, a large probabilistic medical diagnostic system. We show that TLSBP often improves upon the accuracy of the BP solution, at the expense of increased computation time. We also show that the performance of TLSBP strongly depends on the degree of interaction between the variables. For weak interactions, truncating the series leads to significant improvements, whereas for strong interactions it can be ineffective, even if a high number of terms is considered.Comment: 31 pages, 12 figures, submitted to Journal of Machine Learning Researc

Wildgänse in Europa : gestern, heute und in Zukunft

In der zweiten Hälfte des 20. Jahrhunderts haben die Bestände vieler Gänsearten im Westen Europas zugenommen. Aufgrund vorliegender Daten scheint es nicht unrealistisch zu sein, dass die westpaläarktischen Bestände der Bless-, Saat- und Graugänse seit Mitte des 19. Jahrhunderts drastisch abgenommen haben und sich seit Mitte des 20. Jahrhunderts auf einem relativ niedrigen Niveau stabilisiert und regional verlagert haben. Diese Entwicklung zeigt, dass eine regional positive Bestandsentwicklung bei einer wandernden Vogelart nicht unbedingt mit einer positiven Bestandsentwicklung der Gesamtpopulation verbunden ist, und dass die Einschätzung einer Bestandsentwicklung als positiv oder negativ stark von dem berücksichtigten Zeitraum abhängig ist. Die Daten zeigen auch, dass die Gänsejagdstrecke seit den 1950er Jahren zugenommen hat, während der jährliche Fortpflanzungserfolg bei den meisten arktischen Gänsearten seitdem stetig zurückgegangen ist. Diese Entwicklung lässt befürchten, dass die meisten arktischen Gänsearten in den kommenden Jahren wieder einen Bestandsrückgang zeigen werden.In the second half of the 20th century the populations of the majority of the West-European goose species increased. Based on available data it seems not unrealistic that the western Palearctic population of the White-fronted, Bean and Greylag Goose have decreased dramatically since the middle of the 19th century and have stabilized and shifted within Europe since the middle of the 20th century. This development shows that a regionally positive population development of a migratory bird species not necessarily means that the whole population of the species shows an increasing tendency. At the same time it shows that the assessment of the population development of a species as being positive or negative strongly depends of the considered space of time. Besides the data showed that the goose bag increased since the 1950s, whereas the annual reproductive rate of most goose species over the same period declined steadily. This development feeds the fear that the numbers of most arctic goose species could decline again in the coming years

In-flight measured human pilot describing function and remnant for pitch attitude control

Flight tests have been performed with a variable pitch-rate-command/attitude-hold flight control system in a Beechoraft Queen air-80 aircraft. Some results of in-flight measured runs for two pilots controlling typical easy and difficult dynamics are presented together with the initial results of the same tracking experiment performed on a ground-based flight simulator. Results are compared with results of other investigators using fixed-base flight simulators

The merger of vertically offset quasi-geostrophic vortices

We examine the critical merging distance between two equal-volume, equal-potential-vorticity quasi-geostrophic vortices. We focus on how this distance depends on the vertical offset between the two vortices, each having a unit mean height-to-width aspect ratio. The vertical direction is special in the quasi-geostrophic model (used to capture the leading-order dynamical features of stably stratified and rapidly rotating geophysical flows) since vertical advection is absent. Nevertheless vortex merger may still occur by horizontal advection. In this paper, we first investigate the equilibrium states for the two vortices as a function of their vertical and horizontal separation. We examine their basic properties together with their linear stability. These findings are next compared to numerical simulations of the nonlinear evolution of two spheres of potential vorticity. Three different regimes of interaction are identified, depending on the vertical offset. For a small offset, the interaction differs little from the case when the two vortices are horizontally aligned. On the other hand, when the vertical offset is comparable to the mean vortex radius, strong interaction occurs for greater horizontal gaps than in the horizontally aligned case, and therefore at significantly greater full separation distances. This perhaps surprising result is consistent with the linear stability analysis and appears to be a consequence of the anisotropy of the quasi-geostrophic equations. Finally, for large vertical offsets, vortex merger results in the formation of a metastable tilted dumbbell vortex.Publisher PDFPeer reviewe

Quantum transitions induced by the third cumulant of current fluctuations

We investigate the transitions induced by external current fluctuations on a small probe quantum system. The rates for the transitions between the energy states are calculated using the real-time Keldysh formalism for the density matrix evolution. We especially detail the effects of the third cumulant of current fluctuations inductively coupled to a quantum bit and propose a setup for detecting the frequency-dependent third cumulant through the transitions it induces.Comment: 4 pages, 3 figure

Superconductor-insulator transition in nanowires and nanowire arrays

Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can be tuned by a homogeneous magnetic frustration.Comment: 15 pages, 10 figure