Partition function of two- and three-dimensional Potts ferromagnets for arbitrary values of q>0

A new algorithm is presented, which allows to calculate numerically the partition function Z_q of the d-dimensional q-state Potts models for arbitrary real values q>0 at any given temperature T with high precision. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the distribution of the case q=1 (graph percolation), where the exact result Z_1=1 is known. As application, d=2 and d=3-dimensional ferromagnetic Potts models are studied, and the critical values q_c, where the transition changes from second to first order, are determined. Large systems of sizes N=1000^2 respectively N=100^3 are treated. The critical value q_c(d=2)=4 is confirmed and q_c(d=3)=2.35(5) is found.Comment: 4 pages, 4 figures, RevTe

Primary spinal segment stability with a stand-alone cage: in vitro evaluation of a successful goat model.

Background: Interbody cages have been developed to restore disk height and to increase stability of the spinal segment, and thereby enhance fusion. However, they often prove inadequate as a stand-alone device. It is unknown how much primary stability is required to facilitate fusion. In various goat studies, we have obtained spinal fusion routinely with a stand-alone cage device. However, data covering the mechanical conditions under which these fusions have been obtained are lacking. In this study, we addressed the issue of primary stability. Methods: We used an established goat model for spinal fusion in vitro. 48 native lumbar spine segments were mechanically tested in flexion/extension, axial torsion (left/right), anterior/posterior shear, and left/right lateral bending. Then all segments were provided with a titanium cage using the exact surgical procedure of our earlier in vivo studies, and the mechanical tests were repeated. Under shear force and axial torsion, a significant loss of stiffness was seen in the operated segments as compared to nonoperated controls. No increase in stiffness was found in any of the loading directions. Interpretation: Cage implantation in a lumbar spinal segment does not increase immediate postoperative stability as compared to the native segment in this goat model. This is attributable to both the annular damage during cage implantation and the subsequent loss of segment height. Yet previous in vivo studies using this goat model have generally shown fusion. This implies that high primary segment stability is not required for fusion or, alternatively, that the tested range of motion of the spinal segment in vitro does not occur at these magnitudes in vivo. Copyright© Taylor & Francis 2006

Spatial patterns of large African cats : a large-scale study on density, home range size, and home range overlap of lions Panthera leo and leopards Panthera pardus

Spatial patterns of and competition for resources by territorial carnivores are typically explained by two hypotheses: 1) the territorial defence hypothesis and 2) the searching efficiency hypothesis. According to the territorial defence hypothesis, when food resources are abundant, carnivore densities will be high and home ranges small. In addition, carnivores can maximise their necessary energy intake with minimal territorial defence. At medium resource levels, larger ranges will be needed, and it will become more economically beneficial to defend resources against a lower density of competitors. At low resource levels, carnivore densities will be low and home ranges large, but resources will be too scarce to make it beneficial to defend such large territories. Thus, home range overlap will be minimal at intermediate carnivore densities. According to the searching efficiency hypothesis, there is a cost to knowing a home range. Larger areas are harder to learn and easier to forget, so carnivores constantly need to keep their cognitive map updated by regularly revisiting parts of their home ranges. Consequently, when resources are scarce, carnivores require larger home ranges to acquire sufficient food. These larger home ranges lead to more overlap among individuals' ranges, so that overlap in home ranges is largest when food availability is the lowest. Since conspecific density is low when food availability is low, this hypothesis predicts that overlap is largest when densities are the lowest. We measured home range overlap and used a novel method to compare intraspecific home range overlaps for lions Panthera leo (n = 149) and leopards Panthera pardus (n = 111) in Africa. We estimated home range sizes from telemetry location data and gathered carnivore density data from the literature. Our results did not support the territorial defence hypothesis for either species. Lion prides increased their home range overlap at conspecific lower densities whereas leopards did not. Lion pride changes in overlap were primarily due to increases in group size at lower densities. By contrast, the unique dispersal strategies of leopards led to reduced overlap at lower densities. However, when human-caused mortality was higher, leopards increased their home range overlap. Although lions and leopards are territorial, their territorial behaviour was less important than the acquisition of food in determining their space use. Such information is crucial for the future conservation of these two iconic African carnivores