A fractal set from the binary reflected Gray code

The permutation associated with the decimal expression of the binary reflected Gray code with N bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of an IFS. For large values of N the set is examined from the point of view of time series analysis

A Zoomable Mapping of a Musical Parameter Space Using Hilbert Curves

The final publication is available at Computer Music Journal via http://dx.doi.org/10.1162/COMJ_a_0025

Thrackles: An improved upper bound

A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is 3/2(n-1), and that this bound is best possible for infinitely many values of n. © Springer International Publishing AG 2018

Epilepsy in Dcx Knockout Mice Associated with Discrete Lamination Defects and Enhanced Excitability in the Hippocampus

Patients with Doublecortin (DCX) mutations have severe cortical malformations associated with mental retardation and epilepsy. Dcx knockout (KO) mice show no major isocortical abnormalities, but have discrete hippocampal defects. We questioned the functional consequences of these defects and report here that Dcx KO mice are hyperactive and exhibit spontaneous convulsive seizures. Changes in neuropeptide Y and calbindin expression, consistent with seizure occurrence, were detected in a large proportion of KO animals, and convulsants, including kainate and pentylenetetrazole, also induced seizures more readily in KO mice. We show that the dysplastic CA3 region in KO hippocampal slices generates sharp wave-like activities and possesses a lower threshold for epileptiform events. Video-EEG monitoring also demonstrated that spontaneous seizures were initiated in the hippocampus. Similarly, seizures in human patients mutated for DCX can show a primary involvement of the temporal lobe. In conclusion, seizures in Dcx KO mice are likely to be due to abnormal synaptic transmission involving heterotopic cells in the hippocampus and these mice may therefore provide a useful model to further study how lamination defects underlie the genesis of epileptiform activities

The Most Godless Region of the World: Atheism in East Germany

With a population of 52.1% presently identifying as atheists, East Germany ranks as the most atheistic region of the world. This anomaly can be explained through the economic lenses of supply-side theory and demand-side theory when analyzing the changes instated by the Communist Party during the life of the German Democratic Republic, from 1945 to 1989. Through a process of secularization and religious oppression, the Communist Party lessened the supply of religious goods in East Germany. On the other hand, it also minimized religious demand by providing secular alternatives to traditional religious practices, and institutionalizing anti-religious sentiment. These actions combined have caused the number of citizens subscribing to religious institutions to decrease steadily over the past century

Role of a human digestive strain of Bacteroides thetaiotaomicron in the metabolism of food-borne glucosinolates

International audienc

Packing non-zero AA-paths in group-labelled graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group G and let A¿V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If G is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k -2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem

Packing non-zero AA-paths in group-labelled graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group G and let A¿V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If G is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k -2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem