Aims. Using a reconstruction of sunspot numbers stretching over multiple millennia, we analyze the statistics of the occurrence of grand minima and maxima and set new observational constraints on long-term solar and stellar dynamo models. Methods. We present an updated reconstruction of sunspot number over multiple millennia, from C data by means of a physics-based model, using an updated model...

In the first paper, the author summarized the shortcomings of one previous melody segmentation method, which is LBDM, and then he gave his own method, MDSM. Instead of measuring the accumulated boundary strength and identifying local maxima, this method was trying to calculate the accumulated melodic cohesion between pitch intervals and identify the local minima. Both methods extracted some int...

QBI in 162 directions (b=4500 s/mm2). In panel a), colors encode principal sheet direction and both techniques show good qualitative agreement. However, closer inspection of the SNDFs shows intravoxel sheet crossing which cannot be resolved with conventional DTI. Panel b) illustrates this for the framed voxel from a), where the DTI sheet normal direction lies in between two distinct sheet popul...

This paper continues Nebel and Burckert’s investigation of Allen’s interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P # NP), in addition to their previously reported ORD-Horn subclass. Furthermore, twelve tractable subclasses are identified, whose maximality is not decided. Four of them can express the notion of sequentiulity between intervals,...

Theorem 1. Convergence to local optimum (a) The sequence of iterates Ut of Algorithm 4 satisfies: limt→∞ ||∇f(Ut)|| = 0. This means that the accumulation points of the sequence {Ut}t=1 are critical points of f . (b) Assume the critical points of f are isolated. Let U∗ be a critical point of f . Then U∗ is a local minimum of f if and only if it is asymptotically stable with regard to the sequenc...

We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. In our main result, we prove that this process yields a maximum ...