The model of hierarchical complexity (MHC) provides an analytic a priori measurement of the difficulty of tasks. As part of the theory of measurement in mathematical psychology, the model of hierarchical complexity (Commons and Pekker, 2008) defines a new kind of scale. It is important to note that the orders of hierarchical complexity of tasks are postulated to form an ordinal scale. A formal ...

We provide a decidable hierarchical classification of first-order recurrent neural networks made up of McCulloch and Pitts cells. This classification is achieved by proving an equivalence result between such neural networks and deterministic Büuchi automata, and then translating the Wadge classification theory from the abstract machine to the neural network context. The obtained hierarchy of ne...

The expressiveness of existential monadic second-order logic is investigated over several classes of nite graphs among them the graphs of bounded tree-width. A hierarchical approach to the decomposition of graphs is introduced which is related to the notion of tree decomposition. Among other results we show that existential monadic second-order logic on graphs of bounded tree-width is not close...

ended in the early 1990s, many leading scholars offered a bleak prognosis for East Asia: with the decline of the Soviet Union and the rise of China, the region would move toward an unstable multipolar order, as the United States drew down its forces, Japan remilitarized, China’s economic and military power grew, and other countries in the region began to engage in arms races.1 More than a decad...

Classic multigrid methods are often not directly applicable to nonelliptic problems such as curl-type partial differential equations (PDEs). Curl-curl PDEs require specialized smoothers that are compatible with the gradient-like (near) null space. Moreover, recent developments have focused on replicating the grad-curl-div de Rham complex in a multilevel hierarchy through smoothed aggregation ba...

A floorplan is a rectangular dissection which describes the relative placement of electronic modules on the chip. It is called a mosaic floorplan if there are no empty rooms or cross junctions in the rectangular dissection. We study a subclass of mosaic floorplans called hierarchical floorplans of order k (abbreviated HFOk). A floorplan is a hierarchical floorplan of order k if it can be obtain...

Database design aims to find a database schema that permits the efficient processing of common types of queries and updates on future database instances. Full first-order hierarchical decompositions constitute a large class of database constraints that can provide assistance to the database designer in identifying a suitable database schema. We establish finite axiomatisations of full first-ord...

We address in this paper the issue of computing diffuse global illumination solutions for animation sequences. The principal difficulties lie in the computational complexity of global illumination, emphasized by the movement of objects and the large number of frames to compute, as well as the potential for creating temporal discontinuities in the illumination, a particularly noticeable artifact...

We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used. For nonlinear modeling we use a hierarchical piecewise linear approach based on the notion of decision trees where the space of the regressor vectors is adapti...

We simulate open clusters containing up to 182 stars initially in the form of singles, binaries and triples. Due to the high interaction rate a large number of stable quadruples, quintuples, sextuples, and higher-order hierarchies form during the course of the simulations. For our choice of initial conditions, the formation rate of quadruple systems after about 2 Myr is roughly constant with ti...