Related papers: Slit-slide-sew bijections for oriented planar maps
We are interested in the quantitative analysis of the compaction ratio for two classical families of trees: recursive trees and plane binary increasing trees. These families are typical representatives of tree models with a small depth.…
We consider maps on orientable surfaces. A map is called \emph{unicellular} if it has a single face. A \emph{covered map} is a map (of genus $g$) with a marked unicellular spanning submap (which can have any genus in $\{0,1,...,g\}$). Our…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous…
A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated…
The paper proposes a Bayesian multinomial logit model to analyse spatial patterns of urban expansion. The specification assumes that the log-odds of each class follow a spatial autoregressive process. Using recent advances in Bayesian…
We study the functorial and growth properties of closed orbits for maps. By viewing an arbitrary sequence as the orbit-counting function for a map, iterates and Cartesian products of maps define new transformations between integer…
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…
We propose the Selective Densification method for fast motion planning through configuration space. We create a sequence of roadmaps by iteratively adding configurations. We organize these roadmaps into layers and add edges between…
In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder woods where the number of incoming edges of each color at each vertex is balanced as much as possible. We provide a simple linear-time heuristic leading…
We consider unicellular maps, or polygon gluings, of fixed genus. A few years ago the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
We study random bipartite planar maps defined by assigning nonnegative weights to each face of a map. We prove that for certain choices of weights a unique large face, having degree proportional to the total number of edges in the maps,…
We present unified bijections for maps on the torus with control on the face-degrees and essential girth (girth of the periodic planar representation). A first step is to show that for d>=3 every toroidal d-angulation of essential girth d…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
We study the structure of the relative Hilbert scheme for a family of nodal (or smooth) curves via its natural cycle map to the relative symmetric product. We show that the cycle map is the blowing up of the discriminant locus, which…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
A sweep of a point configuration is any ordered partition induced by a linear functional. Posets of sweeps of planar point configurations were formalized and abstracted by Goodman and Pollack under the theory of allowable sequences of…
Autonomous excavation for hard or compact materials, especially irregular rigid objects, is challenging due to high variance of geometric and physical properties of objects, and large resistive force during excavation. In this paper, we…
The paper develops a method for model reduction of bilinear control systems. It leans upon the observation that the input-output map of a bilinear system has a particularly simple Fliess series expansion. Subsequently, a model reduction…