Related papers: Thurston equivalence for rational maps with cluste…

In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…

Let $D$ be a $k$-regular bipartite tournament on $n$ vertices. We show that, for every $p$ with $2 \le p \le n/2-2$, $D$ has a cycle $C$ of length $2p$ such that $D \setminus C$ is hamiltonian unless $D$ is isomorphic to the special digraph…

A distinguishing $r$-labeling of a digraph $G$ is a mapping $\lambda$ from the set of verticesof $G$ to the set of labels $\{1,\dots,r\}$ such that no nontrivial automorphism of $G$ preserves all the labels.The distinguishing number $D(G)$…

It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

The Globally Coupled Map Lattice (GCML) is one of the basic model of the intelligence activity. We report that, in its so-called turbulent regime, periodic windows of the element maps foliate and systematically control the dynamics of the…

We obtain a recursive formula for the number of rational degree $d$ curves in $\mathbb{P}^3$, whose image lies in a $\mathbb{P}^2$, passing through $r$ lines and $s$ points, where $r + 2s = 3d+2$. This can be viewed as a family version of…

We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…

Let $X \subset \mathbb{P}^n$ be a general Fano complete intersection of type $(d_1,\dots, d_k)$. If at least one $d_i$ is greater than $2$, we show that $X$ contains rational curves of degree $e \leq n$ with balanced normal bundle. If all…

We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…

A {\it cluster of cycles} (or {\it $(r,q)$-polycycle}) is a simple planar 2--co nnected finite or countable graph $G$ of girth $r$ and maximal vertex-degree $q$, which admits {\it $(r,q)$-polycyclic realization} on the plane, denote it by…

We consider the problem of lifting a regular cluster structure on a quasi-affine variety to the ambient affine space and a similar problem of defining a regular pullback of a regular cluster structure under a dominant rational map between…

We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the…

In this paper, we give a family of rational maps whose Julia sets are Cantor circles and show that every rational map whose Julia set is a Cantor set of circles must be topologically conjugate to one map in this family on their…

An important task in trajectory analysis is clustering. The results of a clustering are often summarized by a single representative trajectory and an associated size of each cluster. We study the problem of computing a suitable…

Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation)…

This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we…

Economic policy and research rely on the correct evaluation of the billions of high-frequency data points that we collect every day. Consistent clustering algorithms, like DBSCAN, allow us to make sense of the data in a useful way. However,…