Related papers: Homomesy via Toggleability Statistics
This paper introduces and develops M\"obius homology, a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology and M\"obius functions is classical, we go further by…
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…
We study a simple generalization of the rotation (or circular shift) of the binary sequences. In particular, we show each orbit of this generalized rotation has a certain statistical symmetry. This generalized rotation naturally arises when…
Human mobility clustering is an important problem for understanding human mobility behaviors (e.g., work and school commutes). Existing methods typically contain two steps: choosing or learning a mobility representation and applying a…
With the continuous advancement of robot teleoperation technology, shared control is used to reduce the physical and mental load of the operator in teleoperation system. This paper proposes an alternating shared control framework for object…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural…
The paper surveys more than forty characterizations of scoring methods for preference aggregation and contains one new result. A general scoring operator is {\it self-consistent} if alternative $i$ is assigned a greater score than $j$…
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These…
Discrete and periodic contact switching is a key characteristic of steady-state legged locomotion. This paper introduces a framework for modeling and analyzing this contact-switching behavior through the framework of geometric mechanics on…
The Koopman operator framework offers a way to represent a nonlinear system as a linear one. The key to this simplification lies in the identification of eigenfunctions. While various data-driven algorithms have been developed for this…
A class of network models with symmetry group $G$ that evolve as a Lie-Poisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenberg model studied in statistical mechanics. We considered two…
The algorithm derived in this article, which builds upon the original paper, takes a holistic view of the handedness of an orthonormal eigenvector matrix so as to transfer what would have been labeled as a reflection in the original…
We present a comprehensive study on discrete morphological symmetries of dynamical systems, which are commonly observed in biological and artificial locomoting systems, such as legged, swimming, and flying animals/robots/virtual characters.…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
User's intentions may be expressed through spontaneous gesturing, which have been seen only a few times or never before. Recognizing such gestures involves one shot gesture learning. While most research has focused on the recognition of the…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…