Related papers: Dendriform-Tree Setting for Fully Non-commutative …
In this paper, we propose an explicit, non-strict representation of search trees in constraint-logic object-oriented programming. Our search tree representation includes both the non-deterministic and deterministic behaviour during…
The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of…
The adoption of the distributed paradigm has allowed applications to increase their scalability, robustness and fault tolerance, but it has also complicated their structure, leading to an exponential growth of the applications'…
We define and investigate a family of permutations matrices, called shuffling matrices, acting on a set of $N=n_1\cdots n_m$ elements, where $m\geq 2$ and $n_i\geq 2$ for any $i=1,\ldots, m$. These elements are identified with the vertices…
We consider parabolic PDEs associated with fractional type operators drifted by non-linear singular first order terms. When the drift enjoys some boundedness properties in appropriate Lebesgue and Besov spaces, we establish by exploiting a…
We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision…
The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a…
Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using…
This article introduces two new fractional operators with sine ($\sin$) and cosine ($\cos$) kernels, motivated by their fundamental role in modeling AC signals in electrical circuits. The operators are designed to improve the analysis of…
We introduce the notion of quasi-triangular anti-dendriform bialgebras, which can be induced by the solutions of the AD-YBE whose symmetric parts are invariant. A factorizable anti-dendriform bialgebra leads to a factorization of the…
We develop a classification of composite operators without gradients at Anderson-transition critical points in disordered systems. These operators represent correlation functions of the local density of states (or of wave-function…
We systematically study various aspects of operator-valued multishifts. Beginning with basic properties, we show that the class of multishifts on the directed Cartesian product of rooted directed trees is contained in that of…
We propose a reformulation of some results known on the free dendriform dialgebra on one generator from a parenthesis point of view. This turns out to be more tractable and point out a connection to free probability by identifying…
This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying…
We consider symmetric operators of the form $S := A\otimes I_{\mathfrak T} + I_{\mathfrak H} \otimes T$ where $A$ is symmetric and $T = T^*$ is (in general) unbounded. Such operators naturally arise in problems of simulating point contacts…
This paper presents a novel anti-windup proportional-integral controller for stable multi-input multi-output nonlinear plants. We use tools from projected dynamical systems theory to force the integrator state to remain in a desired…
This paper addresses a motion planning problem of the second-order chained form system. The author presents a novel control approach based on switching a state. The second-order chained form system is composed of three subsystems including…
This paper explores the notions of $\mathcal{F}$-transitivity and topological $\mathcal{F}$-recurrence for backward shift operators on weighted $\ell^p$-spaces and $c_0$-spaces on directed trees, where $\mathcal{F}$ represents a Furstenberg…