Related papers: Two Dimensional Discrete Dynamics of Integral Valu…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Model selection in the large-P small-N scenario is discussed in the framework of two-stage models. Two specific models are considered, namely, two-stage least squares (TSLS) involving instrumental variables (IVs), and mediation models. In…
Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems…
Floquet theory combined with the generalized Van Vleck nearly degenerate perturbation theory, has been widely employed for studying various two-level systems that are driven by external fields via the time-dependent longitudinal (i.e.,…
An interval translation map (ITM) is a map $T \colon I \to I$ defined as a piecewise translation on a finite partition of an interval $I$ into $r \ge 2$ subintervals. Unlike classical interval exchange transformations (IETs), the images of…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
Numerous experimental and theoretical studies have established that intramolecular vibrational energy redistribution (IVR) in isolated molecules has a heirarchical tier structure. The tier structure implies strong correlations between the…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
The study of quantum vortices provides critical insights into non-equilibrium dynamics across diverse physical systems. While previous research has focused on point-like vortices in two dimensions and line-like vortices in three dimensions,…
We propose a periodically driven system whose dimensionality is an emergent property that can be tunable, thus enables us to realize not only many-body phases with arbitrary dimensions, but also phase transitions, instead of crossovers,…
We propose a theory in electromagnetic dynamics, in which time and space are equivalent with each other and have totally twelve dimensions. Then, we solve that with realistic assumptions and find a steady state as a solution. The solution…
In this paper, we discuss duality about components of invariant variety of periodic points(IVPP) and fundamental domain of recurrence equation, and present an algorithm for the derivation of all components of IVPPs of any rational maps. It…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
We show that dynamical quantum phase transitions (DQPTs) in the quench dynamics of two-dimensional topological systems can be characterized by a dynamical topological invariant defined along an appropriately chosen closed contour in…
We derive a functional change of variable formula for {\it non-anticipative} functionals defined on the space of right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may…
We first develop systematic and comprehensive interval observer designs for linear time-invariant (LTI) systems, under standard assumptions of observability and interval bounds on the initial condition and uncertainties. Traditionally, such…
Vision Transformers (ViTs) have shown promising performance compared with Convolutional Neural Networks (CNNs), but the training of ViTs is much harder than CNNs. In this paper, we define several metrics, including Dynamic Data Proportion…
Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order initial value problems (IVPs). By discretizing the dynamics…