Related papers: Classification of Double Saddle-Point Systems
We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track…
This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various…
This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version…
Multimodal classification research has been gaining popularity in many domains that collect more data from multiple sources including satellite imagery, biometrics, and medicine. However, the lack of consistent terminology and architectural…
We consider a class of two-degree-of-freedom Hamiltonian systems with saddle-centers connected by heteroclinic orbits and discuss some relationships between the existence of transverse heteroclinic orbits and nonintegrability. By the…
We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural…
This paper focuses on different reductions of 2-dimensional (2d-)Toda hierarchy. Symmetric and skew symmetric moment matrices are firstly considered, resulting in the differential relations between symmetric/skew symmetric tau functions and…
This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…
The solution of matrices with $2\times 2$ block structure arises in numerous areas of computational mathematics, such as PDE discretizations based on mixed-finite element methods, constrained optimization problems, or the implicit or steady…
Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where…
In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling…
Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…
To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
Dense Associative Memory (DAM) models have been attracting renewed attention since they were shown to be robust to adversarial examples and closely related to cutting edge machine learning paradigms, such as the attention mechanism and…
A general and exact critical condition of saddle-node bifurcation is derived in closed form for the buck converter. The critical condition is helpful for the converter designers to predict or prevent some jump instabilities or coexistence…
We study the steerability for arbitrary dimensional bipartite systems based on the correlation matrices given by local special unitary groups. We present families of steering criteria for bipartite quantum states in terms of parameterized…
Higher-dimensional automata, i.e., pointed labeled precubical sets, are a powerful combinatorial-topological model for concurrent systems. In this paper, we show that for every (nonempty) connected polyhedron there exists a shared-variable…
Combining an old idea of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators we classify compatible trios of two-component homogeneous Hamiltonian operators. The trios yield pairs of…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…