Related papers: T-systems with boundaries from network solutions
We prove a number of \textit{a priori} estimates for weak solutions of elliptic equations or systems with vertically independent coefficients in the upper-half space. These estimates are designed towards applications to boundary value…
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 $T$-designs in the nonbinary Johnson scheme. This scheme generalizes both the Johnson and Hamming schemes and admits a bivariate $Q$-polynomial structure. Zhu (2021) provided a combinatorial characterization of $T$-designs in this…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Given a thin torus $T_K$ around a knot $K\subset \mathbb{R}^3$, we construct Morse models of cord algebra $Cord(T_K)$ with $\mathbb{Z}$ and loop space coefficients. Using the Multiple time scale dynamics we identify $Cord(T_K; \mathbb{Z})$…
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is…
In this paper, we revisit the problem of classifying real algebraic and semialgebraic sets by their topological types, focusing on establishing the effectiveness of bounds rather than deriving new quantitative estimates. Building on Hardt's…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…
Let $T\subset \R^{m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partial T$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed intial point $A\in X$, a…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…
The general solutin to the constraints that define relativistic spin networks vertices is given and their relations with 3-dimensional quantum tetrahedra is dicussed. An alternative way to handle the constraints is also presented.
For an infinite Toeplitz matrix $T$ with nonnegative real entries we find the conditions, under which the equation $\boldsymbol{x}=T\boldsymbol{x}$, where $\boldsymbol{x}$ is an infinite vector-column, has a nontrivial bounded positive…
In arXiv:2112.09122, we analyzed the reflected entropy ($S_R$) in random tensor networks motivated by its proposed duality to the entanglement wedge cross section (EW) in holographic theories, $S_R=2 \frac{EW}{4G}$. In this paper, we…
We consider a potential $W:R^m\rightarrow R$ with two different global minima $a_-, a_+$ and, under a symmetry assumption, we use a variational approach to show that the Hamiltonian system \begin{equation} \ddot{u}=W_u(u), \hskip 2cm (1)…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure…