Related papers: T-systems with boundaries from network solutions
We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters…
This is a sequel to my paper "The Octagonal PET I: Renormalization and Hyperbolic Symmetry". In this paper we use the renormalization scheme found in the first paper to classify the limit sets of the systems according to their topology. The…
In this work we consider the Kitaev Toric Code with specific open boundary conditions. Such a physical system has a highly degenerate ground state determined by the degrees of freedom localised at the boundaries. We can write down an…
We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the…
Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite…
Ropelength, L, is a parameter characterizing the minimum contour length of a knot or link. There exist upper and lower bounds on ropelength with respect to crossing number, C, including a universal lower bound constraining $L\geq\alpha_0…
Utilizing Bott index vectors formulated through a series of polynomials of position operators under open boundary conditions, we establish a universal, rigorous, and complete correspondence between the Bott index vector and topological…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…
In the framework of the spatial circular Hill three-body problem we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbit families. The extensive collection of families within this…
We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free…
We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the $A-$amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl $m-$function associated with the…
In this note, we present an alternative proof of a quantified Tauberian theorem for vector-valued sequences first proved in \cite{Sei15_Tauberian}. The theorem relates the decay rate of a bounded sequence with properties of a certain…
We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state…
We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the elliptic tangent bundle. Using this Lie algebroid, we…
This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem (i) we propose a metric…
Threshold-linear networks (TLNs) are models of neural networks that consist of simple, perceptron-like neurons and exhibit nonlinear dynamics that are determined by the network's connectivity. The fixed points of a TLN, including both…
Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…
The T-graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the T = (K^*)^n action on the Hilbert scheme induced from the T-action on A^n. It has vertices the T-fixed points, and edges the one-dimensional…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…