相关论文: Recursion Relations for Long-Range Integrable Spin…

We discuss the transition from a metal to charge or spin insulating phases characterized by the opening of a gap in the charge or spin excitation spectra, respectively. These transitions are addressed within the context of two exactly…

Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary…

We show that boundary contributions of BCFW recursions can be interpreted as the form factors of some composite operators which we call 'boundary operators'. The boundary operators can be extracted from the operator product expansion of…

A systematic method to construct the complete set of conserved quantities of the Haldane-Shastry type spin chains is proposed. The hidden relationship between the Yang-Baxter relation and the conservation laws of the long-range interacting…

Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.

The Motzkin spin chain is a spin-1 model introduced in \cite{shor} as an example of a system exhibiting a high degree of quantum fluctuations whose ground state can be mapped to Motzkin paths that are generated with local equivalence moves.…

The long-range, spin-dependent forces between D0-branes are related to long-range fundamental string interactions using duality. These interactions can then be computed by taking the long distance non-relativistic expansion of string…

Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the…

Reversible logic is experience renewed interest as we are approach the limits of CMOS technologies. While physical implementations of reversible gates have yet to materialize, it is safe to assume that they will rely on faulty individual…

We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recursion relations in the length of the chain. These relations…

Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate more easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models…

Successful recurrent models such as long short-term memories (LSTMs) and gated recurrent units (GRUs) use ad hoc gating mechanisms. Empirically these models have been found to improve the learning of medium to long term temporal…

This paper presents the design concept, modeling and motion planning solution for the aerial robotic chain. This design represents a configurable robotic system of systems, consisting of multi-linked micro aerial vehicles that…

It is shown that transient spin-spin correlations in one-dimensional spin S>>1 chain can be enhanced for initially factorized and individually squeezed spin states. Such correlation transfer form "internal" to "external" degrees of freedom…

General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial…

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.

The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function…

We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, crystal, in characteristic relationship to each other. As the parameters of the model are varied one obtains characteristic patterns of phase…

We analyze correlations among stock returns via a series of widely adopted parameters which we refer to as explanatory variables. We subsequently exploit the results to propose a long only quantitative adaptive technique to construct a…

We study Ising models for describing data and show that autoregressive methods may be used to learn their connections, also in the case of asymmetric connections and for multi-spin interactions. For each link the linear Granger causality is…