Related papers: Motifs, Coherent Configurations and Second Order N…
It has been known that several objects such as cluster variables, coefficients, seeds, and $Y$-seeds in different cluster patterns with common exchange matrices share the same periodicity under mutations. We call it synchronicity phenomenon…
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…
Although neural module networks have an architectural bias towards compositionality, they require gold standard layouts to generalize systematically in practice. When instead learning layouts and modules jointly, compositionality does not…
We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms for composition, tensor product, construction of diagrams from…
To understand a scene in depth not only involves locating/recognizing individual objects, but also requires to infer the relationships and interactions among them. However, since the distribution of real-world relationships is seriously…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…
It is well understood that the structure of a social network is critical to whether or not agents can aggregate information correctly. In this paper, we study social networks that support information aggregation when rational agents act…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
The paper addresses the problem of consensus seeking among second-order linear agents interconnected in a specific ring topology. Unlike the existing results in the field dealing with one-directional digraphs arising in various cyclic…
The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
We develop a new method to efficiently sample synthetic networks that preserve the d-hop neighborhood structure of a given network for any given d. The proposed algorithm trades off the diversity in network samples against the depth of the…
This paper is devoted to constructing a quantum version of the famous KP hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear $\hat{W}_{\infty}$ algebra. This is achieved by quantizing the conformal noncompact…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual…
We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract…
The Cartan scheme $\cal X$ of a finite group $G$ with a $(B,N)$-pair is defined to be the coherent configuration associated with the action of $G$ on the right cosets of the Cartan subgroup $B\cap N$ by the right multiplications. It is…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
Scene graph generation aims to produce structured representations for images, which requires to understand the relations between objects. Due to the continuous nature of deep neural networks, the prediction of scene graphs is divided into…