相关论文: Characterizing co-NL by a group action

Let a complex algebraic reductive group $\bf G$ act on a complex algebraic manifold $\bf X$. For a $\bf G$-invariant subvariety $\Xi$ of the nilpotent cone $\mathcal{N}(\mathfrak{g}^*)\subset \mathfrak{g}^*$ we define a notion of…

This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.

Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…

Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes…

Previous work combines word-level and character-level representations using concatenation or scalar weighting, which is suboptimal for high-level tasks like reading comprehension. We present a fine-grained gating mechanism to dynamically…

The study of rare events is one of the major challenges in atomistic simulations, and several enhanced sampling methods towards its solution have been proposed. Recently, it has been suggested that the use of the committor, which provides a…

Let ${\rm GK}(G)$ be the prime graph associated with a finite group $G$ and $D(G)$ be the degree pattern of $G$. A finite group $G$ is said to be $k$-fold OD-characterizable if there exist exactly $k$ non-isomorphic groups $H$ such that…

We propose a new algorithm for compiling Bayesian network classifier (BNC) into class formulas. Class formulas are logical formulas that represent a classifier's input-output behavior, and are crucial in the recent line of work that uses…

We show that the left regular representation of Neretin groups is factorial, providing the first example of a non-discrete simple group with this property. This is based on a new criterion of factoriality for totally disconnected groups.…

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism…

A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…

Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology…

The key in agglomerative clustering is to define the affinity measure between two sets. A novel agglomerative clustering method is proposed by utilizing the path integral to define the affinity measure. Firstly, the path integral descriptor…

Generating explanations for neural networks has become crucial for their applications in real-world with respect to reliability and trustworthiness. In natural language processing, existing methods usually provide important features which…

Let G be a finite, complex reflection group and f its discriminant polynomial. The fibers of f admit commuting actions of G and a cyclic group. The virtual $G\times C_m$ character given by the Euler characteristic of the fiber is a…

In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…

Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes,…

We present an algorithm turning any term of a linear quantum $\lambda$-calculus into a quantum circuit. The essential ingredient behind the proposed algorithm is Girard's geometry of interaction, which, differently from its well-known uses…

Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…