相关论文: Topological Representation of Double Boolean Algeb…
Double Boolean algebras are algebras $\underline{D}=(D;\sqcap,\sqcup,\neg,\lrcorner,\bot,\top)$ of type $(2,2,1,1,0,0)$ introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Every double Boolean…
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…
A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor…
The completion $\overline{A}[\tau]$ of a locally convex *-algebra $A [ \tau ]$ with not jointly continuous multiplication is a *-vector space with partial multiplication $xy$ defined only for $x$ or $y \in A_{0}$, and it is called a…
Recent studies on computer vision mainly focus on natural images that express real-world scenes. They achieve outstanding performance on diverse tasks such as visual question answering. Diagram is a special form of visual expression that…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
Binary Tree States (BTS) are states whose decomposition on a quantum register basis formed by a set of qubits can be made sequentially. Such states sometimes appear naturally in many-body systems treated in Fock space when a global symmetry…
A quasi-twilled associative algebra is an associative algebra $\mathbb{A}$ whose underlying vector space has a decomposition $\mathbb{A} = A \oplus B$ such that $B \subset \mathbb{A}$ is a subalgebra. In the first part of this paper, we…
The asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal…
Textual Concept Bottleneck Models (TCBMs) are interpretable-by-design models for text classification that predict a set of salient concepts before making the final prediction. This paper proposes Complete Textual Concept Bottleneck Model…
Conversational text-to-speech (TTS) aims to synthesize speech with proper prosody of reply based on the historical conversation. However, it is still a challenge to comprehensively model the conversation, and a majority of conversational…
Background / introduction. Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of symbolic data, such as documents, syntactic structures, or semantic frames. Methods. We present a rigorous…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
Unlabeled data is often used to learn representations which can be used to supplement baseline features in a supervised learner. For example, for text applications where the words lie in a very high dimensional space (the size of the…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
Under a general categorical procedure for the extension of dual equivalences as presented in this paper's predecessor, a new algebraically defined category is established that is dually equivalent to the category $\bf LKHaus$ of locally…
The widespread adoption of artificial intelligence (AI) in next-generation communication systems is challenged by the heterogeneity of traffic and network conditions, which call for the use of highly contextual, site-specific, data. A…
Multimodalpersonalityunderstandingplaysacriticalroleinhuman centered artificial intelligence. Previous work mainly focus on learn-ing rich multimodal representations for video personality under standing. However, they often suffer from…
There are a wide range of applications that involve multi-modal data, such as cross-modal retrieval, visual question-answering, and image captioning. Such applications are primarily dependent on aligned distributions of the different…