The Dijkstra algorithm is a classical method for solving the shortest path problem on weighted graphs. There are several variations of the Dijkstra algorithm, including algorithms for the widest path problem and for two-player games. In this paper, we introduce the coalgebraic shortest path problem (CSPP), a unifying framework for a broad class of optimization problems on state-transition systems. This framework encompasses not only the aforementioned problems but also new ones such as the shortest binary tree problem. We further present a coalgebraic Dijkstra algorithm for solving the CSPP efficiently under a suitable condition. Our condition is necessary and sufficient for the algorithm to return correct solutions, thereby providing a precise criterion for when Dijkstra-style acceleration is possible. We also show that the proposed algorithm achieves asymptotic complexity comparable to that of the classical Dijkstra algorithm.

We introduce a new programming language and its categorical semantics in order to design and implement neural networks within the framework of algebraic effects and handlers for arrows. Our language enables us to construct neural networks symbolically, in the same manner as algebraic effects, and to assign implementations—such as backpropagation computations—to them via handlers. The advantage of this language design is that network descriptions become abstract and high-level, while implementations can be flexibly assigned to networks. We establish a rigorous foundation for our language by developing a type system, an operational semantics, a categorical semantics, and soundness and adequacy theorems. The technical core is the introduction of reverse handlers , a novel handler mechanism for arrows for implementing backpropagation, together with new algebras of strong promonads on reverse differential restriction categories (RDRCs), whose string diagrams provide a formal graphical syntax and semantics for neural networks.

Abstract We present an arrow calculus with operations and handlers and its operational and denotational semantics. The calculus is an extension of Lindley, Wadler and Yallop’s arrow calculus. The denotational semantics is given using a strong (pro)monad $\mathcal{A}$ in the bicategory of categories and profunctors. The construction of this strong monad $\mathcal{A}$ is not trivial because of a size problem. To build denotational semantics, we investigate what $\mathcal{A}$ -algebras are, and a handler is interpreted as an $\mathcal{A}$ -homomorphisms between $\mathcal{A}$ -algebras. The syntax and operational semantics are derived from the observations on $\mathcal{A}$ -algebras. We prove the soundness and adequacy theorem of the operational semantics for the denotational semantics.

We describe our ongoing work on generalizing some quantitatively constrained notions of weak simulation up-to that are recently introduced for deterministic systems modeling program execution. We present and discuss a new notion dubbed preorder-constrained simulation that allows comparison between words using a preorder, instead of equality.

Previous neuroimaging studies have reported that the ventral temporal cortex (VTC) processes visual stimuli and thereby establish visual categories, which can be detected in electrophysiological signals such as electrocorticography (ECoG). However, most of the studies are based on visual stimulation through a computer. Thus, the degree to which those categories can be generalized is unclear under real-world conditions. This study extends the findings of a previous experiment, which aimed in real-time detection of visual perception, and investigated whether neural face and kanji categories obtained by computer stimuli can be confirmed in a real-world scenario. The real-time decoder accuracy and latency of two patients with epilepsy revealed that real-world faces and kanji can be detected with 79.9% and 28.4% accuracy, respectively, showing an average online detection latency of 447 ms with respect to presentation time. Hence, the VTC cortex elicits robust and similar responses to computer stimuli and real-world face, leading to a powerful brain-computer interface to track a person's attention in a real-world scenario.