We derive two types of representation results for increasing convex functionals in terms countably additive measures. The first is a max-representation defined on spaces real-valued continuous functions and the second sup-representa

My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...

The method of spectral distribution only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. The idea of calculation of the probability amplitudes for continuous-time quantum walk, in terms of the spectral distribution associated with the adjacency matrix of graphs was firs...

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N -fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K2 graphs (Complete graph with two vertices) and the probability of observing wal...

Our interest is in the design process that spans the gap between the requirements acquisition process and the implementation process, in which the basic architecture of a system is defined, and functions are allocated to software, hardware, and human agents. We call this process composite system design. Our goal is an interactive model of composite system design incorporating deficiency-driven ...

This paper investigates second-order representations in the sense of Kawamura and Cook for spaces of integrable functions that regularly show up in analysis. It builds upon prior work about the space of continuous functions on the unit interval: Kawamura and Cook introduced a representation inducing the right complexity classes and proved that it is the weakest second-order representation such ...

Just as semantic hashing [Salakhutdinov and Hinton2009] can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for nodes in a graph. By imagining the embeddings as independent coin flips of varying bias, continuous optimization techniques can be...

A class of optimal hybrid control problems involving model and state jump systems is considered. The calculation of optimal switching times amounts to minimizing a cost function. A continuous representation of these problems – based on convergence results – is introduced. This representation simplifies the study of the initial problem as it is shown, while applying variational formalism to dete...

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...