Three tokens in Herman’s algorithm

Herman’s algorithm is a synchronous randomized protocol for achieving self-stabilization in a token ring consisting of N processes. The interaction of tokens makes the dynamics of the protocol very difficult to analyze. In this paper we study the distribution of the time to stabilization, assuming that there are three tokens in the initial configuration. We show for arbitrary N and for an arbitrary timeout t that the probability of stabilization within time t is minimized by choosing as the initial three-token configuration the configuration in which the tokens are placed equidistantly on the ring. Our result strengthens a corollary of a theorem of McIver and Morgan (Inf. Process Lett. 94(2): 79–84, 2005), which states that the expected stabilization time is minimized by the equidistant configuration.     

Formalization of Shannon’s Theorems

The most fundamental results of information theory are Shannon’s theorems. These theorems express the bounds for (1) reliable data compression and (2) data transmission over a noisy channel. Their proofs are non-trivial but are rarely detailed, even in the introductory literature. This lack of formal foundations is all the more unfortunate that crucial results in computer security rely solely on information theory: this is the so-called “unconditional security”. In this article, we report on the formalization of a library for information theory in the SSReflect extension of the Coq proof-assistant. In particular, we produce the first formal proofs of the source coding theorem, that introduces the entropy as the bound for lossless compression, and of the channel coding theorem, that introduces the capacity as the bound for reliable communication over a noisy channel.     

An analysis of a firm’s capacity in Mazda’s Keiretsu

Capacity is defined as the power resulting from the specific position of a company in a network organization. This article extends the theory of network organizations to examine Mazda’s Yokokai Keiretsu, and proposes a new approach to calculating a firm’s capacity in a network. Capacity is divided into two categories, take-in capacity and take-out capacity, and the gap between them is called the capacity difference. We analyze the impact of capacity difference as a determinant of corporate performance in network organizations, thus providing a new perspective for successful corporate management.     

Design of robotic arm’s action to imitate the mechanism of an animal’s consciousness

We are attempting to develop a system so that a user is able to let robots perform an intellectual action that has a healing and friendly feeling. Based on the development process of the actions and consciousness of animals, we constructed a structure model which connects consciousness and action hierarchically, built a valuation function for action selection, and developed software to control the action of a robot. This software is called Consciousness-Based Architecture (CBA). With it, our aim is to connect a user and robot as closely as possible and to allow smooth communications between them by developing an emotional system that takes notice of consciousness. In our system, the robotic arm’s finger is outfitted with a small Web camera, which allows the arm to recognize external information so that the robot can select various actions that comply with certain factors in the outside environment. Furthermore, by using the actuator of the robotic arm, the system we have built provides a correspondence between the robot’s internal states, such as the degree of rotation angle, and the outside temperature. In the present study, a motivation model which considers the outside environment and the internal states has been built into the CBA, and the behavior of the robotic arm has been verified.     

The Resolution of Keller’s Conjecture

Journal of Automated Reasoning - We consider three graphs, $$G_{7,3}$$ , $$G_{7,4}$$ , and $$G_{7,6}$$ , related to Keller’s conjecture in dimension 7. The conjecture is false for this...     

Quantum dynamics of Friedmann’s universe

In the dynamics of three-dimensional space in global time, the global scale takes the form of a discrete variable whose dynamics is described by Friedmann models. Due to a nonzero Hamiltonian, a differential equation is formed for a vacuum configuration. This equation has exact discrete solutions with the spectrum ε _n = ±\(\sqrt {2n} \). Three Hilbert spaces are connected with this equation. We study the dynamics of wave packets on the basis of a small number of eigenfunctions.     

On Floridi’s Method of Levels of Abstraction

Abstraction is arguably one of the most important methods in modern science in analysing and understanding complex phenomena. In his book The Philosophy of Information, Floridi (The philosophy of information. Oxford University Press, Oxford, 2011) presents the method of levels of abstraction as the main method of the Philosophy of Information. His discussion of abstraction as a method seems inspired by the formal methods and frameworks of computer science, in which abstraction is operationalised extensively in programming languages and design methodologies. Is it really clear what we should understand by levels of abstraction? How should they be specified? We will argue that levels of abstraction should be augmented with annotations, in order to express semantic information for them and reconcile the method of level of abstraction (LoA’s) with other approaches. We discuss the extended method when applied e.g. to the analysis of abstract machines. This will lead to an example in which the number of LoA’s is unbounded.     

A Reinterpretation of Beall’s ‘Off-Topic’ Semantics

Journal of Logic, Language and Information - Jc Beall’s off-topic interpretation of Weak Kleene logic offers a logic of ‘true-and-topic’ preservation. However, Nissim Francez has...     

A series of revisions of David Poole’s specificity

In the middle of the 1980s, David Poole introduced a semantic, model-theoretic notion of specificity to the artificial-intelligence community. Since then it has found further applications in non-monotonic reasoning, in particular in defeasible reasoning. Poole tried to approximate the intuitive human concept of specificity, which seems to be essential for reasoning in everyday life with its partial and inconsistent information. His notion, however, turns out to be intricate and problematic, which — as we show — can be overcome to some extent by a closer approximation of the intuitive human concept of specificity. Besides the intuitive advantages of our novel specificity orderings over Poole’s specificity relation in the classical examples of the literature, we also report some hard mathematical facts: Contrary to what was claimed before, we show that Poole’s relation is not transitive in general. The first of our specificity orderings (CP1) captures Poole’s original intuition as close as we could get after the correction of its technical flaws. The second one (CP2) is a variation of CP1 and presents a step toward similar notions that may eventually solve the intractability problem of Poole-style specificity relations. The present means toward deciding our novel specificity relations, however, show only slight improvements over the known ones for Poole’s relation; therefore, we suggest a more efficient workaround for applications in practice.     

On the order of convergence of Broyden’s method

Calcolo - We derive results on equivalence of piecewise polynomial approximations of a given function in the Sobolev space $${varvec{H}}{mathrm{(curl)}}$$ . We namely show that the global-best...     

Postoptimal analysis of bicriteria boolean problems of selecting investment projects with Wald’s and Savage’s criteria

Lower and upper feasible bounds on the stability radius of the Pareto-optimal portfolio in the bicriteria Boolean investment problem with the Wald maximin efficiency criterion and the Savage minimax risk criterion are obtained in the case when the Chebyshev metric is defined in the space of varying parameters.     

A Historical View of Studies of Women’s Work

Computer Supported Cooperative Work (CSCW) - This paper places observational studies of women’s work in historical perspective. We present some of the very early studies (carried out in the...