Barnett’s Theorems About the Greatest Common Divisor of Several Univariate Polynomials Through Bezout-like Matrices

This article provides a new presentation of Barnett’s theorems giving the degree (resp. coefficients) of the greatest common divisor of several univariate polynomials with coefficients in an integral domain by means of the rank (resp. linear dependencies of the columns) of several Bezout-like matrices. This new presentation uses Bezout or hybrid Bezout matrices instead of polynomials evaluated in a companion matrix as in the original Barnett’s presentation. Moreover, this presentation also allows us to compute the coefficients of the considered greatest common divisor in an easier way than in the original Barnett’s theorems.     

Analytical Properties of Shannon’s Capacity of Arbitrarily Varying Channels under List Decoding: Super-Additivity and Discontinuity Behavior

The common wisdom is that the capacity of parallel channels is usually additive. This was also conjectured by Shannon for the zero-error capacity function, which was later disproved by constructing explicit counterexamples demonstrating the zero-error capacity to be super-additive. Despite these explicit examples for the zero-error capacity, there is surprisingly little known for nontrivial channels. This paper addresses this question for the arbitrarily varying channel (AVC) under list decoding by developing a complete theory. The list capacity function is studied and shown to be discontinuous, and the corresponding discontinuity points are characterized for all possible list sizes. For parallel AVCs it is then shown that the list capacity is super-additive, implying that joint encoding and decoding for two parallel AVCs can yield a larger list capacity than independent processing of both channels. This discrepancy is shown to be arbitrarily large. Furthermore, the developed theory is applied to the arbitrarily varying wiretap channel to address the scenario of secure communication over AVCs.     

Finding academic experts on a multisensor approach using Shannon’s entropy

Expert finding is an information retrieval task concerned with the search for the most knowledgeable people, in some topic, with basis on documents describing peoples activities. The task involves taking a user query as input and returning a list of people sorted by their level of expertise regarding the user query. This paper introduces a novel approach for combining multiple estimators of expertise based on a multisensor data fusion framework together with the Dempster–Shafer theory of evidence and Shannon’s entropy. More specifically, we defined three sensors which detect heterogeneous information derived from the textual contents, from the graph structure of the citation patterns for the community of experts, and from profile information about the academic experts. Given the evidences collected, each sensor may define different candidates as experts and consequently do not agree in a final ranking decision. To deal with these conflicts, we applied the Dempster–Shafer theory of evidence combined with Shannon’s Entropy formula to fuse this information and come up with a more accurate and reliable final ranking list. Experiments made over two datasets of academic publications from the Computer Science domain attest for the adequacy of the proposed approach over the traditional state of the art approaches. We also made experiments against representative supervised state of the art algorithms. Results revealed that the proposed method achieved a similar performance when compared to these supervised techniques, confirming the capabilities of the proposed framework.     

Fluid flow-based description of the geometrical features in fluidic channels using the Shannon’s information theory: an exploratory study

Microfluidic analytical devices manufactured on paper and similar inexpensive substrates (µ-PADs) have shown considerable promise for disease diagnostics in resource-limited regions. However, current commercialization approaches can be improved substantially by addressing existing technical challenges associated with µ-PADs. Among these, off-device plasma separation from whole blood is a critical challenge in µ-PAD technology that limits commercialization. Existing µ-PADs made by combining multiple components require extra fabrication steps and manufacturing material. Our approach utilizes a two-step plasma process to fabricate single-layer semi-enclosed µ-PADs directly on a commercially available blood plasma separation membrane to incorporate blood plasma separation functionality into the device. The semi-enclosed µ-PADs are bonded with low-cost adhesive plastic tape to provide mechanical support to the device and make it more mechanically robust for field applications. Detection zones of the µ-PADs have also been modified with a cellulose nanocrystal (CNC) to increase colorimetric signal homogeneity, thus enhancing signal quality. The CNC-modified µ-PADs have been used for colorimetric detection of two model analytes (glucose and albumin) in whole blood. Colorimetric signals for both glucose and albumin from whole blood samples were consistent with the calibration curves generated using stock solutions.

     

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.     

Rényi Extrapolation of Shannon Entropy

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide a lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann entropy of a mixed quantum state, its linear entropy and traces.     

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.     

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.     

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...     

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...     

New Proofs of Important Theorems of Untyped Extensional λ Calculus

This paper contains new proofs of the following two theorems of the untyped extensional λ-calculus: the Curry theorem stating that any λ-term has a βη-normal form if and only if it has a β-normal form and the normalization theorem for βη-reduction. The proposed approach is based on the following well-known results: the postponement theorem of η-reduction and the strong normalization property of η-reduction that allow one to naturally extend some propositions from the usual λ-calculus to the extensional case.     

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...     

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.