1,287 research outputs found
Relational Galois connections between transitive fuzzy digraphs
Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering
Arithmetic Operations in Multi-Valued Logic
This paper presents arithmetic operations like addition, subtraction and
multiplications in Modulo-4 arithmetic, and also addition, multiplication in
Galois field, using multi-valued logic (MVL). Quaternary to binary and binary
to quaternary converters are designed using down literal circuits. Negation in
modular arithmetic is designed with only one gate. Logic design of each
operation is achieved by reducing the terms using Karnaugh diagrams, keeping
minimum number of gates and depth of net in to consideration. Quaternary
multiplier circuit is proposed to achieve required optimization. Simulation
result of each operation is shown separately using Hspice.Comment: 12 Pages, VLSICS Journal 201
Towards a generalisation of formal concept analysis for data mining purposes
In this paper we justify the need for a generalisation of Formal
Concept Analysis for the purpose of data mining and begin the
synthesis of such theory. For that purpose, we first review semirings and
semimodules over semirings as the appropriate objects to use in abstracting
the Boolean algebra and the notion of extents and intents, respectively.
We later bring to bear powerful theorems developed in the field
of linear algebra over idempotent semimodules to try to build a Fundamental
Theorem for K-Formal Concept Analysis, where K is a type of
idempotent semiring. Finally, we try to put Formal Concept Analysis in
new perspective by considering it as a concrete instance of the theory
developed
Binding Social and Cultural Networks: A Model
Until now, most studies carried onto social or semantic networks have
considered each of these networks independently. Our goal here is to bring a
formal frame for studying both networks empirically as well as to point out
stylized facts that would explain their reciprocal influence and the emergence
of clusters of agents, which may also be regarded as ''cultural cliques''. We
show how to apply the Galois lattice theory to the modeling of the coevolution
of social and conceptual networks, and the characterization of cultural
communities. Basing our approach on Barabasi-Albert's models, we however extend
the usual preferential attachment probability in order to take into account the
reciprocal influence of both networks, therefore introducing the notion of dual
distance. In addition to providing a theoretic frame we draw here a program of
empirical tests which should give root to a more analytical model and the
consequent simulation and validation. In a broader view, adopting and actually
implementing the paradigm of cultural epidemiology, we could proceed further
with the study of knowledge diffusion and explain how the social network
structure affects concept propagation and in return how concept propagation
affects the social network.Comment: 8 pages, 3 figures (v2: typos, minor corrections in section 3.2) (v3:
examples, figures added
Resource theories of knowledge
How far can we take the resource theoretic approach to explore physics?
Resource theories like LOCC, reference frames and quantum thermodynamics have
proven a powerful tool to study how agents who are subject to certain
constraints can act on physical systems. This approach has advanced our
understanding of fundamental physical principles, such as the second law of
thermodynamics, and provided operational measures to quantify resources such as
entanglement or information content. In this work, we significantly extend the
approach and range of applicability of resource theories. Firstly we generalize
the notion of resource theories to include any description or knowledge that
agents may have of a physical state, beyond the density operator formalism. We
show how to relate theories that differ in the language used to describe
resources, like micro and macroscopic thermodynamics. Finally, we take a
top-down approach to locality, in which a subsystem structure is derived from a
global theory rather than assumed. The extended framework introduced here
enables us to formalize new tasks in the language of resource theories, ranging
from tomography, cryptography, thermodynamics and foundational questions, both
within and beyond quantum theory.Comment: 28 pages featuring figures, examples, map and neatly boxed theorems,
plus appendi
Permutations of Massive Vacua
We discuss the permutation group G of massive vacua of four-dimensional gauge
theories with N=1 supersymmetry that arises upon tracing loops in the space of
couplings. We concentrate on superconformal N=4 and N=2 theories with N=1
supersymmetry preserving mass deformations. The permutation group G of massive
vacua is the Galois group of characteristic polynomials for the vacuum
expectation values of chiral observables. We provide various techniques to
effectively compute characteristic polynomials in given theories, and we deduce
the existence of varying symmetry breaking patterns of the duality group
depending on the gauge algebra and matter content of the theory. Our examples
give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur
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