1,915 research outputs found
A Covariant Information-Density Cutoff in Curved Space-Time
In information theory, the link between continuous information and discrete
information is established through well-known sampling theorems. Sampling
theory explains, for example, how frequency-filtered music signals are
reconstructible perfectly from discrete samples. In this Letter, sampling
theory is generalized to pseudo-Riemannian manifolds. This provides a new set
of mathematical tools for the study of space-time at the Planck scale: theories
formulated on a differentiable space-time manifold can be completely equivalent
to lattice theories. There is a close connection to generalized uncertainty
relations which have appeared in string theory and other studies of quantum
gravity.Comment: 4 pages, RevTe
Gegenbauer-solvable quantum chain model
In an innovative inverse-problem construction the measured, experimental
energies , , ... of a quantum bound-state system are assumed
fitted by an N-plet of zeros of a classical orthogonal polynomial . We
reconstruct the underlying Hamiltonian (in the most elementary
nearest-neighbor-interaction form) and the underlying Hilbert space
of states (the rich menu of non-equivalent inner products is offered). The
Gegenbauer's ultraspherical polynomials are chosen for
the detailed illustration of technicalities.Comment: 29 pp., 1 fi
A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language")
is a fuzzy logic programming language with implicit/explicit truth degree
annotations, a great variety of connectives and unification by similarity.
FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic
Programming, a fuzzy logic language with explicitly annotated rules) and
Bousi~Prolog (which uses a weak unification algorithm and is well suited for
flexible query answering). Hence, it properly manages similarity and truth
degrees in a single framework combining the expressive benefits of both
languages. This paper presents the main features and implementations details of
FASILL. Along the paper we describe its syntax and operational semantics and we
give clues of the implementation of the lattice module and the similarity
module, two of the main building blocks of the new programming environment
which enriches the FLOPER system developed in our research group.Comment: In Proceedings PROLE 2014, arXiv:1501.0169
Pregeometric Concepts on Graphs and Cellular Networks as Possible Models of Space-Time at the Planck-Scale
Starting from the working hypothesis that both physics and the corresponding
mathematics have to be described by means of discrete concepts on the
Planck-scale, one of the many problems one has to face is to find the discrete
protoforms of the building blocks of continuum physics and mathematics. In the
following we embark on developing such concepts for irregular structures like
(large) graphs or networks which are intended to emulate (some of) the generic
properties of the presumed combinatorial substratum from which continuum
physics is assumed to emerge as a coarse grained and secondary model theory. We
briefly indicate how various concepts of discrete (functional) analysis and
geometry can be naturally constructed within this framework, leaving a larger
portion of the paper to the systematic developement of dimensional concepts and
their properties, which may have a possible bearing on various branches of
modern physics beyond quantum gravity.Comment: 16 pages, Invited paper to appear in the special issue of the Journal
of Chaos, Solitons and Fractals on: "Superstrings, M, F, S ... Theory" (M.S.
El Naschie, C. Castro, Editors
Gene Expressio Array Exploration Using K-Formal Concept Analysis
Proceeding of: 9th International Conference, ICFCA 2011, Nicosia, Cyprus, May 2-6, 2011.DNA micro-arrays are a mechanism for eliciting gene expression values, the concentration of the transcription products of a set of genes, under different chemical conditions. The phenomena of interest—up-regulation, down-regulation and co-regulation—are hypothesized to stem from the functional relationships among transcription products. In [1,2,3] a generalisation of Formal Concept Analysis was developed with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the usual Boolean carrier set. In this paper, we use (Rmin+)- and (Rmax+) to analyse gene expression data for Arabidopsis thaliana. We introduce the mechanism to render the data in the appropriate algebra and profit by the wealth of different Galois Connections available in Generalized Formal Concept Analysis to carry different analysis for up- and down-regulated genes.Spanish Government-Comision Interministerial de Ciencia y TecnologĂa projects 2008-06382/TEC and 2008-02473/TEC and the regional projects S-505/TIC/0223 (DGUI-CM) and CCG08-UC3M/TIC- 4457 (Comunidad Aut onoma de Madrid - UC3M)
Ordering objects via attribute preferences
We apply recent results on the construction of suitable orderings for the existence of right adjoint to the analysis of the following problem: given a preference ordering on the set of attributes of a given context, we seek an induced preference among the objects which is compatible with the information provided by the context.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
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