3,644 research outputs found
Fuzzy Quasi-Metric Spaces: Bicompletion, Contractions on Product Spaces, and Applications to Access Predictions
Desde que L.A. Zadeh presentó la teorÃa de conjuntos difusos en 1965, esta se ha usado en una amplia serie de áreas de las matemáticas y se ha aplicado en una gran variedad de escenarios de la vida real. Estos escenarios cubren procesos complejos sin modelo matemático sencillo tales como dispositivos de control industrial, reconocimiento de patrones o sistemas que gestionen información imprecisa o altamente impredecible.
La topologÃa difusa es un importante ejemplo de uso de la teorÃa de L.A. Zadeh. Durante años, los autores de este campo han buscado obtener la definición de un espacio métrico difuso para medir la distancia entre elementos según grados de proximidad.
El presente trabajo trata acerca de la bicompletación de espacios casi-métricos difusos en el sentido de Kramosil y Michalek. Sherwood probó que todo espacio métrico difuso admite completación que es única excepto por isometrÃa basándose en propiedades de la métrica de Lévy. Probamos aquà que todo espacio casi-métrico difuso tiene bicompletación usando directamente el supremo de conjuntos en [0,1] y lÃmites inferiores de secuencias en [0,1] en lugar de usar la métrica de Lévy.
Aprovechamos tanto la bicompletitud y bicompletación de espacios casi-métricos difusos como las propiedades de los espacios métricos difusos y difusos intuicionistas para presentar varias aplicaciones a problemas del campo de la informática.
Asà estudiamos la existencia y unicidad de solución para las ecuaciones de recurrencia asociadas a ciertos algoritmos formados por dos procedimientos recursivos. Para analizar su complejidad aplicamos el principio de contracción de Banach tanto en un producto de casi-métricas no-Arquimedianas en el dominio de las palabras como en la casi-métrica producto de dos espacios de complejidad casi-métricos de Schellekens.
Estudiamos también una aplicación de espacios métricos difusos a sistemas de información basados en localidad de accesos.Castro Company, F. (2010). Fuzzy Quasi-Metric Spaces: Bicompletion, Contractions on Product Spaces, and Applications to Access Predictions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8420Palanci
A kernel-based framework for learning graded relations from data
Driven by a large number of potential applications in areas like
bioinformatics, information retrieval and social network analysis, the problem
setting of inferring relations between pairs of data objects has recently been
investigated quite intensively in the machine learning community. To this end,
current approaches typically consider datasets containing crisp relations, so
that standard classification methods can be adopted. However, relations between
objects like similarities and preferences are often expressed in a graded
manner in real-world applications. A general kernel-based framework for
learning relations from data is introduced here. It extends existing approaches
because both crisp and graded relations are considered, and it unifies existing
approaches because different types of graded relations can be modeled,
including symmetric and reciprocal relations. This framework establishes
important links between recent developments in fuzzy set theory and machine
learning. Its usefulness is demonstrated through various experiments on
synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication.
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Bringing Up a Quantum Baby
Any two infinite-dimensional (separable) Hilbert spaces are unitarily
isomorphic. The sets of all their self-adjoint operators are also therefore
unitarily equivalent. Thus if all self-adjoint operators can be observed, and
if there is no further major axiom in quantum physics than those formulated for
example in Dirac's `Quantum Mechanics', then a quantum physicist would not be
able to tell a torus from a hole in the ground. We argue that there are indeed
such axioms involving vectors in the domain of the Hamiltonian: The
``probability densities'' (hermitean forms) \psi^\dagger \chi for \psi,\chi in
this domain generate an algebra from which the classical configuration space
with its topology (and with further refinements of the axiom, its C^K and
C^infinity structures) can be reconstructed using Gel'fand - Naimark theory.
Classical topology is an attribute of only certain quantum states for these
axioms, the configuration space emergent from quantum physics getting
progressively less differentiable with increasingly higher excitations of
energy and eventually altogether ceasing to exist. After formulating these
axioms, we apply them to show the possibility of topology change and to discuss
quantized fuzzy topologies. Fundamental issues concerning the role of time in
quantum physics are also addressed.Comment: 23 pages, 2 figures ( ref. updated, no other changes
On theories of random variables
We study theories of spaces of random variables: first, we consider random
variables with values in the interval , then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type
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