5,187 research outputs found
Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra
Mathematics, and more generally computational sciences, intervene in several
aspects of music. Mathematics describes the acoustics of the sounds giving
formal tools to physics, and the matter of music itself in terms of
compositional structures and strategies. Mathematics can also be applied to the
entire making of music, from the score to the performance, connecting
compositional structures to acoustical reality of sounds. Moreover, the precise
concept of gesture has a decisive role in understanding musical performance. In
this paper, we apply some concepts of category theory to compare gestures of
orchestral musicians, and to investigate the relationship between orchestra and
conductor, as well as between listeners and conductor/orchestra. To this aim,
we will introduce the concept of gestural similarity. The mathematical tools
used can be applied to gesture classification, and to interdisciplinary
comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of
Mathematics and Musi
Ideal-quasi-Cauchy sequences
An ideal is a family of subsets of positive integers which
is closed under taking finite unions and subsets of its elements. A sequence
of real numbers is said to be -convergent to a real number , if
for each \; the set belongs
to . We introduce -ward compactness of a subset of , the set
of real numbers, and -ward continuity of a real function in the senses that
a subset of is -ward compact if any sequence of
points in has an -quasi-Cauchy subsequence, and a real function is
-ward continuous if it preserves -quasi-Cauchy sequences where a sequence
is called to be -quasi-Cauchy when is
-convergent to 0. We obtain results related to -ward continuity, -ward
compactness, ward continuity, ward compactness, ordinary compactness, ordinary
continuity, -ward continuity, and slowly oscillating continuity.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1005.494
On algebraic supergroups, coadjoint orbits and their deformations
In this paper we study algebraic supergroups and their coadjoint orbits as
affine algebraic supervarieties. We find an algebraic deformation quantization
of them that can be related to the fuzzy spaces of non commutative geometry.Comment: 37 pages, AMS-LaTe
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated
Gauge Theories on Deformed Spaces
The aim of this review is to present an overview over available models and
approaches to non-commutative gauge theory. Our main focus thereby is on gauge
models formulated on flat Groenewold-Moyal spaces and renormalizability, but we
will also review other deformations and try to point out common features. This
review will by no means be complete and cover all approaches, it rather
reflects a highly biased selection.Comment: v2 references added; v3 published versio
The structure of classical extensions of quantum probability theory
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed
Duality Symmetries and Noncommutative Geometry of String Spacetime
We examine the structure of spacetime symmetries of toroidally compactified
string theory within the framework of noncommutative geometry. Following a
proposal of Frohlich and Gawedzki, we describe the noncommutative string
spacetime using a detailed algebraic construction of the vertex operator
algebra. We show that the spacetime duality and discrete worldsheet symmetries
of the string theory are a consequence of the existence of two independent
Dirac operators, arising from the chiral structure of the conformal field
theory. We demonstrate that these Dirac operators are also responsible for the
emergence of ordinary classical spacetime as a low-energy limit of the string
spacetime, and from this we establish a relationship between T-duality and
changes of spin structure of the target space manifold. We study the
automorphism group of the vertex operator algebra and show that spacetime
duality is naturally a gauge symmetry in this formalism. We show that classical
general covariance also becomes a gauge symmetry of the string spacetime. We
explore some larger symmetries of the algebra in the context of a universal
gauge group for string theory, and connect these symmetry groups with some of
the algebraic structures which arise in the mathematical theory of vertex
operator algebras, such as the Monster group. We also briefly describe how the
classical topology of spacetime is modified by the string theory, and calculate
the cohomology groups of the noncommutative spacetime. A self-contained,
pedagogical introduction to the techniques of noncommmutative geometry is also
included.Comment: 70 pages, Latex, No Figures. Typos and references corrected. Version
to appear in Communications in Mathematical Physic
Mathematical problems for complex networks
Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy
is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
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