7,874 research outputs found
Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models
In the previous study, we formulate a matrix model renormalization group
based on the fuzzy spherical harmonics with which a notion of high/low energy
can be attributed to matrix elements, and show that it exhibits locality and
various similarity to the usual Wilsonian renormalization group of quantum
field theory. In this work, we continue the renormalization group analysis of a
matrix model with emphasis on nonlocal interactions where the fields on
antipodal points are coupled. They are indeed generated in the renormalization
group procedure and are tightly related to the noncommutative nature of the
geometry. We aim at formulating renormalization group equations including such
nonlocal interactions and finding existence of nontrivial field theory with
antipodal interactions on the fuzzy sphere. We find several nontrivial fixed
points and calculate the scaling dimensions associated with them. We also
consider the noncommutative plane limit and then no consistent fixed point is
found. This contrast between the fuzzy sphere limit and the noncommutative
plane limit would be manifestation in our formalism of the claim given by Chu,
Madore and Steinacker that the former does not have UV/IR mixing, while the
latter does.Comment: 1+47 pages, no figure; Ver. 2, references and some comments are
added; Ver. 3, typos corrected. Version to appear in JHE
Noncommutative geometry, Quantum effects and DBI-scaling in the collapse of D0-D2 bound states
We study fluctuations of time-dependent fuzzy two-sphere solutions of the
non-abelian DBI action of D0-branes, describing a bound state of a spherical
D2-brane with N D0-branes. The quadratic action for small fluctuations is shown
to be identical to that obtained from the dual abelian D2-brane DBI action,
using the non-commutative geometry of the fuzzy two-sphere. For some of the
fields, the linearized equations take the form of solvable Lam\'e equations. We
define a large-N DBI-scaling limit, with vanishing string coupling and string
length, and where the gauge theory coupling remains finite. In this limit, the
non-linearities of the DBI action survive in both the classical and the quantum
context, while massive open string modes and closed strings decouple. We
describe a critical radius where strong gauge coupling effects become
important. The size of the bound quantum ground state of multiple D0-branes
makes an intriguing appearance as the radius of the fuzzy sphere, where the
maximal angular momentum quanta become strongly coupled.Comment: 34 pages, Latex; v2: Minor correction in conformal transformation of
couplings, references adde
Complexity of fuzzy answer set programming under Łukasiewicz semantics
Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Łukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules – a syntactic generalization which does not affect the expressivity of ASP in the classical case – the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully characterizing the complexity of FASP in this more general setting is not likely to have an easy solution
Renormalization group approach to matrix models via noncommutative space
We develop a new renormalization group approach to the large-N limit of
matrix models. It has been proposed that a procedure, in which a matrix model
of size (N-1) \times (N-1) is obtained by integrating out one row and column of
an N \times N matrix model, can be regarded as a renormalization group and that
its fixed point reveals critical behavior in the large-N limit. We instead
utilize the fuzzy sphere structure based on which we construct a new map
(renormalization group) from N \times N matrix model to that of rank N-1. Our
renormalization group has great advantage of being a nice analog of the
standard renormalization group in field theory. It is naturally endowed with
the concept of high/low energy, and consequently it is in a sense local and
admits derivative expansions in the space of matrices. In construction we also
find that our renormalization in general generates multi-trace operators, and
that nonplanar diagrams yield a nonlocal operation on a matrix, whose action is
to transport the matrix to the antipode on the sphere. Furthermore the
noncommutativity of the fuzzy sphere is renormalized in our formalism. We then
analyze our renormalization group equation, and Gaussian and nontrivial fixed
points are found. We further clarify how to read off scaling dimensions from
our renormalization group equation. Finally the critical exponent of the model
of two-dimensional gravity based on our formalism is examined.Comment: 1+42 pages, 4 figure
Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System
Due to the inherent aleatory uncertainties in renewable generators, the
reliability/adequacy assessments of distributed generation (DG) systems have
been particularly focused on the probabilistic modeling of random behaviors,
given sufficient informative data. However, another type of uncertainty
(epistemic uncertainty) must be accounted for in the modeling, due to
incomplete knowledge of the phenomena and imprecise evaluation of the related
characteristic parameters. In circumstances of few informative data, this type
of uncertainty calls for alternative methods of representation, propagation,
analysis and interpretation. In this study, we make a first attempt to
identify, model, and jointly propagate aleatory and epistemic uncertainties in
the context of DG systems modeling for adequacy assessment. Probability and
possibility distributions are used to model the aleatory and epistemic
uncertainties, respectively. Evidence theory is used to incorporate the two
uncertainties under a single framework. Based on the plausibility and belief
functions of evidence theory, the hybrid propagation approach is introduced. A
demonstration is given on a DG system adapted from the IEEE 34 nodes
distribution test feeder. Compared to the pure probabilistic approach, it is
shown that the hybrid propagation is capable of explicitly expressing the
imprecision in the knowledge on the DG parameters into the final adequacy
values assessed. It also effectively captures the growth of uncertainties with
higher DG penetration levels
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