15,737 research outputs found
Quantum Moduli Spaces of String Theories
Generically, string models with supersymmetry are not expected to have
moduli beyond perturbation theory; stringy non-perturbative effects as well as
low energy field-theoretic phenomena such as gluino condensation will lift any
flat directions. In this note, we describe models where some subspace of the
moduli space survives non-perturbatively. Discrete symmetries forbid any
inherently stringy effects, and dynamical considerations control the
field-theoretic effects. The surviving subspace is a space of high symmetry;
the system is attracted to this subspace by a potential which we compute.
Models of this type may be useful for considerations of duality and raise
troubling cosmological questions about string theory. Our considerations also
suggest a mechanism for fixing the expectation value of the dilaton.Comment: 26 pages; uses harvmac. Footnote re fixing dilaton adde
Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
The holomorphic anomaly equations describe B-model closed topological strings
in Calabi-Yau geometries. Having been used to construct perturbative
expansions, it was recently shown that they can also be extended past
perturbation theory by making use of resurgent transseries. These yield formal
nonperturbative solutions, showing integrability of the holomorphic anomaly
equations at the nonperturbative level. This paper takes such constructions one
step further by working out in great detail the specific example of topological
strings in the mirror of the local CP2 toric Calabi-Yau background, and by
addressing the associated (resurgent) large-order analysis of both perturbative
and multi-instanton sectors. In particular, analyzing the asymptotic growth of
the perturbative free energies, one finds contributions from three different
instanton actions related by Z_3 symmetry, alongside another action related to
the Kahler parameter. Resurgent transseries methods then compute, from the
extended holomorphic anomaly equations, higher instanton sectors and it is
shown that these precisely control the asymptotic behavior of the perturbative
free energies, as dictated by resurgence. The asymptotic large-order growth of
the one-instanton sector unveils the presence of resonance, i.e., each
instanton action is necessarily joined by its symmetric contribution. The
structure of different resurgence relations is extensively checked at the
numerical level, both in the holomorphic limit and in the general
nonholomorphic case, always showing excellent agreement with transseries data
computed out of the nonperturbative holomorphic anomaly equations. The
resurgence relations further imply that the string free energy displays an
intricate multi-branched Borel structure, and that resonance must be properly
taken into account in order to describe the full transseries solution.Comment: 63 pages, 54 images in 24 figures, jheppub-nosort.sty; v2: corrected
figure, minor changes, final version for CM
Superposition frames for adaptive time-frequency analysis and fast reconstruction
In this article we introduce a broad family of adaptive, linear
time-frequency representations termed superposition frames, and show that they
admit desirable fast overlap-add reconstruction properties akin to standard
short-time Fourier techniques. This approach stands in contrast to many
adaptive time-frequency representations in the extant literature, which, while
more flexible than standard fixed-resolution approaches, typically fail to
provide efficient reconstruction and often lack the regular structure necessary
for precise frame-theoretic analysis. Our main technical contributions come
through the development of properties which ensure that this construction
provides for a numerically stable, invertible signal representation. Our
primary algorithmic contributions come via the introduction and discussion of
specific signal adaptation criteria in deterministic and stochastic settings,
based respectively on time-frequency concentration and nonstationarity
detection. We conclude with a short speech enhancement example that serves to
highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio
Sampling from a system-theoretic viewpoint: Part I - Concepts and tools
This paper is first in a series of papers studying a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. In this paper we present the paradigm and revise underlying technical tools, such as the lifting technique and some topics of the operator theory. This material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems, recovering many hitherto considered different solutions and leading to new results. Some of these applications are discussed in the second part
Probability & incompressible Navier-Stokes equations: An overview of some recent developments
This is largely an attempt to provide probabilists some orientation to an
important class of non-linear partial differential equations in applied
mathematics, the incompressible Navier-Stokes equations. Particular focus is
given to the probabilistic framework introduced by LeJan and Sznitman [Probab.
Theory Related Fields 109 (1997) 343-366] and extended by Bhattacharya et al.
[Trans. Amer. Math. Soc. 355 (2003) 5003-5040; IMA Vol. Math. Appl., vol. 140,
2004, in press]. In particular this is an effort to provide some foundational
facts about these equations and an overview of some recent results with an
indication of some new directions for probabilistic consideration.Comment: Published at http://dx.doi.org/10.1214/154957805100000078 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Binary Hypothesis Testing Game with Training Data
We introduce a game-theoretic framework to study the hypothesis testing
problem, in the presence of an adversary aiming at preventing a correct
decision. Specifically, the paper considers a scenario in which an analyst has
to decide whether a test sequence has been drawn according to a probability
mass function (pmf) P_X or not. In turn, the goal of the adversary is to take a
sequence generated according to a different pmf and modify it in such a way to
induce a decision error. P_X is known only through one or more training
sequences. We derive the asymptotic equilibrium of the game under the
assumption that the analyst relies only on first order statistics of the test
sequence, and compute the asymptotic payoff of the game when the length of the
test sequence tends to infinity. We introduce the concept of
indistinguishability region, as the set of pmf's that can not be distinguished
reliably from P_X in the presence of attacks. Two different scenarios are
considered: in the first one the analyst and the adversary share the same
training sequence, in the second scenario, they rely on independent sequences.
The obtained results are compared to a version of the game in which the pmf P_X
is perfectly known to the analyst and the adversary
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