234 research outputs found
Restriction of the Fourier transform to some complex curves
The purpose of this paper is to prove a Fourier restriction estimate for certain 2-dimensional surfaces in R-2d, d >= 3. These surfaces are defined by a complex curve gamma (z) of simple type, which is given by a mapping of the form z bar right arrow gamma (z) = (z, z(2), ..., z(d-1), phi(z)) where phi(z) is an analytic function on a domain Omega subset of C. This is regarded as a real mapping z = (x, y) bar right arrow gamma (x, y) from Omega subset of R-2 to R-2d. Our results cover the case phi(z) = z(N) for any nonnegative integer N, in all dimensions d >= 3. The main result is a uniform estimate, valid when d = 3, where phi(z) may be taken to be an arbitrary polynomial of degree at most N. It is uniform in the sense that the operator norm is independent of the coefficients of the polynomial. These results are analogues of the uniform restricted strong type estimates in [5], valid for polynomial curves of simple type and some other classes of curves in R-d, d >= 3. (C) 2013 Elsevier Inc. All rights reserved.X1111Ysciescopu
Holographic Correlation Functions for Open Strings and Branes
In this paper, we compute holographically the two-point and three-point
functions of giant gravitons with open strings. We consider the maximal giant
graviton in and the string configurations corresponding to the ground
states of Z=0 and Y=0 open spin chain, and the spinning string in AdS
corresponding to the derivative type impurities in Y=0 or Z=0 open spin chain
as well. We treat the D-brane and open string contribution separately and find
the corresponding D3-brane and string configurations in bulk which connect the
composite operators at the AdS boundary. We apply a new prescription to
treat the string state contribution and find agreements for the two-point
functions. For the three-point functions of two giant gravitons with open
strings and one certain half-BPS chiral primary operator, we find that the
D-brane contributions to structure constant are always vanishing and the open
string contribution for the Y=0 ground state is in perfect match with the
prediction in the free field limit.Comment: 25 page
More three-point correlators of giant magnons with finite size
In the framework of the semiclassical approach, we compute the normalized
structure constants in three-point correlation functions, when two of the
vertex operators correspond to heavy string states, while the third vertex
corresponds to a light state. This is done for the case when the heavy string
states are finite-size giant magnons with one or two angular momenta, and for
two different choices of the light state, corresponding to dilaton operator and
primary scalar operator. The relevant operators in the dual gauge theory are
Tr(F_{\mu\nu}^2 Z^j+...) and Tr(Z^j). We first consider the case of AdS_5 x S^5
and N = 4 super Yang-Mills. Then we extend the obtained results to the
gamma-deformed AdS_5 x S^5_\gamma, dual to N = 1 super Yang-Mills theory,
arising as an exactly marginal deformation of N = 4 super Yang-Mills.Comment: 14 pages, no figure
Holographic three-point functions of giant gravitons
Working within the AdS/CFT correspondence we calculate the three-point
function of two giant gravitons and one pointlike graviton using methods of
semiclassical string theory and considering both the case where the giant
gravitons wrap an S^3 in S^5 and the case where the giant gravitons wrap an S^3
in AdS_5. We likewise calculate the correlation function in N=4 SYM using two
Schur polynomials and a single trace chiral primary. We find that the gauge and
string theory results have structural similarities but do not match perfectly,
and interpret this in terms of the Schur polynomials' inability to interpolate
between dual giant and pointlike gravitons.Comment: 21 page
How citation boosts promote scientific paradigm shifts and Nobel Prizes
Nobel Prizes are commonly seen to be among the most prestigious achievements
of our times. Based on mining several million citations, we quantitatively
analyze the processes driving paradigm shifts in science. We find that
groundbreaking discoveries of Nobel Prize Laureates and other famous scientists
are not only acknowledged by many citations of their landmark papers.
Surprisingly, they also boost the citation rates of their previous
publications. Given that innovations must outcompete the rich-gets-richer
effect for scientific citations, it turns out that they can make their way only
through citation cascades. A quantitative analysis reveals how and why they
happen. Science appears to behave like a self-organized critical system, in
which citation cascades of all sizes occur, from continuous scientific progress
all the way up to scientific revolutions, which change the way we see our
world. Measuring the "boosting effect" of landmark papers, our analysis reveals
how new ideas and new players can make their way and finally triumph in a world
dominated by established paradigms. The underlying "boost factor" is also
useful to discover scientific breakthroughs and talents much earlier than
through classical citation analysis, which by now has become a widespread
method to measure scientific excellence, influencing scientific careers and the
distribution of research funds. Our findings reveal patterns of collective
social behavior, which are also interesting from an attention economics
perspective. Understanding the origin of scientific authority may therefore
ultimately help to explain, how social influence comes about and why the value
of goods depends so strongly on the attention they attract.Comment: 6 pages, 6 figure
Universal features of correlated bursty behaviour
Inhomogeneous temporal processes, like those appearing in human
communications, neuron spike trains, and seismic signals, consist of
high-activity bursty intervals alternating with long low-activity periods. In
recent studies such bursty behavior has been characterized by a fat-tailed
inter-event time distribution, while temporal correlations were measured by the
autocorrelation function. However, these characteristic functions are not
capable to fully characterize temporally correlated heterogenous behavior. Here
we show that the distribution of the number of events in a bursty period serves
as a good indicator of the dependencies, leading to the universal observation
of power-law distribution in a broad class of phenomena. We find that the
correlations in these quite different systems can be commonly interpreted by
memory effects and described by a simple phenomenological model, which displays
temporal behavior qualitatively similar to that in real systems
Correlation functions of three heavy operators - the AdS contribution
We consider operators in N=4 SYM theory which are dual, at strong coupling,
to classical strings rotating in S^5. Three point correlation functions of such
operators factorize into a universal contribution coming from the AdS part of
the string sigma model and a state-dependent S^5 contribution. Consequently a
similar factorization arises for the OPE coefficients. In this paper we
evaluate the AdS universal factor of the OPE coefficients which is explicitly
expressed just in terms of the anomalous dimensions of the three operators.Comment: 49 pages, 3 figures; v.2 references corrected; v3: corrected
discussion in section 5, results unchange
Long-lived pressure-driven coherent structures in KSTAR plasmas
Highly coherent structures associated with an extremely long-lived saturated magnetohydrodynamic instability have been observed in KSTAR tokamak under a long-pulse and steady-state operation. They persist essentially unchanged for the full duration of a discharge up to 40 s, much longer than any dynamical or dissipative time scales in the system. Analysis of the data, supported by numerical simulations, indicates that they may be associated with a pressure-driven mode causing some degradation in the toroidal rotation, electron, and ion energy confinement. Published by AIP Publishing.open1121Ysciescopu
The General Age of Leadership: Older-Looking Presidential Candidates Win Elections during War
As nation-state leaders age they increasingly engage in inter-state militarized disputes yet in industrialized societies a steady decrease in testosterone associated with aging is observed – which suggests a decrease in dominance behavior. The current paper points out that from modern societies to Old World monkeys increasing both in age and social status encourages dominant strategies to maintain acquired rank. Moreover, it is argued this consistency has shaped an implicit prototype causing followers to associate older age with dominance leadership. It is shown that (i) faces of older leaders are preferred during intergroup conflict and (ii) morphing U.S. Presidential candidates to appear older or younger has an overriding effect on actual election outcomes. This indicates that democratic voting can be systematically adjusted by activating innate biases. These findings appear to create a new line of research regarding the biology of leadership and contextual cues of age
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