1,304 research outputs found
A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models
We present a procedure in which known solutions to reflection equations for
interaction-round-a-face lattice models are used to construct new solutions.
The procedure is particularly well-suited to models which have a known fusion
hierarchy and which are based on graphs containing a node of valency . Among
such models are the Andrews-Baxter-Forrester models, for which we construct
reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe
Holomorphic anomaly equations and the Igusa cusp form conjecture
Let be a K3 surface and let be an elliptic curve. We solve the
reduced Gromov-Witten theory of the Calabi-Yau threefold for all
curve classes which are primitive in the K3 factor. In particular, we deduce
the Igusa cusp form conjecture.
The proof relies on new results in the Gromov-Witten theory of elliptic
curves and K3 surfaces. We show the generating series of Gromov-Witten classes
of an elliptic curve are cycle-valued quasimodular forms and satisfy a
holomorphic anomaly equation. The quasimodularity generalizes a result by
Okounkov and Pandharipande, and the holomorphic anomaly equation proves a
conjecture of Milanov, Ruan and Shen. We further conjecture quasimodularity and
holomorphic anomaly equations for the cycle-valued Gromov-Witten theory of
every elliptic fibration with section. The conjecture generalizes the
holomorphic anomaly equations for ellliptic Calabi-Yau threefolds predicted by
Bershadsky, Cecotti, Ooguri, and Vafa. We show a modified conjecture holds
numerically for the reduced Gromov-Witten theory of K3 surfaces in primitive
classes.Comment: 68 page
Meson Decay Constants from the Valence Approximation to Lattice QCD
We evaluate , , , and , extrapolated to physical quark mass, zero
lattice spacing and infinite volume, for lattice QCD with Wilson quarks in the
valence (quenched) approximation. The predicted ratios differ from experiment
by amounts ranging from 12\% to 17\% equivalent to between 0.9 and 2.8 times
the corresponding statistical uncertainties.Comment: uufiles encoded copy of 40 page Latex article, including 14 figures
in Postscript. The long version of hep-lat/9302012, IBM/HET 93-
Curve counting via stable pairs in the derived category
For a nonsingular projective 3-fold , we define integer invariants
virtually enumerating pairs where is an embedded curve and
is a divisor. A virtual class is constructed on the associated
moduli space by viewing a pair as an object in the derived category of . The
resulting invariants are conjecturally equivalent, after universal
transformations, to both the Gromov-Witten and DT theories of . For
Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing
formula in the derived category.
Several calculations of the new invariants are carried out. In the Fano case,
the local contributions of nonsingular embedded curves are found. In the local
toric Calabi-Yau case, a completely new form of the topological vertex is
described.
The virtual enumeration of pairs is closely related to the geometry
underlying the BPS state counts of Gopakumar and Vafa. We prove that our
integrality predictions for Gromov-Witten invariants agree with the BPS
integrality. Conversely, the BPS geometry imposes strong conditions on the
enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page
Accelerating the Universe with Gravitational Waves
Inflation generically produces primordial gravitational waves with a red
spectral tilt. In this paper we calculate the backreaction produced by these
gravitational waves on the expansion of the universe. We find that in radiation
domination the backreaction acts as a relativistic fluid, while in matter
domination a small dark energy emerges with an equation of state w=-8/9.Comment: 18 pages, 4 figures. Replaced with version published by JCAP - some
discussion and references added concerning second-order gravitational waves,
typeset in JHEP styl
A Rule-Based Approach to Analyzing Database Schema Objects with Datalog
Database schema elements such as tables, views, triggers and functions are
typically defined with many interrelationships. In order to support database
users in understanding a given schema, a rule-based approach for analyzing the
respective dependencies is proposed using Datalog expressions. We show that
many interesting properties of schema elements can be systematically determined
this way. The expressiveness of the proposed analysis is exemplarily shown with
the problem of computing induced functional dependencies for derived relations.
The propagation of functional dependencies plays an important role in data
integration and query optimization but represents an undecidable problem in
general. And yet, our rule-based analysis covers all relational operators as
well as linear recursive expressions in a systematic way showing the depth of
analysis possible by our proposal. The analysis of functional dependencies is
well-integrated in a uniform approach to analyzing dependencies between schema
elements in general.Comment: Pre-proceedings paper presented at the 27th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur,
Belgium, 10-12 October 2017 (arXiv:1708.07854
Cosmological Backreaction from Perturbations
We reformulate the averaged Einstein equations in a form suitable for use
with Newtonian gauge linear perturbation theory and track the size of the
modifications to standard Robertson-Walker evolution on the largest scales as a
function of redshift for both Einstein de-Sitter and Lambda CDM cosmologies. In
both cases the effective energy density arising from linear perturbations is of
the order of 10^-5 the matter density, as would be expected, with an effective
equation of state w ~ -1/19. Employing a modified Halofit code to extend our
results to quasilinear scales, we find that, while larger, the deviations from
Robertson-Walker behaviour remain of the order of 10^-5.Comment: 15 pages, 8 figures; replaced by version accepted by JCA
Distributed Testing of Excluded Subgraphs
We study property testing in the context of distributed computing, under the
classical CONGEST model. It is known that testing whether a graph is
triangle-free can be done in a constant number of rounds, where the constant
depends on how far the input graph is from being triangle-free. We show that,
for every connected 4-node graph H, testing whether a graph is H-free can be
done in a constant number of rounds too. The constant also depends on how far
the input graph is from being H-free, and the dependence is identical to the
one in the case of testing triangles. Hence, in particular, testing whether a
graph is K_4-free, and testing whether a graph is C_4-free can be done in a
constant number of rounds (where K_k denotes the k-node clique, and C_k denotes
the k-node cycle). On the other hand, we show that testing K_k-freeness and
C_k-freeness for k>4 appear to be much harder. Specifically, we investigate two
natural types of generic algorithms for testing H-freeness, called DFS tester
and BFS tester. The latter captures the previously known algorithm to test the
presence of triangles, while the former captures our generic algorithm to test
the presence of a 4-node graph pattern H. We prove that both DFS and BFS
testers fail to test K_k-freeness and C_k-freeness in a constant number of
rounds for k>4
International VLBI Service for Geodesy and Astrometry: Delivering high-quality products and embarking on observations of the next generation
© 2016 Springer-Verlag Berlin HeidelbergThe International VLBI Service for Geodesy and Astrometry (IVS) regularly produces high-quality Earth orientation parameters from observing sessions employing extensive networks or individual baselines. The master schedule is designed according to the telescope days committed by the stations and by the need for dense sampling of the Earth orientation parameters (EOP). In the pre-2011 era, the network constellations with their number of telescopes participating were limited by the playback and baseline capabilities of the hardware (Mark4) correlators. This limitation was overcome by the advent of software correlators, which can now accommodate many more playback units in a flexible configuration. In this paper, we describe the current operations of the IVS with special emphasis on the quality of the polar motion results since these are the only EOP components which can be validated against independent benchmarks. The polar motion results provided by the IVS have improved continuously over the years, now providing an agreement with IGS results at the level of 20â25 (Formula presented.)as in a WRMS sense. At the end of the paper, an outlook is given for the realization of the VLBI Global Observing System
Quark Mass Corrections to the Perturbative Thrust and its Effect on the determination of
We consider the effects of quark masses to the perturbative thrust in
annihilation. In particular we show that perturbative power
corrections resulting from non-zero quark masses considerably alters the size
of the non-perturbative power corrections and consequently, significantly
changes the fitted value of .Comment: Latex, 6 pages, 2 figures, minor change in text, added one referenc
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