37 research outputs found
Gluon quasidistribution function at one loop
We study the unpolarized gluon quasidistribution function in the nucleon at
one loop level in the large momentum effective theory. For the quark
quasidistribution, power law ultraviolet divergences arise in the cut-off
scheme and an important observation is that they all are subjected to Wilson
lines. However for the gluon quasidistribution function, we first point out
that the linear ultraviolet divergences also exist in the real diagram which is
not connected to any Wilson line. We then study the one loop corrections to
parton distribution functions in both cut-off scheme and dimensional
regularization to deal with the ultraviolet divergences. In addition to the
ordinary quark and gluon distributions, we also include the quark to gluon and
gluon to quark splitting diagrams. The complete one-loop matching factors
between the quasi and light cone parton distribution functions are presented in
the cut-off scheme. We derive the evolution equation for quasi parton
distribution functions, and find that the evolution kernels are identical
to the DGLAP evolution kernels.Comment: 26 pages,8 figures;accepted by Eur.Phys.J
Personalized Recommendations Based On Usersâ Information-Centered Social Networks
The overwhelming amount of information available today makes it difficult for users to find useful information and as the solution to this information glut problem, recommendation technologies emerged. Among the several streams of related research, one important evolution in technology is to generate recommendations based on usersâ own social networks. The idea to take advantage of usersâ social networks as a foundation for their personalized recommendations evolved from an Internet trend that is too important to neglect â the explosive growth of online social networks. In spite of the widely available and diversified assortment of online social networks, most recent social network-based recommendations have concentrated on limited kinds of online sociality (i.e., trust-based networks and online friendships). Thus, this study tried to prove the expandability of social network-based recommendations to more diverse and less focused social networks. The online social networks considered in this dissertation include: 1) a watching network, 2) a group membership, and 3) an academic collaboration network. Specifically, this dissertation aims to check the value of usersâ various online social connections as information sources and to explore how to include them as a foundation for personalized recommendations.
In our results, users in online social networks shared similar interests with their social partners. An in-depth analysis about the shared interests indicated that online social networks have significant value as a useful information source. Through the recommendations generated by the preferences of social connection, the feasibility of usersâ social connections as a useful information source was also investigated comprehensively. The social network-based recommendations produced as good as, or sometimes better, suggestions than traditional collaborative filtering recommendations. Social network-based recommendations were also a good solution for the cold-start user problem. Therefore, in order for cold-start users to receive reasonably good recommendations, it is more effective to be socially associated with other users, rather than collecting a few more items. To conclude, this study demonstrates the viability of multiple social networks as a means for gathering useful information and addresses how different social networks of a novelty value can improve upon conventional personalization technology
The DAG Visit Approach for Pebbling and I/O Lower Bounds
We introduce the notion of an r-visit of a Directed Acyclic Graph DAG G = (V,E), a sequence of the vertices of the DAG complying with a given rule r. A rule r specifies for each vertex v ? V a family of r-enabling sets of (immediate) predecessors: before visiting v, at least one of its enabling sets must have been visited. Special cases are the r^(top)-rule (or, topological rule), for which the only enabling set is the set of all predecessors and the r^(sin)-rule (or, singleton rule), for which the enabling sets are the singletons containing exactly one predecessor. The r-boundary complexity of a DAG G, b_r(G), is the minimum integer b such that there is an r-visit where, at each stage, for at most b of the vertices yet to be visited an enabling set has already been visited. By a reformulation of known results, it is shown that the boundary complexity of a DAG G is a lower bound to the pebbling number of the reverse DAG, G^R. Several known pebbling lower bounds can be cast in terms of the r^{(sin)}-boundary complexity. The main contributions of this paper are as follows:
- An existentially tight ?(?{d_{out} n}) upper bound to the r^(sin)-boundary complexity of any DAG of n vertices and out-degree d_{out}.
- An existentially tight ?(d_{out}/(log? d_{out}) log? n) upper bound to the r^(top)-boundary complexity of any DAG. (There are DAGs for which r^(top) provides a tight pebbling lower bound, whereas r^(sin) does not.)
- A visit partition technique for I/O lower bounds, which generalizes the S-partition I/O technique introduced by Hong and Kung in their classic paper "I/O complexity: The Red-Blue pebble game". The visit partition approach yields tight I/O bounds for some DAGs for which the S-partition technique can only yield a trivial lower bound
Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case
We propose a Kronecker product model for correlation or covariance matrices
in the large dimensional case. The number of parameters of the model increases
logarithmically with the dimension of the matrix. We propose a minimum distance
(MD) estimator based on a log-linear property of the model, as well as a
one-step estimator, which is a one-step approximation to the quasi-maximum
likelihood estimator (QMLE). We establish rates of convergence and central
limit theorems (CLT) for our estimators in the large dimensional case. A
specification test and tools for Kronecker product model selection and
inference are provided. In a Monte Carlo study where a Kronecker product model
is correctly specified, our estimators exhibit superior performance. In an
empirical application to portfolio choice for SP500 daily returns, we
demonstrate that certain Kronecker product models are good approximations to
the general covariance matrix
Torsion homology growth and cycle complexity of arithmetic manifolds
Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold.
We conjecture that there is a basis for the second homology of M, where each basis
element is represented by a surface of âlowâ genus, and give evidence for this. We explain
the relationship between this conjecture and the study of torsion homology growth
Algebraic Multigrid for Meshfree Methods
This thesis deals with the development of a new Algebraic Multigrid method (AMG) for the solution of linear systems arising from Generalized Finite Difference Methods (GFDM). In particular, we consider the Finite Pointset Method, which is based on GFDM. Being a meshfree method, FPM does not rely on a mesh and can therefore deal with moving geometries and free surfaces is a natural way and it does not require the generation of a mesh before the actual simulation. In industrial use cases the size of the linear systems often becomes large, which means that classical linear solvers often become the bottleneck in terms of simulation run time, because their convergence rate depends on the discretization size. Multigrid methods have proven to be very efficient linear solvers in the domain of mesh-based methods. Their convergence is independent of the discretization size, yielding a run time that only scales linearly with the problem size. AMG methods are a natural candidate for the solution of the linear systems arising in the FPM, as this thesis will show. They need to be tuned to the specific characteristics of GFDM, though. The AMG methods that are developed in this thesis achieve a speed-up of up to 33x compared to the classical linear solvers and therefore allow much more accurate simulations in the future.Diese Dissertation beschĂ€ftigt sich mit der Entwicklung einer neuen Algebraischen Mehrgittermethode fĂŒr die Lösung linearer Gleichungssysteme aus Generalisierten Finite Differenzen Methoden. Im Speziellen betrachten wir die sogenannte Finite Pointset Method, eine gitterfreie Lagrange Methode, welche auf Generalisierten Finite Differenzen Methoden basiert. Die Finite Pointset Method wurde insbesondere fĂŒr Simulationen von VorgĂ€ngen mit freien OberflĂ€chen und bewegten Geometrien entwickelt, bei denen der gitterfreie Charakter der Methode besonders groĂe Vorteile liefert: An den freien OberflĂ€chen und nahe der Geometrie muss zu keinem Zeitpunkt â auch nicht zu Beginn der Simulation â ein Gitter erstellt oder angepasst werden. Dies ist ein groĂer Vorteil gegenĂŒber klassischen gitterbasierten Methoden. Wie in gitterbasierten Methoden entstehen auch in der Finite Pointset Method und anderen Generalisierten Finite Differenzen Methoden groĂe, dĂŒnn besetze lineare Gleichungssysteme. Das Lösen dieser Gleichungssysteme wird bei fein aufgelösten Simulationen, wie sie in der Industrie oft nötig sind, schnell zum zeitlichen Flaschenhals der Gesamtsimulation. Ohne eine geeignete Methode zur Lösung dieser Gleichungssysteme dauern Simulationen oft sehr lange oder sind praktisch nicht durchfĂŒhrbar. Auch kann es vorkommen, dass klassische Lösungsverfahren divergieren und die Simulation damit unmöglich wird. Im Kontext von gitterbasierten Methoden sind Mehrgittermethoden ein etabliertes Werkzeug, um die entstehenden linearen Gleichungssysteme effizient und robust zu lösen. Besonders hervorzuheben ist dabei die lineare Skalierbarkeit dieser Methoden in der GröĂe der Matrix. Damit eignen sie sich besonders fĂŒr fein aufgelöste Simulationen. Algebraische Mehrgittermethoden sind natĂŒrliche Kandidaten fĂŒr die Lösung der Gleichungssysteme aus Generalisierten Finite Differenzen Methoden, wie diese Dissertation zeigen wird. AuĂerdem entwickeln wir eine neue Algebraische Mehrgittermethode, die auf den Einsatz in der Finite Pointset Method zugeschnitten ist und die Besonderheiten dieser Methode beachtet. Dazu zĂ€hlen die Eigenschaften der einzelnen Matrizen, die wir ebenfalls analysieren werden, und auch die VerĂ€nderung der Matrizen ĂŒber mehrere Zeitschritte hinweg, die im Vergleich mit gitterbasierten Verfahren eine gröĂere Schwierigkeit darstellt. Wir evaluieren unsere neue Methode anhand von akademischen und realen Beispielen, sowohl mit nur einem Prozess als auch mit mehreren (MPI-)Prozessen. Die hier neu entwickelte Algebraische Mehrgittermethode ist um ein Vielfaches schneller als klassische Verfahren zur Lösung linearer Gleichungssysteme und erlaubt damit neue, genauere Simulationen mit gitterfreien Methoden