494 research outputs found
Einstein energy associated with the Friedmann -Robertson -Walker metric
Following Einstein's definition of Lagrangian density and gravitational field
energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A.,
Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I.
Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general
formula for the total matter plus gravitational field energy () of an
arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C.,
{\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962));
Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in
quasi-Cartesian coordinates, this formula leads to the well known result , where is the
determinant of the metric tensor and is the energy momentum tensor of
the {\em matter}. Though in the literature, this is known as "Tolman Mass", it
must be realized that this is essentially "Einstein Mass" because the
underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz
obtained the same expression for the "inertial mass" of a static isolated
system without using any pseudo-tensor at all and which points to physical
significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz,
E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed.,
1962)! For the first time we apply this general formula to find an expression
for for the Friedmann- Robertson -Walker (FRW) metric by using the same
quasi-Cartesian basis. As we analyze this new result, physically, a spatially
flat model having no cosmological constant is suggested. Eventually, it is seen
that conservation of is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the
journal version is uploade
Bayesian nonparametric models for name disambiguation and supervised learning
This thesis presents new Bayesian nonparametric models and approaches for their development,
for the problems of name disambiguation and supervised learning. Bayesian
nonparametric methods form an increasingly popular approach for solving problems
that demand a high amount of model flexibility. However, this field is relatively new,
and there are many areas that need further investigation. Previous work on Bayesian
nonparametrics has neither fully explored the problems of entity disambiguation and
supervised learning nor the advantages of nested hierarchical models. Entity disambiguation
is a widely encountered problem where different references need to be linked
to a real underlying entity. This problem is often unsupervised as there is no previously
known information about the entities. Further to this, effective use of Bayesian
nonparametrics offer a new approach to tackling supervised problems, which are frequently
encountered.
The main original contribution of this thesis is a set of new structured Dirichlet process
mixture models for name disambiguation and supervised learning that can also
have a wide range of applications. These models use techniques from Bayesian statistics,
including hierarchical and nested Dirichlet processes, generalised linear models,
Markov chain Monte Carlo methods and optimisation techniques such as BFGS. The
new models have tangible advantages over existing methods in the field as shown with
experiments on real-world datasets including citation databases and classification and
regression datasets.
I develop the unsupervised author-topic space model for author disambiguation that
uses free-text to perform disambiguation unlike traditional author disambiguation approaches.
The model incorporates a name variant model that is based on a nonparametric
Dirichlet language model. The model handles both novel unseen name variants and
can model the unknown authors of the text of the documents. Through this, the model
can disambiguate authors with no prior knowledge of the number of true authors in the
dataset. In addition, it can do this when the authors have identical names.
I use a model for nesting Dirichlet processes named the hybrid NDP-HDP. This
model allows Dirichlet processes to be clustered together and adds an additional level of
structure to the hierarchical Dirichlet process. I also develop a new hierarchical extension
to the hybrid NDP-HDP. I develop this model into the grouped author-topic model
for the entity disambiguation task. The grouped author-topic model uses clusters to model the co-occurrence of entities in documents, which can be interpreted as research
groups. Since this model does not require entities to be linked to specific words in a
document, it overcomes the problems of some existing author-topic models. The model
incorporates a new method for modelling name variants, so that domain-specific name
variant models can be used.
Lastly, I develop extensions to supervised latent Dirichlet allocation, a type of supervised
topic model. The keyword-supervised LDA model predicts document responses
more accurately by modelling the effect of individual words and their contexts directly.
The supervised HDP model has more model flexibility by using Bayesian nonparametrics
for supervised learning. These models are evaluated on a number of classification
and regression problems, and the results show that they outperform existing supervised
topic modelling approaches. The models can also be extended to use similar information
to the previous models, incorporating additional information such as entities and
document titles to improve prediction
Energy Distribution associated with Static Axisymmetric Solutions
This paper has been addressed to a very old but burning problem of energy in
General Relativity. We evaluate energy and momentum densities for the static
and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen
and the gamma metrics, belonging to the Weyl class. We apply four well-known
prescriptions of Einstein, Landau-Lifshitz, Papaterou and Mller to
compute energy-momentum density components. We obtain that these prescriptions
do not provide similar energy density, however momentum becomes constant in
each case. The results can be matched under particular boundary conditions.Comment: 18 pages, accepted for publication in Astrophysics and SpaceScienc
Energy and Momentum Densities Associated with Solutions Exhibiting Directional Type Singularities
We obtain the energy and momentum densities of a general static axially
symmetric vacuum space-time described by the Weyl metric, using Landau-Lifshitz
and Bergmann-Thomson energy-momentum complexes. These two definitions of the
energy-momentum complex do not provide the same energy density for the
space-time under consideration, while give the same momentum density. We show
that, in the case of Curzon metric which is a particular case of the Weyl
metric, these two definitions give the same energy only when .
Furthermore, we compare these results with those obtained using Einstein,
Papapetrou and M{\o}ller energy momentum complexes.Comment: 10 pages, references added, minor corrections [Admin note:
substantial overlap with gr-qc/0403097 , gr-qc/0403039
An Experimental Investigation of Colonel Blotto Games
"This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a 'guerilla warfare' strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a 'stochastic complete coverage' strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields." (author's abstract)"Dieser Artikel untersucht das Verhalten von Individuen in einem 'constant-sum Colonel Blotto'-Spiel zwischen zwei Spielern, bei dem die Spieler mit unterschiedlichen Ressourcen ausgestattet sind und die erwartete Anzahl gewonnener Schlachtfelder maximieren. Die experimentellen Ergebnisse bestätigen alle wichtigen theoretischen Vorhersagen. Im Durchgang, in dem wie in einer Auktion der Sieg in einem Schlachtfeld deterministisch ist, wenden die Spieler, die sich im Nachteil befinden, eine 'Guerillataktik' an, und verteilen ihre Ressourcen stochastisch auf eine Teilmenge der Schlachtfelder. Spieler mit einem Vorteil verwenden eine Strategie der 'stochastischen vollständigen Abdeckung', indem sie zufällig eine positive Ressourcenmenge auf allen Schlachtfeldern positionieren. Im Durchgang, in dem sich der Gewinn eines Schlachtfeldes probabilistisch wie in einer Lotterie bestimmt, teilen beide Spieler ihre Ressourcen gleichmäßig auf alle Schlachtfelder auf." (Autorenreferat
On the energy of charged black holes in generalized dilaton-axion gravity
In this paper we calculate the energy distribution of some charged black
holes in generalized dilaton-axion gravity. The solutions correspond to charged
black holes arising in a Kalb-Ramond-dilaton background and some existing
non-rotating black hole solutions are recovered in special cases. We focus our
study to asymptotically flat and asymptotically non-flat types of solutions and
resort for this purpose to the M{\o}ller prescription. Various aspects of
energy are also analyzed.Comment: LaTe
Bergmann-Thomson energy-momentum complex for solutions more general than the Kerr-Schild class
In a very well-known paper, Virbhadra's research group proved that the
Weinberg, Papapetrou, Landau and Lifshitz, and Einstein energy-momentum
complexes ``coincide'' for all metrics of Kerr-Schild class. A few years later,
Virbhadra clarified that this ``coincidence'' in fact holds for metrics more
general than the Kerr-Schild class. In the present paper, this study is
extended for the Bergmann-Thomson complex and it is proved that this complex
also ``coincides'' with those complexes for a more general than the Kerr-Schild
class metric.Comment: RevTex, 12 page
Exponential Metric Fields
The Laser Interferometer Space Antenna (LISA) mission will use advanced
technologies to achieve its science goals: the direct detection of
gravitational waves, the observation of signals from compact (small and dense)
stars as they spiral into black holes, the study of the role of massive black
holes in galaxy evolution, the search for gravitational wave emission from the
early Universe. The gravitational red-shift, the advance of the perihelion of
Mercury, deflection of light and the time delay of radar signals are the
classical tests in the first order of General Relativity (GR). However, LISA
can possibly test Einstein's theories in the second order and perhaps, it will
show some particular feature of non-linearity of gravitational interaction. In
the present work we are seeking a method to construct theoretical templates
that limit in the first order the tensorial structure of some metric fields,
thus the non-linear terms are given by exponential functions of gravitational
strength. The Newtonian limit obtained here, in the first order, is equivalent
to GR.Comment: Accepted for publication in Astrophysics and Space Science, 17 page
The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications
There exist at least a few different kind of averaging of the differences of
the energy-momentum and angular momentum in normal coordinates {\bf NC(P)}
which give tensorial quantities. The obtained averaged quantities are
equivalent mathematically because they differ only by constant scalar
dimensional factors. One of these averaging was used in our papers [1-8] giving
the {\it canonical superenergy and angular supermomentum tensors}.
In this paper we present another averaging of the differences of the
energy-momentum and angular momentum which gives tensorial quantities with
proper dimensions of the energy-momentum and angular momentum densities. But
these averaged relative energy-momentum and angular momentum tensors, closely
related to the canonical superenergy and angular supermomentum tensors, {\it
depend on some fundamental length }.
The averaged relative energy-momentum and angular momentum tensors of the
gravitational field obtained in the paper can be applied, like the canonical
superenergy and angular supermomentum tensors, to {\it coordinate independent}
analysis (local and in special cases also global) of this field.
We have applied the averaged relative energy-momentum tensors to analyze
vacuum gravitational energy and momentum and to analyze energy and momentum of
the Friedman (and also more general) universes. The obtained results are very
interesting, e.g., the averaged relative energy density is {\it positive
definite} for the all Friedman universes.Comment: 30 pages, minor changes referring to Kasner universe
The Non-linear Dynamics of Meaning-Processing in Social Systems
Social order cannot be considered as a stable phenomenon because it contains
an order of reproduced expectations. When the expectations operate upon one
another, they generate a non-linear dynamics that processes meaning. Specific
meaning can be stabilized, for example, in social institutions, but all meaning
arises from a horizon of possible meanings. Using Luhmann's (1984) social
systems theory and Rosen's (1985) theory of anticipatory systems, I submit
equations for modeling the processing of meaning in inter-human communication.
First, a self-referential system can use a model of itself for the
anticipation. Under the condition of functional differentiation, the social
system can be expected to entertain a set of models; each model can also
contain a model of the other models. Two anticipatory mechanisms are then
possible: one transversal between the models, and a longitudinal one providing
the modeled systems with meaning from the perspective of hindsight. A system
containing two anticipatory mechanisms can become hyper-incursive. Without
making decisions, however, a hyper-incursive system would be overloaded with
uncertainty. Under this pressure, informed decisions tend to replace the
"natural preferences" of agents and an order of cultural expectations can
increasingly be shaped
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