31 research outputs found
Vertex operator algebras and operads
Vertex operator algebras are mathematically rigorous objects corresponding to
chiral algebras in conformal field theory. Operads are mathematical devices to
describe operations, that is, -ary operations for all greater than or
equal to , not just binary products. In this paper, a reformulation of the
notion of vertex operator algebra in terms of operads is presented. This
reformulation shows that the rich geometric structure revealed in the study of
conformal field theory and the rich algebraic structure of the theory of vertex
operator algebras share a precise common foundation in basic operations
associated with a certain kind of (two-dimensional) ``complex'' geometric
object, in the sense in which classical algebraic structures (groups, algebras,
Lie algebras and the like) are always implicitly based on (one-dimensional)
``real'' geometric objects. In effect, the standard analogy between
point-particle theory and string theory is being shown to manifest itself at a
more fundamental mathematical level.Comment: 16 pages. Only the definitions of "partial operad" and of "rescaling
group" have been improve
Interval total colorings of graphs
A total coloring of a graph is a coloring of its vertices and edges such
that no adjacent vertices, edges, and no incident vertices and edges obtain the
same color. An \emph{interval total -coloring} of a graph is a total
coloring of with colors such that at least one vertex or edge
of is colored by , , and the edges incident to each vertex
together with are colored by consecutive colors, where
is the degree of the vertex in . In this paper we investigate
some properties of interval total colorings. We also determine exact values of
the least and the greatest possible number of colors in such colorings for some
classes of graphs.Comment: 23 pages, 1 figur
Tamari Lattices and the symmetric Thompson monoid
We investigate the connection between Tamari lattices and the Thompson group
F, summarized in the fact that F is a group of fractions for a certain monoid
F+sym whose Cayley graph includes all Tamari lattices. Under this
correspondence, the Tamari lattice operations are the counterparts of the least
common multiple and greatest common divisor operations in F+sym. As an
application, we show that, for every n, there exists a length l chain in the
nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page
The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys
The collisionless accretion shock at the outer boundary of a galaxy cluster
should primarily heat the ions instead of electrons since they carry most of
the kinetic energy of the infalling gas. Near the accretion shock, the density
of the intracluster medium is very low and the Coulomb collisional timescale is
longer than the accretion timescale. Electrons and ions may not achieve
equipartition in these regions. Numerical simulations have shown that the
Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter
Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can
be biased if non-equipartition effects are not properly taken into account.
Using a set of hydrodynamical simulations, we have calculated three potential
systematic biases in the Y-mass relations introduced by non-equipartition
effects during the cross-calibration or self-calibration when using the galaxy
cluster abundance technique to constraint cosmological parameters. We then use
a semi-analytic technique to estimate the non-equipartition effects on the
distribution functions of Y (Y functions) determined from the extended
Press-Schechter theory. Depending on the calibration method, we find that
non-equipartition effects can induce systematic biases on the Y functions, and
the values of the cosmological parameters Omega_8, sigma_8, and the dark energy
equation of state parameter w can be biased by a few percent. In particular,
non-equipartition effects can introduce an apparent evolution in w of a few
percent in all of the systematic cases we considered. Techniques are suggested
to take into account the non-equipartition effect empirically when using the
cluster abundance technique to study precision cosmology. We conclude that
systematic uncertainties in the Y-mass relation of even a few percent can
introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical
Journal, abstract abridged slightly. Typos corrected in version
Bayesian Based Comment Spam Defending Tool
Spam messes up user's inbox, consumes network resources and spread worms and
viruses. Spam is flooding of unsolicited, unwanted e mail. Spam in blogs is
called blog spam or comment spam.It is done by posting comments or flooding
spams to the services such as blogs, forums,news,email archives and guestbooks.
Blog spams generally appears on guestbooks or comment pages where spammers fill
a comment box with spam words. In addition to wasting user's time with unwanted
comments, spam also consumes a lot of bandwidth. In this paper, we propose a
software tool to prevent such blog spams by using Bayesian Algorithm based
technique. It is derived from Bayes' Theorem. It gives an output which has a
probability that any comment is spam, given that it has certain words in it.
With using our past entries and a comment entry, this value is obtained and
compared with a threshold value to find if it exceeds the threshold value or
not. By using this concept, we developed a software tool to block comment spam.
The experimental results show that the Bayesian based tool is working well.
This paper has the major findings and their significance of blog spam filter.Comment: 14 Pages,4 Figures, International Journal of Network Security & Its
Applications (IJNSA), Vol.2, No.4, October 201